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THE PLANET JUPITER
As seen with the 26 inch telescope at "Washington, 1875, June 24.
AMERICAN SCIENCE SERIES, BRIEFER COURSE.
ASTEONOMT
SIMON NEWCOMB, LL.D.
SUPERINTENDENT AMERICAN EPHSMERI3 AND NAUTICAL ALMANAC
AND
EDWARD S. HOLDEN, M.A.
DIRECTOR OF THE WA8HBURN OBSERVATORY
SECO
ox, REVISED AKD ENLARGED.
1STEW YORK
HENRY HOLT AND COMPANY
1885
Copyright, 1883
BY
HENRY HOLT & Co.
PBEFACE.
THE present treatise is a condensed edition of the Astronomy of
the American Science Series. The book has not been shortened by
leaving out anything that was essential, but by omitting some of the
details of practical astronomy, thus giving to the descriptive por-
tions a greater relative extension.
The most marked feature of this condensation is, perhaps, the
omission of most of the mathematical formulae of the larger treatise.
The present work requires for its understanding only a fair acquaint-
ance with the principles of algebra and geometry and a slight
knowledge of elementary physics. The space which has beeo gained
by these omissions has been utilized in giving a fuller discussion of
the more elementary parts of the subject, and in treating the funda-
mental principles from various points of view.
A familiar and secure knowledge of these is essential to the
students' real progress. The full index makes the work of value as
a reference-book to a student who has studied it and put it aside.
As in the larger work, the matter is given in two sizes of type. It
will be found that the larger type contains a course practically com-
plete in itself, and that the matter of the smaller type is chiefly ex-
planatory of the former. It is highly desirable, however, that the
book should be read as a whole, while the actual class -work may be
confined to the subjects treated in the larger type, if the class is
pressed for time. A celestial globe, and a set of star-maps (PROC-
TOR'S " New Star- Atlas" is as good as any), will be found to be of
use in connection with the study ; and if the class has access to a small
telescope, even, much can be learned in this way. A mere opera-
glass will suffice to give a correct notion of the general features of
the moon's surface, and a very small telescope, if properly used, will
do the same for the larger planets.
CONTENTS.
PAET I.
INTRODUCTION.
PAGE
Astronomy Defined How to Study Astronomy Angles: their
Measure Plane Triangles The Sphere Power of the Eye
to See Small Objects Latitude and Longitude Symbols
and Abbreviations 1
CHAPTER I.
RELATION OF THE EARTH TO THE HEAVENS.
The Earth's Shape and Dimensions The Celestial Sphere The
Horizon The Diurnal Motion Diurnal Motion in Different
Latitudes Correspondence of the Terrestrial and Celestial
Spheres 13
CHAPTER II.
RELATION OP THE EARTH TO THE HEAVENS (Continued).
The Celestial Sphere Systems of Coordinates Relation of Time
to the Sphere Sidereal Time Solar Time Determinations
of Terrestrial Longitudes Where does the Day Change ?
Determination of Latitudes Parallax 37
CHAPTER III.
ASTRONOMICAL INSTRUMENTS.
The Telescope Chronometers and Clocks The Transit Instru-
mentThe Meridian Circle The Equatorial The Sextant
The Nautical Almanac. .....,,,. .,,,,,.,,.,,,, 60
v i CONTENTS.
CHAPTER IV.
MOTIONS OF THE EARTH.
FAGK
Ancient Ideas of the Planets Annual Revolution of the Earth
The Sun's Apparent Path Obliquity of the Ecliptic
The Seasons Celestial Latitude and Longitude 81
CHAPTER V.
THE PLANETARY MOTIONS.
Apparent and Real Motions of the Planets The Copernican
System of the World Kepler's Laws of Planetary Motion . . 96
CHAPTER VI.
UNIVERSAL GRAVITATION.
Newton's Laws of Motion Gravitation in the Heavens Mutual
Action of the Planets Remarks on the Theory of Gravi-
tation 113
CHAPTER VII.
THE MOTIONS AND ATTRACTION OF THE MOON.
The Moon's Motions and Phases The Tides Effect of the
Tides upon the Earth's Rotation 123
CHAPTER VIII.
ECLIPSES OF THE SUN AND MOON.
The Earth's Shadow Eclipses of the Moon Eclipses of the
Sun The Recurrence of Eclipses 129
CHAPTER IX.
THE EARTH.
Mass and Density of the Earth Laws of Terrestrial Gravitation
Figure and Magnitude of the Earth Geodetic Surveys
Motions of the Earth's Axis, or Precession of the Equinoxes
Sidereal and Equinoctial Year The Causes of Precession 142
CONTENTS. Vii
CHAPTER X.
CELESTIAL MEASUREMENTS OF MASS AND DISTANCE.
PAGE
The Celestial Scale of Measurement Measures of the Solar and
Lunar Parallax Methods of Determining the Solar Parallax
Relative Masses of the Sun and Planets '. 158
CHAPTER XI.
THE REFRACTION AND ABERRATION OF LIGHT ; TWILIGHT.
Atmospheric Refraction Quantity and Effects of Refraction
Twilight Aberration and the Motion of Light Discovery
and Effects of Aberration 169
CHAPTER XII.
CHRONOLOGY.
Astronomical Measures of Time Formation of Calendars
Kinds of Months and Years, Old and New Style Divi-
sions of the Day Equation of Time 180
PAET II.
THE SOLAR SYSTEM IN DETAIL.
CHAPTER I.
STRUCTURE OF THE SOLAR SYSTEM.
Planets Asteroids Comets Planetary Aspects Tables of the
Elements of the Solar System 190
CHAPTER II.
THE SUN.
General Summary The Photosphere Light and Heat from
the Photosphere Amount of Heat Emitted by the Sun
Solar Temperature Sun-Spots and Faculse Solar Axis
and Equator Nature of Sun-Spots Number and Periodic-
ity of Solar Spots The Sun's Chromosphere and Corona
Gaseous Nature of the Prominences The Coronal Spec-
trum Sources of the Sun's Heat Theories of the Sun's
Constitution.. .... 200
Vlii CONTENTS.
CHAPTER IIL
THE INFERIOR PLANETS.
PAGE
Motions and Aspects Atmosphere and Rotation of Mercury
Atmosphere and Rotatiou of Veu us Transits of Mercury
and Venus Supposed Intramercurial Planets 221
CHAPTER IV.
THE MOON.
Character of the Moon's Surface Lunar Atmosphere Light
and Heat of the Moon Is there any Change on the Surface
of the Moot? 228
CHAPTER V.
THE PLANET MARS.
Description of the Planet Rotation Surface Satellites of
Mars 233
CHAPTER VI.
THE MINOR PLANETS
The Number of Small Planets Their Magnitudes Forms of
their Orbits Origin 237
CHAPTER VII.
JUPITER AND ins SATELLITES.
The Planet Jupiter Satellites of Jupiter 240
CHAPTER VIIL
SATURN AND HIS SYSTEM.
General Description The Rings of Saturn Satellites of Saturn 246
CHAPTER IX.
THE PLANET URANUS.
Discovery Satellites . 353
CONTENTS. i x
CHAPTER X.
THE PLANET NEPTUNE.
PAGE
Reasons for believing in its Existence Discovery Its Satellite. . 256
CHAPTER XI.
THE PHYSICAL CONSTITUTION OF THE PLANETS.
Mercury and Venus The Earth and Mars Jupiter and Saturn
Uranus and Neptune 261
CHAPTER XII.
METEORS.
Phenomena and Causes of Meteors Meteoric Showers Relation
of Meteors and Comets The Zodiacal Light 265
CHAPTER XIIL
COMETS.
Aspect of Comets The Vaporous Envelopes Physical Consti-
tution Motions Remarkable Comets Encke's Comet
The Resisting Medium 274
PAET III.
INTRODUCTION 285
CHAPTER I.
CONSTELLATIONS.
General Aspect of the Heavens The Galaxy Lucid Stars
Telescopic Stars Magnitudes of the Stars The Constella-
tions and Names of the Stars Numbering and Cataloguing
the Stars 288
CHAPTER II.
VARIABLE AND TEMPORARY STARS.
Stars Regularly Variable Temporary or New Stars 296
X CONTENTS.
CHAPTER m.
MULTIPLE STABS.
Character of Double and Multiple Stars Binary Systems 301
CHAPTER IV.
NEBULAE AND CLUSTERS.
Discovery of Nebulae Classification of Nebulae Clusters Star
Clusters Spectra of Nebulae, Clusters, and Fixed Stars-
Motion of Stars in the Line of Sight 304
CHAPTER V.
MOTIONS AND DISTANCES OF THE STARS.
Proper Motions Proper Motion of the Sun Distances of the
Fixed Stars 312
CHAPTER VI.
CONSTRUCTION OP THE HEAVENS.
Star-gauging The Milky Way 318
CHAPTER VII.
COSMOGONY.
Laplace's Nebular Hypothesis General Conclusions 323
APPENDIX.
Spectrum Analysis The Spectroscope The Solar Spectrum
Results of Spectroscopic Observations Description and
Maps of the Constellations 833
INDEX . 347
ASTRONOMY.
INTRODUCTION.
Astronomy Defined. Astronomy (affrrfp a star, and
vof^o? a law) is the science which has to do with the
heavenly bodies, their appearances, their nature, and the
laws governing their real and their apparent motions.
In approaching the study of this the oldest of the
sciences depending upon observation, it must be borne in
mind that its progress is most intimately connected with
that of the race, it having always been the basis of geog-
raphy and navigation, and the soul of chronology. Some
of the chief advances and discoveries in abstract mathe-
matics have been made in its service, and the methods
both of observation and analysis once peculiar to its prac-
tice now furnish the firm bases upon which rest that great
group of exact sciences which we call Physics.
It is more important to the student that he should be-
come penetrated with the spirit of the methods of astron-
omy than that he should recollect its minutia3 ; and it is
most important that the knowledge which he may gain
from this or other books should be referred by him to its
true sources. For example, it will often be necessary to
speak of certain planes or circles, the ecliptic, the equa-
tor, the meridian, etc., and of the relation of the appa-
ASTRONOMY.
rent positions of stars and planets to them; but his labor
will be useless if it has not succeeded in giving him a pre-
cise notion of these circles and planes as they exist in the
sky, and not merely in the figures of his text-book. Above
all, the study of this science, in which not a single step
could have been taken without careful and painstaking
observation of the heavens, should lead its student himself
to attentively regard the phenomena daily and hourly pre-
sented to him by the heavens.
Does the sun set daily in the same point of the horizon?
Does a change of his own station affect this and other
aspects of the sky? At what time does the full moon rise?
Which way are the horns of the young moon pointed?
These and a thousand other questions are already answered
by the observant eyes of the ancients, who discovered not
only the existence, but the motions, of the various planets,
and gave special names to no less than fourscore stars.
The modern pupil is more richly equipped for observation
than the ancient philosopher. If one could have put a
mere opera-glass in the hands of HIPPARCHUS the world
need not have waited two thousand years to know the
nature of that early mystery, the Milky Way, nor would it
have required a GALILEO to discover the phases of Venus
and the spots on the sun.
Astronomy furnishes the principles and the methods by
means of which thousands of ships are navigated with
safety and certainty from port to port ; by which the
dimensions of the earth itself are fixed with high precision;
by which the distances of the sun, the planets, and the
brighter stars are measured and determined. The details
of these methods cannot be given in an elementary work ;
but the general principles and even the spirit of the special
INTRODUCTION. 3
methods can be entirely mastered by the faithful student.
All the attention which he can bring will be richly reward-
ed by the insight he will gain into the noblest of the physi-
cal sciences.
How to Study Astronomy. There are a few principles
of Mathematics of Geography, of Physics, which must be
clearly understood by the student commencing astronomy,
so that he may go on with advantage. They are all quite
simple, but they must be entirely fixed in the mind, in
order that the attention may be directed to the astronomical
principle and not diverted by an attempt to recollect a fact
from another science. Any patience and concentration
which the student may bestow upon them at the outset
should *be rewarded by the facility with which they will
enable him to grasp the more interesting portions of the
subject. The few definitions which are given in italics
should be memorized in the words of the text. In all other
cases it is preferable that the student should give his own
explanations in his own words.
First we will go briefly over some of the essential mathe-
matical principles alluded to.
Angles : their Measurement. An angle is the amount
of divergence of two right lines. For example, the angle
between the two right lines 8 1 E and
8*E is the amount of divergence of
these lines. The angle 8*E8* is the
amount of divergence of the two lines
S S E and S*K The eye sees at once
that the angle S 3 ES* in the figure is
greater than the angle S 1 ES*, and
that the angle 8*ES* is greater than
either of them.
4 ASTRONOMY.
In order to compare them and to obtain their numerical
ratio, we must have a unit-angle.
The unit angle is obtained in this way: The circumfer-
ence of any circle is divided into 360 equal parts. The
points of division are joined with the centre. The angles
between any two adjacent radii are called degrees. In the
figure, S'fiS* is about 12, S'ES* is about 22, S'ES* is
about 30, and S l S 4 is about 64. The vertex of the
angle is at the centre E ': the measure of the angle is on
the circumference S 1 S*S*S', or on any other circumference
drawn from E as a centre.
In this way we have come to speak of the length of one
three-hundred-and-sixtieth part of any circumference as a
degree, because radii drawn from the ends of this part
make an angle of 1.
For convenience in expressing the ratios of different
angles we have subdivided the degree into minutes and
seconds. The degree is too large a unit for some of the
purposes of astronomy, just as the metre is too large a unit
for use in the machine-shop, where fine work is concerned.
One circumference = 360 = 21600' = 1296000*
1 = 60' = 360'
1' = 60'
When we wish to express smaller angles than seconds,
we use decimals of a second. Thus one-quarter of a second
is 0*.25; one quarter of a minute is 15'.
The Radius of the Circle in Angular Measure. If 'R is
the radius of a circle, we know from geometry that 1 cir-
cumference = 2 n R, where n 3.1416. That is,
2 it M - 360 = 21600' = 1296000'
or R = 57. 3 = 3437'.? = 206264'. 8.
INTRODUCTION. 5
By this we mean that if a flexible cord equal in length
to the radius of any circle were laid round the circumfer-
ence of that circle, and if two radii were then drawn to the
ends of this cord, the angle of these radii would be 57. 3,
3437'.7, or 206264". 8.
It is important that this should be perfectly clear to the
student.
For instance, how far off must you place a foot-rule in
order that it may subtend an angle of 1 at your eye?
Why, 57.3 feet away. How far must it be in order to sub-
tend an angle of a minute ? 3437.7 feet. How far for a
second ? 206264.8 feet, or over 39 miles.
Again, if an object subtends an angle of 1 at the eye,
we know that its diameter must be ^-5 as great as its dis-
57 .o
tance from us. If it subtends an angle of 1", its distance
from us is over 200,000 times as great as its diameter.
The instruments employed in astronomy may be used to
measure the angles subtended at the eye by the diameters of
the heavenly bodies. In other ways we determine their dis-
tance from us in miles. A combination of these data will
give us the actual dimensions of these bodies in miles.
For example, the sun is about 93,000,000 miles from the
earth. The angle subtended by the sun's diameter at this
distance is 1922*. What is the diameter of the sun in miles ?
An idea of angular dimensions in the sky may be had by
remembering that the angular diameters of the moon and
of the sun are about 30'. It is 180 from the west point to
the east point counting through the point immediately
overhead. How many moons placed edge to edge would it
take to reach from horizon to horizon ? The student may
guess at the answer first and then compute it.
Q ASTRONOMY.
Perhaps a more convenient measure is the apparent dis-
tance apart of the " pointers" in the Great Dipper, which
is 5. (See Fig. 7, page &i.)
Plane Triangles. The angles of which we have been
speaking are angles in a plane. In any plane triangle there
are three sides and three angles six parts. If any three of
these parts (except the three angles) are given we can
construct the triangle. If the three angles alone are given
we can make a triangle which shall be of the right shape,
and that is all.
Fro. 2.
Spherical Triangles. Besides plane angles and triangles,
we have to do with those drawn on the surface of a sphere
spherical triangles. This is necessary since the heavenly
bodies are spherical in shape, and since they are seen pro-
jected against the concave surface of the sky.
The Sphere: its Planes and Circles. In the figure, is
the centre of the sphere and ABE is one of its circles.
Suppose a plane AB passing through the centre and cut-
INTRODUCTION. 7
\
ting the sphere into two hemispheres. It will intersect the
surface of the sphere in a circle AEBF which is called a
great circle of the sphere. A great circle of the sphere is
one cut from the surface by a plane passing through the
centre of the sphere. Suppose a right line POP' perpen-
dicular to this plane. The points P and P f in which it
intersects the surface of the sphere are everywhere 90
from the circle AEBF. They are the poles of that circle.
The poles of the great circle CEDF are Q and Q'.
The following relations exist between the angles made
in the figure:
I. The angle POQ between the poles is equal to the in-
clination of the planes to each other.
II. The arc BD which measures the greatest distance
between the two circles is equal to the arc PQ which
measures the angle POQ.
III. The points E and F, in which the two great cir-
cles intersect each other, are the poles of the great circle
PQACP'Q'BD which passes through the poles of the first
two circles.
The Spherical Triangle. In the last figure there are
several spherical triangles, as EDB, FAC, ECP'Q'B, etc.
In astronomy we need consider only those whose sides
are formed by arcs of great circles. The angles of the
triangle are angles between two arcs of great circles; or what
is the same thing, they are angles between the two planes
which cut the two arcs from the surface of the sphere.
In spherical triangles, as in plane, there are six parts,
three angles and three sides. Having any three parts the
other three can be constructed.
The sides as well as the angles of spherical triangles are
expressed in degrees, minutes, and seconds. If the student
g ASTRONOMY.
has a globe before him, let him mark on it the triangle
whose angles are
A 128 44' 45M,
B 33 11' 12'.0,
G 1815'31M,
and whose sides are (a is opposite to A, I to B, c to C.)
a = 10, b = 7, c = 4.
Power of the Eye to see Small Objects. When a round
object subtends an angle of 1' (that is, when it is about
3437 of its own diameters away), it is just at the limit of
visibility, under ordinary circumstances. At the Transit of
Venus in 1874, the planet Venus was between the earth
and the sun, and appeared as a small black spot, just visi-
ble to the naked eye, projected on the sun's face. It was
67* in diameter.
If two such discs are nearer together than 1' 12', few
eyes can distinguish them as two distinct objects. If a
body is long and narrow, its angular dimensions (width)
may be reduced to 10* or 15* before it is indistinguishable
to the eye. For example, a spider line hanging in the air.
If an object is very much brighter than the background
on which it is seen, there is no limit below which it is nec-
essarily invisible. Its visibility depends, in such a case,
only on its brightness. It is probable that the diameters
of the brightest stars subtend an angle no greater than
O'.Ol.
Latitude and Longitude of a Place on the Earth's Surface.
Geography teaches us that the earth is a sphere. Positions
on its surface are defined by giving their latitude and
longitude. According to geography, the latitude of a place
on the earth's surface is its angular distance north or south
of the equator.
INTRODUGTION. $
The longitude of a place on the earth's surface is its
angular distance east or west of a given first meridian,
If P in the figure is the north pole of the earth, the
latitude of the point B is 60 north; of Z it is 30 north;
of / it is 27-J south. All places having the same latitude
are situated on the same parallel of latitude. In the figure
the parallels of latitude are represented by straight lines.
All places having the same longitude are situated on the
Fia. 3.
same meridian. "We shall give the astronomical definitions
of these terms further on.
It is found convenient in astronomy to modify the geo-
graphical definition of longitude. In geography we say
that Washington is 77 west of Greenwich, and that Syd-
ney (Australia) is 151 east of Greenwich. For astro-
nomical purposes it is found more convenient to count the
10 ASTRONOMY.
longitude of a place from the first meridian (usually
Greenwich) always towards the west. Thus Sydney is 209
west of Greenwich. 360-151=209.
The earth turns on its axis once in 24 hours. In this
time a point on its surface moves through 360 degrees, or
such a point moves at the rate of 15 per hour. 360 divided
by 24 is 15.
Hence we may express the longitude of a place either in
time or arc. Washington is 5 h 8 m west of Greenwich, and
Sydney is 13 h 56 m west of Greenwich.
It is also indifferent which first meridian we choose.
We may refer all longitudes to Paris, to Berlin, or to Wash-
ington. Sydney is 8 h 48 m west of Washington, and Green-
wich is 18 h 52 m west of Washington.
In the figure, suppose F to be west of the first meridian.
All the places on the straight line PQ have a longitude of
15 or 1 hour ; all on the curve P5 h Q have a longitude
of 75 or 5 hours; and so on.
The difference of longitude of any two places on the earth
is the angular distance between the terrestrial meridians
passing through the two places.
Thus Washington is 77 west of Greenwich, and Sydney
is 209 west of Greenwich. Hence Sydney is 132 west of
Washington, and this is the difference of longitude of the
two places.
SYMBOLS AND ABBREVIATIONS
SIGNS OP THE PLANETS, ETC.
or
The Sun.
The Moon.
Mercury.
Venus.
The Earth.
Mars.
Jupiter.
Saturn.
Uranus.
Neptune.
The asteroids are distinguished by a circle enclosing a number,
which number mdicates the order of discovery, or by their names,
or by both, as (100) ; Hecate.
Spring (
signs. }
Summer \
signs. )
1.
2.
3.
4.
5.
6.
T
n
<l
m
SIGNS OF T
Aries.
Taurus.
Gemini.
Cancer.
Virgo.
HE ZODIAC.
Autumn
signs.
Winter
signs.
!*
[ 9.
;10.
! lle
!l2.
== Libra.
TTL Scorpius.
# Sagittarius.
V3 Capricornus,
? Aquarius.
K Pisces.
The Greek alphabet is here inserted to aid those who are not already
familiar with it in reading the parts of the text in which its letters
occur :
Letters.
Names.
A a
Alpha
B ft
Beta
r r
Gamma
A S
Delta
E s
Epsilon
ZC
Zeta
Hrf
Eta
050
Theta
It
Iota
K K
Kappa
A A
Lambda
M //
Mu
Letters.
N v
O o
n TtTt
PP
2 6 $
T r
TV
Names.
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
Chi
Psi
Omega
12 ASTRONOMY.
THE METRIC SYSTEM.
THE metric system of weights and measures being employed in
this volume, the following relations between the units of this system
most used and those of our ordinary one will be found convenient for
reference :
MEASURES OP LENGTH,
1 kilometre = 1000 metres = 0-62137 mile.
1 metre = the unit = 39-370 inches.
1 millimetre = ^fa of a metre = 0-03937 inctu
MEASURES OP WEIGHT.
1 kilogramme = 1000 grammes = 2-2046 pounds.
1 gramme = the unit = 15-432 grains.
The following rough approximations may be memorized :
The kilometre is a little more than T * ff of a mile, but less than f of
a mile.
The mile is l T 6 ff kilometres.
The kilogramme is 2\ pounds.
The pound is less than half a kilogramme.
One metre is 3-3 feet.
One metre is 39-4 inches.
CHAPTEB L
THE RELATION OF THE EARTH TO THE HEAVENS.
THE EARTH'S SHAPE AND DIMENSIONS.
The earth is a globe whose dimensions are gigantic
when compared with our ordinary and daily ideas of size.
Its shape is nearly a sphere, as has been abundantly
proved by the accurate geodetic surveys which have been
made by various nations.
Of its size we may get a rough idea by remembering
that at the present time it requires about three months to
travel completely around it.
To these familiar facts we may add two propositions
which are fundamental in astronomy.
I. The earth is completely isolated in space. The most
obvious proof of this is that men have visited nearly every
part of the earth's surface without finding anything to the
contrary.
II. The earth is one of a vast number of globular bodies,
familiarly known as stars and planets, moving according
to certain laws and separated by distances so immense that
the magnitudes of the bodies themselves are insignificant in
comparison to these distances. The first conception which
the student of astronomy has to form is that of living on
the surface of a spherical earth which, although it seems of
immense size to him, is really but a point in comparison
14 ASTRONOMY.
with the distances which separate him from the stars which
he nightly sees in the sky.
THE CELESTIAL SPHEKE.
When we look at a star at night we seem to see it set
against the dark surface of a holloy sphere in whose centre
we are.
All the stars seem to be at the same distance from us.
When we stop to consider, we see that it is quite possible
that some one of the many stars visible may be nearer
than some other, but as we have no immediate method
of knowing which of two stars is the nearer, we are driven
to speak of their apparent positions just as if they were
bright points studded over the inner surface of a large
hollow globe, and all at the same distance from us. The
radius of this globe is unknown. We do not, however,
think of any of the stars as beyond the surface and
shining through it. We therefore suppose the radius of
the sphere to be equal to or greater than the distance of
the remotest star.
Students generally fail at the outset to realize two very
important facts in relation to the celestial sphere. First,
that for all the purposes of our present knowledge the
relative positions of the stars on its surface do not vary.
Maps were made of these positions centuries ago which are
as correct now as old maps of portions of the earth. The
motions of the earth present different portions of the celes-
tial sphere to our observation at different times, and one
who has not thought at all of the subject might by that
fact be led to suppose that changes are taking place in the
relative positions of the stars themselves. Most people,
however, know that they can find the same groups of stars
RELATION OF THE EARTH TO THE HEAVENS. 15
" constellations, " as they are called in different direc-
tions from the observer's location on the earth, night after
night; the difference in the directions being due to the
earth's motions. Reflection on the foregoing will help the
student to realize the second important fact alluded to in the
beginning of this paragraph that for most practical pur-
poses of astronomy the earth may be regarded as a point
FIG. 4.
in the centre of a hollow globe whose inside surface is
spotted over with the stars, that hollow globe corresponding
to the celestial sphere. In fact ingenious instruments to
illustrate some of the truths of astronomy have been made
of large globes of glass or other transparent substances,
with the stars painted in their unvarying positions on the
16 ASTRONOMY.
inside surface, and the earth suspended at the centre by
supports rendered as nearly invisible as possible.
Suppose an observer at the point in the figure. If he
sees a star at the point Q it is clear that the real star may
be anywhere in space on the line OQ, as at q for example,
and still appear to be at Q.
Again, stars which appear to be at the points P, V, U,
T, S, R, may in fact be anywhere on the lines OP, V,
OU, OT, OS, OR. Thus, if there were three stars along
the line T, they would all be projected at the point T of
the celestial sphere, and would appear as one star.
The celestial sphere is the surface upon which we im-
agine the stars to be projected.
The projection of a body upon the celestial sphere is the
point in which this body appears to be, when seen from
the earth. This point is also called the apparent position
of the body. Thus to an observer at 0, T is the apparent
position of any of the stars whose true positions are t, t, t.
Hence it follows that positions on the celestial sphere re-
present the directions of the heavenly bodies from the ob-
server, but have no necessary relation to their distances.
If the observer changes his position, the apparent posi-
tions of the stars will also change.
We need some method of describing the apparent posi-
tions of stars on the celestial sphere; to do this we im-
agine a number of great circles to be drawn on its surface,
and to these circles we refer the apparent positions of the
stars.
A consideration of Fig. 2 will show the correctness of
the following propositions, which it is necessary should be
clearly understood:
I, Every straight line through the observer, when pro-
RELATION OF THE EARTH TO THE HEAVENS. 17
duced indefinitely, intersects the celestial sphere in two
opposite points.
II. Every plane through the observer intersects the
sphere in a great circle.
III. For every such plane there is one line through the
observer's position which intersects the plane at light
angles. This line meets the sphere at the poles of the
great circle which is cut from the sphere by the plane.
Example: P P' , Fig. 2, is a line through perpendicular
to the plane A B. P, P' are the poles of A B.
IV. Every line through the centre has one plane perpen-
dicular to it, which plane cuts the sphere in a great circle
whose poles are the intersection of the line with the
sphere.
Example: The Hue Q Q' has one plane C D through
perpendicular to it, and only this one.
THE HORIZON.
A level plane touching the spherical earth at the point
where an observer stands is called the horizon of that
observer.
This plane cuts the celestial sphere in a great circle,
which is called the celestial horizon. The celestial horizon
is therefore the boundary between the visible and the in-
visible hemispheres to that observer.
The Vertical Line. The vertical Jine of any observer is
the direction of a plumb-line where he stands. This line
is perpendicular to his horizon. It intersects the celestial
sphere in two points, called the zenith and the nadir of
that observer^
The zenith of an observer is thejpoint where his vertical
line cuts the celestial sphere above his head.
18 ASTRONOMY.
The nadir of an observer is the point where his vertical
line cuts the celestial sphere below his feet.
The zenith and nadir are the poles of the horizon.
Vertical Planes and Circles. A vertical plane with re-
spect to any observer is a plane which contains his vertical
line. It must pass through his zenith and nadir and must
be perpendicular to his horizon.
A vertical plane cuts the celestial sphere in a vertical
circle.
As soon as we imagine an observer to be at any point on
the earth's surface bis horizon
is at once fixed; bis zenith
and nadir arc also fixed. From
his zenith radiate a -number
of vertical circles which cut the
celestial horizon perpendicu-
larly, and unite again at his
nadir. This is a system of
lines and circles which every
. 5. person carries about with
him, as it were, and which may serve him for lines to
which to refer the apparent position of every star which he
Some one of these vertical circles will pass through any
and every star visible to this observer.
v The altitude of a heavenly body is its elevation above the
plane of the horizon measured on a vertical circle through
the star.
The zenith distance of a star is its angular distance from
the zenith measured on a vertical circle.
In the figure, Z 8 is the zenith distance () of S, and
(a) is its altitude. Z S H is an arc of a great circle;
RELATION OF THE EARTH TO THE HEAVENS. 19
the vertical circle through the star. ZS H = a -f = 90,
and <? = 90 - a or a = 90 - <?.
The altitude of a star in the zenith is 90; half way from
the zenith to the horizon it is 45; in the horizon it is 0.
T/ie azimuth of a star is the angular distance from the point
where the vertical circle through it meets the horizon, to the
north (or south) point of the horizon.
In the figure, NH is the azimuth of 8. The azimuth
of a star in the east or west is 90.
The prime vertical of an observer is that one of his verti-
cal circles which passes through his east and west points.
Co-ordinates of a Star. The apparent position of a heav-
enly body is completely fixed by means of its altitude and
azimuth. If we know the altitude and azimuth of a star
we can point to it.
If, for example, its azimuth is 20 from north towards
the west and if its altitude is 30, we can point to the star by
measuring an angle of 20 from the north point towards
the west, which will fix the foot of a vertical circle through
the star. The star itself will be on the vertical circle, 30
above the horizon.
This point, and this alone, will correspond to the posi-
tion of the star as determined by its altitude and azimuth.
Numbers (or quantities) which exactly define the position
of a body are called its co-ordinates.
Hence altitude and azimuth form a pair of co-ordinates
which fix the apparent position of a star on the celestial
sphere.
It must be remembered that these two co-ordinates give
only the position of the projection of the star on the celes-
tial sphere, and give no knowledge of its distance from the
observer. The body may be any where on the line defined
20 ASTRONOMY.
by the position on the celestial sphere and the place of the
observer.
If we also know the distance of the star from the obser-
ver, we know every possible fact as to its place in space.
Thus, three co-ordinates suffice to fix the absolute position
of a body in space ; two co-ordinates suffice to determine its
apparent position on the celestial sphere.
These propositions suppose the place of the observer to
be fixed, since the altitude and azimuth refer to an obser-
ver in some one definite position. If the observer should
change his place, the star remaining fixed, the apparent
position of the star on the celestial sphere would change to
him, owing to his own motion. The numbers which ex-
press this apparent position the altitude and azimuth of
the star would also change.
But wherever the observer is, if he has these two co-
ordinates for a star, the apparent place of the star is fixed
for him.
The Horizon. Since the earth is spherical in form, and
the horizon is a plane touching this sphere, every different
place must have a different horizon. Wherever an observer
goes on the earth's surface he carries an horizon, a zenith,
and a nadir with him, and a set of vertical circles to which
he can refer the positions of all the stars he sees. If lie
stays at a fixed point on the earth's surface his horizon is
always fixed with relation to his vertical line. But the
earth on which he stands is turning round its axis, and his
horizon being tangent to the earth is moving also v and the
vertical line moves with ifo The stars stay in the same abso-
lute places from year to year. The earth on which the
observer stands is turning round from west to east. His
horizon is thus brought successively to the east of the various
RELATION OF THE EARTH TO THE HEAVENS. 21
stars, which thus appear to rise higher and higher above
it.
The earth continues its motion, and the plane of his ho-
rizon finally approaches the same stars from the west and
they set below it, only to repeat this phenomenon with
every rotation of the earth.
The horizon appears to each observer to be the stable
thing, and the motion is referred to the stars. As a matter
of fact it is the stars that stand still and the horizon which
moves below them, causing them to appear to rise, and then
above them, causing them to appear to set.
THE DUTBNAL MOTION.
/ The diurnal motion is that apparent motion of the sun,
moon, and stars from east to west in consequence of which
they rise and, set>
We call it the diurnal motion because it repeats itself
from day to day. The diurnal motion is caused by a daily
rotation of the earth on an axis passing through its centre
called the axis of the earth.
This axis intersects the earth's surface in two opposite
points called the north and south poles of the earth. If the
earth's axis be prolonged in both directions, it meets the
celestial sphere in two points which are called the poles of
the celestial sphere or the celestial poles. The north celes-
tial pole corresponds to the north end of the earth's axis;
the south celestial pole to the south end.
The plane of the equator is that plane which passes
through the earth's centre perpendicular to its axis. This
plane intersects the earth's surface in a great circle of the
earth's sphere which is called the earth's equator (e q in
Fig. 6).
22 ASTRONOMY.
^
This plane intersects the celestial sphere in a great circle
of this sphere which is called the celestial equator or equi-
noctial (EQ in Fig. 6).
The celestial equator is everywhere half way between the
two celestial poles and thus 90 from each. The celestial
poles are thus the poles of the celestial equator.
Apparent Diurnal Motion of the Celestial Sphere. The
Fio.6.
observer on the earth is unconscious of its rotation, and
the celestial sphere appears to him to revolve from east to
west around the earth, while the earth appears to remain
at rest. The case is much the same as if he was on a
steamer which is turning round, and as if he saw the har-
bor-shores, the ships, and the houses apparently turning in
an opposite direction,
RELATION OF THE EARTH TO THE HEAVENS. 23
So far as appearances are concerned, it is quite the same
thing whether we conceive the earth to be at rest and the
heavens to turn about it, or whether we conceive the stars
to remain at rest and the earth to move on its axis. We
can explain all the phenomena of the diurnal motion in
either way. We must, however, remember that it really is
the earth which turns on its axis and successively presents
to the observer different parts of the celestial sphere. The
parts to his east are just coming into view (rising above his
horizon). The parts to his west are about to disappear,
(setting below his horizon).
Since the diurnal motion is an apparent rotation of the
celestial sphere about a fixed axis, it follows that there
must be two points of this sphere that remain at rest;
namely, the two celestial poles. Moreover, since the celes-
tial poles are opposite points, one pole must be above the
horizon and therefore a visible point of this sphere, and
the other pole must be below the horizon and therefore in-
visible.
The celestial pole visible to observers in the northern
hemisphere is the north pole. To locate its place in the
sky let the student look at the northern sky on any clear
evening.
He will see the stars somewhat as they are represented in
the figure.
In fact Fig. 7. shows the stars as they will appear to
an observer -in the month of August in the early hours of
the evening. But the configurations of the stars can be
recognized at any other time.
The first star to be identified is Polaris, or the Pole Star.
It may be found by means of the Pointers, two stars in the
constellation Ursa Major, familiarly known as the Great
24 ASTRONOMY.
Dipper. The straight line through theae stare, as shown
in the figure, passes near Polaris. Polaris is 1 degrees
from the true pole. There is no star exactly at the pole
itself.
The altitude of the pole-star above the horizon of any
place is equal to the latitude of the place, as will be shown
Fio. 7.
hereafter. Hence in most parts of the United States the
north pole is from 30 to 45 above the horizon. In Eng-
land it is 51, in Norway 60.
The north-polar distance of a star is its angular distance
from the north celestial pole.
RELATION OF THE EARTH TO THE HEAVENS. 25
The following laws of the diurnal motion will now be
clear:
I. Every star in the heavens appears to describe a circle
around the pole as a centre in consequence of the diurnal
motion.
II. The greater the star's, north-polar distance the larger
is the circle %
III. All- the stars -describe their diurnal orbits in the
same interval of time, which is the time required for the
earth to turn once on its axis.
The circle which & star appears to describe in the sky in
consequence of the diurnal motion of the earth is called the
diurnal orbit of that star.
These law* can be proved by observation. The student
can satisfy himself of their correctness in any clear night.
If the star's north-polar distance is less than the altitude
of the pole, the circle which the star describes will not
meet the horizon at all, and the star will therefore neither
rise nor set, but will simply perform an apparent diurnal
revolution round the pole. Such stars are shown in the
figure. The apparent diurnal motion of the stars is in the
direction shown by the arrows in the cut. Below the
pole the stars appear to move from left to right, west to
east;* above the pole they appear to move from east to
west.
The circle within which the stars neither rise nor set is
called the circle of perpetual apparition. The radius of
this circle is equal to the altitude of the pole above the
horizon, or to the north polar distance of the north point
of the horizon.
As a result of this apparent motion each individual con-
stellation changes its configuration with respect to the
26 ASTRONOMY.
horizon. That part of the constellation which is highest
when the group is above the pole becomes lowest when it
is below the pole. This is shown in the figure, which
represents a supposed constellation at different times of the
night as it revolves round the pole. The culmination of a
star occurs when it is at its highest point above the hori-
zon. The point of culmination is midway between the
points of rising and setting.
If the polar distance of a star exceeds the altitude of the
NORTH
FIG. 8.
pole, the star will dip below the horizon for a part of its
diurnal orbit, and the greater the polar distance of the
star the longer it will be below the horizon.
A star whose polar distance is 90 lies on the celestial
equator, and one half of its diurnal orbit is above and
one half below the horizon.
The sun is in the celestial equator about March 21st and
September 21st of each yeai, so that at these times the
RELATION OF THE EARTH TO THE HEAVENS. 27
days and nights are of equal length. This is why the
celestial equator was formerly called the equinoctial.
Looking further south at the celestial sphere, we shall
see stars which rise a little to the east of the south point of
the horizon and set a little to the west of this point, being
1 above the horizon but a short time. The south pole is as
far below the horizon of any place as the north pole is above
it. Hence stars near the south pole never rise in our
latitudes. The circle within which stars never rise is called
the circle of perpetual occultation.
It is clear that the positions of the circles of perpetual
apparition and occultation depend upon the position of the
observer upon the earth, and hence that they will change
"their positions as the observer changes his.
By going to Florida we may see groups of stars which
are not visible in the latitude of New York.
The Meridian. The plane ofjhe meridian of an observer
is that one of his vertical planes which contains the earth's
axis. Being a vertical plane it must contain the zenith
and nadir of the observer ; as it contains the earth's axis
it must contain the north and south celestial poles.
Different observers have different meridian planes, since
they have different zeniths.
The terrestrial meridian of an observer is the line in
which the plane of his meridian intersects the surface of
the earth. It is his north and south line.
It follows that if several observers are due north and
south of each other, they have the same terrestrial meridian.
The celestial meridian of an observer is the great circle
cut from the celestial sphere by the plane of that observer's
meridian. Persons on the same terrestrial meridian have
the same celestial meridian.
28 ASTRONOMY.
Terrestrial meridians are considered as belonging to the
places through which they pass. For example, we speak
of the meridian of Greenwich or of the meridian of Wash-
ington, and by this we mean the (terrestrial or celestial)
meridian lines cut out by the meridian plane of the Royal
Observatory at Greenwich or the Naval Observatory at
Washington.
THE DITTRNAL MOTION IN DIFFERENT LATITUDES.
As we have seen, the celestial horizon of an observer will
change its place on the celestial sphere as the observer travels
Fio. 9. THB PARALLEL SPHERE.
from place to place on the surface of the earth. If he
moves directly toward the north his zenith will approach the
north pole; but as the zenith is not a visible point, the
motion will be naturally attributed to the pole, which will
seem to approach the point overhead. The new apparent
position of the pole will change the aspect of the observer's
sky, as the higher the pole appears above the horizon the
RELATION OP THE EARTH 10 THE HEAVENS. 29
greater the circle of perpetual apparition, and therefore the
greater the number of stars which never set.
If the observer is at the north pole his zenith and the
pole itself will coincide : half of the stars only will be vis-
ible, and these will never rise or set, but appear to move
around in circles parallel to the horizon. The horizon and
the celestial equator will coincide. The meridian will be
indeterminate since Z and. P coincide; there will be no east
and west line, and no direction but south. The sphere in
this case is called & parallel sphere. (See Fig. 9.)
FIG. 10. THE RIGHT SPHERE.
If instead of travelling to the north the observer should
go toward the equator, the north pole would seem to ap-
proach his horizon. When he reached the equator both
poles would be in the horizon, one north and the other
south. All the stars in succession would then be visible,
and each would be an equal time above and below the
horizon. (See Fig. 10.)
The sphere in this case is called a right sphere, because
the diurnal motion is at right angles to the horizon. If
30 ASTRONOMY.
now the observer travels southward from the equator, the
south pole will become elevated above his horizon, and in
the southern hemisphere appearances will be reproduced
which we have already described for the northern, except
that the direction of the motion will, in one respect, be
different. The heavenly bodies will still rise in the east
and set in the west, but those near the equator will pass
north of the zenith instead of south of it, as in our lati-
tudes. The sun, instead of moving from left to right,
there moves from right to left. The bounding line be-
tween the two directions of motion is the equator, where
the sun culminates north of the zenith from March till
September, and south of it from September till March.
If the observer travels west or east of his first station,
his zenith will still remain at the same angular distance
from the north pole as before, and as the phenomena
caused by the earth's diurnal motion at any place depend
only upon the altitude of the elevated pole at that place,
these will not be changed except as to the times of their
occurrence. A star which appears to pass through the
zenith of his first station will also appear to pass through
the zenith of the second (since each star remains at a con-
stant angular distance from the pole), but later in time,
since it has to pass through the zenith of every place be-
tween the two stations. The horizons of the two stations
will intercept different portions of the celestial sphere at
any one instant, but the earth's rotation will present the
same portions successively, and in the same order, at both.
RELATION OF THE EARTH TO THE HEAVENS. 31
CORRESPONDENCE OF THE TERRESTRIAL AND CELESTIAL
SPHERES.
We have seen that the altitude of the pole above the
horizon of any observer changes as the observer changes
his place on the earth's surface. The exact relation of the
altitude of the pole and the horizon of any observer is
expressed in the following THEOREM: The altitude of the
celestial pole above the horizon of any place on the earth's
surface is equal to the lati-
tude of that place.
Let L be a place on the
earth P Ep Q, Pp being
the earth's axis and E Q its
equator. Z is the zenith of
the place, and H R its hori-
zon. L Q is the latitude
of L according to ordinary
geographical definitions; i.e.,
it is the angular distance of
L from the equator. Pro-
long OP indefinitely to P' FIG. n.
and draw L P" parallel to it. P' and P" are points on
the celestial sphere infinitely distant from L. In fact
they appear as one point since the dimensions of the earth
are vanishingly small compared with the radius of the
celestial sphere, which may be taken as large as we please.
We have then to prove that L Q = P" L H. P OQ
and Z L Hare right angles, and therefore equal. Z LP"
= ZOP' by construction. Hence ZLH-ZLP" =
P Q - Z P', or the latitude of the point L is meas-
ured by either of the equal angles L Q or P
32 ASTRONOMY.
If we denote the latitude by cp it follows that the N.P.D.
(north-polar distance) of Z is 90 - (p. As an observer
moves to various parts of tKe earth, his zenith changes
position with him. In every' position the N.P.D. of his
zenith is 90 <p. If he is at the equator his cp is and
his zenith is 90 from the north pole, which must there-
fore be in his horizon. If he is at the north pole, q> = -|-
90 and the N.P.D. of his zenith is 0, or his zenith co-
incides with the north pole. If he is at the south pole
(cp = - 90) the N.P.D. of his zenith is 90 - (- 90)
or 180. That is, his zenith is 180 from the north pole,
or it must coincide with the south pole ; and so in other
cases.
All this has just been shown (pages 28-30) in another
way, but it is of the first importance that it should be not
only clear but familiar to the student. When he sees any
astronomical diagram in which the north pole and the hori-
zon are laid down he can at once tell for what latitude this
diagram is constructed. The elevation of the pole above
the horizon measures the latitude of the observer, to whose
station this particular diagram applies.
Change of the Position of the Zenith of an Observer by
the Diurnal Motion. In Fig. 12 suppose n e s q to repre-
sent the earth and NE S Q the celestial sphere. The earth,
as we know, is rotating on the axis N S. We have now to
inquire what are the real circumstances of this motion.
The apparent phenomena have been previously described.
Eemember that the vertical line of an observer is (practi-
cally) that of a radius of the earth passing through his
station. If the observer is at n his zenith is at N P.
If he is at s his zenith is at S P. If the observer
ig in 45 north latitude, he is carried round by the
RELATION OF THE EARTH TO THE HEAVENS. 33
rotation of the earth in a small circle of the earth's surface
whose plane is perpendicular to the earth's axis. This is
the parallel of 45, so called,^nd is indicated in the figure.
His zenith is always directly^bove him, and therefore his
zenith must describe each day a circle M L on the celestial
sphere corresponding to this parallel on the earth; that is,
Fio. 12.
a circle half way between the celestial pole and the celestial
equator. Now, suppose the observer to be on the equator
e q. His zenith will then be 90 from either pole. As the
earth revolves on its axis his zenith will describe a great
circle E Q on the celestial sphere. This circle is the celestial
equator. An observer at 45 south latitude will ha*ve a
34 ASTRONOMY.
parallel SO marked out on the celestial sphere by the
motion of his zenith due to the earth's rotation, and so on.
Thus, for each parallel of la^ude on the earth we have a
corresponding circle on thcelestial sphere, and each of
these latter circles has its poles at the celestial poles.
Not only are there circles of the celestial sphere which
correspond to parallels of latitude on the earth, but there
are also celestial meridians corresponding to the various
terrestrial meridians. The plane of the meridian of any
place contains the zenith of that place ;md the two celestial
poles. It cuts from the earth's surface the terrestrial
meridian and from the celestial sphere that great circle
which we have defined as the celestial meridian. To fix
the ideas let us suppose an observer at some one point of
the earth's surface. A north and south line on the earth
at that point is the visible representative of his terrestrial
meridian. A plane through the centre of the earth and
that line contains his zenith, and cuts from the celestial
sphere the celestial meridian. As the earth rotates on its
axis his zenith moves around the celestial sphere in a
parallel as Z L in the last figure. Suppose that the east
point is in front of the picture, the west point being be-
hind it. Then as the earth rotates the zenith Z will move
along the line Z L from Z towards L. The celestial meri-
dian always contains the celestial poles and the point Z,
wherever it may be. Hence the arcs of great circles join-
ing N.P. and S.P. in the figure are representatives of the
celestial meridian of this observer, at different times dur-
ing the period of the earth's rotation. They have been
drawn to represent ;the places of the meridian at intervals
of 1 hour* That is, 12 of them are drawn to represent
12 consecutive positions of the meridian during a semi-
RELATION OF THE EARTH TO THE HEAVENS. 35
revolution of the earth. In this time Z moves from Z to
L. In the next semi-revolution Z moves from L to Z,
along the other half of the parallel Z L. In 24 hours
the zenith Z of the observer has moved from Z to L and
from L back to Z again. The celestial meridian has also
swept across the heavens from the position N.P., Z, Q, S,
8. P. through every intermediate position to N.P., L, E, 0,
., and from this last position back to N.P., Z, Q, 8,
8. P. The terrestrial meridian of the observer has been
under it all the time. This real revolution of the celestial
meridian is incessantly repeated with every revolution of
the earth. The sky is studded with stars all over the
sphere. The celestial meridian of any place approaches
these various stars from the west, passes them, and leaves
them. This is the real state of things. Apparently the
observer is fixed. His terrestrial and celestial meridians
seem to him to be fixed, not only with reference to himself,
as they are, but to be fixed in space. The stars appear to
him to approach his celestial meridian from the east, to
pass it, and to move away from it towards the west.
When a star crosses the celestial meridian it is said to
culminate. The pa-sage of the star across the meridian is
called the transit of that star. This phenomenon takes
place successively for each observer on the earth. Suppose
two observers, A and B, A being one hour (15) east of
B in longitude. This means that the angular distance of
their terrestrial meridians is 15 (see page 10). From what
we have just learned it follows that their celestial meri-
dians are also 15 apart. When B's meridian is N.P.,
Z, Q, R, S.P., A's will be the first one (in the figure)
beyond it; when B's meridian has moved to this first posi-
tion, A's will be in the second, and so on, always 15
36 ASTRONOMY.
(1 hour) in advance. A group of stars which has just come
to A's meridian will not pass B's for 1 hour. When they
are on B's meridian they will be 1 hour west of A's, and
so on. Notice also that A's zenith is always 15 east of
B's.
The same stars will successively rise, culminate, and set
to each observer, but the phenomena will be presented to
the eastern observer sooner than to the other.
FIG. 12.
If N be the earth, and a a spectator whose zenith is at
Z &t the instant chosen for making the picture, and Z', Z"
at subsequent times, his horizon must successively take the
positions H, H', H". . . The stars near E (the east point)
will successively appear to rise, as the horizon falls below
them, while those near W will successively appear to set.
It is obvious that the observer I will see these appearances
earlier than a.
CHAPTER II.
THE RELATION OF THE EARTH TO THE HEAVENS
(Continued.)
THE CELESTIAL SPHERE.
Systems of Co-ordinates. The great circles of the celestial
sphere which pass through the two celestial poles are called
hour-circles. Each hour-circle is the celestial meridian of
some place on the earth.
The hour-circle of any particular star is that one which
passes through the star at the time. As the earth revolves,
different hour-circles, or celestial meridians, come to the
star.
In Fig. 13 let be the position of the earth in the centre of
the celestial sphere NZ SD. Let Zbe the zenith of the ob-
server at a given instant, and P, p, the celestial poles. By
definition P ZSpnNP is his celestial meridian. (Each
of these points has a name; let the student give the names
in order.) N S is the horizon of the observer at the instant
chosen. PO N is his latitude. If P is the north pole, he
is in latitude 34 north. (See page 31.)
E WD is the celestial equator; E and W are the east
and west points. The earth is turning from W to E. That
is, the celestial meridian which at the instant chosen in the
picture contains P Zp was in the position P D Rp twelve
hours earlier.
38 ASTRONOMY.
PC, PB 9 PV, PD are parts of hour-circles. If A is
a star, P B is the hour-circle of that star. As the earth
turns PB turns with it, and directly P B will have moved
away from A towards the top of the picture and soon P V
will pass through the star A, which stands still. When it
does, PV will be the hour-circle of A. At the instant
chosen P B is the hour-circle of A. The stars inside the
circle NK are always above the observer's horizon. Im is
FIG. 13.
half of the diurnal orbit of one of the north stars. All the
stars inside the circle SR are perpetually invisible to the
observer, or is half of the orbit of one of these southern
stars. The north-polar distance of all those stars perpetu-
ally aboTe the horizon is less than or equal ioPN\ the
south-polar distance of all the stars perpetually invisible is
less than or equal to p S, which is equal to P N.
RELATION OP THE EARTH TO THE HEAVENS. 39
Altitude and Azimuth. Z G is the vertical circle of the
star A at the instant chosen for making the picture. In
a few moments Z will have moved eastwards and a new
vertical circle will have to be drawn. G A is the altitude
of A at the instant; in a few moments it will be less. For
as Z moves towards the eastward, N W S, the western hori-
zon of the observer, will move upwards (in the drawing)
and come nearer to A, which stands still. Therefore the
altitude of A will diminish progressively. It is now GA.
The azimuth of A is now NG, counted from the north
point. It will change as Z changes. Having the altitude
and azimuth of A at the instant, the observer at can find
it in the sky. (See page 18.)
North-Polar Distance and Hour- Angle. The north-polar
distance of A is PA. This will serve as one of a pair of
co-ordinates to point out the apparent position of A- in the
sky.
The hour-angle of a star is the angular distance between
the celestial meridian of the place and the hour-circle of
that star. The hour-angle is counted from the meridian
towards the west from to 360, or from O h to 24 h . The
hour-angle of A, at this instant, is Z P B. The hour-
angle of a star K is 0.
The hour-angle is measured by the arc of the equator
between the celestial meridian and the foot of the hour-
circle through the star. The arc C B measures the hour-
angle of A at the instant. Directly, Z will have moved away
to the east and will move away also along the dotted part
of the line representing the equator, W CUD.
Having the two co-ordinates PA and C B, the observer
at" can find the star A. It will be noticed that these two
co-ordinates, polar distance and hour-angle, differ in one
40 ASTRONOMT.
respect from the two co-ordinates altitude and azimuth.
Both the latter change as the earth revolves on its axis. Of
the former only one changes; viz., the hour-angle. The
polar distance of a star remains the same, since it is the dis-
tance from a fixed point, the pole, to a fixed point, the star.
Right Ascension and North-Polar Distance. We can
devise a pair of co-ordinates neither of which shall change
as the earth revolves. This will clearly be convenient, for
this pair of co-ordinates will be the same for every observer
and for every hour of the day, whereas the others vary with
the time, and with the situation of the observer.
To select such a pair we have simply to use fixed points
in the celestial sphere to count from. The north pole will
do for one of these, and the north-polar distance of the star
will serve for one co-ordinate. This is measured, for the
star A y on the hour-circle P B. Let us choose some fixed
point V on the equator to measure our other co-ordinate
from, and let us always measure it on the equator towards
the east from to 360 (from O h to 24 h ). That is, from
V through B, C, E y D, W, successively.
V B is the right ascension of A. The right ascension of
a star is the angular distance of the foot of the hour-circle
through the star from the vernal equinox, measured on tlte
celestial equator, towards the east.
Exactly what the vernal equinox is we shall find out
later on; for the present it is sufficient to define it as a
certain fixed point on the celestial equator.
If we have the right ascension and north-polar distance
of a star, we can point it out. Thus V B and PA define
the position of A. As long as the pole, the star, and the
vernal equinox do not move relatively to each other these
two co-ordinates fix the position of the star. Their relative
RELATION OF THE EARTH TO THE HEAVENS. 41
positions are not affected by the rotation of the earth, nor
by the position of the observer upon its surface. He may
be in any latitude or any longitude, and his zenith may be
anywhere in, the whole sky, but the right ascension and
the north-polar distance of each star remain the same nev-
ertheless.
The right ascension of the star K is V 0. Of a star at E
it is V CE-, of a star at D it is VGED\ of a star at W
it is V C ED W, and so on.
Right Ascension and Decimation. Sometimes in place
of the north-polar distance of a star it is convenient to
use its declination.
The declination of a star is its angular distance north or
south of the celestial equator.
The declination of A is BA y which is 90 minus PA.
The relation between N. P. D. and d is
N. P. D. = 90 - tf; d = 90 - N. P. D.
North declinations are -J-; South declinations are .
The declination of Z is C Z. CZ is equal to P N, since
each is equal to 90 PZ. PN measures the latitude of
the observer whose zenith is Z. (See page 31.)
TJie latitude of a place on the earth's surface is measured
ly the declination of its zenith,
This is the definition of the latitude which is used in
astronomy.
Co-ordinates of a Star. In what has gone before we have
seen that there are various ways of expressing the apparent
positions of stars on the surface of the celestial sphere.
That one most commonly used in astronomy is to give the
right ascension and north-polar distance (or declination) of
the star. The apparent position of the star is fixed by these
42 ASTRONOMY.
two co-ordinates. If we know its distance also, the abso-
lute position of the star in space is fixed by the three co-
ordinates. Thus we have a complete method of describing
the positions of the heavenly bodies.
Co-ordinates of an Observer. To describe the position of
an observer on the surface of the earth we have to give his
latitude and longitude. His latitude is the declination of
his zenith; his longitude is the fixed angle between his
celestial meridian and the celestial meridian of Greenwich
(or Washington). Declination in the sky is analogous to
Latitude on the earth. Right ascension in the sky is anal-
ogous to Longitude on the earth. Both of these co-ordi-
nates depend upon the position of his zenith, since his
longitude is nothing but the angular distance of his zenith
west of the zenith of Greenwich.
All this is extremely simple, but if it is clearly under-
stood the student has it in his power to answer a great
many interesting questions for himself.
We know, for example, that the sun is in the equator and at the
vernal equinox on March 21st of each year.
The student can determine for himself what appearances will be
presented on that day next year. He may proceed in this way: Draw
a circle to represent the celestial sphere. Take a point, P, of it to
be the position of the north pole in the sky. If the observer lives
in a place whose latitude is <p degrees north, his zenith will be
90 <p from the north pole measured towards the south. Measure
off 9(T q> on the circle from P. The end of that arc is the zenith
of that observer, Z. PZ is an arc of his celestial meridian. Meas-
ure from P through Z 90, and the end of that arc is on the equator,
Q say. Join P with the centre, 0, of the circle. This line is the
direction of the celestial pole. Join and Q, and this line (perpen-
dicular to P 0) is the direction of that point of the equator which is
highest above his horizon. Draw the liueZO; this is the vertical
line. Through draw NOS perpendicular to Z 0. This is the north
and south line of his horizon. Draw the ovals which represent (in
RELATION Of THE EARTH TO THM HEAVENS. 43
perspective) the circles of the equator and of the horizon. Assume
a point, V, of the celestial equator. On March 21st of each year the
sun is there. When the sun is at the highest point Q of the equatoi
it is noon to this observer. The sun is on his meridian. Six hours
before this time the sun will rise to him; six hours after he will
set. It requires twenty-four hours for the point Fto be apparently
carried all round the equator, and the sun appears to go with the
point. Three months later the sun is about 90 of right ascension
and has a north polar distance of 66|. The student can determine
in the same way the circumstances under which the sun will appear
to him to move on the 21st of next June when its north-polar distance
is 664, or on December 21st, when its K P. D. is 113f.
The example that is here given is not for the purpose of teaching
the student what the motion of the sun is; that will be considered in
its proper order in this book. But it is to show him that if he wishes
to know about it he can find out for himself.
When he reads about the midnight sun that is visible in the Arctic
regions he can verify the facts for himself. Let him construct the
diagram we have described for a place whose latitude is 80 north
and see what sort of a diurnal orbit the sun will describe on the 21st
of June when its N. P. D. is 66^.
RELATION OF TIME TO THE SPHEEE.
Sidereal Time. The earth rotates uniformly on its axis;
that is, it turns through equal angles in equal intervals of
time.
This rotation can be used to measure any intervals of
time when once a unit of time is agreed upon. The most
natural and convenient unit is a day. There are various
kinds of days, and we have to take them as they are.
A sidereal day is the interval of time required for the
earth to rotate once on its axis. Or what is the same thing,
it is the interval of time between two consecutive tran-
sits of any star over the same celestial meridian. The
sidereal day is divided into 24 sidereal hours; each hour is
divided into 60 minutes; each minute into 60 seconds. In
making one revolution the earth turns through 360, so that
44 ASTRONOMY.
24 hours = 360; also,
1 hour = 15; 1 = 4 minutes.
1 minute = 15'; 1' = 4 seconds.
1 second = 15*; 1' = 0.066 second.
When a star is on the celestial meridian of any place its
hour-angle is zero, by definition (see page 39). It is then
at its transit or culmination.
As the earth rotates, the meridian moves away (east-
wardly) from this star, whose hour-angle continually in-
creases from to 360, or from hours to 24 hours.
Sidereal time can then be directly measured by the hour-
angle of any star in the heavens which is on the meridian
at an instant we agree to call sidereal hours. When this
star has an hour-angle of 90, the sidereal time is 6 hours;
when the star has an hour angle of 180 (and is again on
the meridian, but invisible unless it is a circumpolar star), it
is 12 hours ; when its hour-angle is 270, the sidereal time
is 18 hours; and, finally, when the star reaches the upper
meridian again, it is 24 hours or hours. (See Fig. 13,
where E C WD is the apparent diurnal path of a star in
the equator. It is on the meridian at C.)
Instead of choosing a star as the determining point
whose transit marks sidereal hours, it is found more con-
venient to select that point in the sky from which the right
ascensions of stars are counted the vernal equinox the
point V in the figure. The fundamental theorem of si-
dereal time is: The hour-angle of tie vernal equinox, or the
sidereal time, is equal to the right ascension of the meri-
dian; that is, C V= VO.
To avoid continual reference to the stars, we set a clock
so that its hands shall mark hours minutes seconds
RELATION OF THE fiAllTII TO THE HEAVENS. 45
at the transit of the vernal equinox, and regulate it so that
its hour-hand revolves once in 24 sidereal hours. Such a
clock is called a sidereal clock.
Solar Time. Time measured by the hour-angle of the
sun is 'called true or apparent solar time. An apparent
solar day is the interval of time between two consecutive
transits of the sun over the upper meridian. The instaut
of the -transit of the sun. over the meridian of anyplace
is the apparent noon of that place, or local apparent noon.
When the sun's hour-angle is 12 hours or 180, it is
local apparent midnight.
The ordinary sun-dial marks apparent solar time. As
a matter of fact, apparent solar days are not equal. The
reason for this will be fully explained later. Hence our
clocks are not made to keep this kind of time, for if once
set right they would sometimes lose and sometimes gain
on such time.
Mean Solar Time. A modified kind of solar time is
therefore used, called mean solar time. This is the time
kept by ordinary watches and clocks. It is sometimes
called civil time. Mean solar time is measured by the hour-
angle of the mean sun, a fictitious body which is imagined
to move uniformly in the equator. The law according to
which the mean sun is supposed to move enables us to com-
pute its exact position in the heavens at any instant, and to
define this position by the two co-ordinates right ascension
and declination. Thus we know the position of this imagi-
nary body just as we know the position of a star whose
co-ordinates are given, and we may speak of its transit as
if it were a bright material point in the sky. A mean
solar day is the interval of time between two consecutive
transits of the mean sun over the upper meridian. Mean
46 ASTRONOMY.
noon at any place on the earth is the instant of the mean
sun's transit over the meridian of that place. Twelve hours
after local mean noon is local mean midnight. The mean
solar day is divided into 24 hours of 60 minutes each. Each
minute of mean time contains 60 mean solar seconds.
Astronomers begin ^the mean solar day at noon, which is
hours, and count round to 24 hours.
"We have thus three kinds of time. They are alike in one point:
each is measured by the hour-angle of some body, real or assumed.
The body chosen determines the kind of time, and the absolute length
of the unit the day. The simplest unit is that determined by the
uniformly rotating earth the sidereal day; the most natural unit is
that determined by the sun itself the apparent solar day, which,
however, is a variable unit; the most convenient unit is the mean
solar day, and this is the one chosen for use in our daily life.
Comparative Lengths of the Mean Solar and Sidereal
Day. As a fact of observation, it is found that the sun
appears to move from west to east among the stars, about
1 daily, making a complete revolution around the sphere
in a year. It requires 365 days to move through 360.
Hence an apparent solar day will be longer than a side-
real day. For suppose the sun to be at the vernal equinox
exactly at sidereal noon (0 hours) of Washington time on
March 21st; that is, the vernal equinox and the sun are
both on the meridian of Washington at the same instant.
In 24 sidereal hours the vernal equinox will again be on the
same meridian, but the sun will have moved eastwardly by
about a degree, and the earth will have to turn through
this angle and a little more in order that the sun shall
again be on the Washington meridian, or in order that it
may be apparent noon on March 22d. For the meridian
to overtake the sun requires about 4 minutes of ^sidereal
RELATION OF THE EARTH TO THE HEAVENS. 47
time. The true sun does not move, as we have said, uni-
formly. The mean sun is supposed to move uniformly,
and to make the circuit of the heavens in the same time as
the real sun. Hence a mean solar day will also be longer
than a sidereal day, for the same reason that the apparent
solar day is longer. The exact relation is:
1 sidereal day = 0^997 mean solar day,
24 sidereal hours = 23 h 56 m 4 s -091 mean solar time,
1 mean solar day = 1-003 sidereal days,
24 mean solar hours = 24 h 3 m 56 s -555 sidereal time,
and
366-24222 sidereal days = 365-24222 mean solar days.
Local Time. When the mean sun is on the meridian of
a place, as Boston, it is mean noon at Boston. When the
mean sun is on the meridian of St. Louis, it is mean noon
at St. Louis. St. Louis being west of Boston, and the
earth rotating from west to east, the local noon of Boston
occurs before the local noon at St. Louis. In the same
way the local sidereal time at Boston at any given instant
is expressed by a larger number than the local sidereal time
of St. Louis at that instant.
The sidereal time of mean noon is given in the astro-
nomical ephemeris for every day of the year. It can be
found within ten or twelve minutes at any time by remem-
bering that on March 21st it is sidereal hours about
noon, on April 21st it is about two hours sidereal time at
noon, and so on through the year. Thus, by adding two
hours for each month, and four minutes for each day after
the 21st day last preceding, we have the sidereal time at
the noon we require. Adding to it the number of hours
since noon, and, one minute more for every fourth of a day
48 ASTRONOMY.
on account of the constant gain of the clock (4 m daily), we
have the sidereal time at any moment,
Example. Find the sidereal time on July 4th, 1381, at 4 o'clock
A.M. We have:
h m
June 21st, 3 mouths after March 21st; to be X 2, 60
July 3d, 12 days after June 21st; X 4, 48
4 A.M., 16 hours after noon, nearly f of a day, 16 3
22 51
This result is within a miuute of the exact value.
Relation of Time and Longitude. Considering our civil
time which depends on the sun, it will be seen that it is
noon at any and every place on the earth when the sun
crosses the meridian of that place, or, to speak with more
precision, when the meridian of the place passes under the
sun. In the lapse of 24 hours the rotation of the earth on
its axis brings all its meridians under the sun in succession,
or, which is the same thing, the sun appears to pass in suc-
cession over all the meridians of the earth. Hence noon
continually travels westward at the rate of 15 in an hour,
making the circuit of the earth in 24 hours. The differ-
ence between the time of day, or the Inntl lime as it is called,
at any two places will be in proportion to their difference
of longitude, amounting to one hour for every 15 degrees of
longitude, four minutes for every degree, and so on. Vice
versa, if at the same real moment of time we can determine
the local times at two different places,* the difference of these
times multiplied by 15 will give the difference of longitude.
The longitudes of places are determined astronomically
on this principle. Astronomers are, however, in the habit
of expressing the longitude of places on the earth like the
* And compare the two, by telegraph for example.
RELATION OF THE xmRTH TO THE HEAVEN 8. 49
right ascensions of the heavenly bodies, not in degrees, but
in hours. For instance, instead of saying that Washington
is 77 3' west of Greenwich, we commonly say that it is 5
hours 8 minutes 12 seconds west, meaning that when it is
noon at Washington it is 5 hours 8 minutes 12 seconds
after noon at Greenwich. This course is adopted to prevent
the trouble and confusion which might arise from constantly
having to change hours into degrees and the reverse.
Where does the Day Change? A question frequently
asked in this connection is, Where does the day change?
It is, we will suppose, Sunday noon at Washington. That
noon travels all the wny round the earth, and when it gets
back to Washington again it is Monday. Where or when
did it change from Sunday to Monday ? We answer,
wherever people choose to make the change. Navigators
make the change occur in longitude 180 from Greenwich.
As this meridian lies in the Pacific Ocean, and meets
scarcely any land through its course, it is very convenient for
this purpose. If its use wore universal, the day in question
would be Sunday to all the inhabitants east of this line, and
Monday to every one west of it. But in practice there have
been some deviations. As a general rule, on those islands
of the Pacific which were settled by men travelling east the
day would at first be called Monday, even though they
might cross the meridian of 180. Indeed the Russian
settlers carried their count into Alaska, so that when our
people took possession of that territory they found that
the inhabitants called the day Monday when they them-
selves called it Sunday. These deviations have, however,
almost entirely disappeared, and with few exceptions the
day is changed by common consent in longitude 180 from
Greenwich,
50 ASTRONOMY.
DETERMINATIONS OF TEBRESTBIAL LONGITUDES
Owing to the rotation of the earth, there is no such fixed
correspondence between meridians on the earth and among
the stars as there is between latitude on the earth and de-
clination in the heavens. The observer can always deter-
mine his latitude by finding the declination of his zenith,
but he cannot find his longitude from the right ascension
of his zenith with the sumo facility, because that right as-
cension is constantly changing. To determine the longi-
tude of a place, the element of time as measured by the
diurnal motion of the earth necessarily comes in. Con-
sider the plane of the meridian of a place extended out to
the celestial sphere so as to mark out on the latter the
celestial meridian of the place. Take two such places,
Washington and San Francisco for example ; then there
will be two such celestial meridians cutting the celes-
tial sphere so as to make an angle of about forty-five de-
grees with each other in this case. Let the observer imagine
himself at San Francisco. Then he may conceive the
meridian of Washington to be visible on the celestial sphere,
and to extend from the pole over toward his south-east
horizon so as to pass at a distance of about forty-five degrees
east of his own meridian. It would appear to him to be at
rest, although really both his own meridian and that of
Washington are moving in consequence of the earth's rota-
tion. Apparently the stars in their course will first pass
the meridian of Washington, and about three hours later
will pass his own meridian. Now it is evident that if he
can determine the interval which the star requires to pass
from the meridian of Washington to that of his own place,
he will at once have the difference of longitude of the two
RELATION OF THE EAETH TO THE HEAVENS. 51
places by simply turning the interval in time into degrees
at the rate of fifteen degrees to each hour.
FIG. 14.
The difference of longitude between any two places de-
pends upon the angular distance of the terrestrial (or celes-
tial) meridians of these two places and not upon the motion
of the star or sun which is used to determine this angular
difference, and hence the longitude of a place is the same
whether expressed as the difference of two sidereal or of
two solar times. The longitude of Washington west from
Greenwich is 5 h 8 m or 77, and this is in fact the ratio of
the angular distance of the meridian of Washington from
that of Greenwich, to 24 hours or 360. The angle between
the two meridians is -gfo of 24 hours, or of a whole circum-
ference.
52 ASTRONOMY.
It is thus plain that the difference of longitude of any tivo
places is the same as the difference of their simultaneous
local times ; and this whether the local times spoken of
are both sidereal or both solar.
METHODS OF DETERMINING THE DIFFERENCE OF LONGI-
TUDE OF Two PLACES ON THE EARTH.
Every purely astronomical method depends upon the
principle we have just laid down.
It is of vital importance to seamen to be able to deter-
mine the longitude of their vessels. The voyage from Liv-
erpool to New York is made weekly by scores of steamers,
and the safety of the voyage depends upon the certainty
with which the captain can mark the longitude and lati-
tude of his vessel upon the chart.
The method used by a sailor is this : with a sextant (see
Chapter III.) the local time of the ship's position is deter-
mined by an observation of the sun. That is, on a given
day he can set his watch so that its hands point to twelve
hours when the sun is on his meridian on that day. He
carries a chronometer (which is merely a very fine watch)
whose hands point always to Greenwich time. Suppose
that when the ship's time is O h or noon the Greenwich
time is 3 h 20 m . Evidently he is west of Greenwich 3 h 20 ra ,
since that is the difference of the simultaneous local times,
and since the Greenwich time is later. Hence he is some-
where on the meridian of 50 west. If he has determined
the altitude of the pole or the declination of his zenith in
any way, then he has his latitude also. If this should be
45 north, the ship is in the regular track between New
York and Liverpool, and he can go on with safety.
RELATION OF THE EARTH TO THE HEAVENS. 53
When the steamer Faraday was laying the direct cable she got her
longitude every day by comparing her ship's time (found by obser-
vation on board) with the Greenwich time telegraphed along the cable
and received at the end of it which she had on her deck. Longitudes
may be determined in the same way on shore.
From an observatory, as Washington, the beats of a clock are sent
out by telegraph along the lines of railway; at every railway station
and telegraph office the telegraph sounder beats the seconds of the
Washington clock. Any one who can set his watch to the local time
of his station and who can compare it with the signals of the Wash-
ington clock (which are sent at Washington noon, daily except Sun.
day) can determine for himself the difference of the simultaneous
local times of Washington and of his station, and thus his own longi-
tude east or west from Washington.
METHODS OF DETERMINING THE LATITUDE OF A PLACE
ON THE EARTH.
Latitude from Circumpolar Stars. In the figure sup-
pose Z to be the zenith of the observer, H ZRN his me-
90 - cp = p -f z',
90 - <p = z" -p,
90 - <p = \(z' + z");
p = i(z" - z').
Fia. 15.
ridian, P the north pole, H R his horizon. Suppose Sand.
S' to be the two points where a circumpolar star crosses
the meridian, as it moves around the pole in its apparent
54
ASTRONOMY.
diurnal orbit. P 8 = P S' is the star's north-polar dis-
tance, and P H = (p = the observer's latitude.
ZS+ZS'
Therefore
<p = 90 -
= ZP = 90 - (p.
ZS+ZS'
We can measure Z S and Z S', the zenith distances of the
star in the two positions, by the meridian circle or by the
sextant, as will be explained in the next chapter. Hence
having these zenith distances we have the latitude of the
place.
Latitude by the Meridian Altitude of the Sun or a Star.
In the figure let Z be the observer's zenith, P the pole,
and Q the intersection of
the celestial equator with the
meridian H Z H. The alti-
tude of the star S is meas-
ured when the star is on the
meridian. It is known to
be on the meridian when we
find its altitude to be a max-
Fl0 - 16 - imum. From the measured
altitude of the star S we deduce its zenith distance Z S = 2
= 90 HS. Its declination is taken from a catalogue of
stars if it is a star, or from the Nautical Almanac if it is
the sun. In either case the declination Q S is known.
ZQ = QS + ZS-,
If the body culminates north of the zenith at /S",
ZQ=QS'-ZS'i
<z= 6 -2.
vT
RELATION OF THE EARTH TO THE HEAVENS. 55
This is the method uniformly employed at sea, where the
altitude of the sun at apparent noon is daily measured.
PARALLAXES AND SEMIDIAMETERS OF THE HEAVENLY
BODIES.
The apparent position of a body on the celestial sphere
remains the same as long as the observer is fixed, as has
been shown (see page 20). If the observer changes his
place and the star remains in the same position, the ap-
Fio. 17.
parent position of the star will change. To show this let
CH' be the earth, C being its centre. 8' and S" are the
places of two observers on the surface. Z' and Z" are
their zeniths in the celestial sphere H' P" . P is a star.
S' will see P in the apparent position P f . S" will see P
in the apparent position P". That is, two different ob-
servers see the same object in two different apparent
positions. If the observer 8' moves along the surface
directly to S", the apparent position of P on the celes-
tial sphere will appear to move from P' to P".
This change is due to the parallax of P.
56 ASTRONOMY.
The parallax of a body due to a change in the position
of the observer, is the alteration in the apparent position
of the body caused by that change.
If the observer at S' could move to the centre of the
earth along the line S'C 9 the apparent position of P would
move from P* to P t . If the observer at S" could move
from S* to C along S'C, the apparent position of P would
move from P" to P t .
In the triangle P S'C the following parts are known:
C P = A = the geocentric distance of P,
C S' = p' = the radius of the earth at S',
and the angle S'PC= P'PP, is \\\cparallax of P.
For the change of apparent position of P from P' to P t
is due to the change of the point of observation from S' to
C.
Similarly the angle S'PC = P"PP t is the parallax of P
relative to a change of the observer fiom S" to C.
Horizontal Parallax. Clearly the parallax of P differs
for observers differently situated on the earth, and it is
necessary to take some standard parallax for each observer.
Such a standard is the horizontal parallax. Suppose P
to be in the horizon of the observer '; then Z'S'P
will be 90, as will also the angle PS'C. In the triangle
S'PC three parts "will then be known and the horizontal
parallax (the angle at P when P is in the horizon) can be
found. It will be the same for the observer at S". When
P is in the horizon of S", Z"S"P is a right angle, as is also
PS"C. C P and C S' are known and thus the horizontal
parallax of P is determined.
If CP, the distance of P, increases, other things remain-
ing the same, the parallax of P will diminish.
DELATION OF THE EARTH TO THE HEAVENS. 57
The student can prove this for himself by drawing the
figure on the same scale as here given, making GP larger.
The angles at P (the parallaxes) will become smaller and
smaller the larger GP is taken. Hence the magnitude of
the parallax of a star or a planet depends upon its distance
from us.
Suppose an observer at the point P looking at the earth's
radius S'C. The angle subtended by that semidiameter
is the same as the parallax of P. Hence we may say that
the parallax of a body with reference to an observer on the
earth is measured by the angle subtended at the body by
that semidiameter of the earth which passes through the
observer's station.
As the point P is carried further and further away from
the earth, the angle subtended by S f C, for example, becomes
less and less. If P were at the distance of the moon, this
angle would be about 57'; if at the distance of the sun,
it would be about 8-J". S'C is roughly 4000 miles; it
subtends an angle of 57' at the distance of the moon. 70
miles would subtend an angle of about 1', and 3437'
would be about 240,000 miles. This is the distance of the
moon from the earth. (See pages 4, 5.)
Again, 4000 miles subtends an angle of 8*. 5 at the dis-
tance of the sun. 470. 7 miles would subtend an angle of
I", and 206,264". 8 would be 97,000,000 miles, and this is
about the distance of the sun. By taking the exact values
of the radius of the earth and of the solar parallax, this dis-
tance is found to be about 93,000,000 miles.
The example shows the method of calculating the sun's
distance when we have two things accurately given: first,
the dimensions of the earth; and second, the parallax e
the sun.
58 ASTRONOMY
Annual Parallax. "We have seen that for the moon the
parallax is about 1; for the sun it is only 8*; for some of
the more distant planets it is considerably less.
For Jupiter it is about 2*; for Saturn less than 1*; for
Neptune about 0*.3.
Let us remember what this means. It means that 4000
miles, the earth's radius, would subtend at the distance of
Neptune an angle of only ^ of a single second of arc.
The parallax of the moon is determined by observation,
and the observation consists in measuring the angle which
the radius of the earth ivould subtend if viewed from the
moon's centre. 57' is an angle large enough to be deter-
mined quite accurately in this way. There would be but a
small per cent of error. Even S", the sun's parallax, can be
measured so as to have an error of not more than 2 or 3
per cent.
But this method will not do to measure anything much
smaller than 8". The parallax of a fixed star, for example,
is not sTnsWir P ar ^ * large as the sun's parallax: and this
is too minute a quantity to be deduced by these methods.
We therefore use for distant bodies a parallax which does
not depend on the radius of the earth, but upon the radius
of the earth's orbit around the sun.
Tlie annual parallax of a body is the angle subtended at
the body by the radius of the earth's orbit seen at right
angles.
For example, in Fig. 18 suppose that C now represents
the fiun, around which the earth S' moves in the nearly
circular orbit S'S"H'. S'Cis no longer 4000 miles as in
the last example, but it is 93,000,000 miles. Suppose P to
be, again, a body whose annual parallax is S'P G (suppos-
ing PS'Cto be a right angle).
RELATION OF THE EAHTH TO THE HEAVENS. 59
Some of the nearest fixed stars have an annual parallax
of nearly If. Hence the nearest of them are not nearer
than 206,2^4 times 93,000,000 miles. The greater number
of them have a parallax of not more than -fa".
Hence their distances cannot be less than
10 X 206,264 X 93,000,000 miles.
To the student who has understood the simple rules given
on pages 4 and 5 these deductions will be plain.
FIG. 18.
Semidiameters of the Heavenly Bodies. The angular
semidiameter of the sun as seen from the earth is 961 ff .
Hence its diameter is 1922". Its real diameter in miles is
therefore about 880,000, as its distance is 93,000,000 miles.
The angular semidiameter of the moon as seen from the
earth is about 15^'. Hence its real diameter is about 2000
miles, its distance being about 240,000 miles.
In the same way, knowing the distance of any planet and
measuring its angular semidiameter, we can compute its
dimensions in miles.
CHAPTER III.
ASTRONOMICAL INSTRUMENTS.
General Account. In a general way we may divide the
instruments of astronomy into two classes, seeing instru-
ments and measuring instruments.
The seeing instruments are telescopes ; they have for
their object either to enable the observer to see faint objects
as comets or small stars, or to enable him to see brighter
stars with greater precision than he could otherwise do.
How they accomplish this we shall shortly explain. The
measuring instruments are of two classes. The first class
measures intervals of time. The second measures angles.
A clock is a familiar example of the first class; a divided
circle of the second.
Let us take these in the order named.
The Refracting Telescope. The refracting telescope is
composed of two essential parts, the object-glass or objec-
tive and the eye-piece.
The object-glass is for the sole purpose of collecting the
rays of light which emanate from the thing looked at, and
for making an image of this thing at a point which is called
the focus of the objective.
The eye-piece has for its sole object to magnify the image
so that the angular dimensions of the thing looked at will
appear greater when the telescope is used than when it is
not.
ASTRONOMICAL INSTRUMENTS. 61
For example, in the figure suppose BI to
be a luminous surface. Every point of it is
throwing off rays of light in straight lines in
every possible direction. Let us consider the
point /. The rays from / proceed in every
direction in which we can draw a straight line
through /. Suppose all such straight lines
drawn. Let 00' be the objective of a tele-
scope pointed towards BI. All the rays from
/ which fall on 00' lie between the lines 10,
and 10'. No others can reach the objective,
and all others which proceed from / are
wasted so far as seeing / with this particu-
lar telescope is concerned.
The action of the convex lens 00' is to
bend every ray which passes through it to-
wards its axi^ BA. 10 is bent down to 01' \
10' is bent up to OT; and so for every
other ray except the ray from / through the
centre of 00' which is bent neither up nor
down, but which goes straight on to I' and
beyond.
Every one of the rays of light sent out by
/between the limits JO and 10' finally passes
through /'. / is a point of light, and so is
/'. The point /' is the focus of 00' with
respect to /.
Similarly B sends out light in every direc-
tion. Only those rays which chance to fall
between BO and BO' are useful for seeing
B with this particular telescope. Every one
of this bundle of rays comes to & focus on the
"FIO. 19.
62 ASTRONOMY.
intersection of the lines /' and BA. In the same way
every point of the object .#/has a corresponding image on
the line /' somewhere between 1' and the axis BA.
I' is the focal plane of the objective with respect to
the object BI, and the image of BI lies in this focal plane.
The objective has now done all it can; it has gathered
every possible ray from the object BI and presents every
one of these rays concentrated in an image of this object
in the focal plane at F
Notice two things: first, the image is inverted with re-
spect to the object; / is above B; the image of / is below
the image of B\ second, the rays from B /do not
stop at /' , but go on indefinitely to the left, always
diverging from the image.
The Eye-piece. The eye-piece is essentially a microscope
which is simply to magnify the angular dimensions of the
object as it is seen in the telescope; that is, to magnify the
image. To see well with a microscope it must be close to
the thing magnified. It cannot be placed near to BI in
general, for BI may be a mile or ten millions of miles
away. So the place to put it is near to the image of BI, a
little above the focal plane F in the figure.
The eye must be placed a little further above still,
at such a position as to see well with the eye-piece. That
is, close to it. Now fix an objective in one end of a tube
and an eye-piece in the other end and you have a refracting
telescope. The more powerful the microscope used as an
eye-piece the higher the magnifying power of the combina-
tion. We increase the magnifying power of any telescope
by changing the eye-piece.
The Objective. As a matter of fact the objective is usu-
ally made of two glasses like the figure, where the arrow
ASTRONOMICAL INSTRUMENTS. 63
shows the direction in which the rays come to it from the
object. If we use a dngle ob-
jective we find that the image of
the object is colored ; that is, of
different colors from its natural
tints. We find that by using a
double objective made of two FIQ. 20.
different kinds of glass this can be corrected. This is ex-
plained in Optics under the head of Achromatism or Chro-
matic Aberration.
Light-gathering Power. It is not merely by magnifying
that the telescope assists the vision, but also by increasing
the quantity of light which reaches the eye from the object
at which we look. Indeed, should we view an object
through an instrument which magnified but did not in-
crease the amount of light received by the eye, it is evident
that the brilliancy would be diminished in proportion as
the surface of the image was enlarged, since a constant
amount of light would be spread over an increased surface;
and thus, unless the light were very bright, the object might
become so darkened as to be less plainly seen than with the
naked eye. How the telescope increases the quantity of
light will be seen by considering that when the unaided
eye looks at any object, the retina can only receive so many
rays as fall upon the pupil of the eye. By the use of the
telescope it is evident that as many rays can be brought to
the retina as fall on the entire object-glass. The pupil of
the human eye, in its normal state, has a diameter of about
one fifth of an inch, and by the use of the telescope it is
virtually increased in surface in the ratio of the square of
the diameter of the objective to the square of one fifth of
an inch; that is ? in the ratio of the surface of the objective
64 ASTRONOMY.
to the surface of the pupil of the eye. Thus, with a two-
inch aperture to our telescope, the number of rays collected
is one hundred times as great as the number collected with
the naked eye.
With a 5-inch object-glass the ratio is 625 to 1
" 10 " " " " 2,500 to 1
" 15 " " " 5.625 to 1
" 20 " " " " 10 000 to 1
" 26 " " " 16,900 to 1
When a minute object, like a small star, is viewed, it is
necessary that a certain number of rays should fall on the
retina in order that the star may be visible at all. It is
therefore plain that the use of the telescope enables an
observer to see much fainter stars than he could detect with
the naked eye, and also to see faint objects much better
than by unaided vision alone. Thus, with a -20-inch tele-
scope we may see stars so minute that it would rorjuire the
collective light of many thousands to be vi.-ible to the
unaided eye.
Eye-piece. In the skeleton form of telescope before de-
scribed the eye-piece as well as the objective was considered
as consisting of but a single lens. But with such an eye-
piece vision is imperfect, except in the centre of the field,
from the fact that the image does not throw rays in every
direction, but only in straight lines away from the objec-
tive. Hence the rays from near the edges of the focal
image fall on or near the edge of the eye- piece, whence
arises distortion of the image formed on the retina, and loss
of light. To remedy this difficulty a lens is inserted at or
very near the place where the focal image is formed, for the
purpose of throwing the different pencils of rays which
emanate from the several parts of the image, toward the
ASTRONOMICAL INSTRUMENTS. 65
axis of the telescope, so that they shall all pass nearly
through the centre of the eye-lens proper. These two
lenses are together called the eye-piece.
There are some small differences of detail in the con-
struction of eye-pieces, but the general principle is the
same in all
The figure shows an eye-piece drawn accurately to scale. 01 is
one of the converging pencils from the object-glass which forms one
point (/) of the focal image la. This image is viewed by the field-
lens F of the eye-piece as if it were a real object, and the shaded pencil
between ^and E shows the course of these rays after deviation by F.
If there were no eye-lens E, an eye properly placed beyond F would
see an image at 1' a 1 . The eye-lens Z receives the pencil of rays, and
deviates it to the observer's eye placed at such a point that the whole
incident pencil will pass through the pupil and fall on the retina, and
thus be effective. As we saw in the figure of the refracting telescope,
FIG 21.
every point of the object produces a pencil similar to 01, and the
whole surfaces of the lenses Faud J57are covered with rays. All of
these pencils passing through the pupil go to make up the retinal
image. This image is referred by the mind to the distance of distinct
vision (about ten inches), and the image AF' represents the dimen-
sion of the final image relative to the ima^e al as formed by the ob-
AI"
jective, and is evidently the magnifying power of this particular
Ob J.
eye-piece used in combination with this particular objective.
66 ASTRONOMY.
Reflecting Telescopes. As we have seen, one essential part of a
refracting telescope is the objective, which brings all the incident rays
from an object to one focus, forming there an image of that object
In reflecting telescopes (reflectors) the objective is a mirror of specu-
lum metal or silvered glass ground to the shape of a paraboloid. The
figure shows the action of such a mirror on a bundle of parallel rays,
which, after impinging on it, are brought by reflection to one focus
F. The image formed at this focus may be viewed with an eye-
piece, as in the case of the refracting telescope.
The eye-pieces used with such a mirror are of the kind already
described. In the figure the eye-piece would have to be placed to
Fio. 22.
the right of the point F, and the observer's head would thus interfere
with the incident light. Various devices have been proposed to rem-
edy this inconvenience, of which the most simple is to interpose a
small plane mirror, which is inclined 45 to the line AC, just to the
left of F. This mirror will reflect the rays which are moving towards
the focus ^down (in the figure) to another focus outside of the main
beam of rays. At this second focus the eye-piece is placed and the
observer looks into it in a direction perpendicular to AG.
The Telescope in Measurement, A telescope is generally
thought of only as an instrument to assist the eye by its
magnifying and light-gathering power in the manner we
have described. But it has a very important additional
function in astronomical measurements by enabling the
astronomer to point at a celestial object with a certainty
and accuracy otherwise unattainable. This function of
the telescope was not recognized for more than half a cen-
ASTRONOMICAL INSTRUMENTS. 57
tury after its invention, and after a long and rather acri-
monious contest between two schools of astronomers.
Until the middle of the seventeenth century, when an
astronomer wished to determine the altitude of a celestial
object, or to measure the angular distance between two
stars, he was obliged to point his sextant or other meas-
uring instrument at the object by means of "pinnules."
These served the same purpose as the sights on a rifle. In
using them, however, a difficulty arose. It was impossible
for the observer to have distinct vision both of the object
and of the pinnules at the same time, because when the
eye was focused on either pinnule, or on the object, it was
necessarily out of focus for the others. The only way to
diminish this difficulty was to lengthen the arm on which .
the pinnules were fastened so that the latter should be as
far apart as possible. Thus TYCHO BRAHE, before the
year 1600, had measuring instruments very much larger
than any in use at the present time. But this plan only
diminished the difficulty and could not entirely obviate it,
because to be manageable the instrument must not be very
large.
About 1670 the English and French astronomers found
that by simply inserting fine threads or wires exactly in
the focus of the object-glass, and then pointing it at the
object, the image of that object formed in the focus could
be made to coincide with the threads, so that the observer
could see the two exactly superimposed upon each other.
When thus brought into coincidence, it was obvious that
the point of the object on which the wires were set was in
a straight line passing through the wires, and through the
centre of the object-glass. So exactly could such a point-
ing be made, that if the telescope did not magnify at all
68 ASTRONOMY.
(the eye-piece and object-glass being of equal focal length),
a very important advance would still be made in the ac-
curacy of astronomical measurements. This line, passing
centrally through the telescope, we call the line of colli-
mation of the telescope, A B in Fig. 19. If we have any
way of determining it, it is as if we had an indefinitely long
pencil extended from the earth to the sky. If the observer
simply sets his telescope in a fixed position, looks through
it and notices what stars pass along the threads in the eye-
piece, he knows that all those stars lie in the axis of col-
limation of his telescope at that instant,
By the diurnal motion a pencil-mark, as it were, is thus
drawn on the surface of the celestial sphere among the
stars, and the direction of this pencil-mark can be deter-
mined with far greater precision by the telescope than with
the naked eye.
CHRONOMETERS AND CLOCKS,
We have seen that it is important for various purposes
that an observer should be able to determine his local time
(see page 52). This local time is determined most accu-
rately by observing the transits of stars over the celestial
meridian of the place where the observer is. In order to
determine the moment of transit with all required accuracy,
it is necessary that the time-pieces by which it is measured
shall go with the greatest possible precision. There is no
great difficulty in making astronomical measures to a sec-
ond of arc, and a star, by its diurnal motion, passes over
this space in one fifteenth of a second of time (see page
44). It is therefore desirable that the astronomical clock
shall not vary from a uniform rate more than a few
ASTRONOMICAL INSTRUMENTS. 69
hundredth s of a second in the course of a day. It is
not, however, necessary that it should always be perfectly
correct; it may go too fast or too slow without detracting
from its character for accuracy, if the intervals of time
which it tells off hours, minutes, or seconds are always
of exactly the same length, or, in other words, if it gains
or loses exactly the same amount every hour and every
day.
The time-pieces used in astronomical observation are the
chronometer and the clock.
The chronometer is merely a very perfect watch with
a balance-wheel so constructed that changes of tempera-
ture have the least possible effect upon the time of its
oscillation. Such a balance is called a condensation bal-
ance.
The ordinary house-clock goes faster in cold than in
warm weather, because the pendulum-rod shortens under
the influence of cold. This effect is such that the clock
will gain about one second a day for every fall of 3 Cent.
(5. 4 Fahr.) in the temperature, supposing the pendulum-
rod to be of iron. Such changes of rate would be entirely
inadmissible in a clock used for astronomical purposes.
The astronomical clock is therefore provided with a com-
pensation pendulum, by which the disturbing effects of
changes of temperature are avoided.
The correction of a clock is the quantity which it is necessary to
add to the indications of the hands to obtain the true time. Thus if
the correction of a sidereal clock is -f- l m 10 s . 07 and the hands point
to 21 h 13 m 14". 50, the correct sidereal time is 21 h 14 m 24 s . 57.
The rate of a clock is the daily change of its correction; i.e., what
it gains or loses daily.
70
ASTRONOMY.
THE TRANSIT INSTRUMENT.
The Transit Instrument is used to observe the transits
of stars over the celestial meridian. The times of these
FIG. 23.
transits are noted by the sidereal clock, which is an indis-
pensable adjunct of the transit instrument.
ASTRONOMICAL INSTRUMENTS. 71
It consists essentially of a telescope TT mounted on an axis VV
at right angles to it. The ends of this axis terminate in accurately
cylindrical pivots which rest in metallic bearings VV which are
shaped like the letter Y, and hence called the Y's.
These are fastened to two pillars of stone, brick, or iron. Two
counterpoises TFTFare connected with the axis as in the plate, so as
to take a large portion of the weight of the axis and telescope from
the Y's, and thus to diminish the friction upon these and to render
the rotation about V V more easy and regular. In the ordinary use
of the transit, the line V V is placed accurately level and also perpen-
dicular to the meridian, or in the east and west line. To effect this
"adjustment" there are two sets of adjusting screws, by which the
ends of F Fin the Y's may be moved either up and down, or north
and south. The plate gives the form of transit used in permanent
observatories, and shows the observing chair C, the reversing carriage
R, and the level L. The arms of the latter have Y's, \\lrcli can be
placed over the pivots FF.
The line of cottimalion of the transit, telescope is the line drawn
through the centre of the objective perpendicular to the rotation
axis VV,
The reticle is a network of fine spider-lines placed in the focus of
the objective.
In Fig. 24 the circle represents the field of view of a transit as seen
through the eye-piece. The seven vertical
lines, I, II, III, IV, V, VI, VII, are seven
fine spider-lines tightly stretched across a
hole in a metal plate, and so adjusted as
to be perpendicular to the direction of a
star's apparent diurnal motion. The hori-
zontal wires, guide-wires, a and b, mark the
centre of the field. The field is illuminated
at night by a lamp at the end of the axis
which shines through the hollow interior of
the latter, and causes the field to appear
bright. The wires are dark against a bright
ground. The line of sight is a line joining the centre of the objective
and the central one, IV, of the seven vertical wires.
The whole transit is in adjustment when, first, the axis FFis
horizontal ; second, when it lies east and west ; and third, when the
line of sight and the line of collimation coincide. When these condi-
tions are fulfilled the line of sight intersects the celestial sphere in the
meridian of the place, and when TT is rotated about F Fthe line of
sight marks out the celestial meridian of the place on the sphere.
72 ASTRONOMY.
The clock stands near the transit instrument. The times
when a star passes the wires I-VII are noted. The average
of these is the time when the star was on the middle thread,
or, what is the same thing, on the celestial meridian. At
that instant its hour-angle is zero. (See page 39.)
The sidereal time at that instant is the hour-angle of the
vernal equinox (see page 44). This is measured from the
meridian towards the west. The right ascension of the
star which is observed is the same quantity, measured from
the vernal equinox towards the east. As the star is on
the meridian, the two are equal. Suppose we know the
right ascension of the star and that it is a. Suppose the
clock time of transit is T. It should have been a if the
clock were correct. The correction of the clock at this
instant is thus a T.
This is the use we make of stars of known right ascen-
sions. By observing any one of them we can get a value of
the clock correction.
Suppose the clock to be correct, and suppose we note that
a star whose right ascension is unknown is on the wire IV
at the time a' by the clock, a' is then the right ascension
of that star. In this way the positions of stars, or of the
sun and planets (in right ascension only), are determined,
THE MERIDIAN CIRCLE.
The meridian circle is a combination of the transit in-
strument with a graduated circle fastened to its axis and
moving with it. A meridian circle is shown hi Fig. 25.
It has two circles finely divided on their sides. The grad-
aatiou of each circle is viewed by four microscopes. The
microscopes are 90 apart. The cut shows also the hang-
ing level by which the error of level of the axis is found.
ASTRONOMICAL INSTRUMENTS.
73
The instrument can be used as a transit to determine
right ascensions, as before described. It can be also used
to measure declinations in the following way : If the
telescope is pointed to the nadir, a certain division of
FIG. 25.
the circles, as N, is under the first microscope.* "We can
make the nadir a visible point by placing a basin of quick-
silver below the telescope and looking in it through the tel-
escope. We shall see the wires of the reticle and also their
* Or opposite to a stationary pointer fixed to the pier.
74 ASTliONOMY.
reflected images in the quicksilver. When these coincide,
the telescope points to the nadir. If it is then pointed to
the pole, the reading will change by the angular distance
between the nadir and the pole, or by 90 -\- g>, (p being the
latitude of the place (supposed to be known). The polar
reading P of the circle is thus known when the nadir
reading Nia found. If the telescope is then pointed to
various stars of unknown polar distances, ;/, p", p'", etc.,
as they successively cross the meridian, and if the circle
readings for these stars are P', P", P'", etc., it follows
that p'=P'P; p" = P" P; p'" = P'" P; etc.
Thus the meridian circle serves to determine by observa-
tion loth co-ordinates of the apparent position of a body.
THE EQUATORIAL.
An equatorial telescope is one mounted in such a way that
a star may be followed through its diurnal orbit by turning
the telescope about one axis only. The equatorial mount-
ing consists essentially of a pair of axes at right angles
to each other. One of these S N (the polar axis) is direct-
ed toward the elevated pole of the heavens, and it there-
fore makes an angle with the horizon equal to the latitude
of the place (p. 31). This axis can be turned about its own
axial line. On one extremity it carries another axis LD
(the declination axis), which is fixed at right angles to it,
but which can again be rotated about its axial line.
To this last axis a telescope is attached, which may either
be a reflector or a refractor. It is plain that such a tele-
scope may be directed to any point of the heavens; for we
can rotate the declination axis until the telescope points to
any given polar distance or declination. Then, keeping
the telescope fixed in respect to the declination axis, we can
ASTRONOMICAL INSTRUMENTS. 75
FIG. 26.
76 ASTRONOMY.
rotate the whole instrument as one mass about the polar
axis until the telescope points to any portion of the parallel
of declination defined by the given right ascension or hour-
angle. Fig. 20 is an equatorial of 9J-inch aperture, with
driving-clock inside the pedestal.
If we point such a telescope to a star when it is rising (doing this
by rotating the telescope first about its declination axis and then
about the polar axis), and fix the telescope in this position, we can,
by simply rotating the whole apparatus on the polar axis, cause the
telescope to trace out on the celestial sphere the apparent diurnal
path which this star will appear to follow from rising to setting. In
such telescopes a driving-clock is so arranged that it can turn the
telescope round the polar axis at the same rate at which the earth it-
self turns about its own axis of rotation, but in a contrary direction.
Hence such a telescope once pointed at a star will continue to point
at it as long as the driving-clock is in operation, thus enabling the
astronomer to make such an examination or observation of it as is
required.
THE SEXTANT.
The sextant is a portable instrument by which the altitudes of
celestial bodies or the angular distances between them may be
measured. It is used chiefly by navigators for determining the lati-
tude and the local time of the position of the ship. Knowing the
local time, and comparing it with a chronometer regulated on Green-
wich time, the longitude becomes known and the ship's place is
fixed. (See page 52.)
It consists of an arc of a divided circle usually 60 in extent,
whence the name. This arc is in fact divided into 120 equal parts,
each marked as a degree, and these are again divided into smaller
spaces, so that by means of the vernier at the end of the index arm
MS an arc of 10" (usually) may be read.
The index-arm MS carries the index-glass M, which is a silvered
plane mirror set perpendicular to the plane of the divided arc. The
horizon-glass m is also a plane mirror fixed perpendicular to the plane
of the divided circle.
This last glass is fixed ia position, while the first revolves with the
index-arm. The horizon-glass is divided into two parts, of which
the lower one is silvered, the upper half being transparent. E is a
telescope of low power pointed toward the horizon- glass. By it any
ASTRONOMICAL INSTRUMENTS.
77
object to which it is directly pointed can be seen through the unsilvered
half of the horizon-glass. Any other object in the same plane can be
brought into the same field by rotating the index-arm (and the index-
glass with it), so that a beam of light from this second object shall
strike the index-glass at the proper angle, there to be reflected to the
horizon -glass, and again reflected down the telescope E. Thus the
images of any two objects in the plane of the sextant may be brought
together in the telescope by viewing one directly and the other by
reflection.
Fro. 27.
This instrument is used daily at sea to determine the
ship's position by measuring the altitude of the sun. This
is done by pointing the telescope, E J9, to the sea-horizon,
H in the figure, which appears like a line in the field of the
telescope, and by moving the index-arm till the image of
78 ASTRONOMY.
the sun, S, coincides with the horizon. The arc read from
the sextant at this time is the sun's altitude. From the
altitude of the sun on the meridian the ship's latitude is
known (see page 54). From its altitude at another hour
Fio
the local time can be computed. The difference between
the local time and the Greenwich time, as shown by the
ship's chronometer, gives the ship's longitude. By means
of this simple instrument the place of a vessel can be found
witnin a mile or so.
The above are the instruments of astronomy which best
illustrate the principles of astronomical observations.
Practical Astronomy is the science which teaches the
theory of these instruments and of their application to ob-
servation, and it includes the art of so combining the
observations and so using the appliances as to get the best
results.
ASTRONOMICAL EPHEMERIS. 79
THE ASTRONOMICAL EPHEMERIS, OB NAUTICAL ALMANAC,
The Astronomical Ephemeris, or, as it is more commonly called,
the Nautical Almanac, is a work in which celestial phenomena and
the positions of the heavenly bodies are computed in advance.
The usefulness of such a work, especially to the navigator, de-
pends upon its regular appearance on a uniform plan and upon the
fulness and accuracy of its data; it was therefore necessary that its
i'ssue should be taken up as a government work. An astronomical
ephemeris or nautical almanac is now published annually by each of
the governments of Germany, Spain, Portugal, France, Great Britain,
and the United States. They are printed three years or more be-
forehand, in order that navigators going on long voyages may supply
themselves in advance.
The Ephemeris furnishes the fundamental data from which all our
household almanacs are calculated.
The principal quantities given in the American Ephemeris for
each year are as follows:
The positions (R. A. and 8) of the sun and the principal large
planets for Greenwich noon of every day in each year.
The right ascension and declination of the moon's centre for every
Greenwich hour in the year.
The distance of the moon from certain bright stars and planets for
every third Greenwich hour of the year.
The right ascensions and declinations of upward of two hundred
of the brighter fixed stars, corrected for precession, nutation, and
aberration, for every ten days.
The positions of the principal planets at every visible transit over
the meridian of Washington.
Complete elements of all the eclipses of the sun and moon, with
maps showing the passage of the moon's shadow or penumbra over
those regions of the earth where the eclipses will be visible, and
tables whereby the phases of the eclipses can be accurately computed
for any place.
Tables for predicting the occultations of stars by the moon.
Eclipses of Jupiter's satellites and miscellaneous phenomena.
Catalogues of Stars. Of the same general nature with the Ephe-
meris are catalogues of the fixed stars. The object of such a cata-
logue is to give the right ascension and declination of a number of
stars for some epoch, the beginning of the year 1875 for instance,
with the data by which the position of each star can be found at any
other epoch.
80
ASTRONOMY.
To give the student a still further idea of the Ephemeris, we present
a small portion of one of its pages for the year 1882 :
FEBRUARY, 1882 AT GREENWICH MEAN NOON.
1
I' i 1 licit JMI1
. !
Ijg .
THE SUN'S
or time
jj
Sidereal
the
week.
I 1
to be
subtracted
from
mean
time.
i
time
or right
ascension
of
mean sun.
Apparent
Bright
ascension.
Diff.
forl
hour.
Apparent
declination.
Diff.
forl
hour.
B. M. 8.
8.
e /
.
M. 8.
8.
H. M. 8.
Wed.
1
21 13.04 10.175
S17 2 22.4
+42.82 18 51.34
0.31820 46 21.70
Thur.
2
21 4 16.8410.141
16 45 5.4
43.57 13 58.58
0.28420 50 18.26
Frid.
8
21 8 19.82
10.107
16 27 30.9
44.30
14 5.01
0.250
20 54 14.81
Sat
4
21 12 21 98
10.073
16 9 39.2
+44.99
14 10.61
0.216
20 58 11.87
Sun.
5
21 16 23 33 10.040
15 51 808
4:, ;-.
14 15.41
0.18J21 2 7.92
MOD.
6
21 20 23.88
10.007
15 33 6.1
46.36
14 19.40
0.150
21 6 4.48
Tues.
7
21 24 23 63
9.974
15 14 25.4
+47.03
14 22 60
0.117
21 10 1.03
Wed.
8
21 28 22 60 9.941
14 55 29.1
47 66
14 25 01
008421 13 57.59
Thur.
9
21 82 20 79
'.I.'JW
14 36 17.7
48.28
14 26.65
0.052
21 17 54.14
Frid.
10
21 36 18.21
9.877
14 16 51.6
48.88
14 27.51
0.020
21 21 50 70
Sat.
11
21 40 14.88
it sic,
13 57 11.2
49 47
14 27. 63
0.011 21 25 47.25
Sun.
12
21 44 10.80
9.8n
13 37 16.9
50.03
14 26.99
0.042
21 29 43.81
Mon.
13
21 48 5.98
9.784
13 17 91
+50.59
14 25.63
073
21 33 40 35
Tues.
14
21 52 0.43
I.7H
12 56 48 8
51.12 14 2:1 M
0.10421 37 36.91
Wed.
15
21 55 54.16
9.723
12 36 14.9
51.65 14 20.70
0.134
21 41 33 46
Thur.
16
21 59 47.17
MM
12 15 29.3
+52.14
14 17.15
164
21 45 30.02
Frid.
17
22 3 89.47
-.) mi
11 54 82 1
V> A*>
14 12 90
19321 49 26.57
Sat.
18
22 7 31.07
9.635
11 33 M i;
53^07
14 7.94
022221 58 23.13
1
The third column shows the R. A. of the sun's centre at Green-
wich mean noon of each day. The fourth column shows the hourly
change of this quantity (9.815 on Feb. 12). At Greenwich hours
the sun's R. A. was 21 h 44 m lO'.SO. Washington is 5 h 8 m (5M3)
west of Greenwich. At Washington mean noon, on the 12th. the
Greenwich mean time was 5 h . 13. 9.815 X 5.13 is 50'.35. This is to
be added, since the R. A. is increasing. The sun's R. A. at Wash-
ington mean noon is therefore 21 h 45 m 1". 15. A similar process will
give the sun's declination for Washington mean noon. In the same
manner, theR. A. and Dec. of the sun for any place whose longitude
is known can be found.
The column "Equation of Time" gives the quantity to be sub-
tracted from the Greenwich mean solar time to obtain the Green-
wich apparent solar time (see page 188). Thus, for Feb. 1, the
Greenwich mean time of Greenwich mean noon is O h 0*. The
true sun crossed the Greenwich meridian (apparent noon) at 23 h 46 m
08*. 66 on the preceding day; i.e., Jan. 31.
When it was O h O m 6 s of Greenwich mean time on Feb. 13. it was
also 21 h 33 m 40.35 of Greenwich local sidereal time (see the last
column of the table).
CHAPTER IV.
MOTION OF THE EARTH.
ANCIENT IDEAS OF THE PLANETS.
IT was observed by the ancients that while the great
mass of the stars maintained their positions relatively to
each other month after month and year after year, there
were visible to them seven heavenly bodies which cJianged
their positions relatively to the stars and to each other.
These they called planets or wandering stars. It was found
that the seven planets performed a very slow revolution
around the celestial sphere from west to east, in periods
ranging from one month in the case of the moon to thirty
years in that of Saturn.
The idea of the fixed stars being set in a solid sphere was
in perfect accord with their diurnal revolution as observed
by the naked eye. But it was not so with the planets.
The latter, after continued observation, were found to
move sometimes backward and sometimes forward; and it
was quite evident that at certain periods they were nearer
the earth than at other periods. These motions were en-
tirely inconsistent with the theory that they were fixed in
solid spheres.
These planets (which are visible to the naked eye),
together with the earth, and a number of other bodies
which the telescope has made known to us, form a family
or system by themselves, the dimensions of which, although
82 ASTRONOMY.
inconceivably greater than any which we have to deal with
at the surface of the earth, are quite insignificant when
compared with the distance which separates us from the
fixed stars. The sun being the great central body of this
system, it is called the Solar System. There are eight
large planets, of which the earth is the third in the order of
distance from the sun, and these bodies all perform a regular
revolution around the sun. Mercury, the nearest, performs
its revolution in three months ; Neptune, the farthest, in
164 years.
ANNUAL REVOLUTION OF THE EARTH.
To an observer on the earth the sun seems to perform
an annual revolution among the stars, a fact which has
been known from early ages. This motion is due to the
annual revolution of the earth round the sun.
In Fig. 29 let S represent the sun, ABCD the orbit
of the earth around it, and E FGH the sphere of the
fixed stars. This sphere, being supposed infinitely distant,
must be considered as infinitely larger than the circle
ABCD. Suppose now that 1, 2, 3, 4, 5, 6 are a number
of consecutive positions of the earth in its orbit. The line
IS drawn from the sun to the earth in any given position is
called the radius-vector of the earth. Suppose this line
extended infinitely so as to meet the celestial sphere in the
point 1'. It is evident that to an observer on the earth at
1 the sun will appear projected on the sphere in the direc-
tion of 1'; when the earth reaches 2 it will appear in the
direction of 2', and so on. In other words, as the earth
revolves around the sun, the latter will seem to perform a
revolution among the fixed stars, which are immensely
more distant than itself. The points 1', 2', etc., can be
MOTIONS OF THE EARTH. 83
fixed by their relations to the various fixed stars, whose
places are known.
It is also evident that the point in which the earth would
be projected if viewed from the sun is always exactly
opposite that in which the sun appears as projected from
the earth. Moreover, if the earth moves more rapidly in
Fio. 29. REVOLUTION OF THE EARTH.
some points of its orbit than in others, it is evident that
the sun will also appear to move more rapidly among the
stars, and that the two motions must always accurately
correspond to each other.
The radius-vector of the earth in its annual course de-
Bribes a plane, which in the figure may be represented by
84 ASTRONOMY.
that of the paper. This plane continued to infinity in
every direction will cut the celestial sphere in a great cir-
cle ; and it is clear that the sun will always appear to
move in this circle. The plane and the circle are indiffer-
ently termed the ecliptic. The plane of the ecliptic is gen-
erally taken as the fundamental one, to which the positions
of all the bodies in the solar system are referred. It
divides the celestial sphere into two equal parts. In think-
ing of the celestial motions, it is convenient to conceive of
this plane as horizontal. Then if we draw a vertical line
through the sun at right angles to this plane (perpendicular
to the plane of the paper on which the figure is represent-
ed), the point at which this line intersects the celestial
sphere will be the pole of the ecliptic.
Let us now study the apparent annual revolution of the
sun produced by the real revolution of the earth in its orbit.
When the earth is at 1 in the figure the sun will appear
to be at 1', near some star, as drawn. Now by the diurnal
motion* of the earth the sun is made to rise, to culminate,
and to set successively for each meridian on the globe. This
star being near the sun rises, culminates, and sets with it;
it is on the meridian of any place at the local noon of that
place (and is therefore not visible except in a telescope). The
star on the right-hand side of the figure near the line CSl
prolonged is nearly opposite to the sun. When the sun is
rising at any place, that star will be setting; when the sun
is on the meridian of the place, this star is on the lower
meridian; when the sun is setting, this star is rising. It
is about 180 from the sun. Now suppose the earth to
move to 2. The sun will be seen at 2', near the star there
marked. 2' is east of 1'; the sun appears to move among
the stars (in consequence of the earth's annual motion)
MOTIONS OF THE EARTH. 85
from west to east. The star near 2' will rise, culminate,
and set with the sun at every place on the earth. The star
near 1' being west of 2' will rise "before the sun, culminate
before him, and set before he does.
If, for example, the star 1' is near the equator when the
sun is 15 east of 1', the star will rise about 1 hour earlier
than the sun. When the sun is 30 east of 1' (at 3', for
example), the star will rise 2 hours before the sun. When
the sun is 90 east of 1', the star will rise 6 hours before the
,un, and so on. That is, when the sun is rising at any
place, this star will be on the meridian of the place. When
the sun appears in the line I'CS 1 prolonged to the right
in the figure, the star 1' will be on the meridian at mid-
night, and is then said to be in opposition to the sun. It
is 180 from it. When the sun appears to be near H, the
star 1' will be about 45 or 3 hours east of the sun. The
sun will rise first to any place on the earth, and the star
will rise 3 hours later, say at 9 A.M. Finally the sun will
come back to the same star again and they will rise, culmi-
nate, and set together.
We know that this cycle is about 365 days in length.
In this time the sun moves 360, or about 1 daily.* This
cycle is perpetually repeated. Its length is a sidereal year;
that is, the interval of time required for the sun to move in
the sky from one star back to the same star again, or for the
earth to make one revolution in its orbit among the stars.
The ancients were familiar with this phenomenon. They
knew most of the brighter stars by name. The heliacal
rising of a bright star (its rising with Helios, the sun)
marked the beginning of a cycle. At the end of it, seasons
and crops and the periodical floods of the Nile had repeat-
* 1 is twice the sun's apparent diameter.
86 A8TBQNOMT.
ed themselves. It was in this way that the first accurate
notions of the year arose.
The apparent position of a body as seen from the earth
is called its geocentric place. The apparent position of a
body as seen from the sun is called its heliocentric place.
In the last figure, suppose the sun to be at #, and the
earth at 4. 4' is the geocentric place of the sun, and G is
the heliocentric place of the earth.
THE SUN'S APPARENT PATH.
It is evident that if the appurmt path of the sun lay in
the equator, it would, during the entire- year, rise exactly
in the east and set in the west, and would always cross the
meridian at the same altitude. The days would always be
twelve hours long, for the same muson that a star in the
equator is always twelve hours above the horizon and twelve
hours below it. But we know that this is not the case, the
sun being sometimes north of the equator and sometimes
south of it, and therefore it has a motion in declination.
To understand this motion, suppose that on March 10th,
1879, the sun had been observed with a meridian circle and a
sidereal clock at the moment of transit over the meridian of
Washington. Its position would have been found to be this:
Right Ascension, 23 h 55 m 23 s ; Declination, 30' south.
Had the observation been repeated on the 20th and fol-
lowing days, the results would have been:
March 20, R. Ascen. 23 h 59 m 2 s ; Dec. 6' South.
21, " O h 2 m 40 8 ; " 17' North.
22, " O h 6 m 19 s ; " o 41' North.
If we lay these positions down on a chart, we shall find
them to be as in Fig. 30, the centre of the sun being south
MOTIONS OF THE EARTH. 87
of the equator in the first two positions, and north of it in
the last two. Joining the successive positions by a line, we
shall have a representation of a small portion of the appa-
rent path of the sun on the celestial sphere, or of the ecliptic.
It is clear from the observations and the figure that the
sun crossed the equator between six and seven o'clock on
the afternoon of March 20th, and therefore that the equa-
tor and ecliptic intersect at the point where the sun was at
that hour. This point is called the vernal equinox, the
first word indicating the season, while the second expresses
FIG. 30. THE SUN CROSSING THE EQUATOR.
the equality of the nights and days which occurs when the
sun is on the equator. It will be remembered that this
equinox is the point from which right ascensions are count-
ed in the heavens, in the same way that we count longi-
tudes on the earth from Greenwich or Washington. A
sidereal clock at any place is therefore so set that the hands
shall read hours minutes seconds at the moment
when the vernal equinox crosses the meridian of the place.
Continuing our observations of the sun's apparent course
for six months from March 20th till September 23d, we
ASTRONOMY.
should find it to be as in Fig. 31. It will be seen that Fig.
30 corresponds to the right-
hand end of 31, but is on a
much larger scale. The sun,
moving along the great circle
of the ecliptic, will reach its
greatest northern declination
about June 21st. This point
is indicated on the figure as
90 from the vernal equinox,
and is called the >//>/////>/ W-
stice. The sun's right ascen-
sion is then six hours, and its
declination 23 north. The
student should complete the
figure by drawing the half not
irivt-n IKMV.
The course of the sun now
inclines toward the south, and
it again crosses the equator
about September 22d at a point
diametrically opposite the ver-
nal equinox. All great circles
intersect each other in two op-
posite points, and the ecliptic
and equator intersect at the two
opposite equinoxes. The equi-
nox which the sun crosses on
September 22d is called the
autumnal equinox.
During the six months from
September to March the sun's
MOTIONS OF THE EAETB. 89
course is a counterpart of that from March to Septem-
ber, except that it lies south of the equator. It attains
its greatest south declination about December 22d, in
right ascension 18 hours and south declination 23 30'.
This point is called the winter solstice. It then begins to
incline its course toward the north, reaching the vernal
equinox again on March 20th, 1880.
The two equinoxes and the two solstices may be re-
garded as the four cardinal points of the sun's apparent
annual circuit around the heavens. Its passage through
these points is determined by measuring its altitude or de-
clination from day to day with a meridian circle. Since in
our latitude greater altitudes correspond to greater declina-
tions, it follows that the summer solstice occurs on the day
when the altitude of the sun is greatest, and the winter
solstice on that when it is least. The mean of these alti-
tudes is that of the equator, and may therefore be found
by subtracting the latitude of the place from 90. The
time when the sun reaches this altitude going north, marks
the vernal equinox, and that when it reaches it going south
marks the autumnal equinox.
These passages of the sun through the cardinal points have been
the subjects of astronomical observation from the earliest ages on
account of their relations to the change of the seasons. An ingeni.
ous method of finding the time when the sun reached the equinoxe*.
was used by the astronomers of Alexandria about the beginning 01
our era. In the great Alexandrian Museum, a large ring or whee
was set up parallel to the plane of the equator; in other words, it
was so fixed that a star at the pole would shine perpendicularly 01
the wheel. Evidently its plane if extended must have passed througl
the east and west points of the horizon, while its inclination to the
vertical was equal to the latitude of the place, which was not far
from 30. When the sun reached the equator going north or south,
and shone upon this wheel, its lower edge would be exactly covered
by the shadow of the upper edge; whereas in any other position the
90 ASTRONOMY.
sun would shine upon the lower inner edge. Thus the time at which
the sun reached the equinox could be determined, at least to a frac-
tion of a day. By the more exact methods of modern limes it can
be determined within less than a minute.
It will be seen that this method of determining the annual appar-
ent course of the sun by its declination or altitude is entirely inde-
pendent of its relation to the fixed stars; and it could be equally well
applied if no stars were ever visible. There are, therefore, two en-
tirely distinct ways of finding when the sun or the earth has completed
its apparent circuit around the celestial sphere; the one by the transit
instrument and sidereal clock, which show when the sun returns to
the same position among tlte stars, the other by the measurement of
altitude, which shows when it returns to the same e</uin<u: By the
former method, already described, we conclude that it has completed
an annual circuit when it returns to the same star; by the latter when
it returns to the same equinox. These two methods will give slightly
different results for the length of the year, for a reason to be here-
after described.
The Zodiac and its Divisions. The zodiac is a belt in the heavens,
commonly considered as extending some 8 on each side of the
ecliptic, and therefore about 16 wide. The planets known to the
ancients are always seen within this belt. At a very early day the
zodiac was mapped out into twelve signs known as the signs of the
zodiac, the names of which have been handed down to the present
time. Each of these signs was supposed to be the seat of a constella-
tion after which it was called. Commencing at the vernal equinox,
the first thirty degrees through which the sun passed, or the region
among the stars in which it was found during the month following,
was called the sign Aries. The next thirty degrees was called
Taurus. The names of all the twelve signs in their proper order,
with the approximate time of the sun's entering upon each, are as
follows:
Aries, the Ram, March 20.
Taurus, the Bull, April 20.
Gemini, the Twins, May 20.
Cancer, the Crab, June 21.
Leo, the Lion, July 22.
Virgo, the Virgin, August 22.
Libra, the Balance, September 22.
Scorpius, the Scorpion, October 23.
Sagittarius, the Archer, November 23.
Capricornus, the Goat, December 21.
Aquarius, the Water-bearer, January 20.
Pisces, the Fishes, February 19.
MOTIONS OF THE EAHT1L 91
Each of these signs coincides roughly with a constellation in the
heavens; and thus there are twelve constellations called by the
names of these signs, but the signs and the constellations no longer
correspond. Although the sun now crosses the equator and enters
the sign Aries on the 20th of March, he does not reach the constella-
tion Aries until nearly a month later. This arises from the preces-
sion of the equinoxes, to be explained hereafter.
OBLIQUITY OF THE ECLIPTIC.
We have already stated that when the sun is at the sum-
mer solstice it is about 23 north of the equator, and when
at the winter solstice, about 23$ south. This shows that
the ecliptic and equator make an angle of about 23| with
each other. This angle is called the obliquity of the eclip-
tic, and its determination is very simple. It is only neces-
sary to find by repeated observation the sun's greatest north
declination at the summer solstice, and its greatest south
declination at the winter solstice. Either of these declina-
tions, which must be equal if the observations are accurate-
ly made, will give the obliquity of the ecliptic. It has been
continually diminishing from the earliest ages at a rate of
about half a second a year, or, more exactly, about 47* in
a century. This diminution is due to the gravitating
forces of the planets, and will continue for several thousand
years to come. It will not, however, go on indefinitely,
but the obliquity will only oscillate between comparatively
narrow limits.
In the preceding paragraphs we have explained the
apparent annual circuit of the sun relative to the equator,
and shown how the seasons are related to this course. In
order that the student may clearly grasp the entire subject,
it is necessary to show the relation o2 these apparent move-
ments to the actual movement of the earth around the
sun.
92 ASTRONOMY.
To understand the relation of the equator to the ecliptic, we must
rememl>er that the celestial pole and the celestial equator have really
no reference whatever to the heavens, but depend solely on the direc-
tion of the earth's axis of rotation.* The pole of the heavens is noth-
ing more than that point of the celestial sphere toward which the
earth's axis happens to point. If the direction of this axis changes, the
position of the celestial pole among the stars will change also; though
to an observer on the earth, unconscious of the change, it would
seem as if the starry sphere moved while the pole remained at rest.
Again, the celestial equator being merely the great circle in which
the plane of the earth's equator, extended out to infinity in every
direction, cuts the celestial sphere, any change in the direction of the
pole of the earth would necessarily change the position of ihe equator
among the stars. Now the positions of the celestial pole and the
celestial equator among the stars seem to remain unchanged through-
out the year. (There is, indeed, a minute change, but it does not
affect our present reasoning.) This shows that, as the earth revolves
around the sun, its axis is constantly directed toward nearly the
same point of the celestial sphere.
THE SEASONS.
The conclusions to which we are thus led respecting the
real revolution of the earth are shown in Fig. 32. Here S
represents the sun, with the orbit of the earth surrounding it,
but viewed nearly edgeways so as to be much foreshortened.
A B CD are the four cardinal positions of the earth which
correspond to the cardinal points of the apparent path of the
.sun already described. In each figure of the earth N S is
the axis, N being its north and 8 its south pole. Since
this axis points in the same direction relative to the stars
during an entire year, it follows that the different lines N S
are all parallel. Again, since the equator does not coincide
with the ecliptic, these lines are not perpendicular to the
ecliptic, but are inclined from this perpendicular by 23^.
When the earth is at A the sun's north-polar distance (the
* Just as the horizon and zenith depend only on the situation of the observer.
MOTIONS OF THE EARTH.
93
angle at the centre of the earth at A between the lines to
the north pole and to the sun) is 113^; at B it is 90; at
G it is 66^; at D it is again 90, and between 66 and
113^ the north-polar distance continually varies. This
may be plainer if the student draws the lines S A, SB,
SC 9 SD, and prolongs the lines N8 at each position of
the earth.
Now the sun shines on only one half of the earth; viz.,
that hemisphere turned toward him. This hemisphere is
left bright in each of the figures of the earth at A, B, 0, D.
FIG. 32. CAUSES OF THE SEASONS.
Consider the diagram at A, and remember that the earth
is turning round so that every observer is carried round
his parallel of latitude every 24 hours. The parallels are
drawn in the cut, and it is plain that a person near JVwill
remain in darkness all the 24 hours ; any one in the north-
ern hemisphere is less than half the time in the light that
is, the sun is less than half the time above his horizon
and a person in the southern hemisphere is more than half
the time in the light. At the equator the days and nights
94 ASTRONOMY.
are always equal. At the south pole it is perpetual day.
The spectator near the south pole is carried round in a
parallel of latitude which is perpetually shined upon.
This is the winter solstice (midwinter in the northern
hemisphere, midsummer in the southern).
Next suppose the earth at B : is 90 from A ; that is,
3 months later. The sun's rays just graze the north and
south poles; each parallel of latitude is half light and half
dark ; the days and nights are equal. This is the equinox
of spring the vernal equinox. The sun's north-polar dis-
tance is 90. At C we have the *?/ninn'r solstice (summer
in the northern hemisphere, winter in the southern).
Here is perpetual day at the north pole, perpetual night at
the south; long days to all the northern hemisphere, long
nights in the southern. Three months later we have the
auhutnwt equinox at D.
This change of the seasons depends upon the change of
the sun's north-polar distance.
The exact phenomena at each place may be studied by
constructing a diagram for the latitude of that place 1 (sec
page 42) and assuming the sun's north-polar distance as
follows :
March 21, N.P.D. 90, Vernal Equinox.
June 20, N.P.D. GG^, Summer Solstice.
September 21, N.P.D. 90, Autumnal Equinox.
December 21, N.P.D. 113J, Winter Solstice.
Two such diagrams are given in the text-book (page 28).
The student should be able to pro^e that the sun is always
in the zenith of some place in the torrid zone.
MOTIONS OF THE EARTH. 95
CELESTIAL LATITUDE AND LONGITUDE.
To describe the positions of the sun and planets in space
we need two new co-ordinates.
The Celestial Latitude of a star is its angular distance
north or south of the ecliptic.
The Celestial Longitude of a star is its angular distance
from the vernal equinox measured on the ecliptic from
west to east. Having the right ascension and declination
of a body (which can be had by observation), we can com-
pute its celestial latitude and longitude. These co-ordinates
are no longer observed (as they were by the ancients), but
deduced from observations of right ascension and declina-
tion.
CHAPTER V.
THE PLANETARY MOTIONS.
APPARENT AND REAL MOTIONS OF THE PLANETS.
Definitions. The solar system comprises a number of
bodies of various orders of magnitude and distance, sub-
jected to many complex motions. Our attention will be
particularly directed to the motions of the great planets.
These bodies may, with respect to their apparent motions,
be divided into three classes.
Speaking, for the present, of the sun as a planet, the
first class comprises the sun and moon. We have seen that
if, upon a star chart, we mark down the positions of the
sun day by day, they will all fall into a regular circle which
marks out the ecliptic. The monthly course of the moon
is found to be of the same nature; and although its motion
is by no means uniform in a month, it is always toward the
east, and always along or very near a certain great circle.
The second class comprises Venus and Mercury. The
apparent motion of these bodies is an oscillating one on
each side of the sun. If we watch for the appearance of
one of these planets after sunset from evening to evening,
we shall find it to appear above the western horizon. Night
after night it will be farther and farther from the sun until
it attains a certain maximum distance; then it will appear
to return towards the sun again, and for a while to be lost
THE PLANETARY MOTIONS. 97
in its rays. A few days later it will reappear to the west
of the sun, and thereafter be visible in the eastern horizon
before sunrise. In the case of Mercury the time required
for one complete oscillation back and forth is about four
months; and in the case of Venus it is more than a year
and a half.
The third class comprises Mars, Jupiter, and Saturn, as
well as a great number of planets not visible to the naked
eye. The general or average motion of these planets is
toward the east, a complete revolution in the celestial
sphere being performed in times ranging from two years in
the case of Mars to 164 years in that of Neptune. But,
instead of moving uniformly forward, they seem to have a
swinging motion; first, they move forward or toward the
east through a pretty long arc, then backward or westward
through a short one, then forward through a longer one,
etc. It is by the excess of the longer arcs over the shorter
ones that the circuit of the heavens is made.
The general motion of the sun, moon, and planets among
the stars being toward the east, motion in this direction is
called direct; motions toward the west are called retrograde.
During the periods between direct and retrograde motion
the planets will for a short time appear stationary.
The planets Venus and Mercury are said to be at greatest
elongation when at their greatest angular distance from the
sun. The elongation which occurs with the planet east of
the sun, and therefore visible in the western horizon after
sunset, is called the eastern elongation, the other the west-
ern one.
A planet is said to be in conjunction with the sun when
it is in the same direction as seen from the earth, or when,
as it seems to pass by the sun, it approaches nearest to it.
98 ASTRONOMY.
It is said to be in opposition to the sun when exactly in the
opposite direction rising when the sun sets, and vice
versa.* If, when a planet is in conjunction, it is between
the earth and the sun, the conjunction is said to be an
inferior one; if beyond the sun, it is said to be superior.
FIG. 33. ORBITS OF THE PLANETS.
Arrangements and Motions of the Planets, The sun is
the real centre of the solar system, and the planets proper
revolve around it as the centre of motion. The order of
the five innermost large planets, or the relative position of
* A planet is in conjunction with the sun when it has the same
geocentric longitude; in opposition when the longitudes differ 1$Q.
THE PLANETARY MOTIONS. 99
their orbits, is shown in Fig. 33. These orbits are all
nearly, but not exactly, in the same plane. The planets
Mercury and Venus which, as seen from the earth, never
appear to recede very far from the sun, are in reality those
which revolve inside the orbit of the earth. The planets
of the third class, which perform their circuits at all dis-
tances from the sun, are what we call the superior planets,
and are more distant from the sun than the earth is. Of
these the orbits of Mars, Jupiter, and a swarm of telescopic
planets are shown in the figure; next outside of Jupiter
comes Saturn, the farthest planet readily visible to the
naked eye, and then Uranus and Neptune, telescopic plan-
ets. On the scale of Fig. 33 the orbit of Neptune would
be more than two feet in diameter. Finally, the moon is
a small planet revolving around the earth as its centre, and
carried with the latter as it moves around the sun.
Inferior planets are those whose orbits lie inside that of
the earth, as Mercury and Venus.
Superior planets are those whose orbits lie outside that
of the earth, as Mars, Jupiter, Saturn, etc.
The farther a planet is situated from the sun the slower
is its orbital motion. Therefore, as we go from the sun,
the periods of revolution are longer, for the double reason
that the planet has a larger orbit to describe and moves
more slowly in its orbit. It is to this slower motion of the
outer planets that the occasional apparent retrograde mo-
tion of the planets is due, as may be seen by studying Fig.
34. The apparent position of a planet, as seen from the
earth, is determined by the line joining the earth and
planet. Supposing this line to be continued so as to inter-
sect the celestial sphere, the apparent motion of the planet
will be defined by the motion of the point in which the line
100
ASTRONOMY.
intersects the sphere. If this motion is toward the east, it
is direct ; if toward the west, retrograde.
The Apparent Motion of a Superior Planet. In the figure
let S be the sun, ABCDEF the orbit of the earth, and
HIKLMN the orbit of a superior planet, as Mars.
When the earth is at A suppose Mars to be at H, and let
B and /, C and K, D and L, E and M, F and N be corre-
sponding positions. As the earth moves faster than Mars
FIG
the arcs AB, BC, etc., correspond to greater angles at the
centre than H I, IK, etc.
When the earth is at A, Mars will be seen on the celestial
sphere at the apparent position 0. When the earth is at
B, Mars will be seen at P. As the earth describes AB,
Mars will appear to describe OP moving in the same direc-
tion as the earth's orbital motion; i.e., direct. When tho
earth is at C, Mars is at K (in opposition to the sun), and
its motion is retrograde along the small arc beyond QP in
THE PLANETARY MOTIONS. 101
the figure. When the earth reaches D the planet has fin-
ished its retrograde arc. As the earth moves from D to E
the planet moves from L to M, and the lines joining earth
and planet are parallel and correspond to a fixed position
on the celestial sphere. The planet is at a station. As the
earth moves from E to F the apparent motion of Mars is
direct from Q to R; and in the same way the apparent
motion of any outer planet can be determined by drawing
its orbit outside of the earth's orbifc ABODE Fsn\d laying
off on this orbit positions which correspond to the points
ABCD EF and joining the corresponding positions. It
will be found that all outer planets have a retrograde mo-
tion at opposition, etc.
The Apparent Motion of an Inferior Planet. To deter-
mine the corresponding phenomena for an inferior planet
the same figure maybe used. Suppose HIKL M to be
the orbit of the earth, and A B C D E F t\\Q orbit of Mer-
cury, and suppose H and A, I and B, etc., to be corre-
sponding positions. Suppose H A to be tangent to Mer-
cury's orbit. The angle A H S is the elongation of Mer-
cury, and it is the greatest elongation it can ever have.
Let the student construct the apparent positions of Mer-
cury as seen from the earth from the data given in the
figure. From the apparent positions he can determine the
apparent motions. As Mercury moves from A B its ap-
parent motion is direct. On both sides of the inferior con-
junction C its motion is retrograde. From D to E it is
stationary. Also let him construct the apparent positions
of the sun at different times by drawing the linos H S, IS,
K S, etc., towards the right. The angles between the ap-
parent positions of Mercury and the sun will be the elonga-
tions of Mercury at various times.
102 ASTRONOMY.
Theory of Epicycles. Complicated as the apparent motions of the
planets were, it was seen by the ancient astronomers that they could
be represented by a combination of two motions. First, a small circle
or epicycle was supposed to move around tlie earth (not the sun)
with a regular, though not uniform, forward motion, and then the
planet was supposed to move around the circumference of this circle.
The relation of this theory to the true one was this: The regular
forward motion of the epicycle represents the real motion of the
planet around the sun, while the motion of the planet around the
circumference of the epicycle is an apparent one arising from the
revolution of the eurth around the
sun. To explain this we must under-
stand some of the laws of relative mo-
tion.
It is familiarly known that if an
observer in unconscious motion looks
upon an object ait rest, the object will
appear to him to move in a direction
opposite that in which he moves. As
a result of this law, if the observer is
uncon.-ciously describing a circle, an
object at rest will appear to him to
describe a circle of equal si/e. This
is shown by the following figure. Let
<S represent the sun, and ADCDEF
the orbit of the earth. Let us sup-
pose the observer on the earth carried
around in this orbit, but imagining
himself at rest at S, the centre of mo-
tion. Suppose he keeps observing the
direction and distance of the planet P,
which for the present we suppose to
be at rest, since it is only the relative
motion that we shall have to consider.
When the observer is at A he really
sees the planet in a direction and distance AP, but imagining himself
at S he thinks he sees the planet at the point a determined by drawing
a line Sa parallel and equal to A P. As he passes from A to B the
planet will seem to him to move in the opposite direction from a to
b, the point b being determined by drawing S b equal and parallel
to BP. As he recedes from the planet through the arc BCD, the
planet seems to recede from him through b c d; and while he moves
from left to right through DE the planet seems to move from right
PLANKTAET MOTTONS. 103
to left through de. Finally, as he approaches the planet through
the arc E FA the planet seems to approach him through efa, and
when he returns to A the planet will appear at a, as in the begin-
ning. Thus the planet, though really at rest, would seem to him to
move over the circle abcdef corresponding to that in which the
observer himself was carried around the sun.
The planet being really in motion, it is evident that the combined
effect of the real motion of the planet and the apparent motion
around the circle abcdef will be represented by carrying the centre
of this circle P along the true orbit of the planet. The motion of
the earth being more rapid than that of an outer planet, it follows
that the apparent motion of the planet through a b is more rapid
than the real motion of P along the orbit. Hence in this part of the
orbit the movement of the planet will be retrograde. In every other
part it will be direct, because the progressive motion of P will at
least overcome, sometimes be added to, the apparent motion around
the circle.
In the ancient astronomy the apparent small circle abcdef was
called the epicycle.
In the case of the inner planets Mercury and Venus the relation of
the epicycle to the true orbit is reversed. Here the epicyclic motion
is that of the planet round its real orbit; that is, the true orbit of the
planet around the sun was itself taken for the epicycle, while the
forward motion was really due to the apparent revolution of the sun
produced by the annual motion of the earth.
In Fig. 29 the sun would successively appear to be at 1', 2', 3', 4',
5', and at each of these points the inferior planet would really revolve
about 1', 2', 3', 4', 5'.
Although the observations of two thousand years ago
could be tolerably well explained by these epicycles, yet
with every increase of accuracy in observation new compli-
cations had to be introduced, until at the time of COPER-
NICUS (1542) the confusion was very great.
The Copernican System of the World, COPERNICUS re-
vived a belief taught by some of the ancients that the sun
was the centre of the system, and that the earth and plan-
ets moved about him in circular orbits. While this was a
step, and a great step, forward, purely circular orbits for
the planets would not explain all the facts.
104 ASTRONOMY.
From the time of COPERNICUS (1542) till that of KEP-
LER and GALILEO (1600 to 1630) the whole question of the
true system of the universe was in debate. The circular
orbits introduced by COPERNICUS also required a complex
system of epicycles to account for some of the observed
motions of the planets, and with every increase in accuracy
of observation new devices had to be introduced into the*
system to account for the new phenomena observed. In
short, the system of COPERNICUS accounted for so many
facts (as the stations and retrogradations of the planets)
that it could not be rejected, and had so many difficulties
that without modification it could not be accepted.
KEPLER'S LAWS OF PLANETARY MOTION.
Kepler and Galileo. KEPLER (born 1571, d. 1630) was
ii genius of the first order. He had a thorough acquaint-
ance with the old systems of astronomy and a thorough be-
lief in the essential accuracy of the Copernican system,
whose fundamental theorem was that the sun and not the
earth was the centre of our system. He lived nt the same
time with GALILEO, who was the first person to observe the
heavenly bodies with a telescope of his own invention, and
he had the benefit of accurate observations of the planets
made by TYCHO BRAKE. The opportunity for determin-
ing the true laws of the motions of the planets existed then
as it never had before; and fortunately he was able,
through labors of which it is difficult to form an idea to-
day, to reach a true solution.
The Periodic Time of a Planet. The time of revolution
of a planet in its orbit round the sun (its periodic time)
can be learned by continuous observations of the planet's
course among the stars.
THE PLANETARY MOTIONS. 105
From ancient times the geocentric positions of the
planets had been observed. These positions were referred
to the places of the brightest fixed stars, and the relative
places of these stars had been fixed with a tolerable ac-
curacy. The time required for a planet to move from one
star to the same star again was the time of revolution of
the planet referred to the earth.
The real motion of the earth was known from observa-
tions of the apparent motion of the sun. By calculation
it was possible to refer the motions as observed (i.e., with
reference to the earth) to the real motions (i.e., those about
the sun).
It was thus found that the periodic times of the known
planets were:
For Mercury about 88 days.
Venus " 225 "
Earth " 365 "
For Mars about 687 days
Jupiter " 4,333 "
Saturn " 10,759 "
These values were known to the predecessors of COPER-
KICUS. He also showed (what is evident when we examine
Fig. 34) that to an observer on the sun the motions of
the planets would be always direct, and that no stations or
retrogradations of the planets would be seen from the sun.
We may determine the relative distances of a planet and
the sun from each other by the method illustrated in Fig.
36. 8 is the sun, E the earth, and M the planet when the
planet is in opposition to the sun. The time at which the
planet is in opposition is known by noting the date when it
is on the meridian at midnight. After a certain period,
say one hundred days, the planet will have moved to M'
and the earth to E' . Since we know the periodic times
of the earth and planet, we can calculate the angles M' 8 M
106 ASTRONOMY.
and E' S E which the planet and earth will move over in
any interval.
At this date we can observe the angle M' E' S, which is
the angular distance between the sun and planet. (This
is called the planet's elongation.)
In the triangle M' S E' we shall know the angle at E',
by observation, the angle at S, since it is the difference
between the known angles E S E' and M S M', and hence
FIG. 36.
the angle at M' . Therefore a triangle can be constructed
which has the same shape as M* S E', and the relative
length of S M' and S E' thus becomes known.
Nothing is known from this calculation of the absolute
values of S E or S Mm miles, but observations of this sort
on all the planets give their relative distances from the
sun. If we call 8 E the astronomical unit, it was known
to the ancients that
PLANETARY MOTIONSt** 107
For Mercury ^ = 0.3871
Venus a* = 0.7233
Earth a 3 = 1.0000
Jfors a 4 = 1.5237
Jupiter a 6 = 5.2028
= 9.5388
The calculation which we have described could be made
for every position of each planet, and thus its distances from
the sun at every point of its orbit could be determined.
The radius- vector of a planet is the line which joins it to
the sun.
The relative lengths of the radii-vectores of each planet
at any time were thus found by observation, in terms of
the earth's radius-vector = 1.
FIG. 37.
Suppose Sto be the sun, and draw lines SP, SP l9
S P n , etc., to the heliocentric positions of a planet at dif-
ferent times. On these lines lay off distances SP, SP l9
S P 9 , etc., proportional to the lengths of the planet's radii-
vectores determined as above. Join the points P, P l9 P 9 ,
P,, etc. The line joining these is a visible representation
108 ASTRONOMY.
of the shape of the planet's orbit, drawn to scale. This
shape is not that of a circle, but it is an ellipse, and the
sun, 8, is not at the centre but at a focus of the ellipse.
An ellipse is a curve such that the sum of the distances
of every point of the curve from two fixed points (the foci)
is a constant quantity.
Fio. 88
The Ellipse. A D tf P is an ellipse ; S and S f are the foci. By the
definition of an ellipse SP-\-P8= A C, and this is true for every
point. S is the focus occupied by the sun, " the filled focus." A S
is the least distance of the planet from the sun, its perihelion distance;
and A is the perihelion, that point nearest the sun. C is the aphelion,
the point farthest from the sun. 8 A, SD, SC, SB, SP are radii-
vectores at different parts of the orbit. A C is the major axis
of the orbit = 2a. This major axis of the orbit is twice the mean
distance of the planet from the sun, a. BD is the minor axis, 26.
The ratio of 08 to OA is the eccentricity of the ellipse. By the
definition of the ellipse, again, BS+BS'= A C; and B8 = BS= a.
S 3 , or 08= 4/a*-^ and the eccentricity of the
.OS Vtf^V
ellipse is _=__.
Kepler's Laws. By computations based on the observa-
tions of Mars made by TYCHO BRAHE, KEPLER deduced
THE PLANETAHY MOTIONS. 109
his first two laws of motion in the solar system. The first
law of KEPLER is
/. Each planet moves around the sun in an ellipse, hav-
ing the sun at one of its foci. To understand Law II:
Suppose the planet to be at the points P, P l9 P,, P,, P 4 ,
etc., at the times T, T lt T^ T t , T 4 , etc. (Fig. 37).
Suppose the times T^- T, T 3 - T t , T 6 - T 4 to be equal.
KEPLER computed the areas of the surfaces P 8 P iy P a $P 3 ,
P 4 SP 6 and found that these areas were equal also, and
that this was true for each planet. The second law of KEP-
LER is
//. The radius-vector of each planet describes equal areas
in equal times.
These two laws are true for each planet moving in its
own ellipse about the sun.
For a long time KEPLER sought for some law which
should connect the motion of one planet in its ellipse with
the motion of another planet in its ellipse. Finally he
found such a relation between the mean distances of the
different planets (see table on page 107) and their periodic
times (see table on p. 105).
His third law is:
///. The squares of the periodic times of the planets are
proportional to the cubes of their mean distances from the
sun.
That is, if T lt T^ T 3 , etc., are the periodic times of the
different planets whose mean distances are a l9 # s , etc.,
then
etc. etc.
110 ASTRONOMY.
If T t and 0, are the periodic time and the mean distance
of the earth, and if T t (= 1 year) is taken as the unit of
time and a, as the unit of distance, then we shall have
and so on.
The data which KEPLER had were not quite so accurate
as those which we have given, and the table below shows
the very figures on which KEPLER'S conclusion was based:
PLANET. fll T T '-=- O\
Mercury .............. 0.2378 0.2408 years 1.013
Venus ................ 0.6104 0.6151 1.008
Earth ................ 1.0000 1.0000 1.000
Mars ................. 1.8740 1.8810 1.004
Jupiter ............... 11.914 11.8764 0.996
Saturn ............... 28.058 29.4605 1.050
Although the numbers in the third column were not
strictly the same, their differences were no greater than
might easily have been produced by the errors of the obser-
vations which KEPLER used; and on the evidence here
given he advanced his third law. The order of discovery
of the true theory of the solar system was, then
I. To prove that the earth moved in space;
II. To prove that the centre of this motion was the sun;
III. To establish the three laws of KEPLER, which gave
the circumstances of this motion.
By means of the first two laws of KEPLER the motions of each
planet in its own ellipse became known; that is, the position of the
planet at any future time could be predicted. For example, if the
planet was at P at a time 7, and the question was as to its place at a
subsequent time T, this could be solved by computing, first, how
THE PLANETARY MOTIONS. HI
large an area would be described by the radius-vector in the interval
T T ; and second, what the angle at 8 of the sector having this
area would be. Then drawing a line through S making this angle
with the line P(say SP,), and laying off the length of the radius-
vector S P,, the position of the planet became known.
From the third law the relative values of the mean distances
ai, a y , a 4 , a 6 , etc., could be determined with great and increasing ac-
curacy.
T
From the equation = 1, a could be determined so soon as I 7 was
known. With each revolution of the planet T became known more
accurately, as did also a.
These laws are the foundations of our present theory of the solar
system. They were based on observation pure and simple. We may
anticipate a little to say that these laws have been compared with
the most precise observations we can m;ike at the present time, and
discussed in all their consequences by processes unknown to KEP-
LER, and that they are strictly true if we make the following modifi-
cations.
If there were only one planet revolving about the sun, then it
would revolve in a perfect ellipse, and obey the second law exactly.
In a system composed of the sun and more than one planet each
planet disturbs the motion of every other slightly, by attracting it
from the orbit which it would otherwise follow.
Thus neither the first nor the second law can be precisely true of
any planet, although they are very nearly so. In the same way the
relation between the orbits of any two planets as expressed in the
third law is not precise, although it is a very close approximation.
Elements of a Planet's Orbit. When we know a and b for any orbit,
the shape and size of the orbit is known.
Knowing a we also know T, the periodic time; in fact a is found
from I by KEPLETC'S law III.
If we know the planet's celestial longitude (L) at a given epoch,
say December 31st, 1850, we have all the elements necessary for
finding the place of the planet in its orbit at any time, as has been
explained (page 110).
The orbit lies in a certain plane; this plane intersects the plane of
the ecliptic at a certain angle, which we call the inclination i. Know-
ing i, the plane of the planet's orbit is fixed. The plane of the
orbit intersects the plane of the ecliptic in a line, the line of the nodes.
Half of the planet's orbit lies below (south of) the plane of the
ecliptic and half above. As the planet moves in its orbit it must
pass through the plane of the ecliptic twice for every revolution.
112 ASTRONOMY.
The point where it passes through the ecliptic going from the south
half to the north half of its orbit is the ascending node; the point
where it passes through the ecliptic going from north to south is
the descending node of the planet's orbit. If we have only the in-
clination given, the orbit of the planet may lie anywhere in the plane
whose angle with the ecliptic is t. If we fix the place of the nodes,
or of one of them, the orbit is thus fixed in its plane. This we do
by giving the (celestial) longitude of the ascending node/}.
Now everything is known except the relation of the planet's orbit
to the sun. This is fixed by the longitude of t/ie perilielion, or P.
Thus the elements of a planet's orbit are:
i, the inclination to the ecliptic, which fixes the plane of the planet's
orbit;
fi,, the longitude of the node, which fixes the position of the line of
intersection of the orbit and the ecliptic;
P, the longitude of the perihelion, which fixes the position of the
major axis of the planet's orbit with relation to the sun, and hence
in space;
a and e, the mean distance and eccentricity of the orbit, which fix
the shape and size of the orbit;
2 and M, the periodic time and the longitude at epoch, which enable
the place of the planet in its orbit, and hence in space, to be fixed at
any future or past time.
The elements of the older planets of the solar system are now
known with great accuracy, and their positions for two or three cen-
turies past or future can be predicted with a close approximation to the
accuracy with which these positions can be observed.
CHAPTER VI.
UNIVERSAL GRAVITATION.
NEWTON'S LAWS OF MOTION
THE establishment of the theory of universal gravitation
furnishes one of the best examples of scientific method
which is to be found. We shall describe its leading features,
less for the purpose of making known to the reader the
technical nature of the process than for illustrating the
true theory of scientific investigation, and showing that such
investigation has for its object the discovery of what we
may call generalized facts. The real test of progress is
found in our constantly increased ability to foresee either
the course of nature or the effects of any accidental or arti-
ficial combination of causes. So long as prediction is not
possible, the desires of the investigator remain unsatisfied.
When certainty of prediction is once attained, and the
laws on which the prediction is founded are stated in their
simplest form, the work of science is complete.
To the pre-Newtonian astronomers the phenomena of
the geometrical laws of planetary motion, which we have
just described, formed a group of facts having no connection
with anything on the earth's surface. The epicycles of
HIPPARCHUS and PTOLEMY were a truly scientific concep-
tion, in that they explained the seemingly erratic motions
of the planets by a single simple law. In the heliocentric
114 ASTRONOMY.
theory of COPERNICUS this law was still further simplified
by dispensing in great part with the epicycle, and replacing
the latter by a motion of the earth around the sun, of the
same nature with the motions of the planets. But COPER-
NICUS had no way of accounting for, or even of describing
with rigorous accuracy, the small deviations in the motions
of the planets around the sun. In this respect he made no
real advance upon the ideas of the ancients.
KEPLER, in his discoveries, made a great advance in rep-
resenting the motions of all the planets by a single set of
simple and easily understood geometrical laws. Had the
planets followed his laws exactly, the theory of planetary
motion would have been substantially complete. Still,
further progress was desired for two reasons. In the first
place, the laws of KEPLER did not perfectly represent all
the planetary motions. When observations of the greatest
accuracy were made, it was found that the planets deviated
by small amounts from the ellipse of KEPLER. Some small
emendations to the motions computed on the elliptic theory
were therefore necessary. Had this requirement been ful-
filled, still another step would have been desirable; namely,
that of connecting the motions of the planets with motions
upon the earth, and reducing them to the same laws.
Notwithstanding the great step which KEPLER made in
describing the celestial motions, he unveiled none of the
great mystery in which they were enshrouded. When KEP-
LER said that observation showed the law of planetary mo-
tion to be that around the circumference of an ellipse, as
asserted in his law, he said all that it seemed possible to
learn, supposing the statement perfectly exact. And it
was all that could be learned from the mere study of the
planetary motions. In order to connect these motions with
UNIVERSAL GRAVITATION. 115
those on the earth, the next step was to study the laws of
force and motion here around us. Singular though it may
appear, the ideas of the ancients on this subject were far
more erroneous than their conceptions of the motions of
the planets. We might almost say that before the time of
GALILEO scarcely a single correct idea of the laws of motion
was generally entertained by men of learning. Among
those who, before the time of NEWTON, prepared the way
for the theory in question, GALILEO, HUYGHENS, and
HOOKE are entitled to especial mention. The general laws
of motion laid down by NEWTON were three in number.
Law First: Every body preserves its state of rest or of
uniform motion in a right line, unless it is compelled to
change that state by forces impressed thereon.
It was formerly supposed that a body acted on by no force tended
to come to rest. Here lay one of the greatest difficulties which the
predecessors of NEWTON fouud, in accounting for the motion of the
planets. The idea that the sun in some way caused these motions
was entertained from the earliest times. Even PTOLEMY had a vague
idea of a force which was always directed toward the centre of the
earth, or, which was to him the same thing, toward the centre of the
universe, and which not only caused heavy bodies to fall, but bound
the whole universe together. KEPLER, again, distinctly affirms the
existence of a gravitating force by which the sun acts on the planets;
but he supposed that the sun must also exercise an impulsive forward
force to keep the planets in motion. The reason of this incorrect
idea was, of course, that all bodies in motion on the surface of the
earth had practically come to rest. But what was not clearly seen
before the time of NEWTON, or at least before GALILEO, was that
this arose from the inevitable resisting forces which act upon all
moving bodies upon the earth.
Law Second: TJie alteration of motion is ever propor-
tional to the moving force impressed) and is made in the
direction of the right line in which that force acts.
116 ASTRONOMY.
The first law might be considered as a particular case of this sec-
ond one which arises when the force is supposed to vanish. The ac-
curacy of both laws can be proved only by very carefully conducted
experiments. They are now considered as conclusively proved.
Law Third: To every action there is always opposed an
equal reaction ; or the mutual actions of two bodies upon
each other are always equal, and in opposite directions.
That is, if a body A acts in any way upon a body B, B will exert
a force exactly equal on A in the opposite direction.
These laws once established, it became possible to calculate the mo-
tion of any body or system of bodies when once the forces which act
on them were known, and, rice versa, to define what forces were re-
quisite to produce any given motion. The question which presented
itself to the mind of NEWTON and his contemporaries was this : Under
what law of force will planets mote round t/ie gun in accordance with
KEPLER'S laws f
Supposing a body to move around in a circle, and putting R the
radius of the circle, T the period of revolution, HUYGIIENB had shown
that the centrifugal force of the body, or, which is the same thing,
the attractive force toward the centre which would keep it in the
3
circle, was proportional to -=^. But by KEPLER'S third law T* is pro-
portional to #*. Therefore this centripetal force is proportional to
-j=;that Is, to-nf. Thus it followed immediately from KEPLER'S
third law that the central force which would keep the planets in their
orbits was in verily as the square of the distance from the sun, sup-
posing each orbit to be circular. The first law of motion once com-
pletely understood, it was evident that the planet needed no force
impelling it forward to keep up its motion, but that, once started, it
would keep on forever.
The next step was to solve the problem, What law of force will
make a planet describe an ellipse around the sun, having the latter
in one of its foci? Or, supposing a planet to move round the sun,
the latter attracting it with a force inversely as the square of the dis-
tance; what will be the form of the orbit of the planet if it is not cir-
cular? A solution of either of these problems was beyond the power
of mathematicians before the time of NEWTON; and it thus remained
uncertain whether the planets moving under the influence of the
sun's gravitation would or would not describe ellipses. Unable, at
UNIVERSAL GRAVITATION. 117
first, to reach a satisfactory solution, NEWTON attacked the problem
in another direction, starting from the gravitation, not of the sun,
but of the earth, as explained in the following section.
GRAVITATION IN THE HEAVENS.
The reader is probably familiar with the story of NEW-
TON and the falling apple. Although it has no authorita-
tive foundation, it is strikingly illustrative of the method
by which NEWTON must have reached a solution of the
problem. The course of reasoning by which he ascended
from gravitation on the earth to the celestial motions was as
follows : We see that there is a force acting all over the earth
by which all bodies are drawn toward its centre. This
force is called gravitation. It extends without sensible
diminution to the tops not only of the highest buildings,
but of the highest mountains. How much higher does it
extend? Why should it not extend to the moon? If it
does, the moon would tend to drop toward the earth, just
as a stone thrown from the hand drops. As the moon
moves round the earth in her monthly course, there must
be some force drawing her toward the earth; else, by the
first law of motion, she would fly entirely away in a straight
line. Why should not the force which makes the apple
fall be the same force which keeps her in her orbit? To
answer this question, it was not only necessary to calculate
the intensity of the force which would keep the moon her-
self in her orbit, but to compare it with the intensity of
gravity at the earth's surface. It had long been known
that the distance of the moon was about sixty radii of the
earth, from measures of her parallax (see page 57). If
this force diminished as the inverse square of the distance,
then at the moon it would be only -^-^ as great as at the
118 ASTRONOMY.
surface of the earth. On the earth a body falls sixteen feet
in a second. If, then, the theory of gravitation were cor-
rect, the moon ought to fall towards the earth ygV^ of this
amount, or about -fa of an inch in a second. The moon
being in motion, if we imagine it moving in a straight line
at the beginning of any second, it ought to be drawn away
from that line -fa of an inch at the end of the second.
When the calculation was made it was found to agree ex-
actly with this result of theory. Thus it was shown that
the force which holds the moon in her orbit is the same
force that makes the stone fall, diminished as the inverse
square of the distance from the centre of the earth.
It thus appeared that central forces, both toward the sun
and toward the earth, varied inversely as the squares of the
distances. KEPLER'S second law showed that the line drawn
from the planet to the sun would describe equal areas in
equal times. NEWTON showed that this could not be true
unless the force which held the planet was directed toward
the sun. We have already stated that the third law showed
that the force was inversely as the square of the distance,
and thus agreed exactly with the theory of gravitation. It
only remained to consider the results of the first law, that
of the elliptic motion. After long and laborious efforts,
NEWTON was enaoled to demonstrate rigorously that this
law also resulted from the law of the inverse square, and
could result from no other. Thus all mystery disappeared
from the celestial motions; and planets were shown to be
simply heavy bodies moving according to the same laws that
were acting here around us, only under very different cir-
cumstances. All three of KEPLER'S laws were embraced in
the single law of gravitation toward the sun. The sun at-
tracts the planets as the earth attracts bodies here around us.
UNIVERSAL GRAVITATION. 119
Mutual Action of the Planets. By NEWTON'S third law of motion,
each planet must attract the sun with a force equal to that which the
sun exerts upon the planet. The moon also must attract the earth
as much as the earth attracts the moon. Such being the case, it
must be highly probable that the planets attract each other. If so,
KEPLER'S laws can only be an approximation to the truth. The sun,
being immensely more massive than any of the planets, overpowers
their attraction upon each other, and makes the law of elliptic mo-
tion very nearly true. But still the comparatively small attraction
of the planets must cause some deviations. Now, deviations from
the pure elliptic motion were known to exist in the case of several of
the planets, notably in that of the moon, which, if gravitation were
universal, must move under the influence of the combined attraction
of the earth and of the sun. NEWTON, therefore, attacked the com-
plicated problem of the determination of the motion of the moon
under the combined action of these two forces. He showed in a
general way that its deviations would be of the same nature as those
shown by observation. But the complete solution of the problem,
which required the answer to be expressed in numbers, was beyond
his power.
Gravitation Resides in each Particle of Matter, Still
another question arose. Were these mutually attractive
forces resident in the centres of the several bodies attracted,
or in each particle of the matter composing them? NEW-
TON* showed that the latter must be the case, because the
smallest bodies, as well as the largest, tended to fall toward
the earth, thus showing an equal gravitation in every sepa-
rate part. It was also shown by NEWTON that if a planet
were on the surface of the earth or outside of it, it would
be attracted with the same force as if the whole mass
of the earth were concentrated in its centre. Putting
together the various results thus arrived at, NEWTON"
was able to formulate his great law of universal gravita-
tion in these comprehensive words: "Every particle of
matter in the universe attracts every other particle with
a force directly as the masses of the two particles, and
120 AST&ONOMY.
inversely as the square of the distance which separates
them."
To show the nature of the attractive forces among these various
particles, let us represent by m and iri the masses of two attracting
bodies. We may conceive the body m to be composed of m par-
ticles, and the other body to be composed of m' particles. Let us
conceive that each particle of one body attracts each particle of the
other with a force . Then every particle of m will be attracted by
each of the m' particles of the other, and therefore the total attractive
m'
force on each of the m particles will be 5-. Each of the m particles
being equally subject to this attraction, the total attractive force be-
tween the two bodies will be . When a given force acts upon
a body, it will produce less motion the larger the body is, the Mftrf-
erntiug force being proportional to the total attracting force divided
by the mass of the body moved. Therefore the accelerating force
which acts on the body in', and which determines the amount of
motion, will be -^; and conversely the accelerating force acting on
the body m will be represented by the fraction ^-.
REMARKS ON THE THEORY OF GRAVITATION.
The real nature of the great discovery of NEWTON is so
frequently misunderstood that a little attention may be
given to its elucidation. Gravitation is frequently spoken
of as if it were a theory of NEWTON'S, and very generally
received by astronomers, but still liable to be ultimately
rejected as a great many other theories have been. Not
infrequently people of greater or less intelligence are found
making great efforts to prove it erroneous. NEWTON did
not discover any new force, but only showed that the
motions of the heavens could be accounted for by a force
which we all know to exist. Gravitation (Latin g radius
UNIVERSAL GRAVITATION. 121
weight, heaviness) is the force which makes all bodies
here at the surface of the earth tend to fall downward;
and if any one wishes to subvert the theory of gravitation,
he must begin by proving that this force does not exist.
This no one would think of doing. What NEWTON did
was to show that this force, which, before his time, had
been recognized only as acting on the surface of the earth,
really extended to the heavens, and that it resided not only
in the earth itself, but in the heavenly bodies also, and in
each particle of matter, however situated. To put the
matter in a terse form, what NEWTON discovered was not
gravitation, but the universality of gravitation.
It may be inquired, is the induction which supposes
gravitation universal so complete as to be entirely beyond
doubt? We reply that within the solar system it certainly
is. The laws of motion as established by observation and
experiment at the surface of the earth must be considered
as mathematically certain. It is an observed fact that the
planets in their motions deviate from straight lines in a
certain way. By the first law of motion, such deviation
can be produced only by a force; and the direction and
intensity of this force admit of being calculated once that
the motion is determined. When thus calculated, it is
found to be exactly represented by one great force con-
stantly directed toward the sun, and smaller subsidiary
forces directed toward the several planets. Therefore no
fact in nature is more firmly established than that of uni-
versal gravitation, as laid down by NEWTON, at least within
the solar system.
We shall find, in describing double stars, that gravita-
tion is also found to act between the components of a great
number of such stars. It is certain, therefore, that at
ASTRONOMY.
least some stars gravitate toward each other, as the bodies
of the solar system do; but the distance which separates
most of the stars from each other and from our sun is so
immense that no evidence of gravitation between in dividual
stars and the sun has yet been given by observation. Still,
that they do gravitate according to NEWTON'S law can
hardly be seriously doubted by any one who understands
the subject.
The student may now l>e supposed to see the absurdity
of supposing that the tlioory of gravitation can ever be
subverted. It is not, however, absurd to suppose that it
may yet be shown to be the result of some more general
law. Attempts to do this arc made from time to time
by men of a philosophic spirit; but thus far no theory of
the subject having much probability in its favor has been
propounded.
CHAPTER VII.
THE MOTIONS AND ATTRACTION OF THE MOON.
EACH of the planets, except Mercury and Venus, is at-
tended by one or more satellites, or moons as they are
sometimes familiarly called. These objects revolve around
their several planets in nearly circular orbits, accompany-
ing them in their revolutions around the sun. Their dis-
tances from their planets are very small compared with the
distances of the latter from each other and from the sun.
Their magnitudes also are very small compared with those
of the planets around which they revolve. Considering
each system by itself, the satellites revolve around their
central planets, or " primaries," in nearly circular orbits,
and in each system KEPLER'S laws govern the motion of the
satellites about the primary. Each system is carried around
the sun without any derangement of the motion of its sev-
eral bodies among themselves.
Our earth has a single satellite accompanying it in this
way, the moon. It revolves around the earth in a little
less than a month. The nature, causes, and consequences
of this motion form the subject of the present chapter.
THE MOON'S MOTIONS AND PHASES.
That the moon performs a monthly circuit in the heavens is a fact
with which we are all familiar from childhood. At certain times we
see her newly emerged from the sun's rays in the western twilight,
and then we call her the new moon. On each succeeding evening
124 ASTRONOMY.
we see her further to the east, so that in two weeks she is opposite
the sun, rising in the east as he sets in the west. Continuing her
course two weeks more, she has approached the sun on the other
side, or from the west, and is once more lost in his rays. At the end
of twenty- nine or thirty days, we see her again emerging as new
moon, and her circuit is complete. The sun has been apparently
moving toward the east among the stars during the whole month, so
that during the interval from one new moon to the next the moon
has to make a complete circuit relatively to the stars, and to move
forward some 30 further to overtake the sun, which has also been
moving toward the east at the rate of 1 daily. The revolution of
the moon among the stars is performed in about 27 days,* so that if
we observe when the moon is very near some star, we shall find her
in the same position relative to the star at the end of this interval.
The motion of the moon in this circuit differs from the apparent
motions of the planets in l>eing always forward. We have seen that
the planets, though, on the whole, moving toward the east, are
effected with an apparent retrograde motion at certain intervals, ow-
ing to the motion of the earth around the sun. But the earth is Die
real centre of the moon's motion, and carries the moon along with it
in its annual revolution around the sun. To form a correct idea of
the real motion of these three bodies, we must imagine, the earth per-
forming its circuit around the sun in one year, and carrying with it
the moon, which makes a revolution around it in 27 days, at a dis-
tance only about ffa that of the sun.
Phases of the Moon. The moon, being a non-luminous
body, shines only by reflecting the light falling on her from
some other body. The principal source of light is the sun.
Since the moon is spherical in shape, the sun can illumi-
nate one half her surface. The appearance of the moon
varies according to the amount of her illuminated hemi-
sphere which is turned toward the earth, as can be seen by
studying Fig. 39. Here the central globe is the earth;
the circle around it represents the orbit of the moon. The
rays of the sun fall on both earth and moon from the
right, the distance of the sun being, on the scale of the
* More exactly, 27.32166- 1 .
MOTIONS AND ATTRACTION OF THE MOON. 125
figure, some 30 feet. Eight positions of the moon are
shown around the orbit at A, E, C, etc., and the right-
hand hemisphere of the moon is illuminated in each posi-
tion. Outside these eight positions are eight others show-
ing how the moon looks as seen from the earth in each
position.
At A ifc is "new moon," the moon being nearly between
FIG. 39.
the earth and the sun. Its dark hemisphere is then turn-
ed toward the earth, so that it is entirely invisible. The
sun and moon then rise and set together.
At E the observer on the earth sees about a fourth of
the illuminated hemisphere, which looks like a crescent, as
shown in the outside figure. In this position a great deal
of light is reflected from the earth to the moon, rendering
126 ASTRONOMY.
the dark part of the latter visible by a gray light. This
appearance is sometimes called the "old moon in the new
moon's arms." At O the moon is said to be in her "first
quarter," and one half her illuminated hemisphere is visi-
ble. The moon is on the meridian at 6 P.M. At G three
fourths of the illuminated hemisphere is visible, and at B
the whole of it. The latter position, when the moon is
opposite the sun, is called "full moon." The moon rises
at sunset. After this, at //, D, F, the same appearances
are repeated in the reversed order, the position D being
called the " last quarter."
THE TIDES.
It is not possible in an elementary treatise to give a complete ac-
count of the theory of the tides of the ocean due to the effect of the
sun and moon. A general account may be presented which will be
sufficient to show the nature of the effects produced and of their
causes. (See Fig. 39*.)
Let us consider the earth to be composed of a solid centre sur-
rounded by an ocean of uniform (and not very great) depth. The
moon exercises an attraction upon every particle of the earth's mass,
solid and fluid alike. The attraction of the whole moon (M) upon
a particle m is ~, where p is the distance from the centre of the
moon to m. If m is one of the solid particles of the earth, it cannot
move towards M in obedience to the attraction unless all the other
solid particles move, since the earth proper is rigid.
If m is a fluid particle, it is free to move in obedience to the forces
impressed upon it. The attraction of M is proportional to ; that is,
P 9
the particles nearest M are most attracted, and, on the whole, the
water on the part of the earth nearest the moon will be raised to-
ward M.
The moon also attracts the solid parts of the earth more than she
attracts the water most distant from her, and this produces exactly
the same effect as if there was another moon M' exactly opposite to
M. The elevation of the water under M' will not be quite as great
as that under M, on account of the increased distance from M.
MOTIONS AND ATTRACTION OF THE MOON. 127
Thus the moon's action tends to elevate the whole mass of water on
the line joining her centre with the centre of the earth, and this is so
not only on the part of this line nearest the moon, but also on that
farthest from her.
This elevation of the waters of the ocean above their mean level is
called the tide. The tidal effect of the moon produces a distortion of
the spherical shell of water which we have supposed to surround the
earth, and elongates this shell into the shape of an ellipsoid, the longer
axis of which is always directed to the moon. Now as the moon
moves around the earth once in 24 h 54 m , this ellipsoidal shape must
also move with her. The crest of the wave directly under M would
come back to the same meridian every 24 1 ' 54 m . The outer crest (under
M' ) would come 12 h 27 m after the first, so there would be two high
tides at any one meridian every (lunar) day. The first (and largest)
high tide would be at the time of the moon's visible transit over the
meridian. The second high tide would be 12 h 27 m later, when the
moon was on the lower meridian of the place.
The high tides occur when there is more water than the mean
depth, anil between these high tides we should have low tides, two
in each lunar day. Similarly there would be two high tides daily at
each meridian, due to the attractive force of the sun. These would
have a period of 24 hours and could not always agree with the lunar
high tides. When Uie solar and lunar high tides coincided (at new
and full moon)^then we should have the highest high tides and the
lowest low tides. (These are the Spring tides, so called.) When the
moon and the sun were 90 apart (moon at first and third quarter),
then we should have the lowest high tides and the highest low tides.
(Neap tides, so called.)
The tide-producing force of the moon is to that of the sun as 800 is
to 355. The great mass of the sun compensates in some degree "for
his relatively great distance.
At spring tides sun and moon work together; at neap tides they
oppose each other. The relative heights are as 800 -f 355 : 800 355,
or as 13 to 5 approximately.
The explanation above relates to an earth covered by an ocean of
uniform depth. To fit it to the facts as they are, a thousand cir-
cumstances must be taken into account, Avhich depend upon the
modifying effects of continents and islands, of deep and shallow
seas, of currents and winds. Practically, the high tide at any sta-
tion is predicted by adding to the time of the moon's transit over
its meridian a quantity determined from observation and not from
theory.
128 ASTRONOMY.
Effects of the Tides upon the Earth's Rotation. As the tide-wave
moves it meets with resistance due to friction. The amount of this
resistance is subtracted daily from the earth's energy of rotation
The tides act on the earth, in a way, as if they were a light friction-
brake applied to an enormously heavy wheel turning rapidly. The
wheel has been set to turning, and, so far as we know, it will never
have any more rotative energy given to it. Every subtraction of
energy, however small, is a positive and irretrievable loss.
The lunar tides are gradually, though very slowly, lengthening the
day. Since accurate astronomical observations began there has been
no observational proof of any appreciable change in the length of the
day, but the change has been going on nevertheless.
Fio. 39.
In the figure M is the moon on the meridian Om of a
place m. It is high water at m and m'. It is low water
at m" and m'". In an hour the moon will have moved -to
1' and the crest of the wave to 1. The tide will be high
at 1 and falling at m. As the moon moves by the diurnal
motion to 2', 3', M' ", M' , the crest will move with it.
When the moon is at M"' it is low water at m and m'.
When the moon is at M', it is again high water at m; and
so on. If we suppose M to be the sun, a similar set of
solar tides will be produced every 24 hours. The actual
tide is produced by the superposition of the solar and
lunar tides.
CHAPTER VIII.
ECLIPSES OF THE SUN AND MOON.
ECLIPSES are phenomena arising from the shadow of one
body being cast upon another, or from a dark body passing
over a bright one. In an eclipse of the sun, the shadow of
the moon sweeps over the earth, and the sun is wholly or
partially obscured to observers on that part of the earth
where the shadow falls. In an eclipse of the moon, the
latter enters the shadow of the earth, and is wholly or
partially obscured in consequence of being deprived of
some or all of its borrowed light. The satellites of other
planets are from time to time eclipsed in the same way by
entering the shadows of their primaries ; among these the
satellites of Jupiter are objects whose eclipses may be
observed with great regularity.
THE EARTH'S SHADOW AND PENUMBRA.
In Fig. 40 let S represent the sun, and E the earth. Draw straight
lines, DBVand D'B'V, each tangent to the sun and the earth.
The two bodies being supposed spherical, these lines will be the
intersections of a cone with the plane of the paper, and may be
taken to represent that cone. It is evident that the cone B VB' will
be the outline of the shadow of the earth, and that within this cone
no direct sunlight can penetrate. It is therefore called the earth's
shadow-cone.
Let us also draw the lines D'BP and DB'P' to represent the
other cone tangent to the sun and earth. It is then evident that
within the region VBP and VB'P' the light of the sun. will be
partially but not entirely cut off.
130
ASTRONOMY.
Dimensions of Shadow. Let us investigate the distance E V from
Hie centre of the earth to the vertex of the shadow. The triangles
V EB and VSD are similar, having a right angle at B and at D.
Hence
VE:EB = VS:SD = ES:(8D-EB).
So if we put
I = VE, the length of the shadow measured from the centre of
the earth,
r = E S, the radius- vector of the earth,
R = SD, the radius of the sun,
p = EB, the radius of the earth,
we have
1= VE =
E8X EB
8D-EB~ R- p
rp
FIG. 40. FORM OK SHADOW.
That is, I is expressed in terms of known quantities, and thus is
known.
The radius of the shadow diminishes uniformly with the distance
as we go outward from the earth. At any distance z from the
earth's centre it will be equal to II -\p, for this formula gives
the radius p when 2 = 0, and the diameter zero when z = I as it
should.*
* It will be noted that this expression is not, rigorously speaking, the semi-
diameter of the shadow, but the shortest distance from a point on its central
line to its conical surface. This distance is measured in a direction EB perpen-
dicular to DB, whereas the diameter would be perpendicular to the axis SE^
and its half length would be a little greater than EB.
ECLIPSES OF THE SUN AND JfcfrMf > % 131
ECLIPSES OF THE MOON.
The mean distance of the moon from the earth is about
60 radii of the latter, and the length E V of the earth's
shadow is 217 radii of the earth. Hence when the moon
passes through the shadow she does so at a point less than
three tenths of the way from E to V. The radius of the
shadow here will be ' 3L ^f SL of the radius E B of the earth,
a quantity which we readily find to be about 4600 kilo-
metres. The radius of the moon being 1736 kilometres, it
will be entirely enveloped by the shadow when it passes
through it within 2864 kilometres of the axis E V of the
shadow. If its least distance from the axis exceed this
amount, a portion of the lunar globe will be outside the
limits B V of the shadow-cone, and will therefore receive a
portion of the direct light of the sun. If the least distance
of the centre of the moon from the axis of the shadow is
greater than the sum of the radii of the moon and the
shadow that is, greater than 6336 kilometres the moon
will not enter the shadow at all, and there will be no eclipse
proper, though the brilliancy of the moon is diminished
wherever she is within the penumbral region.
When an eclipse of the moon occurs, the phases are laid down
in the almanac. (See Fig. 40.) Supposing the moon to be moving
around the earth from below upward, its advancing edge first
meets the boundary BP of the penumbra. The time of this
occurrence is given in the almanac as that of " moon entering
penumbra." A small portion of the sunlight is then cut off from the
advancing edge of the moon, and this amount constantly increases
until the edge reaches the boundary B' V of the shadow. It is
curious, however, that the eye can scarcely detect any diminution in
the brilliancy of the moon until she has almost touched the boundary
of the shadow. The observer must not, therefore, expect to detect the
coming eclipse until very nearly the time given in the almanac as that
ASTRONOMY.
of "moon entering shadow." As this happens, the advancing
portion of the lunar disk will be entirely lost to view, as if it were
cut off by n rather ill-defined line. It takes the moon about an hour
to move pver a distance equal to her own diameter, so that if the
eclipse is nearly central the whole moon will be immersed in the
shadow about an hour after she first strikes it. This is the time of
beginning of total eclipse. So long as only a moderate portion of
the moon's disk is in the shadow, that portion will be entirely
invisible, but if the eclipse becomes total the whole disk of the moon
will nearly always be plainly visible, shining with a red coppery
light. This is owing to the refraction of the sun's rays by the lower
strata of the earth's atmosphere. We shall see hereafter that if a ray
of light D B passes from the sun to the earth, so as just to graze the
latter, it is bent by refraction more than a degree out of its course,
so that at the distance of the moon the whole shadow of the earth
is filled with this refracted light. An observer on the moon would,
during a total eclipse of the latter, see the earth surrounded by u
ring of light, anil this ring would appear red, owing to the absorp-
tion of the blue and green rays by the earth's atmosphere, just as the
sun seems red when setting.
The moon may remain enveloped in the shadow of the earth
during a period ranging from a few minutes to nearly two hours,
according to the distance at \\hicli she passes from the axis of the
shadow and the velocity of her angular motion. When she leaves
the shadow, the phases which we have described occur in reverse
order.
It very often happens that the moon passes through the penumbra
of the earth without touching the shadow at all. The diminution of
light in such cases is scarcely perceptible unless the moon at least
grazes the edge of the shadow.
ECLIPSES OF THE Sire.
In Fig. 40 we may suppose B E B' to represent the
moon. The geometrical theory of the shadow will remain
the same, though the actual length of the shadow in
miles will be much less. The mean length of the moon's
shadow cast by the sun is 377,000 kilometres. This is
nearly equal to the distance of the moon from the earth
when she is in conjunction with the sun. We therefore
ECLIPSES OF THE SUN AN.
conclude that when the moon passes between the earth
and the sun, the former will be very near the vertex F of
the shadow. As a matter of fact, an observer on the
earth's surface will sometimes pass through the region
C V C f , and sometimes on the other side of F.
Now, in Fig. 40, still supposing BEB' to be the moon, and
8 DD' to be the sun, let us draw the lines DB'P and D'BP tan-
gent to both moon and sun, but crossing each other between these
bodies at b. It is evident that an observer outside the space
PBB'P will see the whole sun, no part of the moon being project-
ed upon it; while within this space the sun will be more or less
obscured. The whole obscured space may be divided into three
regions, in each of which the character of the phenomenon is dif-
ferent.
First, we have the region BVB' forming the shadow-cone proper.
Here the sunlight is entirely cut off by the moon, and darkness is
therefore complete, except so far as light may enter by refraction
or reflection. To an observer at V the moon would exactly cover
the sun, the two bodies being apparently tangent to each other all
around.
Secondly, we have the conical region to the right of V between
the lines B V and B' F continued. In this region the moon is seen
wholly projected upon the sun, the visible portion of the latter
presenting the form of a ring of light around the moon. This ring
of light will be wider in proportion to the apparent diameter of the
sun, the farther out we go, because the moon will appear smaller
than the sun, and its angular diameter will diminish in a more rapid
ratio than that of the sun. This region is that of annular eclipse,
because the sun will present the appearance of an annulus or ring of
light around the moon.
Thirdly, we have the region PBV and P'B' V, which we notice
is continuous, extending around the interior cone. An observer
here would see the moon partly projected upon the sun, and there-
fore a certain part of the sun's light would be cut off. Along the
inner boundary B V and B V the obscuration of the sun will be
complete, but the amount of sunlight will gradually increase out to
the outer boundary B P B P , where the whole sun is visible. This
region of partial obscuration is called the penumbra.
To show more clearly the phenomena of solar eclipses, we present
another figure representing the penumbra of the moon thrown upon
134
ASTRONOMY.
the earth.* The outer of the two circles S represents the limb of the
sun. The exterior tangents which mark the boundary of the shadow
cross each other at V before reaching the earth. The earth (K) being
a little beyond the vertex of the shadow, there can be no total eclipse.
In this case an observer in the penumbral region, CO or DO, will
see the moon partly projected on the sun, while if he chance to be
situated at he will see an annular eclipse. To show how this
is, we draw dotted lines fiom tangent to the moon. The angle
between these lines represents the apparent diameter of the moon as
seen from the earth. Continuing them to the sun, they show the
apparent diameter of the moon as projected upon the sun. It will
be seen that, in the case supposed, when the vertex of the shadow
is between the earth and moon the latter will necessarily appear
Fio. 41. FIGURE OF SHADOW FOR ANNULAR ECLIPSE.
smaller than the sun, and the observer will see a portion of the solar
disk on all sides of the moon, as shown in Fig. 42.
If the moon were a little nearer the earth than it is represented
in Fig. 41, its shadow would reach the earth in the neighborhood
of 0. We should then have a total eclipse at each point of the earth
on which it fell. It will be seen, however, that a total or annular
eclipse of the sun is visible only on a very small portion of the earth's
surface, because the distance of the moon changes so little that the
earth can never be far from the vertex V of the shadow. As the
* It will be noted that all the figures of eclipses are necessarily drawn very
much out of proportion. Really the sun is 400 times the distance of the moon,
which again is 60 times the radius of the earth. But it would be entirely im-
possible to draw a figure of this proportion; we are therefore obliged to
represent the earth in Fig. 41 as larger than the sun, and the moon as nearly
half way between the earth and sun.
ECLIPSES OF THE SUN AND MOON.
135
moon moves around the earth from west to east, its shadow, whether
the eclipse be total or annular, moves in the same direction. The
diameter of the shadow at the _
surface of the earth ranges from
zero to 150 miles. It therefore
sweeps along a belt of the
earth's surface of that breadth,
in the same direction in which
the earth is rotating. The
velocity of the moon relative to
the earth being 3400 kilometres
per hour, the shadow would
pass along with this velocity if
the earth did not rotate, but
owing to the earth's rotation
the velocity relative to points
on its surface may range from
Fia. 42. DARK BODY OF MOON PROJECTED
ON SUN DURING AN ANNULAR ECLIPSE.
2000 to 3400 kilometres (1200
to 2100 miles).
The reader will readily understand that in order to see a total
eclipse an observer must station himself beforehand at some point of
the earth's surface over which the shadow is to pass. These points
are generally calculated some years in advance, in the astronomical
ephemerides.
It will be seen that a partial eclipse of the sun may be
visible from a much larger portion of the earth's surface
than a total or annular one. The space CD (Fig. 41) over
which the penumbra extends is generally of about one half
the diameter of the earth. Roughly speaking, a partial
eclipse of the sun may sweep over a portion of the earth's
surface ranging from zero to perhaps one fifth or one sixth
of the whole.
There are really more eclipses of the sun than of the
moon. A year never passes without at least two of the
former, and sometimes five or six, while there are rarely
more than two eclipses of the moon, and in many years
none at all. But at any one place more eclipses of the
136 ASTRONOMT.
moon will be seen than of the sun. The reason of this is
that an eclipse of the moon is visible over the entire hemi-
sphere of the earth on which the moon is shining, and as
it lasts several hours, observers who are not in this hemi-
sphere at the beginning of the eclipse may, by the earth's
rotation, be brought into it before it ends. Thus the
eclipse will be seen over more than half the earth's surface.
But, as we have just seen, each eclipse of the sun can be
seen over only so small a fraction of the earth's surface as
to more than compensate for the greater absolute fre-
quency of solar eclipses.
Fio. 43. COMPARISON OF SHADOW AND PENUMBRA OF EARTH AND MOON. A is
THE POSITION OF THK MOON DURING A SOLAR, B DURING A LUNAR, ECLIPSE.
It will be seen that, in order to have either a total or
annular eclipse visible upon the earth, the line joining
the centres of the sun and moon, being continued, must
strike the earth. To an observer on this line the centres
of the two bodies will seem to coincide. An eclipse in
which this occurs is called a central one, whether it be
total or annular. Fig. 43 will perhaps aid in giving a
clear idea of the phenomena of eclipses of both sun and
moon.
THE RECURRENCE OF ECLIPSES.
If the orbit of the moon around the earth were in or near the
plane of the ecliptic there would be an eclipse of the sun at every
new moon, and an eclipse of the moon at every full moon. But,
ECLIPSES OF THE SUN AND MOON. 137
owing to the inclination of the moon's orbit (five degrees to the
ecliptic), the shadow and penumbra of the moon commonly pass above
or below the earth at the time of new moon, while the moon, at her
full, commonly passes above or below the shadow of the earth. It
is only when the moon is near its node at the moment of new or full
moon that an eclipse can occur.
The question now arises, how near must the moon be to its node
in order that an eclipse may occur ? It is found that if, at the
moment of new moon, the moon is more than 18 -6 from its node
no eclipse of the sun is possible, while if it is less than 13. 7 an
eclipse is certain. Between these limits an eclipse may occur or fail
according to the respective distances of the sun and moon from the
earth. Half way between these limits, or say 16 from the node, it
FIG. 44. Illustrating lunar eclipse at different distances from the node. The
dark circles are the earth's shadow, the centre of which is always in the ecliptic
A B. The moon's orbit is represented by CD. At G the eclipse is central and
total, at F it is partial, and at E there is barely an eclipse.
is an even chance that an eclipse will occur; toward the lower limit
(137)the chances increase to certainty; toward the upper one
(18 -6) they diminish to zero. The corresponding limits for an
eclipse of the moon are 9 and 12$ ; that is, if at the moment of full
moon the distance of the moon from her node is greater than 13^
no eclipse can occur, while if the distance is less than 9 an eclipse
is certain. We may put the mean limit at 11. Since, in the long-
run, new and full moon will occur equally at all distances from the
node, there will be, on the average, sixteen eclipses of the sun to
eleven of the moon, or nearly fifty per cent more.
If, at the moment of new moon, the distance of the moon from
the node is less than 10| there will be a central eclipse of the sun,
and if greater than this there will not be such an eclipse. The
138 ASTRO NOMT.
eclipse limit may range half a degree or more on each side of this
mean value, owing to the varying distance of the moon from the
earth. Inside of 10 a central eclipse may be regarded as certain,
and outside of 11 as impossible.
If the direction of the moon's nodes from the centre of the earth
were invariable, eclipses could occur only at the two opposite mouths
of the year when the sun had nearly the same longitude as one node.
For instance, if the longitudes of the two opposite nodes were re-
spectively 54 and 234, then, since the sun must be within 12 of
the node to allow of an eclipse of the moon, its longitude would have
to be either between 42 and 66, or between 222" and 246. But
the sun is within the first of these regions only in the month of May,
and within the second only during the month of November. Hence
lunar eclipses could then occur only during the months of May and
November, and the same would hold true of central eclipses of the
sun. Small partial eclipses of the latter might be seen occasionally
a day or two from the beginnings or ends of the above months, but
they would be very small and quite rare. Now, the nodes of the
moon's orbit were actually in the above directions in the year 1873.
Hence during that .year eclipses occurred only in May and No-
vember. We may caJl these months the seasons of eclipses for
1873.
There is a retrograde motion of the moon's nodes amounting to
19^ in a year. The nodes thus move back to meet the sun in its
annual revolution, and this meeting occurs about 20 days earlier
every year than it did the year before. The result is that the season
of eclipses is constantly shifting, so that each season ranges through-
out the whole year in 18-6 years. For instance, the season corre-
sponding to that of November, 1873, had moved back to July and
August in 1878, and will occur in May, 1882, while that of May,
1873, will be shifting back to November in 1882.
It may be interesting to illustrate this by giving the days in which
the sun is in conjunction with the nodes of the moon's orbit during
several years.
Ascending Node. Descending Node.
1879. January 24. 1879. July 17.
1880. January 6. 1880. June 27.
1880. December 18. 1881. June 8.
1881. November 30. 1882. May 20.
1882. November 12. 1883. May 1.
1883. October 25. 1884. April 12.
1884. October 8. 1885. March 25.
ECLIPSES OF THE SUN AND MOON. 139
During these years, eclipses of the moon can occur only within 11
or 12 days of these dates, and eclipses of the sun only within 15 or
16 days.
In consequence of the motion of the moon's node, three varying
angles come into play in considering the occurrence of an eclipse:
the longitude of the node, that of the sun, and that of the moon.
One revolution of the moon relatively to the node is accomplished,
on the average, in 27-21222 days. If we calculate the time required
for the sun to return to the node, we shall find it to be 346-6201
days.
Now, let us suppose the sun and moon to start out together from
a node. At the end of 346-6201 days the sun, having apparently
performed nearly an entire revolution around the celestial sphere, will
again be at the same node, which has moved back to meet it. But the
moon will not be there. It will, during the interval, have passed
the node 12 times, and the 13th passage will not occur for a week.
The same thing will be true for 18 successive returns of the sun to
the node; we shall not find the moon there at the same time with
the sun; she will always have passed a little sooner or a little later.
But at the 19th return of the sun and the 242d of the moon, the two
bodies will be in conjunction within half a degree of the node. We
find from the preceding periods that
242 returns of the moon to the node require 6585.357 days.
19 " " sun " " " 6585.780 "
The two bodies will therefore pass the node within 10 hours of
each other. This conjunction of the sun and moon will be the 223d
new moon after that from which we started. Now, one lunation
(that is, the interval between two consecutive new moons) is, in the
mean, 29.530588 days; 223 lunations therefore require 6585.32 days.
The new moon, therefore, occurs a little before the bodies reach the
node, the distance from the latter being that over which the moon
moves in O d .036, or the sun in O d .459. This distance is 28' of arc,
somewhat less than the apparent semidiameter of either body. This
would be the smallest distance from either node at which any new
moon would occur during the whole period. The next nearest ap-
proaches would have occurred at the 35th and 47th lunations respec-
tively. The 35th new moon would have occurred about 6 before
the two bodies arrived at the node from which we started, and the
47th about 1| past the opposite node. No other new moon would
so near a node before the 223d one, which, as we have just
. would occur 28' west of the node. This period of 223 new
140 ASTRONOMY.
moons, or 18 years 11 days, was called the Saros by the ancient as-
tronomers, and by means of it they predicted eclipses.
The possibility of a total eclipse of the sun arises from the occa-
sional very slight excess of the apparent angular diameter of the
moon over that of the sun This excess is so slight that such an
eclipse can never last more than a few minutes. It may be of inter-
est to point out the circumstances which favor a long duration of
totality. These are :
(1) That the moon should be as near as possible to the earth, or,
technically speaking, in perigee, because its angular diameter as
seen from the earth will then be greatest.
(2) That the sun should be near its greatest distance from the
earth, or in apogee, because then its angular diameter will l>e the
least It is now in this position about the end of June; hence the
most favorable time for a total eclipse of very long duration is in the
summer months. Since the moon must be in perigee and also be-
tween the earth and sun, it follows that the longitude of the perigee
must if nearly that of the sun. The longitude of the sun at the
end of June being 100, this is the most favorable longitude of the
moon's perigee.
(3) The moon must be very near the node in order that the centre
of the shadow may fall near the equator. The reason of this condi-
tion is that the duration of a total eclipse may be considerably in-
creased by the rotation of the earth on its axis. We have seen that
the shadow sweeps over the earth from west toward east with a
velocity of about 3400 kilometres per hour. Since the earth rotates
in the same direction, the velocity relative to the observer on the
earth's surface will be diminished by a quantity depending on this
velocity of rotation, and therefore greater the greater the velocity.
The velocity of rotation is greatest at the earth's equator, where it
amounts to 1660 kilometres per hour, or nearly half the velocity of
the moon's shadow. Hence the duration of a total eclipse may, with-
in the tropics, be nearly doubled by the earth's rotation. When all
the favorable circumstances combine in the way we have just de-
scribed, the duration of a total eclipse within the tropics will be-
about seven minutes and a half. In our latitude the maximum du-
ration will be somewhat less, or not far from six minutes, but it is
only on very rare occasions, hardly once in many centuries, that all
these favorable conditions can be expected to concur.
Occultation of Stars by the Moon. A phenomenon which, geomet-
rically considered, is analogous to an eclipse of the sun is the occul-
tatlon of a star by the moon. Since all Hie bodies of the solar system
are nearer than the fixed stars, it is evident that they must from
ECLIPSES OF THE SUN AND MOON. 141
lime to time pass between us and the stars. The planets are, how-
ever, so small that such a passage is of very rare occurrence, and
when it does happen the star is generally so faint that it is rendered
invisible by the superior light of the planet before the latter touches
it. But the moon is so large and her angular motion so rapid that
she passes over some star visible to the naked eye every few days.
Such phenomena are termed occultations of stars by the moon. It
must not, however, be supposed that they can be observed by the
naked eye. In general, the moon is so bright that only stars of the
first magnitude can be seen in actual contact with her limb, and even
then the contact must be with the uuilluminated limb.
CHAPTER IX.
THE EARTH.
OUR object in the present chapter is to trace the effects
of terrestrial gravitation and to study the changes to which
it is subject in various places. Since every part of the
earth attracts every other part as well as every object upon
its surface, it follows that the earth and all the objects
that we consider terrestrial form a sort of system by them-
selves, the parts of which are firmly bound together by
their mutual attraction. This attraction is so strong that
it is found impossible to project any object from the sur-
face of the earth into the celestial spaces. Every particle
of matter now belonging to the earth must, so far as we
can see, remain upon it forever.
MASS AND DENSITY OF THE EARTH.
The mass of a body may be defined as the quantity of matter it con-
tains. It is measured by the product of its volume ( V) by its density
(Z>) . M = V . D. For another body M' = V. 1)', and for equal vol-
umes V = V and M : M' = D : D'. The density of pure water at
about 39 Fahr. is taken as the unit-density. The unit-volume may
be taken as a cubic foot. The unit-mass will then be that of a cubic
foot of pure water at 39 Fahr.
The weight of a body i the force with which it is attracted to the cen-
tre of the earth. A body of mass m is attracted by the earth's mass
M by t where r is the distance M m. (See page 120.) The weight
w of m is then 5. The weight w' of another body m' is w = r s
THE EARTH. 143
If the bodies are at the same place on the earth r = / and w : w' =
m : m', or the weights of bodies at the same place on the earth are
proportional to their masses. It is easy to measure the weights of
bodies by balancing them in scales against certain pieces of metal.
Hence by weighing two bodies of weights w and w' we can deter-
mine the ratio of their masses m and m'. If m is a cubic foot of
water, m' is the absolute mass of the other substance.
The weight w is not the same in all parts of the earth, nor at dif-
ferent heights above the earth's surface. It is therefore a variable
quantity, depending upon the position of the body, while the mass
of the body is something inherent in it, which remains constant
wherever the body may be taken, even if it is carried through the
celestial spaces, where its weight would be reduced to almost noth-
ing.
The unit of mass which we may adopt is arbitrary. Generally the
most convenient unit is the weight of a body at some fixed place on
the earth's surface the city of Washington, for example. Suppose
we take such a portion of the earth as will weigh one kilogramme in
Washington; we may then consider the mass of that particular lot of
earth or rock as the unit of mass, no matter to what part of the uni-
verse we take it. Suppose, also, that we could bring all the matter
composing the earth to the city of Washington, one unit of mass at
a time, for the purpose of weighing- it, returning each unit of mass to
its place in the earth immediately after weighing, so that there should
be no disturbance of the earth itself. The sum-total of the weights
thus found would be the mass of the earth, and would be a perfectly
definite quantity, admitting of being expressed in kilogrammes or
pounds. We can readily calculate the mass of a volume of water
equal to that of the earth because we know the magnitude of the
earth in litres, and the mass of one litre of water. Dividing this
into the mass of the earth, supposing ourselves able to determine
this mass, and we shall have the specific gravity, or what is more
properly called the density, of the earth : D M -*- M' .
What we have supposed for the earth we may imagine for any
heavenly body ; namely, that it is brought to the city of Washington
in small pieces, and there weighed one piece at a time. Thus the
total mass of the earth or any heavenly body is a perfectly defined
and determinate quantity.
It may be remarked in this connection that our units of weight, the
pound, the kilogramme, etc., are practically units of mass rather than
of weight. If we should weigh out a pound of tea in the latitude of
Washington, and then take it to the equator, it would really be less
heavy at the equator than in Washington; but if we take a pound
144 ASTRONOMY.
weight with us, that also would be lighter at the equator, so that the
two would still balance each other, and the tea would be still con-
sidered as weighing one pound. Since things are actually weighed
in this way by weights which weigh one unit at some definite place,
say Washington, and which are carried all over the world without
being changed, it follows that a body which has any given weight in
one place will, as measured in this way, have the same apparent
weight in any other place, although its real weight will vary. But
if a spring- balance or any other instrument for determining absolute
weights were adopted, then we should find that the weight of the
same body varied as we took it from one part of the earth to another.
Since, however, we do not use this sort of an instrument in weigh-
ing, but pieces of metal which arc carried about without change, it
follows that what we call units of weight are properly units of ma>s.
Density of the Earth. We see that all bodies around us tend to fall
toward the centre of the earth. According to the law of gravitation,
this tendency is not simply a single force directed toward ilic centre
of the earth, but is the resultant of an infinity of separate forces
arising from the attractions of all the separate parts which compose
the earth. The question may arise, how do we know that each
particle of the earth attracts a stone which falls, and that the whole
attraction does not reside in the centre ? The proofs of this are
numerous, and consist rather in the exactitude with which the
theory represents a great mass of disconnected phenomena than in
any one principle admitting of demonstration. Perhaps, however,
the most conclusive proof is found in the observed fact that masses
of matter at the surface of the earth do really attract each other as
required by the law of NEWTON. It is found, for example, that
isolated mountains attract a plumb-line in their neighborhood.
It is noteworthy that though astronomy affords us the
means of determining with great precision the relative
masses of the earth, the moon, and all the planets, it does
not enable us to determine the absolute mass of any hea-
venly body in units of the weights we use on the earth.
The sun has about 328,000 times the mass of the earth, and
the moon only -g^ of this mass, but to know the absolute
mass of either of them we must know how many kilo-
grammes of matter the earth contains. To determine this
we must know the mean density of the earth, and this is
THE EARTH. 145
something about which direct observation can give us no in-
formation, because we cannot penetrate more than an in-
significant distance into the earth's interior.
The only way to determine the density of the earth is to find how
much matter it must contain in order to attract bodies on its surface
with a force equal to their observed weight; that is, with such intensity
that at the equator a body shall fall nearly five metres in a second. To
find this we must know the relation between the mass of a body and
its attractive force. This relation can only be found by measuring
the attraction of a body of known mass.
We may measure the attraction of a body of known mass in the
following ingenious way. In Fig. 44 a let 11 1KL be a cube of lead
1 metre on each edge. Two holes are bored through the cube at D F
and E G. A pair of scales A B G
has its scale -pans D E connected
by fine wires to other scale-pans,
F G, below the block. Suppose
the pans empty and everything at
rest.
I. Put a weight W in D, and
balance the scales by weights in G.
At D the total attraction is the
attraction of the earth plus the
attraction of the block, while at ~ FIG.
G we have the attraction of the
earth (downwards) minus the attraction of the block (upwards); hence
(1) Weights in G = weight in D -f- 2 attraction of block.
II. Put the weight Win F, and balance the scales by weights in E.
At F the total attraction is earth minus block, and at EH is earth
plus block ; hence
(2) Weights in E weight in F 2 attraction of block.
Combining these equations (1) and (2), we have
Weights in G weights in E = 4 attraction of block,
after small corrections have been applied for the difference of height
of D, E, F, G, etc.
The attraction of this block, which has a known mass in kilo-
grammes, is thus known, and hence the general relation between mass
in kilogrammes and attractions. The attraction of the earth is known,
since it is such as to attract bodies with forces equal to their observed
weights. Therefore the mass of the earth expressed in kilogrammes
is known. The volume, V, of the earth is known from surveys; its
146 ABTBOffOMT.
mass, M, is now known, and hence its density, D. The relative masses
of the sun and earth (and other planets) are known, and hence their
absolute masses in kilogrammes become known as soon as we have
the earth's absolute mass in kilogrammes, determined as above.
The results of experiment show the earth to be about 5 times as
dense as water. The sun is only \ as dense as the eurih. Other re-
searches give about 5-6 for the density of the eailh; this is more
than double the average specific gravity of the rocks which compose
the surface of the globe: whence it follows that the inner portions of
the earth are much more dense than the outer parts.
LAWS OF TERRESTRIAL GRAVITATION.
The earth being very nearly spherical, certain theorems respecting
the attraction of spheres may be applied to it. The demonstration
of these theorems requires the use of the Integral Calculus, and will
be omitted here, only the conditions and the results being stated.
Let us imagine a hollow shell of matter, of which the internal ami
external surfaces are both spheres, attracting any other mass of
matter, a small particle we may suppose. This particle will be
attracted by every particle cf the shell with a force inversely as the
square of its distance from it. The total attraction of the shell will
In- i he resultant of this infinity of separate attractive forces.
TIU<>I;I M I. If tl' )nirftcle be outxide the shell, it will be attracted
as iftlie whole inasnoftJie thell were concentrated in its centre,
Tm.ouKM II. If the particle he iiixitle. the shell, the opposite attrar-
tt'onx in every dirertimt irffl neutralize -h other, no matter whereabout*
in tJie interior the particle may be, and the resultant attraction of the
shell will therefore be zero.
To apply this to the attraction of a solid sphere, let us first sup-
pose a body either outside the sphere or on its surface. If we con-
ceive the sphere as made up of a great number of spherical shells, the
attracted point will be external to all of
them. Since each shell attracts as if
its whole mass were in the centre, it
follows that the whole sphere attracts
a body upon the outside of its surface
as if its entire mass were concentrated
at its centre.
Let us now suppose the attracted
particle inside the sphere, as at P, Fig.
4o, and imagine a spherical surface
PQ concentric with the sphere and
passing through the attracted particle.
45. All that portion of the sphere lying
THE EARTH. 147
outside this spherical surface will be a spherical shell having the
particle inside of it, and will therefore exert no attraction whatever
on the particle. That portion inside the surface will constitute a
sphere with the particle on its surface, and will therefore attract as
if all this portion were concentrated in the centre. To find what
this attraction will be, let us first suppose the whole sphefe of equal
density. Let us put
a, the radius of the entire sphere.
r, the distance PC of the particle from the centre.
The total volume of matter inside the sphere P Q will then be, by
4
geometry, xr 3 . Dividing by the square of the distance r, we see
o
that the attraction will be represented by
4
that is, inside the sphere the attraction will be directly as the dis-
tance of the particle from the centre. If the particle is at the sur-
4
face we have r = a, and the attraction is it a. Outside the sur-
o
4
face the whole volume of the sphere it a 3 will attract the particle,
4 a z
and the attraction will be it 5 . If we put r = a in this formula,
we shall have the same result as before for the surface attraction.
Let us next suppose that the density of the sphere varies from its
centre to its surface, so as to be equal at equal distances from the
centre. We may then conceive of it as formed of an infinity of con-
centric spherical shells, each homogeneous in density, but not of the
same density as the others. Theorems I. and II. will then still
apply, but their result will not be the same as in the case of a homo-
geneous sphere for a particle inside the sphere. Referring to Fig.
45, let us put
D, the mean density of the shell outside the particle P.
D', the mean density of the portion P Q inside of P.
We shall then have :
4
Volume of the shell, it (a? r 3 ). Volume of the inner sphere,
o
4 it r\ Mass of the shell = vol. X D = -^ it D (a 3 r 3 ). Mass of the
O w
148 ASTRONOMY.
inner sphere = vol. X D 1 = 3-* -ZXr 1 . Mass of the whole sphere =
o
sum of masses of shell and inner sphere = g- TT I D a 3 -{- (2)' D) ? >3 i.
Attraction of the whole sphere upon a point at its surface =
Attraction of the inner sphere (the same as that of the whole shell)
upon a point at P = ^ = -n D'r.
If, as in the case of the earth, the density continually increases to-
ward the centre, the value of D' will increase also, as r diminishes, so
that gravity will diminish less rapidly than in the case of a homo-
geneous sphere, and may, in fact, actually increase as we descend.
To show this, let us subtract the attraction at P from that at the sur-
face. The difference will give :
Diminution at P = t n (j)a -f (D' - D) ^ - D'r)
Now let us suppose r a very little less than a, and put r = a d ;
d will then be the depth of the particle below the surface.
Cubing this value of r, neglecting the higher powers of d, and
ft
dividing by a*, we find 9 = a3d. Substituting in the above
equation, the diminution of gravity at P becomes -$ n (3D 2'D)d.
We see that if 3 D < 2 D' that is, if the density at the surface is
less than $ of the mean density of the whole inner mass this quan-
tity will beeomc negative, showing that the force of gravity will be
less at the surface than at a small depth in the interior. But it must
ultimately diminish, because it is necessarily zero at the centre. It
was on this principle that Professor AIRY determined the density of
the earth by comparing the vibrations of a pendulum at the bottom
of the Harton Colliery, and at the surface of the earth in the neigh-
borhood. At the bottom of the mine the pendulum gained about
2 -5 per day, showing the force of gravity to be greater there than at
the surface.
FIGURE AND MAGNITUDE OF THE EARTH.
If the earth were fluid and did not rotate on its axis, it
would assume the form of a perfect sphere. The opinion
TEE EARTH. 140
is entertained that the earth was once in a molten state,
and that this is the origin of its present nearly spherical
form. If we give such a sphere a rotation upon its axis,
the centrifugal force at the equator acts in a direction op-
posed to gravity, and thus tends to enlarge the circle of
the equator. It is found by mathematical analysis that the
form of such a revolving fluid sphere, supposing it to be
perfectly homogeneous, will be an oblate ellipsoid ; that is,
all the meridians will be equal and similar ellipses, having
their major axes in the equator of the sphere and their
minor axes coincident with the axis of rotation. Our earth,
however, is not wholly fluid, and the solidity of its conti-
nents prevents its assuming the form it would take if the
ocean covered its entire surface. By the figure of the
earth we mean, hereafter, not the outline of the solid and
liquid portions respectively, but the figure which it would
assume if its entire surface were an ocean. Let us
imagine canals dug down to the ocean level in every direc-
tion through the continents, and the water of the ocean to
be admitted into them. Then the curved surface touching
the water in all these canals, and coincident with the sur-
face of the ocean, is that of the ideal earth considered by
astronomers. By the figure of the earth is meant the figure
of this liquid surface, without reference to the inequalities
of the solid surface.
We cannot say that this ideal earth is a perfect ellipsoid,
because we know that the interior is not homogeneous, but
all the geodetic measures heretofore made are so nearly
represented by the hypothesis of an ellipsoid that the lat-
ter is a very close approximation to the true figure. The
deviations hitherto noticed are of so irregular a character
that they have not yet been reduced to any certain law.
150 ASTRONOMY.
The largest which have been observed seem to be due to
the attraction of mountains, or to inequalities in the den-
sity of the rocks beneath the surface.
Method of Triangulation. Since it is practically impossi-
ble to measure around or through the earth, the magnitude
as well as the form of our planet has to be found by com-
bining measurements on its surface with astronomical ob-
servations. Even a measurement on the earth's surface
made in the usual way of surveyors would be impracticable,
owing to the intervention of mountains, rivers, forests, and
other natural obstacles. The method of triangulution is
therefore universally adopted for measurements extending
over large areas.
FIG. 46. A PART OF THE FRKNCH TRIANOULATION NEAR PARIS.
Triangulation is executed in the following way : Two points, a
and b, a few miles apart, are selected as the; extremities of a base-
line. They must he so chosen that their di tunee apart can be accu-
rately measured by rods ; the intervening ground should therefore
be as level and free from obstruction as possible. One or more ele-
vated points, E F, etc., must be visible from one or both ends of the
base-line. By means of a theodolite and by observation of the pole-
star, the directions of these points relative to the meridian are accu-
rately observed from each end of the base, as is also the direction a b
of the base-line itself. Suppose F to be a point visible from each
end of the base, then in the triangle a b F we have the length a b de-
THE EARTH. 151
termined by actual measurement, and the angles at a and b deter-
mined by observations. With these data the lengths of the sides
a F and b Fare determined by a simple computation.
The observer then transports his instruments to F, and determines
in succession the direction of the elevated points or hills D E O HJ,
etc. He next goes in succession to each of these hills, and determines
the direction of all the others which are visible from it. Thus a net-
work of triangles is formed, of which all the angles are observed
with the theodolite, while the sides are successively calculated from
the first base. For instance, we have just shown how the side aFis
calculated; this forms a base for the triangle E Fa, the two remain-
ing sides of which are computed. The side E F forms the base of
the triangle Gr EF, the sides of which are calculated, etc. In this
operation more angles are observed than are theoretically necessary
to calculate the triangles. This surplus of data serves to insure the
detection of any errors in the measures, and to test their accuracy by
the agreement of their results. Accumulating errors are further
guarded against by measuring additional sides from time to time as
opportunity offers.
Chains of triangles have thus been measured in Russia and Sweden
from the Danube to the Arctic Ocean, in England and France from
the Hebrides to Algiers, in this country down nearly our entire At-
lantic coast and along the great lakes, and through shorter distances
in many other countries. An east and west line is now being run
by the Coast Survey from the Atlantic to the Pacific Ocean. Indeed
it may be expected that a network of triangles will be gradually ex-
tended over the surface of every civilized country, in order to con-
struct perfect maps of it.
Suppose that we take two stations, a and.;, Fig. 46, situated north
and south of each other, determine the latitude of each, and calculate
the distance between them by means of triangles, as in the figure.
It is evident that by dividing the distance in kilometres by the dif-
ference of latitude in degrees we shall have the length of one degree
of latitude. Then if the earth were a sphere, we should at once have
its circumference by multiplying the length of one degree by 360.
It is thus found that the length of i degree is a little more than 111
kilometres, or between 69 and 70 English statute miles. Its circum-
ference is therefore about 40,000 kilometres, and its diameter between
12,000 and 13,000.* (25,000 and 8000 miles.)
* When the metric system was originally designed by the French, it was in-
tended that the kilometre should be &,, of the distance from the pole of the
earth to the equator. This would make a degree of the meridian equal, on the
averare, to 111 kilometres. But the me:-- rctually adopted is nearly T fo of
an inch too short.
152 ASTRONOMY.
Owing to the ellipticity of the earth, the length of one degree
varies with the latitude and the direction in which it is im-asim <!.
The next step in the order of accuracy is to find the magnitude and
the form of the earth from measures of long arcs of latitude (and
sometimes of longitude) made in different regions, especially near
the equator and in high latitudes. But we shall still find that dif-
ferent combinations of measures give slightly different results, both
for the magnitude and the ellipticity, owing to the irregularities in
the direction of attraction which we have already described. The
problem is therefore to find what ellipsoid will satisfy the measures
with the least sum-total of error. New and more accurate solutions
will be reached from time to time as geodetic measures are extended
over a wider area. The following are among the most recent results:
Fio. 47.
the earth's polar semidiameter, 6355-270 kilometres; earth's equatorial
semidiameter, 6377 -377 kilometres ; earth's compression, ffa.-g of the
equatorial diameter ; earth's eccentricity of meridian, 0-08319. An-
other result is that of Captain CLARKE of England, who found:
polar semidiameter, 6356-456* kilometres; equatorial semidiameter,
6378-191 kilometres.
Geographic and Geocentric Latitudes. An obvious result of the
ellipticity of the earth is that the plumb-line does not point toward
the earth's centre. Let Fig. 47 represent a meridional section of the
earth, NS being the axis of rotation, E Q the plane of the equator,
and the position of the observer. The line HE, tangent to the
* Captain CLARKE'S results are given in feet, the polar radius being 20,854,895
feet, the equatorial 20,926,202. These numbers are in the proportion 292 : 293.
THE EARTH.
earth at 0, will then represent the horizon of the observer, while the
line ZN' t perpendicular to HE, and therefore normal to the earth
at 0, will be the vertical as determined by the plumb-line. The angle
N'Q, or Z Q', which the observer's zenith makes with the equa-
tor will then be his astronomical or geographical latitude. This is
the latitude which in practice we always have to use, because we
are obliged to determine latitude by astronomical observation, and
not by measurement from the equator. We cannot determine the
direction of the true centre G of the earth by direct observation of
any kind, but only the direction of the plumb-line, or of the perpen-
dicular to a fluid surface. Z Q' is the astronomical latitude. If,
however, we conceive the line CO z drawn from the centre of the
earth through 0, z will be the observer's geocentric zenith, while the
angle C Q will be his geocentric latitude. It will be observed that it
is the geocentric and not the geographic latitude which gives the true
position of the observer relative to the earth's centre. The difference
between the two latitudes is the angle N' or Z Oz ; this is called
the angle of 1he vertical. It is zero at the poles and at the equator, be-
cause here the normals pass through the centre of the ellipse, and it
attains its maximum of 11' 30" at latitude 45. It will be seen that the
geocentric latitude is always less than the geographic. In north
latitudes the geocentric zenith is south of the apparent zenith, and in
southern latitudes north of it; being nearer the equator in each case.
MOTION OF THE EARTH'S Axis, OR PRECESSION OF THE
EQUINOXES.
Sidereal and Equinoctial Year. In describing the appar-
ent motion of the sun, two ways of finding the time of its
apparent revolution around the sphere were described ; in
other words, of fixing the length of a year. One of these
methods consists in finding the interval between successive
passages of the sun through the equinoxes, or, which is the
same thing, across the plane of the equator, and the other
by finding when it returns to the same position among the
stars. Two thousand years ago HIPPARCHUS found, by
comparing his own observations with those made two cen-
turies before by TIMOCHARIS, that these two methods of
154 ASTRONOMY.
fixing the length of the year did not give the same result.
It had previously been considered that the length of a year
was about 365 J days, and in attempting to correct this
period by comparing his observed times of the sun's pass-
ing the equinox with those of TIMOCHARIS, HIPPARCHUS
found that the length required a diminution of seven or
eight minutes. He therefore concluded that the true length
of the equinoctial year was 365 days 5 hours and about 53
minutes. When, however, he considered the return of the
sun not to the equinox, but to the same position relative
to the bright star Spica Vinjinix, he found that it took
some minutes more than 365J days to complete the revolu-
tion. Thus there are two years to be distinguished, the
tropical or equinoctial year and the sidereal year. The
first is measured by the time of the sun's return to the
equinox ; the second by its return to the same position
relative to the stars. Although the sidereal year is the
correct astronomical period of one revolution of the earth
around the sun, yet the equinoctial year is the one to be
used in civil life, because the change of seasons depends
upon that year. Modern determinations show the respec-
tive lengths of the two years to be, in mean solar days:
Sidereal year, 365 d 6 h 9 ra 9 8 = 365 d . 25636.
Equinoctial year, 365 d 5 h 48 m 46 s = 365 d .24220.
It is evident from this difference between the two years
that the position of the equinox among the stars must be
changing, and that it must move toward the west, because
the equinoctial year is the shorter. This motion is called
the precession of the equinoxes, and amounts to about 50"
per year. The equinox being simply the point in which
the equator and the ecliptic intersect, it is evident that it
THE EARTH. 155
can change only through a change in one or both of these
circles. HIPPARCHUS found that the change was in the
equator and not in the ecliptic, because the declinations
of the stars changed, while their latitudes did not. Since
the equator is defined as a circle everywhere 90 distant
from the pole, and since it is moving among the stars, it
follows that the pole must also be moving among the stars.
But the pole is nothing more than the point in which the
earth's axis of rotation intersects the celestial sphere: the
position of this pole in the celestial sphere depends solely
upon the direction of the earth's axis, and is not changed by
the motion of the earth around the sun. Hence precession
shows that the direction of the earth's axis is continually
changing. Careful observations from the time of HIPPAR-
CHUS until now show that the change in question consists
in a slow revolution of the pole of the earth around the pole
of the ecliptic as projected on the celestial sphere. The
rate of motion is such that the revolution will be completed
in between 25,000 and 26,000 years. At the end of this
period the equinox and solstices will have made a complete
revolution in the heavens.
The nature of this motion will be seen more clearly by referring to
Fig. 32, p. 93. We have there represented the earth in four posi-
tions during its annual revolution. We have represented the axis as
inclining to the right in each of these positions, and have described
it as remaining parallel to itself during an entire revolution. The
phenomena of precession show that this is not absolutely true, but
that, in reality, the direction of the axis is slowly changing. This
change is such that, after the lapse of some 6400 years, the north
pole of the earth, as represented in the figure, will not incline to the
right, but^ toward the observer, the amount of the inclination remain-
ing nearly the same. The result will evidently be a shifting of the
seasons. At D we shall have the winter solstice, because the north
pole will be inclined toward the observer and therefore from the sun,
1/56 ASTRONOMY.
while at A we shall have the vernal equinox instead of the winter
solstice, and so on.
In 6400 years more the north pole will be inclined toward the left,
and the seasons will be reversed. Another interval of the same
length, and the north pole will be inclined from the observer, the
seasons being shifted through another quadrant. Finally, at the
end of about 25,8uO years, the axis will have resumed its original
direction.
Precession thus arises from a motion of the earth alone and not of
the heavenly bodies. Although the direction of the earth's axis
changes, yet tlie position of tfiis axis rehitive to flu crust of (he earth
remains invariable. Some have supposed that precession would
result in a change in the position of the north pole on the surface of
Fio
the earth, so that the northern regions would be covered by the
ocean as a result of the different direction in which the ocean would
be carried by the centrifugal force of the earth's rotation. This, how-
ever, is a mistake. It has been shown that the position of the poles,
and therefore of the equator, on the surface of the earth, cannot
change except from some variation in the arrangement of the earth's
interior. Scientific investigation has yet shown nothing to indicate
any probability of such a change.
The motion of precession is not uniform, but is subject to several
small inequalities which are called nutation.
THE CAUSE OF PRECESSION.
The cause of precession, etc., is illustrated in the figure, which
shows a spherical earth surrounded by a ring of matter at the equa-
tor. If the earth were really spherical there would be no precessioa
It is, however, ellipsoidal \vith. a protuberance at the equator. The
THE EAUTH. 157
effect of this protuberance is to be examined. Consider the action
between the sun and earth alone. If the ring of matter were absent,
the earth would revolve about the sun as is shown in Fig. 32, p. 93
(Seasons). \4
We remember that the sun's N. P. D. if 90 at the equinoxes, and
66i and 113 at the solstices. At the equinoxes the sun is in the
direction Cm; that is, NCm is 90. At the winter solstice the sun is
in the direction Cc ; NCc = 113i. It is clear that in the latter case
the effect of the sun on the ring of matter will be to pull it down
from the direction Cm towards the direction Cc. An opposite effect
will be produced by the sun when its polar distance is 66^.
The moon also revolves round the earth in an orbit inclined to the
equator, and in every position of the moon it has a different action
on the ring of matter. The earth is all the time rotating on its axis,
and these varying attractions of sun and moon are equalized and
distributed since different parts of the earth are successively presented
to the attracting body. The result of all the complex motions we
have described is a conical motion of the earth's axis N C about the
line CE.
The earth's shape is not that given in the figure, but it is an ellip-
soid of revolution. The ring of matter is not cou'fined to the equator/
but extends away from it in both directions. The effects of the
forces acting on the earth as it is are however, similar to the effects
we have described.
CHAPTER X.
CELESTIAL MEASUREMENTS OF MASS AND DISTANCE.
THE CELESTIAL SCALE OF MEASUREMENT.
THE units of length and mass employed by astronomers
are necessarily different from those used in daily life. The
distances and magnitudes of the heavenly bodies are never
reckoned in miles or other terrestrial measures for astro-
nomical purposes; when so expressed it is only for the pur-
pose of making the subject clearer to the general reader.
The units of weight or mass are also, of necessity, astro-
nomical and not terrestrial. The mass of a body may be
expressed in terms of that of the sun or of the earth, but
never in kilogrammes or tons, unless in popular language.
There are two reasons for this course. One is that in most
cases celestial distances have first to be determined in
terms of some celestial unit the earth's distance from the
sun, for instance and it is more convenient to retain this
unit than to adopt a new one. The other is that the
values of celestial distances in terms of ordinary terrestrial
units are for the most part uncertain, while the corre-
sponding values in astronomical units are known with
great accuracy.
An extreme instance of this is afforded by the dimensions
of the solar system. By a series of astronomical observa-
tions, investigated by means of KEPLER'S laws and the
theory of gravitation, it is possible to determine the forms
MEASUREMENTS OF MASS AND DISTANCE. 159
of the planetary orbits, their positions, and their dimen-
sions in terms of the earth's mean distance from the sun
as the unit of measure, with great precision. KEPLER'S
third law enables us to determine the mean distance of a
planet from the sun when we know its period of revolu-
tion. All the major planets, as far out as Saturn, have been
observed through so many revolutions that their periodic
times can be determined with great exactness in fact
within a fraction of a millionth part of their whole amount.
The more recently discovered planets, Uranus and Nep-
tune, will, in the course of time, have their periods deter-
mined with equal precision. Then, if we square the peri-
ods expressed in years and decimals of a year, and extract
the cube root of this square, we have the mean distance
of the planet with the same order of precision. This
distance is to be corrected slightly in consequence of the
attractions of the planets on each other, but these correc-
tions also are known with great exactness. Again, the
eccentricities of ihe orbits are exactly determined by care-
ful observations of the positions of the planets during suc-
cessive revolutions. Thus we could make a map of the
planetary orbits so exact that the error would entirely
elude the most careful scrutiny, though the map itself
might be many yards in extent.
On the scale of this same map we could lay down the
magnitudes of the planets with as much precision as our
instruments can measure their angular semidiameters.
Thus we know that the mean diameter of the sun, as seen
from the earth, is 32'-, hence we deduce from formulae
already given on pages 5 and 57 that the diameter of the
sun is .0093083 of the distance of the sun from the earth.
We can. therefore, on our supposed map of the solar system,
160 ASTRONOMY.
lay down the sun in its true size, according to the scale of
the map, from data given directly by observation. In the
same way we can do this for each of the planets, the earth
and moon excepted. There is no immediate and direct
way of finding how large the earth or moon would look
from a planet; whence the exception.
But without further special research into this subject,
we shall know nothing about the scale of our map. That
is, we have no means of knowing how many miles or kilo-
metres correspond in space to an inch or a foot on the map.
It is clear that in order to fix the distances or the magni-
tudes of the planets according to any terrestrial standard,
we must know this scale. Of course if we can learn either
the distance or magnitude of any one of the planets laid
down on the map, in miles or in semidiameters of the
earth, we shall be able at once to find the scale. But this
process is so difficult that the general custom of astrono-
mers is not to attempt to use a scale of miles, but to employ
the mean distance of the sun from the earth as the unit in
celestial measurements. Thus, in astronomical language,
we say that the distance of Mercury from the sun is 0.387,
that of Venus 0.7^3, that of Mars 1.523, that of Saturn
9.539, and so on. But this gives us no information respect-
ing the distances and magnitudes in terms of terrestrial
measures. The unknown quantities of our map are the
magnitude of the earth and its distance from the sun in
terrestrial units of length. Could we only take up a point
of observation on the sun or a planet, and determine ex-
actly the angular magnitude of the earth as seen from that
point, we should be able to lay down the earth of our map
in its correct size. Then, since we already know the size
of the earth in terrestrial units from geodetic surveys we,
MEASUREMENTS OF MASS AND DISTANCE. 161
should be able to find the scale of our map, and thence
the dimensions of the whole system in terms of those
units.
It will be seen that what the astronomer really wants is
not so much the dimensions of the solar system in miles as
to express the size of the earth in celestial measures.
This, however, amounts to the same tiling, because having
one, the other can be readily deduced from the known
magnitude of the earth in terrestrial measures.
The magnitude of the earth is not Ihc only unknown
quantity on our map. From KEPLER'S laws we can deter-
mine nothing respecting the distance of the moon from the
earth, because unless a change is made in the units of time
and space, they apply only to bodies moving around the
sun. We must therefore determine the distance of the
moon as well as that of the sun to be able to complete our
map on a known scale of measurement.
MEASURES OF THE SOLAR AND LUNAR PARALLAX.
The problem of distances in the solar system is reduced
by the preceding considerations to measuring the distances
of the sun and moon in terms of the earth's radius. The
most direct method of doing this is by determining their
respective parallaxes, which we have shown to be the same
as the earth's angular semidiameter as seen from them.
In the case of the sun, the required parallax can be deter-
mined as readily by measuring the parallaxes of any of the
planets as by measuring that of the sun, because any one
measured distance on the map will give us the scale of our
map, Now, the planets Venus and Mars occasionally
come much nearer the earth than the sun ever does, and
tkeir parallaxes also admit of more exact measurement.
162 ASTRONOMY.
The parallax of the sun is therefore determined not by ob-
servations on the sun itself, but on these two planets.
The general principles of the method of determining the
parallax of a planet by simultaneous observations at distant
stations will be seen by referring to the figure. If two
observers, situated at S' and S"> make a simultaneous
observation of the direction of the body P, it is evident
that the solution of a plane triangle S'S"P will give the dis-
tance of P from each station. In practice, however, it would
Fio. 49.
be impracticable to make simultaneous observations at
distant stations; and as the planet is continually in motion,
the problem is a much more complex one than that of
simply solving a triangle.
This is the method of determining the parallax of the
moon. Knowing the actual figure of the earth, observa-
tions of the moon made at stations widely separated in
latitude, as Paris and the Cape of Good Hope, can be com-
bined so as to give the parallax of the moon and thus its
distance. On precisely the same principles the parallaxes
of Venus or Mars have been determined.
MEASUREMENTS OF MASS AND DISTANCE. 163
Solar Parallax from Transits of Venus. When Venus is at inferior
conjunction she is between the sun and the earth. If her orbit lay
in the ecliptic, she would be projected on the sun's disk at every in-
ferior conjunction. The inclination of her orbit is, in fact, about 3|,
and thus transits of Venus occur only when she is near the node of
her orbit at the time of inferior conjunction. In Fig. 49* let E, V, S
be the earth, Venus, and the sun. D (7 is Venus' orbit. An observer
B will see Venus impinge on the sun's disk at /, be just internally
tangent at II, move across the disk to III and off at 1 V. Similar
phenomena will occur for A at 1, 2, 3, 4. When A sees Venus at a,
B will see her at 6. a b is the parallax of Venus with respect to the
change of position A B. (See page 56.) a b : A B :: V a : VA; but
V A : Va as 1:2 nearly (see table p. 198, 3d column), a b there-
fore occupies on the sun's disk a space 2| times as large as the earth's
diameter. If we measure the angular dimension a b in any way,
and divide the resulting angle by 2|, we shall have the angle sub
tended at the sun by the earth's diameter; or if we divide it by 5,
the angle subtended by the earth's radius. This is nothing but the
sun's parallax. (See page 57.)
The angular space a b can be directly measured at a transit of
Venus, or it may be calculated when we know the length of the
chords //, ///, and 2, 3. The length of each chord is known by ob-
FIG. 49 a .
serving the interval of time elapsed from phase // to phase III, or
better by observing all four phases and making the proper allowances.
Other Methods of Determining Solar Parallax. A very
interesting and probably the most accurate method of
measuring the sun's distance depends upon a knowledge of
the velocity of light. We shall hereafter see that the time
164 ASTRONOMY.
required for light to pass from the sun to the earth is known
with considerable exactness, being very nearly 498 seconds.
This time can be determined still more accurately. If
then we can determine experimentally how many miles or
kilometres light moves in a second, we shall at once have
the distance of the sun by multiplying that quantity by
498. The velocity of light is about 300,000 kilometres
per second. This distance would reach about eight times
around the earth. It is seldom possible to see two points
on the earth's surface more than a hundred kilometres
apart, and distinct vision at distances of more than twenty
kilometres is rare. Hence to determine experimentally tin-
time required for light to pass between t\\<> tern-stria! sta-
tions requires the measurement of an interval of time
which, even under the most favorable cases, can be only a
fraction of a thousandth of a second. Methods of doing
it, however, have been devised, and the velocity of light
would seem to be about 299,900 kilometres per second.
Multiplying this by 498, we obtain 149,350,000 kilometres
(a little less than 93,000,000 miles) for the distance of the
sun. The time required for light to pass from the sun to
the earth is still uncertain by nearly a second, but this
value of the sun's distance is probably the best yet ob-
tained. The corresponding value of the sun's parallax is
8'. 81.
Yet other methods of determining the sun's distance
are given by the theory of gravitation. It is found by
mathematical investigation that the motion of the moon is
subject to several inequalities, having the sun's horizontal
parallax as a factor. If the position of the moon could be
determined by observation with the same exactness that
the position of a star or planet can (which it cannot be),
MEASUREMENTS OF MASS AND DISTANCE. 165
this would probably afford the most accurate method of
determining the solar parallax.
Brief History of Determinations of the Solar Parallax. The determi-
nation of the distance of the sun must at all times have been one of
the most interesting scientific problems presented to the human mind.
The first known attempt to effect a solution of the problem was made
by ARISTARCHUS, who flourished in the third century before CHRIST.
It was founded on the principle that the time of the moon's first
quarter will vary with the ratio between the distance of the moon
and sun, which may be shown as follows. In Fig. 50 let JE" represent
the earth, M the moon, and S the sun. Since the sun always
illuminates one half of the lunar globe, it is evident that when one
FIG. 50.
half of the moon's disk appears illuminated the triangle E MS must
be right angled at M. The angle ME S can be determined by
measurement, being equal to the angular distance between the sun
and the moon. Having two of the angles, the third can be deter-
mined, because the sum of the three must make two right angles.
Thence we shall have the ratio between E M, the distance of the moon,
and E S, the distance of the sun, by a trigonometrical computation.
Then knowing the distance of the moon, which can be determined
with comparative ease (see page 162), we have the distance of the sun
by multiplying by this ratio. ARISTARCHUS concluded, from his
supposed measures, that the angle M E S was three degrees less than
JTI -\r -j
a right angle. We should then have -==-^- = r very nearly, since 3
Mi o 17
is yj of 57 and E S = 57 (see page 5). It would follow from this
that the sun was 19 times the distance of the moon, We now know
166 ASTRONOMY.
that this result is entirely wrong, and that it is so because it is im-
possible to determine the time when the moon is exactly half illumi-
nated with any approach to the accuracy necessary in the solution of
the problem. In fact, the greatest angular distance of the earth and
moon, as seen from the sun that is, the angle E SM is only about
one quarter the angular diameter of the moon as seen from the
earth.
The second attempt to determine the distance of the sun is men
tioned by PTOLEMY, though HIPPAKCHUS may be the real inventor
of it. It depends on the dimensions of the earth's shadow-cone dur-
ing a total eclipse of the moon. It is only necessary to state the
result, which was that the sun was situated at the distance of 1210
radii of the earth. This result, like the former, was due only to
errors of observation. So far as all the methods known at the time
could show, the real distance of the sun appeared to be infinite;
nevertheless PTOLEMY'S result was received without question for
fourteen ceiilm i -.
Th? first renlly successful measure of the parallax of a planet was
made upon Mara during the opposition of 1672, by the first of the
two methods already described. An expedition was sent to the
colony of Cayenne to observe the declination of the planet from
ni.irht to night, while corresponding observations were made at the
Paris Observatory. From a discussion >f tlioe observations, CAB-
BINI obtained a solar parallax of 9". 5, which is within a second of
the truth. The next steps forward were made by the transits of
Venus in 1761 and 1769. The lending civilized nations caused obx r-
vations on these transits to be made at various points on the globe.
The method used was very simple, consisting in the determination
of the times at which Venus entered upon the sun's disk and left it
again. The absolute times of ingress and egress, as seen from differ-
ent points of the globe, might differ by 20 minutes or more on ac-
count of parallax. The results, however, were found to be discord-
ant. It was not until more than half a century had elapsed that the
observations were systematically calculated by ENCKE of Germany,
who concluded that, the parallax of the sun was 8" .578, and the dis-
tance 95 millions of miles.
In 1854 it began to be suspected that ENCKE'S value of the parallax
was much too small. HANSEN, from the theory of the moon, found
the parallax of the sun to be 8". 916. This result seemed to be con-
firmed by other observations, especially those of Mars during 1862.
It was therefore concluded that the sun's parallax was probably be
tween 8". 90 and 9". 00. Subsequent researches have, however, been
diminishing this value. In 1867, from a discussion of all the data
MEASUREMENTS OF MASS AND DISTANCE. 167
which were considered of value, it was concluded by one of the
writers that the most probable parallax was 8". 848. The measures
of the velocity of light reduce this value to 8". 81, and it is now
doubtful whether the true value is any larger than this.
All we can say at present is that the solar parallax is probably be-
tween 8". 79 and 8". 83, or, if outside these limits, that it can be very
little outside.
RELATIVE MASSES OF THE SUN AND PLANETS,
In estimating celestial masses as well as distances, it is necessary
to use what we may call celestial units; that is, to take the mass of
some celestial body as a unit, instead of any multiple of the pound or
kilogram. The reason of this is that the ratios between the masses
of the planetary system, or, which is the same thing, the mass of
each body in terms of that of some one body as the unit, can be de-
termined independently of the mass of any one of them. To express
a mass in kilogrammes or other terrestrial units, it is necessary to find
the mass of the earth in such units, as already explained This,
however, is not necessary for astronomical purposes, where only the
relative masses of the several planets are required. In estimating
the masses of the individual planets, that of the sun is generally
taken as a unit. The planetary masses will then all be very small
fractions.
The mass of the sun being 1.00, the mass of Mercury is
Venus is
Earth is
Mars is
Jupiter is
Saturn is
Uranus is
Neptune is
Masses of the Earth and Sun. The mass of the earth is connected
by a very curious relation with the parallax of the sun. Knowing
the latter, we can determine the mass of the sun relative to the earth,
which is the same thing as determining the astronomical mass of the
earth, that of the sun being unity. This may be clearly seen by re-
flecting that when we know the radius of the earth's orbit we can
determine how far the earth moves aside from a straight line in one
second in consequence of the attraction of the sun. This motion
measures the attractive force of the sun at the distance of the earth.
168
ASTRONOMY.
Comparing it with the attractive force of the earth, and making
allowance for the difference of distances from centres of the two
hodies, we determine the ratio between their masses.
The following table shows, for different values of the solar paral-
lax, the corresponding ratio of the musses, and distance of the sun in
terrestrial measures:
DISTANCE or THE SUN
SOLAR
M
PARALLAX.
r
m
In equatorial
radii of the
earth.
In millions of
mile*
In millions of
kil>m'tivs.
8*. 77
835684
28519
93.208
150.001
8". 78
:m5tt
MM
93.102
141.810
8'. 79
:{:{:!:ws
28466
92.996
149.6(50
8'. 80
332262
i:*9
92.890
Its. 490
8'. 81
831132
idtl
92.785
149.:'.--M>
8'. 82
330007
:IS6
92.680
149.151
8*. 83
328887
::l0
92 . 575
148.982
We havesnid that the solar parallax is probably contained between
the limits 8". 79 and 8". 83. It is certainly hardly more than one or
two hundredths of a second without them. So, if we wish to ex-
press the constants relating to the sun in round numbers, we may
say that
Its mans is 330,000 times that of the earth.
Its distance in miles is 93 millions, or perhaps a little less.
Its distance in kilometres is probably between 149 and 150 mil-
lions.
The masses of the planets with satellites are determined by cal-
culating what mass a body must have to produce the observed motion
of the satellites. The planets without satellites have their masses de-
termined by calculating what mass will produce such perturbations
of the motions of the other planets as are actually observed.
CHAPTEK XL
THE REFRACTION AND ABERRATION OF LIGHT AND
TWILIGHT.
ATMOSPHERIC REFRACTION.
WHEN we speak of the place of a planet or star, we usu-
ally mean its true place; i.e., its direction from an ob-
server situated at the centre of the earth. We have shown
in the section on parallax how observations which are
necessarily taken at the surface of the earth are reduced
to what they would have been if the observer were situated
at the earth's centre. We have supposed the star to be
projected on the celestial sphere in the prolongation of
the line joining the observer and the star. The ray from
the star was considered to suffer no deflection in passing
through the stellar spaces and through the earth's atmos-
phere. But from the principles of physics, we know that
such a luminous ray passing from an empty space (as the
stellar spaces probably are), and through an atmosphere,
must suffer a refraction, as every ray of light is known to
do in passing from a rare into a denser medium. As we
see the star in the direction in which its light enters the
eye that is, as we project the star on the celestial sphere
by prolonging this light-beam backward into space there
must be an apparent displacement of the star from refrac-
tion.
We may recall a few definitions from physics. The ray which
leaves the star and impinges on the outer surface of the earth's at-
170 ASTRONOMY.
mospbcre is called the incident ray ; after its deflection by the atmos-
phere it is called the refracted ray. The difference between these
directions is called the astronomical refraction. If a normal is drawn
(perpendicular) to the surface of the refracting medium at the point
where the incident ray meets it, the acute angle between the incident
ray and the normal is called the angle of incidence, and the ncutc angle
between the normal and the refracted
ray is called the angle of refraction.
The refraction itself is the difference
of these angles. The normal and
both incident and refracted rays are
in the same vertical plane. In Fig.
51. SA is the ray incident upon the
surface HA of the refracting medium
II II AN, AC 1 is the refracted ray,
MN the normal, SAM and CAN
the angles of incidence and refrac-
tion respectively. Produce ('A back-
Fio. 51. REFRACTION. " ^ v:ll ' ( l * n the direction AS: 8 A > is
the refraction. An observer at C will
see the star S as if it were at S. AS' is the apparent direction of
the ray coming from the star S, and & is the apparent place of the star
as affected by refraction.
This explanation supposes the space above BE' in the
figure to be entirely empty, and the earth's atmosphere,
equally dense throughout, to fill the space below BB'.
In fact, however, the earth's atmosphere, is most dense
at the surface of the earth, and gradually diminishes in
density to its exterior boundary. Therefore we must sup-
pose the atmosphere to be divided into a great number of
parallel layers of air, and by assuming an infinite num-
ber of these we may also assume that throughout each one
of them the air is equally dense. Hence the preceding
figure will only represent the refraction at a single one of
these layers. The path of a ray of light through the at-
mosphere is not a straight line like A C, but a curve. We
may suppose this curve to be represented in Fig. 52, where
REFRACTION AND ABERRATION OF LIGHT. 171
the number of layers has been taken very small to avoid
confusing the drawing."
Let C be the centre and A a point of the surface of the
earth; let S be a star, and Sea, ray from the star which is
refracted at the various layers into which we suppose the
atmosphere to be divided, and which finally enters the eye
of an observer at A in the apparent direction S'A. He
FIG. 52. REFRACTION OP LAYERS OP AIR.
will then see the star in the direction S' instead of that of
S 9 and SA $', the refraction, will throw the star nearer
to his zenith Z.
The angle S'A Z is the apparent zenith distance of S;
the true zenith distance of S is Z A S, and SA may be
assumed to coincide with S e, as for all heavenly bodies
except the moon it practically does. The line Se pro-
172 ASTRONOMY.
longed will meet the line A Z in a point above A, suppose
aU'.
Quantity and Effects of Refraction. At the zenith the
refraction is 0, at 45 zenith distance the refraction is about
1', and at 90 it is 34' 30"; that is, bodies at the zenith
distances of 45 and 90 appear elevated above their true
places by 1' and 34|' respectively. If the sun has just
risen that is, if its lower limb is just in apparent contact
with the horizon it is in fact entirely below the true
horizon, for the refraction (35') has elevated its centre by
more than its whole apparent diameter (32').
The moon is full when it is exactly opposite the sun,
and therefore, were there no atmosphere, moon-rise of a
full moon and sunset would be simultaneous. In fact,
both bodies being elevated by refraction, we see the full
moon risen before the sun has set. On April 20th, 1837,
the full moon rose eclipsed before the sun had set.
TWILIGHT.
It is plain that one effect of refraction is to lengthen the
duration of daylight by causing the sun to appear above
the horizon before the time of his geometrical rising and
after the time of true sunset.
Daylight is also prolonged by the reflection of the sun's
rays (after sunset and before sunrise) from the small parti-
cles of matter suspended in the atmosphere. This pro-
duces a general though faint illumination of the atmos-
phere, just as the light scattered from the floating particles
of dust illuminated by a sunbeam let in through a crack
in a shutter may brighten the whole of a darkened room.
The sun's direct rays do not reach an observer on the
TWILIGHT. 173
earth after the instant of sunset, since the solid body of
the earth intercepts them. But the sun's direct rays
illuminate the clouds and the suspended particles of the
upper air, and are reflected downwards so as to produce a
general illumination of the atmosphere.
In the figure let A B CD be the earth and A an observer
on its surface, to whom the sun S is just setting. A a is
the horizon of A; El of B; Cc of C; DdofD. Let the
FIG. 53.
circle P Q R represent the upper layer of the atmosphere.
Between A BCD and PQR the air is filled with sus-
pended particles which will reflect light. The lowest ray
of the sun, 8 A M, just grazes the earth at A ; the higher
rays S j^and SO strike the atmosphere above A and leave
it at the points Q and R. Each of the lines S A P M,
SQN, is bent from a straight course by refraction, but
S R is not bent since it just touches the upper limits of
174 ASTROXOMY.
the atmosphere. The space MABCDEia the earth's
shadow. An observer at A receives the (last) direct rays
from the sun, and also has his sky illuminated by the reflec-
tion from all the particles lying in the space P Q Ji T
which is all above his horizon A a.
An observer at B receives no direct rays from the sun.
It is after sunset. Nor does he receive any light from all
that portion of the atmosphere below A P M; but the por-
tion P Rx, which lies above his horizon Bb, is lighted by
the sun's rays, and reflects to B a portion of the incident
rays.
This ttriliijht is strongest at R, and fades away gradu-
ally toward P. The altitude of the twilight is I d.
To an observer at C the twilight is derived from the
illumination of the portion PQz which lies above his
horizon Cc. The altitude of the twilight is cd.
To an observer at D it is night. All of the illuminated
atmosphere is below his horizon Dd.
The student should notice for himself the twilight arch
which appears in the west after sunset. It is more marked
in summer than in winter; in high latitudes than in low
ones. There is no true night in England in midsummer,
for example, the morning twilight beginning before the
evening twilight has ended ; and in the torrid zone there
is no perceptible twilight. Twilight ends when the sun
reaches a point 20 below the horizon.
ABEBRATION AND THE MOTION OF LIGHT.
Besides refraction, there is another cause which prevents
our seeing the celestial bodies exactly in the true direction
in which they lie from us; namely, the progressive mo-
tion of light. We see objects only by the light which
emanates from them and reaches our eyes, and we know
REFRACTION AND ABERRATION OF LIGHT. 175
that this light requires time to pass over the space which
separates us from the luminous object. After the ray of
light once leaves the object, the latter may move away, or
even be blotted out of existence, but the ray of light
will continue on its course. Consequently when we look
at a star, we do not see the star that now is, but the star
that was several years ago. If it should be annihilated, we
should still see it during the years which would be required
for the last ray of light emitted by it to reach us. The
velocity of light is so great that in all observations of ter-
restrial objects our vision may be regarded as instantane-
ous. But in celestial observations the time required for
the light to reach us is quite appreciable and measurable.
The discovery of the propagation of light is among the
most remarkable of those made by modern science. The
fact that light requires time to travel was first learned by
the observations of the satellites of Jupiter. (See Fig. 73.)
Owing to the great magnitude of this planet, it casts a much
longer and larger shadow than our earth does, and its inner
satellite passes throagh this shadow and is eclipsed, at every
revolution. These eclipses can be observed from the earth,
the satellite vanishing from view as it enters the shadow,
and reappearing when it leaves it again. The astronomers
of the seventeenth century made a careful study of the mo-
tions of these bodies. It was, however, necessary to con-
struct tables by which the times of the eclipses could be pre-
dicted. It was found by EOEMEE that these times depended
on the distance of Jupiter from the earth. If he made his
tables agree with observations when the earth was nearest
Jupiter, it was found that as the earth receded from Jupiter
in its annual course around the sun, the eclipses were con-
stantly seen later, until, when at its greatest distance, the
176 ASTRONOMY.
times appeared to be 22 minutes late. KOEMER saw that it
was in the highest degree improbable that the actual motions
of the satellites should be affected with any such inequality;
he therefore propounded the bold theory that it took time
for light to come from Jupiter to the earth. The extreme
differences in the times of the eclipse being 22 minutes, he
assigned this as the time required for light to cross the
orbit of the earth, and so concluded that it came from the
sun to the earth in 11 minutes. This estimate was too
great; the true time for this passage being about 8 minutes
and 18 seconds.
Discovery of Aberration. This theory of ROEMEK was
not fully accepted by his contemporaries. Hut in the year
1729 the celebrated BRADLEY, afterward Astnui'-iiK-r Royal
of England, discovered a phenomenon of an entirely dif-
ferent character, which confirmed the theory, lie was
then engaged in making observations on the star y Dnt-
conis in order to determine its parallax. The effect of
parallax would have been to make the declination of the
star greatest in June and least in December, while in
March and September the star would occupy an interme-
diate or mean position. But the result was entirely dif-
ferent. The declinations of June and December were the
same, showing no effect of parallax; but instead of remain-
ing constant the rest of the year, the declination was some
40 seconds greater in September than in March, when the
effect of parallax would be the same. This showed that
the direction of the star appeared different, not according
to the position of the earth in its orbit, but according to
the direction of the earth's motion around the sun, the
star being apparently displaced in this direction.
To show how this is, let AB be the optical axis of a
REFRACTION AND ABERRATION OF LIGHT. 177
telescope, and 8 a star from which emanates a ray moving
in the true direction SAB'. Per-
haps the student will have a clearer
conception of the subject if he imag-
ines AB to be a rod which an ob-
server at B seeks to point at the star
8. It is evident that he will point
this rod in such a way that the ray
of light shall run accurately along its
length. Suppose now that the ob-
server is moving from B toward B'
with such a velocity that he moves FIG. 54.
from B to B' during the time required for a ray of light to
move from A to B'. Suppose, also, that the ray of light
8A reaches A at the same time that the end of his rod
does. Then it is clear that while the rod is moving from
the position AB to the position A'B', the ray of light
will move from A to B' , and will therefore run accurately
along the length of the rod. For instance, if b is one third
of the way from B to B', then the light, at the instan^of
the rod taking the position b a, will be one third of the way
from A to B', and will therefore be accurately on the rod.
Consequently, to the observer, the rod will appear to be
pointed at the star. In reality, however, the pointing will
not be in the true direction of the star, but will deviate
from it by a certain angle depending upon the ratio of the
velocity with which the observer is carried along to the
velocity of light. This presupposes that the motion of the
observer is at right angles to that of a ray of light. If
this is not his direction, we must resolve his velocity into
two components, one at right angles to the ray and one
parallel to it. The latter will not affect the apparent di-
178 ASTRONOMY.
rection of the star, A rich will therefore depend entirely
upon the former.
Effects of Aberration. The apparent displacement of
the heavenly bodies thus produced is called the aberration
of light. Its effect is to cause each of the fixed stars to
describe an apparent annual oscillation in a very small orbit.
The nature of the displacement may he conceived of in the
following way: Suppose the earth at any moment, in the
course of its annual revolution, to be moving toward a
point of the celestial sphere, which \ve may call /'. Then
a star lying in the direction P or in the opposite direction
will suffer no displacement whatever. A star lying in any
other direction will be displaced in the direction of the
point P by an angle depending upon its angular distance
from P. At 90 from P the displacement will be a maxi-
mum.
Now, if the star lies near the pole of the ecliptic, its di-
rection will always be nearly at right angles to the direc-
tion in which the earth is moving. A little consideration
will show that it will seem to describe a circle in conse-
quence of aberration. If, however, it lies in the plane of
the earth's orbit, then the various points toward which the
earth moves in the course of the year all lying in the eclip-
tic, and the star being in this same plane, the apparent
motion will be an oscillation back and forth in this plane,
and in all other positions the apparent motion will be in an
ellipse more and more flattened as we approach the ecliptic.
The maximum displacement of a star by aberration is 20'. 44.
The connection between the velocity of light and the dis-
tance of the sun is such that knowing one we can infer the
other. Let us assume, for instance, that the time required
for light to reach us from the sun is 498 seconds, which
REFRACTION AND ABERRATION OF LIGHT. 179
is probably accurate within a single second. Then know-
ing the distance of the sun, we may obtain the velocity
of light by dividing it by 498. But, on the other hand,
if we can determine how many miles light moves in a
second, we can thence infer the distance of the sun by
multiplying it by the same factor. During the last cen-
tury the distance of the sun was found to be certainly be-
tween 90 and 100 millions of miles. It was therefore
correctly concluded that the velocity of light was some-
thing less than 200,000 miles per second, and probably
between 180,000 and 200,000. This velocity has since
been determined more exactly by the direct measurements
at the surface of the earth already mentioned.
CHAPTER XII.
CHRONOLOGY.
ASTRONOMICAL MEASURES OF TIME.
THE int:mate relation of astronomy to the daily life of
mankind lias arisen from its affording the only reliable and
accurate measure of intervals of time. The fundamental
units of time in all ages have been the day, the month, and
the year, the first being measured by the revolution of the
earth on its axis, the second, primitively, by that of the
moon around the earth, and the third by that of the earth
round the sun.
Of the three units of time just mentioned, the most nat-
ural and striking is the shortest; namely, the day. It is
so nearly uniform in length that the most refined astro-
nomical observations of modern times have never certainly
indicated any change. This uniformity, and its entire
freedom from all. ambiguity of meaning, have always made
the day a common fundamental unit of astronomers. Ex-
cept for the inconvenience of keeping count of the great
number of days between remote epochs, no greater unit
would ever have been necessary, and we might all date our
letters by the number of days after CHRIST, or after any
other fixed date.
The difficulty of remembering great numbers is such
that a longer unit is absolutely necessary, even in keeping
the reckoning of time for a single generation. Such a unit
CHRONOLOGY. 181
is the year. The regular changes of seasons in all extra-
tropical latitudes renders this unit second only to the day
in the prominence with which it must have struck the
minds of primitive man. These changes are, however, so
slow and ill-marked in their progress that it would have
been scarcely possible to make an accurate determination
of the length of the year from the observation of the sea-
sons. Here astronomical observations came to the aid
of our progenitors, and, before the beginnings of history,
it was known that the alternation of seasons was due to
the varying declination of the sun, as the latter seemed
to perform its annual course among the stars in the
" oblique circle" or ecliptic. The seasons were also marked
by the position of certain bright stars relatively to the sun;
that is, by those stars rising or setting in the morning
or evening twilight. Thus arose two methods of measur-
ing the length of the year the one by the time when the
sun crossed the equinoxes or solstices, the other when it
seemed to pass a certain point among the stars. As we
have already explained, these years were slightly different,
owing to the precession of the equinoxes, the first or equi-
noctial year being a little less and the second or sidereal
year a little greater than 365| days.
The number 01 days in a year is too great to admit of
their being easily remembered without any break; an
intermediate period is therefore necessary. Such a period
is measured by the revolution of the moon around the
earth, or, more exactly, by the recurrence of new moon,
which takes place, on the average, at the end of nearly
29| days. The nearest round number to this is 30 days,
and 12 periods of 30 days each only lack 5i days of being
a year. It has therefore been common to consider a year
182 ASTRONOMY.
as made up of 12 months, the lack of exact correspondence
being filled by various alterations of the length of the
month or of the year, or by adding surplus days to each
year.
The true lengths of the day, the month, and the year
having no common divisor, a difficulty arises in attempting
to make months or days into years, or days into months,
owing to the fractions which will always be left over. At
the same time, some rule bearing on the subject is neces-
sary in order that people may be able to remember the year,
month, and day. Such rules are found by choosing some
cycle or period which is very nearly an exact number of
two units, of months and of days for example, and by
dividing this cycle up as evenly as possible.
FOEMATION OF CALENDARS.
The months now or heretofore in use among the peoples of the
globe nwy for the most part be divided into two classes:
(1) The lunar month pure and simple, or the mean interval be-
tween successive new moons.
(2) An approximation to the twelfth part of a year, without respect
to the motion of the moon.
The Lunar Month. The mean interval between consecutive new
moons being nearly 29$ days, it was common in the use of the pure
lunar month to have months of 29 and 30 <l;ivs alternately. This
supposed period, however, will fall short by a day in about 2| years.
This defect was remedied by introducing cycles containing rather more
months of 30 than of 29 days, the small excess of long months being
spread uniformly through the cycle. Thus the Greeks had a cycle
of 235 months, of which 125 were full or long mouths, ;md 110 were
short or deficient ones. We see that the length of this cycle was
6940 days (125 X 30 -f 110 X 29), whereas the length of 235 true lunar
months is 235 X 29.53088 = 6939.688 days. The cycle was therefore
too long by less than one third of a day, and the error of count would
amount to only one day in more than 70 years. The Mohammedans,
again, took a cycle of 360 months, which they divided into 169 short
and 191 long ones. The length of this cycle was 10631 days, while
CHRONOLOGY. 183
the true length of 360 lunar months is 10631.012 days. The count
would therefore not be a day in error until the end of about 80
cycles, or nearly 23 centuries. This month therefore follows the
moou closely enough for all practical purposes.
Months other than Lunar. The complications of the system just
described, and the consequent difficulty of making the calendar
month represent the course of the moon, are so great that the pure
lunar month was generally abandoned, except among people whose
religion required important ceremonies at the time of new moon. In
such cases the year has been usually divided into 12 months of
slightly different lengths. The ancient Egyptians, however, had 12
mouths of 30 days each, to which they added 5 supplementary days
at the close of each year.
Kinds of Year. As we find two different systems of months to
have been used, so we may divide the calendar years into three
classes, namely :
(1) The lunar year, of 12 lunar months.
(2) The solar year.
(3) The combined luni-solar year.
The Lunar Year. We have already called attention to the fact that
the time of recurrence of the year is not well marked except by
astronomical phenomena which the casual observer would hardly
remark. But the time of new moon, or of beginning of the month,
is always well marked. Consequently it was very natural for people
to begin by considering the year as made up of twelve lunations, the
error of eleven days being unnoticeable in a single year unless care-
ful astronomical observations were made. Even when this error was
fully recognized, it might be considered better to use the regular
year of 12 lunar months than to use one of an irregular or varying
number of months. The Mohammedans use such a year to this day.
The Solar Year. In forming this year, the attempt to measure the
year by revolutions of the moon is entirely abandoned, and its length
is made to depend entirely on the change of the seasons. The solar
year thus indicated is that most used in both ancient and modern
times. Its length has been known to be nearly 365i days from the
times of the earliest astronomers, and the system adopted in our cal-
endar of having three years of 365 days each, followed by one of 366
days, has been employed in China from the remotest historic times.
This year of 365J days is now called by us the Julian Tear, after
JULIUS C^SAR, from whom we obtained it.
The Metonic Cycle. These considerations will enable us to under-
stand the origin of our own calendar. We begin with the Metonic
Cycle of the ancient Greeks, which still regulates some religious fes-
184 ASTRONOMY.
tivals, although it has disappeared from our civil reckoning of time.
The necessity of employing lunar months caused the Greeks great
difficulty in regulating their calendar so as to accord with their rules
for religious feasts, until a solution of the problem was found by
METON, about 433 B.C. The discovery of METON was that u period
or cycle of 6940 days could be divided up into 235 lunar months, and
also into 19 solar years. Of these months, 125 were to be of 30 days
each and 110 of 29 days each, which would, in all, make up the re-
quired 6940 days. To see how nearly this rule represents the actual
motions of the sun and moon, we remark that:
Days. Hours. Min.
235 lunations require 6939 16 31
19 Julian years require 6939 18
19 true solar years require 6939 14 27
We see that though the cycle of 6940 days is a few hours too
long, yet if we take 235 true lunar months, we find their whole dura-
tion to be a little less than 19 Julian years of 365 days each, and a
little more than 19 true solar years.
The problem was to take these 235 months and divide them up
into 19 years, of which 12 should have 12 months each and 7
should have 13 months each. The long years, or those of 13 months,
were probably those corresponding to the numl>ers 3, 5, 8, 11, 13, 16,
and 19, while the first, second, fourth, sixth, etc., were short years.
In general, the months had 29 and 30 days alternately, but it was
necessary to substitute a long month for a short one every two or
three years, so that in the cycle there should be 125 long and 110
short months.
Golden Number. This is simply the number of the year in the
Mrtonic Cycle, and is said to owe its appellation to the enthusiasm
of the Greeks over METON'S discovery, the authorities having ordered
the division and numbering of the years in the new calendar to be
inscribed on public monuments in letters of gold. The rule for find-
ing the golden number is to divide the number of the year by 19 and
add 1 to the remainder. From 1881 to 1899 it may be found by sim-
ply subtracting 1880 from the year. It is employed in our church
calendar for finding the time of Easter Sunday.
The Julian Calendar. The civil calendar now in use throughout
Christendom had its origin among the Romans, and its foundation
was laid by JULIUS CESAR. Before his time, Rome can hardly be
said to have had a chronological system, the length of the year not
being prescribed by any invariable rule, and being therefore changed
from time to time to suit the caprice or to compass the ends of the
CHRONOLOGY. 185
rulers. Instances of this tampering disposition are familiar to the
historical student. It is said, for instance, that the Gauls having to
pay a certain monthly tribute to the Romans, one of the governors
ordered the year to be divided into 14 months, in order that the pay-
days might recur more rapidly. A year was fixed at 365 days, with
the addition of one day to every fourth year. The old Roman months
were afterward adjusted to the Julian year in such a way as to give
rise to the somewhat irregular arrangement of months which we now
have.
Old and New Styles. The mean length of the Julian year is 365
days, about Hi minutes greater than that of the true equinoctial
year, which measures the recurrence of the seasons. This difference
is of little practical importance, as it only amounts to a week in a
thousand years, and a change of this amount in that period is pro-
ductive of no inconvenience. But, desirous to have the year as cor-
rect as possible, two changes were introduced into the calendar by
Pope GREGORY XIII. with this object. They were as follows :
(1) The day following October 4, 1582, was called the 15th instead
of the 5th, thus advancing the count 10 days.
(2) The closing year of each century, 1600, 1700, etc., instead of
being always a leap-year, as in the Julian calendar, is such only
when the number of the century is divisible by 4. Thus while 1600
remained a leap-year, as before, 1700, 1800, and 1900 were to be
common years.
This change in the calendar was speedily adopted by all Catholic
countries, and more slowly by Protestant ones, England holding out
until 1752. In Russia it has never been adopted at all, the Julian
calendar being still continued without change. The Russian reckon-
ing is therefore 12 days behind ours, the ten days dropped in 1582
being increased by the days dropped from the years 1700 and 1800 in
the new reckoning. This modified calendar is called the Gregorian
Calendar, or New Style, while the old system is called the Julian
Calendar, or Old Style.
It is to be remarked that the practice of commencing the year on
January 1st was not universal until comparatively recent times. The
most common times of commencing were, perhaps, March 1st and
March 22d, the latter being the time of the vernal equinox. But
January 1st gradually made its way, and became universal after its
adoption by England in 1752.
Solar Cycle and Dominical Letter. In our church calendars Janu-
ary 1st is marked by the letter A, January 2d by B, and so on to G,
when the seven letters begin over again, and are repeated through
the year in the same order. Each letter there indicates the same day
186 ASTRONOMY.
of the week throughout each separate year, A indicating the day on
which January 1st falls, B the day following, and so on. An excep-
tion occurs in leap years, when February 29th and March 1st are
marked by the same letter, so that a change occurs at the beginning
of March. The letter corresponding to Sunday on this scheme is
called the Dominical or Sunday letter, and when we once know
what letter it is, all the Sundays of the year are indicated by that
letter, and hence all the other days of the week by their letters. In
leap-years there will be two Dominical letters, that for the last ten
months of the year being the one next preceding the letter for
January and February. In the Julian calendar the Dominical letter
must always recur at the end of 28 years (besides three recurrences
at unequal intervals in the me:m time). This period is called the
solar cycle, and determines the days of the week on which the days
of the month fall during each year.
Since any day of any year occurs one day later in the week than
it did the year befon . < r two days later when a 29th of February
has intervened, the Dominical letters recur in the order G, F, E, D,
C, B, A, G, etc. This may also be expressed by saying that any day
of a past year occurred one day earlier in the week for every year
that has elapsed, and, in addition, one day earlier for every 29th of
February that has intervened. This fact will make it easy to calcu-
late the day of the week on which any historical event happened
from the day corresponding in any past or future year. Let us take
the following example:
On what day of the week was WASHINGTON born, the date being
1732, February 22d, knowing that February 22d, 1879, fell on
Saturday? The interval is 147 years: dividing by 4 we have a
quotient of 36 and a remainder of 3, showing that, had every fourth
year in the interval been a leap year, there were either 36 or 37 leap-
years. As a February 29th followed only a week after the date, the
number must be 37;* but as 1800 was dropped from the list of leap-
years, the number was really only 36. Then 147 -f- 36 = 183 days
advanced in the week. Dividing by 7, because the same day of the
week recurs after seven days, we find a remainder of 1. So
February 22d, 1879, is one day further advanced than was Febru-
ary 22d, 1732; so the former being Saturday, WASHINGTON was born
on Friday.
* Perhaps the most convenient way of deciding whether the remainder does
or does not indicate an additional leap-year is to subtract it from the last date,
and see whether a February 29th then intervenes. Subtracting 3 years from
February 22d, 1879, we have February 23d 1876, and a 29th occurs between the
two dates, only a week after the first. _
CHRONOLOGY. 187
DIVISION OF THE DAY.
The division of the day into hours was, in ancient and mediaeval
times, effected in a way very different from that which we practise.
Artificial time-keepers not being in general use, the two funda-
mental moments were sunrise and sunset, which marked the day as
distinct from the night. The first subdivision of this interval was
marked by the instant of noon, when the sun was on the meridian.
The day was thus subdivided into two parts. The night was
similarly divided by the times of rising and culmination of the
various constellations. EURIPIDES (480-407 B.C.) makes the chorus
in RJiesus ask :
" CHORUS. Whose is the guard? Who takes my turn? The first
signs are setting, and the sewn Pleiades are in the sky, and the Eagle
glides midway through heaven. Awake! Why do you delay? Awake
from your beds to watch! See ye not the brilliancy of the moon?
Morn, morn indeed is approaching, and hither is one of the forewin-
ning stars"
The interval between sunrise and sunset was divided into twelve
equal parts called hours, and as this interval varied with the season,
the length of the hour varied also. The night, whether long or
short, was divided into hours of the same character, only when the
night hours were long those of the day were short, and vice versa.
These variable hours were called temporary hours. At the time of
the equinoxes both the day and the night hours were of the same
length with those we use; namely, the twenty-fourth part of the
day ; these were therefore called equinoctial hours.
Instead of commencing the civil day at midnight, as we do, it was
customary to commence it at sunset. The Jewish Sabbath, for
instance, commenced as soon as the sun set on Friday, and ended
when it set on Saturday. This made a more distinctive division of
the astronomical day than that which we employ, and led naturally
to considering the day and the night as two distinct periods, each to
be divided into 12 hours.
So long as temporary hours were used, the beginning of the day
and the beginning of the night, or, as we should call it, six o'clock
in the morning and six o'clock in the evening, were marked by the
rising and setting of the sun; but when equinoctial hours were
introduced, neither sunrise nor sunset could be taken to count from,
because both varied too much in the course of the year. It therefore
became customary to count from noon, or the time at which the sun
passed the meridian. The old habit of dividing the day and the
188 ASTRONOMY.
night each into 12 parts was continued, the first 12 being reckoned
from midnight to noon, and the second from noon to midnight. The
day was made to commence at midnight rather than at noon for
obvious reasons of convenience, although noon was of course the
point at which the time had to be determined.
Equation of Time. To any one who studied the annual motion of
the sun, it must have been quite evident that the intervals between
its successive passages over the meridian, or between one noon and
the next, could not be the same throughout the year, l>ecause the
apparent motion of the sun in right ascension is not constant. It
will be remembered that the apparent revolution of the starry
sphere, or, which is the same thing, the diurnal revolution of the
earth upon its axis, may be regarded as absolutely constant for all
practical purposes. This revolution is measured around in right
ascension as explained in the opening chapter of this work. If the
sun increased its right ascension by the same amount every day, it
would pass the meridian 3 m 56" later every day, as measured by
sidereal time, and hence the intervals between successive passages
would be equal. But the motion of the sun in right ascension is
unequal from two causes: (1) the unequal motion of the earth in its
annual revolution around it, arising from the eccentricity of the
earth's orbit, and (2) the obliquity of the ecliptic. How the first
cause produces an inequality is obvious. The mean motion is 3 m 50* ;
the actual motion varies from 3 m 48* to 4 m 4 s .
The effect of the obliquity of the ecliptic is still greater. When
the sun is near the equinox, the direction of its motion along the
ecliptic makes an angle of 2&J with the parallels of declination.
Since its motion in right ascension is measured along the parallel of
declination, we see that it is less than the motion in longitude. The
days are then 20 seconds shorter than they would be were there no
obliquity. At the solstices the opposite effect is produced. Here
the different meridians of right ascension are nearer together than
they are at the equator; when the sun moves through one degree
along the ecliptic, it changes its right ascension by 1-08; here,
therefore, the days are about 19 seconds longer than they would be
if the obliquity of the ecliptic were zero.
We thus have to recognize two slightly different kinds of days:
solar days and mean days. A solar day is the interval of time
between two successive transits of the sun over the same meridian,
while a mean day is the mean of all the solar days in a year. If we
had two clocks, one going with perfect uniformity, but regulated
so as to keep as near the sun as possible, and the other changing its
rate so as to always follow the sun, the latter would gain or lose on
CHRONOLOGY. 189
the former by amounts sometimes rising to 22 seconds in a day. The
accumulation of these variations through a period of several months
would lead to such deviations that the sun-clock would be 14 minutes
slower than the other during the first half of February, and 16
minutes faster during the first week in November. The time-keepers
formerly used were so imperfect that these inequalities in the solar
day were nearly lost in the necessary irregularities of the rate of the
clock. All clocks were therefore set by the sun as often as was
found necessary or convenient. But during the last century it was
found by astronomers that the use of units of time varying in this
way led to much inconvenience; they therefore substituted mean
time for solar or apparent time.
Mean time is so measured that the hours and days shall always be
of the same length, and shall, on the average, be as much behind the
sun as ahead of it. We may imagine a fictitious or mean sun mov-
ing along the equator at the rate of 3 m 56* in right ascension every
day. Mean time will then be measured by the passage of this
fictitious sun across the meridian. Apparent time was used in
ordinary life after it was given up by astronomers, because it was
very easy to set a clock from time to time as the sun passed a noon-
mark. But when the clock was so far improved that it kept much
better time than the sun did, it was found troublesome to keep put-
ting it backward and forward so as to agree with the sun. Thus
mean time was gradually introduced for all the purposes of ordinary
life.
The common household almanac should give the equation of time,
or the mean time at which the sun passes the meridian, on each day
of the year. Then, if any one wishes to set his clock, he knows the
moment when the sun passes the meridian, or when it is at some noon-
mark, and sets his time-piece accordingly. For all purposes where
accurate time is required, recourse must be had to astronomical
observation. It is now customary to send time-signals every day at
noon, or some other hour agreed upon, from observatories along the
principal lines of telegraph. Thus at the present time the moment
of Washington noon is signalled to New York, and over the principal
lines of railway to the South and West. Each person within reach
of a telegraph-office can then determine his local time by correcting
these signals for the difference of longitude.
PART II.
THE SOLAR SYSTEM IN DETAIL
CHAPTER I.
STRUCTURE OF THE SOLAR SYSTEM.
THE solar system consists of the sun as a central body,
around which revolve the major and minor planets, with
their satellites, a iV\v periodic comets, and an unknown
number of meteor swarms. These an.' piM-manrnt members
of the system. At times other comets appear, and move
usually in parabolas through the system, around the sun,
and away from it into space again, thus visiting the system
without being permanent members of it.
The bodies of the system may be classified as follows :
1. The central body the Sun.
2. The four inner planets Mercury, Venus, the Earth, Mars.
3. A group of small planets, sometimes called Asteroids, revolving
outside of the orbit of Mars.
4. A group of four outer planets Jupiter, Saturn, Uranus, and
Neptune.
5. The satellites, or secondary bodies, revolving about the planets,
their primaries.
6. A number of comets and meteor swarms revolving in very
eccentric orbits about the sun.
The eight planets of Groups 2 and 4 are sometimes classed to-
gether as the major planet^ to distinguish them from the two hun-
dred or more minor plfineta of Group 3. The formal definitions of
the various classes, laid down by Sir WILLIAM HERSCHEL in 1802, are
worthy of repetition :
STRUCTURE OF THE SOLAR
^ SIT I
Planets are celestial bodies of a certain very considefat
They move in not very eccentric ellipses about the sun. The planes
of their orbits do not deviate many degrees from the plane of the
earth's orbit. Their motion about the sun is direct (from west to
east). They may have satellites or rings. They have atmospheres of
FIG. 65. RELATIVE SURFACES or THE PLANETS.
considerable extent, which, however, bear hardly any sensible pro-
portion to their diameters. Their orbits are at certain considerable
distances from each other.
Asteroids, now more generally known as small or minor planet*, are
celestial bodies which move about the sun }n orbits, either of little or
192
ASTROXOMY.
of considerable eccentricity, the planes of which orbits may be in-
clined to the ecliptic at any angle whatsoever. They may or may
not have considerable atmospheres.
Cometi are celestial bodies, generally of a very small mass, though
how far this may be limited is yet unknown. They move in very
Fio. 56. APPARENT MAGNITUDES OF THE SUN AS SEEN FROM DIFFERENT PLANETS.
eccentric ellipses or in parabolic arcs about the tun. The planes of
their motion admit of the greatest variety in their situation. The
direction of their motion is also totally undetermined. They have
atmospheres of very great extent, which show themselves in various
forms us tails, coma, haziness, etc.
STRUCTURE OF THE SOLAR SYSTEM.
193
Relative Surfaces of the Planets. The comparative surfaces of the
major planets, as they would appear to an observer situated at an
equal distance from all of them, is given in the figure on page 191.
The relative apparent magnitudes of the sun, as seen from the
various planets, is shown in the figure on page 192.
Flora and Mnemosyne are two of the asteroids.
A curious relation between the distances of the planets, known as
BODE'S law, deserves mention. If to the numbers
0, 3, 6, 12, 24, 48, 96, 192, 384,
each of which (the second excepted) is twice the preceding, we add
4, we obtain the series
4, 7, 10, 16, 28, 52, 100, 196, 388.
These last numbers represent approximately the distances of the
planets from the sun (except for Neptune, which was not discovered
when the so-called law was announced).
This is shown in the following table :
PLANETS.
Actual
Distance.
BODE'S Law.
3-9
4-0
Venus
7-2
7-0
Earth
10-0
10-0
Mars
15-2
16-0
[Ceres]
27-7
28-0
Jupiter
52-0
52-0
Saturn
95-4
100-0
, Uranus
191-8
96-0
^Neptune ....
300-4
888
It will be observed that Neptune does not fall within this ingenious
scheme. Ceres is one of the minor planets.
The relative brightness of the sun and the various planets has been
measured by ZOLLNER, and the results are given below. The column
per cent shows the percentage of error indicated in the separate re-
sults:
SUN AND
Ratio : 1 to
Percent, of Error.
Moon
618 000
1-6
6 994 000 000
5-8
5 472 000 000
5-7
Saturn (ball alone)
130 980 000 000
5-0
8,486,000,000,000
6-0
Neptune
79 620 000 000 000
5-5
194
ASTRONOMY.
The differences in the density, size, mass, and distance of the
several planets, and in the amount of solar light and heat which they
receive, are immense. The distance of Neptune is eighty times that
of Mercury, and it receives only ^^ as much light and heat from the
sun. The density of the earth is about six times that of water, while
Saturn's mean density is less than that of water.
The mass of the sun is far greater than that of any single planet
in the system, or indeed than the combined mass of all of them. In
general, it is a remarkable fact that the mass of any given planet ex-
ceeds the sum of the masses of all the planets of less mass than itself.
This is shown in the following table, where the masses of the planets
are taken as fractions of the sun's mass, which we here express as
1,000,000,000:
900
324
3,000
51,000 885,580 954,905 1,000,000,000 Masses.
PLANETS
The total mass of the small planets, like their number, is unknown,
but it is probably less than one th<>M-:imltli that of our earth, and
would hardly increase the sum-total of the above masses of the solar
system hy more than one or two units. Tin- sun's mass is thus over
TOO times that of all the other bodies, and hence the fact of its cen-
tral position in the solar system is explained. In fact, the centre of
gratify ot the whole solar system is very little outside the body of the
sun, and will be inside of it when J>i]>it< : r and Saturn are in opposite
directions from it.
Planetary Aspects. The motions of the planets about the sun have
been explained in Chapter V. From what is there said it appears
that the best time to see one of the "outer planets will be when it is
in opposition; that is, when its geocentric longitude or its right as-
cension differs 180 or 12 h from that of the sun. At such a time the
planet will rise at sunset and culminate at midnight. During the
three months following opposition the planet will rise from three to
six minutes earlier every day, so that, knowing when a planet is in
opposition, it is easy to find it at any other time. For example, a
month after opposition the planet will be two or three hours high
about sunset, and will culminate about nine or ten o'clock. Of
course the inner planets never come into opposition, and hence are
best seen about the times of their greatest elongations.
STRUCTURE OF THE SOLAR 81' STEM.
195
Dimensions of the Solar System. The figure gives a rough plan of
part of the solar system as it would appear to a spectator immediately
above or below the plane of the ecliptic. It is drawn approximately
to scale, the mean distance of the earth (= 1) being half an inch.
The mean distance of Saturn would be 4-77 inches, of Uranus 9-59
FIG. 57.
inches, of Neptune 15-03 inches. On the same scale the distance of
the nearest fixed star would be 103,133 inches, or over one and one half
miles.
The arrangement of the planets and satellites is, then
The Inner Group.
Mercury.
Venus.
Earth and Moon.
Mars and 2 moons.
Asteroids.
200 minor planets,
and probably
many more.
The Outer Group.
/ Jupiter and 4 moons.
J Saturn and 8 moons.
J Uranus and 4 moons.
( Neptune and 1 moon.
196 ASTRONOMY.
To avoid repetitions, the elements of the major planets and other
data are collected into the two following tables, to which reference
should be made by the student. The units in termsof which Hie vari-
ous quantities are given are those familiar to us, as miles, days, etc.,
yet some of the distances, etc., are so immensely greater than any
known to our daily experience that we must have recourse to illus-
trations to obtain any idea of them at all. For example, the dis-
tance of the sun is said to be 92* million miles. It is of importance
that some idea should !>< had of this distance, as it is the unit, in
terms of which not only the distances in the sohir system are ex-
pressed, but which serves as a basis for measures in the stellar uni-
verse. Thus when we say that the distance of the nearext star is over
200,000 times the mean distance e.f tin- sun, it becomes necessary to see
if some conception can be obtained of one factor in this. Of the ab-
stract number, 92,500,000. we have no conception. It is far too
great for us to have counted. We have never taken in at one view
even a million similar discrete objects. The largest tree has less
than 500,000 leaves. To count from 1 to 200 requires with very
rapid counting, 60 seconds. Suppose this kept up for a day without
intermission ; at the end we should have counted 288.000, which is
about ,J ff of 92,500,000. Hence over 10 months' uninterrupted
counting by night and day would l>e required simply to enumerate
the number, and long before the expiration of the task all idea of it
would have vanished We may take other and perhaps more strik-
ing examples. We know, for instance, that the time of the fastest
express-trains between New York and Chicago, \\hich average 40
miles per hour, is about a day. Suppose such a train to start for the
sun and to continue running at this rapid rate. It would take 363
years for the journey. Three hundred and sixty-three years ago there
was not a European settlement in America.
A cannon-ball moving continuously across the intervening space
nt its highest speed would require about nine years to reach the sun.
The report of the cannon, if it could be conveyed to the sun with
the velocity of sound in air, would arrive there five years after the
projectile. Such a distance is entirely inconceivable, and yet it is
only a small fraction of those with which astronomy has to deal, even
in our own system. The distance of Neptune is 30 times as great.
If we examine the dimensions of the various orbs, we meet almost
equally inconceivable numbers. The diameter of the sun is 860.000
miles; its radius is but 430,000, and yet this is nearly twice the mean
distance of the moon from the enrth. Try to conceive, in looking at
the moon in a clear sky, that if the centre of the sun could be placed
at the centre of the earth, the moon would be far within the sun's
STRUCTURE OF THE SOLAR SYSTEM. 197
surface. Or again, conceive of the force of gravity at the surface of
the various bodies of the system. At the sun it is nearly 28 times
that known to us. A pendulum beating seconds here would, if
transported to the sun vibrate with a motion more rapid than that
of a watch-balance. The muscles of the strongest man would not
support him erect on the surface of the sun : even lying down he
would crush himself to death under his own weight of two tons.
We may by these illustrations get some rough idea of the meaning of
the numbers in these tables, :md of the incapability of our limited
ideas to comprehend the true dimensions of even the solar system.
198
ASTRONOMY.
STRUCTURE OF THE SOLAR SYSTEM.
199
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CHAPTER H.
THE SUN.
GENERAL SUMMARY.
To enable the nature of the phenomena of the sun to be
clearly understood, we preface our account of its physical
constitution by a brief summary of its main features.
Photosphere. To the simple vision the sun presents the
aspect of a brilliant sphere. The visible shining surface
of this sphere is called the photosphere, to distinguish it
from the body of the sun as a whole. The apparently flat
surface presented by a view of the photosphere is called the
sun's disk.
Spots. When the photosphere is examined with a tele-
scope, small dark patches of varied and irregular outline
are frequently found upon it. These are called the *olar
spots.
Rotation. "When the spots are observed from day to
day, they are found to move over the sun's disk from east to
west in such a way as to show that the sun rotates on its
axis in a period of "25 or 2G days. The sun, therefore, has
axis, poles, and equator, like the earth, the axis being the
line around which it rotates from west to east.
Facnlae. Groups of minute specks brighter than the
general surface of the sun are often seen in the neighbor-
hood of spots or elsewhere. They are called faculce.
THE kUN. 201
Chromosphere, or Sierra. The solar photosphere is cov-
ered by a layer of glowing vapors and gases of very irregu-
lar depth. At the bottom lie the vapors of many metals,
iron, etc., volatilized by the fervent heat which reigns
there, while the ripper portions are composed principally
of hydrogen gas. This vaporous atmosphere is commonly
called the chromosphere, sometimes the sierra. It is en-
tirely invisible to direct vision, whether with the telescope
or naked eye, except for a few seconds about the beginning
or end of a total eclipse, but it may be seen on any clear
day through the spectroscope.
Prominences, Protuberances, or Red Flames. The gases
of the chromosphere are frequently thrown up in irregular
masses to vast heights above the photosphere, it may be
50,000, 100,000, or even 200,000 kilometres. Like the
chromosphere, these masses have to be studied with the
spectroscope, and can never be directly seen except when
the sunlight is cut off by the intervention of the moon
during a total eclipse. They are then seen as rose-colored
flames, or piles of bright red clouds of irregular and fantas-
tic shapes.
Corona. During total eclipses the sun is seen to be en-
veloped by a mass of soft white light, much fainter than
the chromosphere, and extending out on all sides far be-
yond the highest prominences. It is brightest around the
edge of the sun, and fades off toward its outer boundary,
by insensible gradations. This halo of light is called the
corona, and is a very striking object during a total eclipse.
THE PHOTOSPHERE.
Aspect and Structure of the Photosphere. The disk of the snn is cir-
cular in shape, no matter what side of the sun's globe is turned to-
202
ASTRONOMY.
ward us, whence it follows that the sun itself is a sphere. The aspect
of the disk, when viewed with the naked eye, or with a telescope of
low power, is that of a uniform bright, shining surface, hence called
the photosphere. With a telescope of higher power the photosphere
is seen to be diversified with groups of spots, and under good con-
: t\*\"l?*&'' +'****< * *."' ;**'
1
;
!
;W:
Fia. 68. RETICULATED ARRANGEMENT OF THE SUN'S PHOTOSPHERE.
(From a photograph.)
ditions the whole mass has a mottled or curdled appearance. This
mottling is caused by the presence of cloud-like forms, whose out-
lines though faint are yet distinguishable. The background is also
covered with small white clots or forms still smaller than the clouds.
THE SUN. 203
These are the "rice-grains," so called. The clouds themselves are
composed of small, intensely bright bodies, irregularly distributed,
of tolerably definite shapes, which seem to be suspended in or super-
posed on a darker medium or background. The spaces between the
bright dots vary in diameter from 2" to 4" (about 1400 to 2800 kilo-
metres). The rice-grains themselves have been seen to be composed
of smaller granules, sometimes not more than 0".3 (135 miles) in
diameter, clustered together. Thus there have been seen at least
three orders of aggregation in the brighter parts of the photosphere:
the larger cloud-like forms; the rice-grains; and, smallest of all, the
granules.
Light and Heat from the Photosphere, The photosphere
is not equally bright all over the apparent disk. This is at
once evident to the eye in observing the sun with a tele-
scope. The centre of the disk is most brilliant, and the
edges or limbs are shaded off so as to forcibly suggest the
idea of an absorptive atmosphere, which, in fact, is the
cause of this appearance.
Such absorption occurs not only for the rays by which
we see the sun, the so-called visual rays, but for those
which have the most powerful effect in decomposing the
salts of silver, the so-called chemical rays, by which the
ordinary photograph is taken.
The amount of heat received from different portions of
the sun's disk is also variable, according to the part of the
apparent disk examined. This is what we should expect.
That is, if the intensity of any one of these radiations (as
felt at the earth) varies from centre to circumference, that
of every other should also vary, since they are all modifi-
cations of the same primitive motion of the sun's con-
stituent particles. But the constitution of the sun's at-
mosphere is such, that the law of variation for the three
classes is different. The intensity of the radiation in the
sun itself and inside of the absorptive atmosphere is prob-
204 ASTRONOMT.
ably nearly constant. The ray which leaves the centre
of the sun's disk in passing to the earth traverses the
smallest possible thickness of the solar atmosphere, while
the rays from points of the sun's body which appear to us
near the limbs pass, on the contrary, through the maxi-
mum thickness of atmosphere, and are thus longest sub-
jected to its absorptive action.
This is plainly a rational explanation, since the part of
the sun which is seen by us as the limb varies with the
position of the earth in its orbit and with the position of
the sun's surface in its rotation, and has itself no physical
peculiarity. The various absorptions of different (-hisses
of rays correspond to this supposition, the more refrangi-
ble rays, violet and blue, suffering most absorption, as they
must do, being composed of waves of shorter wave-length.
Amount of Heat Emitted by the Sun. Owing to the
absorption of the solar atmosphere, it follows that we re-
ceive only a portion perhaps a very small portion of
the rays emitted by the sun's photosphere.
If the sun had no absorptive atmosphere, it would seem
to us hotter, brighter, and more blue in color.
Exact notions as to how great this absorption is are hard
to gain, but it maybe said roughly that the best authorities
agree that although it is quite possible that the sun's at-
mosphere absorbs half the emitted rays, it probably does
not absorb four fifths of them.
The amount of this absorption is a practical question to
us on the earth. So long as the central body of the sun
continues to emit the same quantity of rays, it is plain that
the thickness of the solar atmosphere determines the num-
ber of such rays reaching the earth. If in former times
this atmosphere was much thicker, then less heat would
THE SUN. 205
have reached the earth. Glacial epochs may be explained
in this way. If the central body of the sun has likewise
had different emissive powers at different times, this again
would produce a variation in the temperature of the earth.
Amount of Heat Radiated. There is at present no way of determin-
ing accurately either the absolute amount of heat emitted from the
central body or the amount of this heat stopped by the solar atmos-
phere itself. All that can be done is to measure (and that only
roughly) the amount of heat really received by the earth, without
attempting to define accurately the circumstances which this radiation
has undergone before reaching the earth.
POUILLET has experimented upon this question, making allowance
for the time that the sun is below the horizon of any place, and for
the fact that the solar rays do not in general strike perpendicularly
but obliquely upon any given part of the earth's surface. His con-
clusions may be stated as follows : if our own atmosphere were re-
moved, the solar rays would have energy enough to melt a layer of
ice 9 centimetres thick over the whole earth daily, or a layer of about
32 metres thick in a year.
This action is constantly at work over the whole of the sun's sur-
face. To produce a similar effect by the combustion of coal would
require that a layer of coal 5 metres thick spread all over the sun
should be consumed every hour. This is equivalent to a continuous
evolution of 10,000 horse-power on every square foot of the sun's
surface. If the sun were of solid coal and produced its own heat by
combustion, it would burn out in 6000 years.
Of this enormous outflow of heat the earth receives only
FSOOO^OOOO- We have expressed the power of even this small frac-
tion of the sun's heat in terms of the ice it would melt daily. If we
compute how much coal it would require to melt the same amount,
and then further calculate how much work this coal would do, we
shall find that the sun sends to the earth an amount of heat which is
equivalent to one horse-power continuously acting for every 30
square feet of the earth's surface. Most of this is expended in main-
taining the earth's temperature; but a small portion, about yg^rr* is
stored away by animals and vegetables, and this slight fraction is
the source upon which the human race depends. If this were with-
drawn the race would perish.
Of the total amount of heat radiated by the sun the earth receives
but an insignificant share. The sun is capable of heating the entire
surface of a sphere whose radius is the earth's mean distance to the
206 ASTHONOMY.
same degree that the earth is now heated. The surface of such a
sphere is 2,170,000,000 times greater than the angular dimensions of
the earth as seen from the sun, and hence the earth receives less than
one two-billionth part of the solar radiation. The rest of the solar
rays are, so far as we know, lost in spun-.
Solar Temperature. From the amount of heat actually radiated by
the sun, attempts have been made to determine the actual tempera-
ture of the solar surface. The estimates reached by various authori-
ties differ widely, as the laws which govern the absorption within
the solar envelope are almost unknown. Some such law of absorp-
tion has to be supposed in any such investigation, and the estimates
have differed widely according to the adopted law.
SKCCHI e>timates this temperature at about 6,100,000 C. Other
estimates are far lower, but, according to all sound philosophy, the
temperature must far exceed any terrestrial temperature. There can
be no doubt that if the temperature of the earth's surface were sud-
denly raised to that of the sun, no single chemical element would re-
main in its present condition. The most refractory materials would
be at once volatili/.ed.
We may concentrate the heat received upon several square feet
(the surface of a huge burning-lens or mirror, for instance), examine
its effects at the focus, and, making allowance for the condensation
by the lens, see what is the minimum possible temperature of the
sun. The temperature at the focus of the lens cannot be higher than
that of the source of heat in the sun ; we can only concentrate the
heat received on the surface of the lens to one point and examine its
effects. If a lens three feet in diameter be used, the most refractory
materials, as fire-clay, platinum, the diamond, are at once melted or
volatilized. The effect of the lens is plainly the same as if the earth
were brought closer to the sun, in the ratio of the diameter of the
focal image to that of the lens. In the case of the lens of three feet,
allowing for the absorption, etc., this distance is yet greater than
that of the moon from the earth, so that it appears that any comet or
planet so close as this to the sun, if composed of materials similar to
those in the earth, must be vaporized.
SUN-SPOTS AND FACULJE.
A very cursory examination of the sun's disk with a small tele-
scope will generally show one or more dark spots upon the photo-
sphere. These are of various sizes, from minute black dots 1" or 2*
in diameter (1000 kilometres or less) to large spots several minutes
of arc in extent.
THE SUN.
207
Solar spots generally have a dark central nucleus or umbra, sur-
rounded by a border or penumbra of grayish tint, intermediate in
shade between the central blackness and the bright photosphere.
By increasing the power of the telescope, the spots are seen to be of
very complex forms. The umbra is often extremely irregular in
shape, and is sometimes crossed by bridges or ligaments of shining
matter. The penumbra is composed of filaments of brighter and
darker light, which are arranged in striae. The general aspect of a
spot under considerable magnifying power is shown in Fig. 59.
The first printed account of solar spots was given by FABRITIUS in
1611, and GALILEO in the same year (May, 1611) also described them.
FIG. 59. UMBRA AND PENUMBRA OF SUN-SPOT.
GALILEO'S observations showed them to belong to the sun itself, and
to move uniformly across the solar disk from east to west. A spot
just visible at the east limb of the sun on any one day travelled slow-
ly across the disk for 12 or 14 days, when it reached the west limb,
behind which it disappeared. After about the same period, it reap-
pears at the eastern limb, unless, as is often the case, it has in the
mean time vanished.
The spots are not permanent in their nature, but are formed some-
where on the sun, and disappear after lasting a few days, weeks, or
months. But so long as they last they move regularly from east to
west on the sun's apparent disk, making one complete rotation iu
208 ASTRONOMY.
about 25 days. This period of 25 days is therefore approximately
the rotation period of the sun itself.
Spotted Region. It is found that the spots are chiefly confined to
two zones, one in each hemisphere, extending from about 10 to 35
or 40 of heliographic latitude. In the polar region spots are
scarcely ever seen, and on the solar equator they are much more rare
than in latitudes 10 north or south. Connected with the spots, but
lying on or above the solar surface, are fticufa, moltlings of light
brighter lhan the general surface of the sun.
Fio. 60. PHOTOGRAPH OF THE Rrx.
Solar Axis and Equator. The spots must revolve with the surface
of the sun about his axis, and the directions of their motions must be
approximately parallel to his equator. Fig. 61 shows the appear-
ances as actually observed, the dotted lines representing the apparent
paths of the spots across the sun's disk at different times of the year.
In June and December these paths, to an observer on the earth, seem
to be right lines, and hence at these times the observer must be in the
plane of the solar equator. At other times the paths are ellipses, and
in March and September the planes of these ellipses are most oblique,
showing the spectator to be then furthest from the plane of the solar
equator. The inclination of the solar equator to the ecliptic is about
7 9', and the axis of rotation is of course perpendicular to it.
THE SUN.
209
Nature of the Spots. The sun-spots are really depres
sions in the photosphere, as was first pointed out by Atf-
DREW WILSON of Glasgow in 1 774. When a spot is seen at
the edge of the disk, it appears as a notch in the limb, and is
FIG. 61. APPARENT PATH OF SOLAR SPOT AT DIFFERENT SEASONS.
elliptical in shape. As the rotation carries it further and
further on to the disk, it becomes more and more nearly
circula-r in shape, and after passing the centre of the disk
the appearances take place in reverse order.
These observations were explained by WILSON, and more fully by
Sir WILLIAM HE$SCHEL, by supposing the sun to consist of an in.
210
ASTRONOMY.
terior dark cool mass, surrounded by two layers of clouds. The
outer layer, which forms the visible photosphere, was supposed ex-
tremely brilliaut. The iuuer layer, which could not be seen except
when a cavity existed in the photosphere, was supposed to be dark.
The appearance of the edges of a spot, which has been described as
the penumbra, was supposed to arise from those dark clouds. The
spots themselves are, according to this view, nothing but openings
through both of the atmospheres, the nucleus of the spot being simply
the black surface of the inner sphere of the sun itself.
This theory, Fig. 62, accounts for the facts as they were known
FIG. 62. APPEARANCE OF A SPOT NKAR THE LIMB AND NEAR THE
CENTRE OF THE SUN.
to HERSCHEL. But when it is confronted with the questions of the
cause of the sun's heat and of the method by which this heat has
been maintained constant in amount for centuries, it breaks down
completely. The conclusions of WILSON and HERSCHEL, that the
spots are depressions in the sun's surface, are undoubted. But the
existence of a cool central and solid nucleus to the sun is now
known to be impossible. The apparently black centres of the spots
are so mostl3 r by contrast. If they were seen against a perfectly
black background, they would appear very bright, as has been
proved by photometric measures. And a cool solid nucleus beneath
TEE SUN.
VC*5f .
.*f
Bucli an atmosphere as HERSCHEL supposed would soon become gas-
eous by the conduction and radiation of the heat of the photosphere.
The supply of solar heat, which has been very nearly constant dur-
ing the historic period, in a sun so constituted would have sensibly
diminished in a few hundred years. For these and other reasons
the hypothesis of HEHSCHEL must be modified, save as to the fact
that the spots are really cavities in the photosphere.
Number and Periodicity of Solar Spots. The number of
solar spots which come into view varies from year to year.
Although at first sight this might seem to be what we call
a purely accidental circumstance, like the occurrence of
cloudy and clear years on the earth, observations of sun-
spots establish the fact that this number varies periodically.
The periodicity of the spots will appear from the following sum-
mary:
From 1828 to 1831 the sun was without spots on only 1 day.
In 1833 " " " 139 days.
From 1836 to 1840 " " " 3 "
In 1843 " " " 147 "
From 1847 to 1851 " " " 2 "
In 1856 " " " 193 "
From If 58 to 1861 " " " no day.
In 1867 " " " 195 days.
Every 11 years there is a minimum number of spots, and about 5
years after each minimum there is a maximum. If, instead of mere-
ly counting the number of spots, measurements arc made on solar
photographs of the extent of spotted area, the period comes out with
greater distinctness. This periodicity of the area of the solar spots
appears to be connected with magnetic phenomena on the earth's
surface, and with the number of auroras visible. It has been sup-
posed to be connected also with variations of temperature, of rain-
fall, and with other meteorological phenomena such as the monsoons
of the Indian Ocean, etc. The cause of this periodicity is as yet un-
known. It probably lies within the sun itself, and is similar to the
cause of the periodic action of a geyser. As the periodic variations
of the spots correspond to variations of the magnetic needle on the
earth, it appears that there is a connection of an unknown nature
between the sun and the earth..
212 ASTRONOMY.
THE SUN'S CHROMOSPHERE AND CORONA.
Phenomena of Total Eclipses. The beginning of a total solar
eclipse is marked simply by the small black notch made in the
luminous disk of the sun by the advancing edge or limb of the
moon. This always occurs on the western half of the sun, as the
moon moves from west to east in ils orbit. An hour or more must
elapse before the moon has advanced sufficiently far in its orbit to
cover the sun's disk. During this time the disk of the sun is gradu-
ally hidden until it becomes a thin crescent.
The actual amount of the sun's light may be diminished to two
thirds or three fourths of its ordinary amount without its being
strikingly perceptible to the eye. What is first noticed is the change
which takes place in the color of the surrounding landscape, which
begins to wear a ruddy aspect. This grows more and more pro-
nounced, and gives to the adjacent country that weird effect which
lends so much to the impress! vcness of a total eclipse. The reason
for the change of color is simple. We have already said that the
sun's atmosphere absorbs a large proportion of the bluer rays, nnd as
this absorption is dependent on the thickness of the solar atmosphere
through which the rays must pass, it is plain that just before the sun
is totally covered the rays by which we see it will be redder than
ordinary sunlight, as they are those which come from points near
the sun's limb, where they have to pass through the greatest thick-
ness of the sun's atmosphere.
The color of the light becomes more and more lurid up to the mo-
ment when the sun has nearly disappeared. If the spectator is upon
the top of a high mountain, he can then begin to see the moon's
shadow rushing toward him at the rate of a kilometre in about a
second. Just as the shadow reaches him there is a sudden increase
of darkness; the brighter stars begin to shine in the dark lurid sky,
the thin crescent of the sun breaks up into small points or dots of
light, which suddenly disappear, and the moon itself, an intensely
black ball, appears to hang isolated in the heavens.
An instant afterward the corona is seen surrounding the black
disk of the moon with a soft effulgence quite different from any
other light known to us. Near the moon's limb it is intensely bright,
and to the naked eye uniform in structure; 5' or KX from the limb
this inner corona has a boundary more or less defined, and from this
extend streamers and wings of fainter and more nebulous light.
These are of various shapes, sizes, and brilliancy. No two solar
eclipses yet observed have been alike in this respect.
THE SUN. 213
These appearances, though changeable, do not change in the time
the moon's shadow requires to pass from Vancouver's Island to
Texas, for example, which is some fifty minutes.
Superposed upon these wings may be seen (sometimes with the
naked eye) the red flames or protuberances which were first discov-
ered during a solar eclipse. These need not be more closely de-
scribed here, as they can now be studied at any time by aid of the
spectroscope.
The total phase lasts for a few minutes (never more than six or
seven), and during this time, as the eye becomes more and more
accustomed to the faint light, the outer corona is seen to stretch
further and further away from the sun's limb. At the eclipse of 1878,
July 29th, it was seen to extend more than 6 (about 9,000,000 miles)
from the sun's limb. Just before the end of the total phase there is
a sudden increase of the brightness of the sky, due to the increased
illumination of the earth's atmosphere near the observer, and in a
moment more the sun's rays are again visible, seemingly as bright as
ever. From the end of totality till the last contact the phenomena
of the first half of the eclipse are repeated in inverse order.
Telescopic Aspect of the Corona, Such are the appearances to the
naked eye. The corona, as seen through a telescope, is, however,
of a very complicated structure. The inner corona is usually com-
posed of bright striae or filaments separated by darker bands, and
some of these latter are sometimes seen to be almost totally black.
The appearances are extremely irregular, but they are often as if the
inner corona were made up of brushes of light on a darker back-
ground.
The corona and red prominences are solar appendages. It was
formerly doubtful whether the corona was an atmosphere belonging
to the sun or to the moon. At the eclipse of 1860 it was proved by
measurements that the red prominences belonged to the sun and not
to the moon, since the moon gradually covered them by its motion,
they remaining attached to the sun. The corona has also since been
shown to be a solar appendage.
Gaseous Nature of the Prominences. The eclipse of 1868 (July)
was total in India, and was observed by many skilled astronomers.
A discovery of M. JANSSEN'S will make this eclipse forever memora-
ble. He was provided with a spectroscope, and by it observed the
prominences. One prominence in particular was of vast size, and
when the spectroscope was turned upon it, its spectrum was discon-
tinuous, showing the bright lines of hydrogen gas.
The brightness of the spectrum was so marked that JANSSEN deter-
mined to keep his spectroscope fixed upon it even after the reappear-
214
ASTRONOMY.
Fid. 63. SUN'S CORONA DURING THK ECLIPSE OF JULY 29, 1878.
THE SUN.
ance of sunlight, to see how long it could be followed. It was found
that its spectrum could still be seen after the return of complete sun-
light; and not only on that day, but on subsequent days, similar
phenomena could be observed.
One great difficulty was conquered in an instant. The red flames
which formerly were only to be seen for a few moments during the
comparatively rare occurrences of total eclipses, and whose observa-
tion demanded long and expensive journeys to distant parts of the
world, could now be regularly observed with all the facilities offered
by a fixed observatory.
This great step in advance was independently made by Mr. LOCK-
Fia. 64. FORMS OF THE SOLAR PROMINENCES AS SEEN WITH THE SPECTROSCOPE.
YER, and his discovery was derived from pure theory, unaided by the
eclipse itself. By this method the prominences have been carefully
mapped day by day all around the sun, and it has been proved that
around this body there is a vast atmosphere of hydrogen gas the
chromosphere or sierra. From out of this the prominences are pro-
jected sometimes to heights of 100,000 kilometres or more.
It will be necessary to recall the main facts of observation which
are fundamental in the use of the spectroscope. When a brilliant
point is examined with the spectroscope, it is spread out by the prism
into a band the spectrum. Using two prisms, the spectrum be-
comes longer, but the light of the surface, being spread over a
216 ASTRONOMY.
greater area, is enfeebled. Three, four, or more prisms spread out
the spectrum proportionally more. If the spectrum is of an incan-
descent solid or liquid, it is always continuous, and it can be en-
feebled to any degree ; so that any part of it cau be made as feeble as
desired.
This method is precisely similar in principle to the use of the tele-
scope in viewing stars in the daytime. The telescope lessens the
brilliancy of the sky, while the disk of the star is kept of the same
intensity, as it is a point in itself. It thus becomes visible. The
spectrum of a glowing gas will consist of a definite number of lines,
say three A, B, C, for example. Now suppose the spectrum of this
gas to be superposed on the continuous spectrum of the sun; by
using only one prism, the solar spectrum is short and brilliant, and
every part of it may be more brilliant than the line spectrum of the gas.
By increasing the dispersion (the number of prisms), the solar spec-
trum is proportionately enfeebled. If the ratio of the light of the
bodic- ihrmxrlves. the sun and the gas, is not too great, the continu-
ous spectrum may be so enfeebled that the line spectrum will be
visible when superposed upon it, and the spectrum of the gas may
then be seen even in the presence of true sunlight. Such was the
process imagined and successfully carried out by Mr. LOCKYER, and
such is in essence the method of viewing the prominences to-day
adopted.
The Coronal Spectrum. In 1869 (August 7th) a total solar eclipse
was visible in the United States. It was probably observed by more
astronomers than any preceding eclipse. Two American astron-
omers, Professor YOUNG, of Dartmouth College, and Professor HARK-
NE88, of the Naval Observatory, especially observed the spectrum of
the corona. This spectrum was found to consist of one faint green-
ish line crossing a faint continuous spectrum. The place of this line
in the maps of the solar spectrum published by KIRCHHOFF was oc-
cupied by a line which he had attributed to the iron spectrum, and
which had been numbered 1474 in his list, so that it is now spoken
of as 1474 K. This line is probably due to some gas which must be
present in large and possibly variable quantities in the corona, and
which is not known to us on the earth, in this form at least. It is
probably a gas even lighter than hydrogen, as the existence of this
line has been traced KX or 30' from the sun's limb nearly all around
the disk.
In the eclipse of July 29th, 1878, which was total in Colorado and
Texas, the continuous spectrum of the corona was found to be
crossed by the dark lines of the solar spectrum, showing that the
coronal light was composed in part of reflected sunlight.
TRE StTtf. 217
SOURCES OF THE SUN'S HEAT.
Theories of the Sun's Constitution. No considerable
fraction of the heat radiated from the sun returns to it
from the celestial spaces. But we know the sun is daily
radiating into space 2,170,000,000 times as much heat as
is daily received by the earth, and it follows that unless
the supply of heat is infinite (which we cannot believe) this
enormous daily radiation must in time exhaust the supply.
When the supply is exhausted,, or even seriously trenched
upon, the result to the inhabitants of the earth will be fatal.
A slow diminution of the daily supply of heat would pro-
duce a slow change of climates from hotter toward colder.
The serious results of a fall of 50 in the mean annual tem-
perature of the earth will be evident when we remember
that such a fall would change the climate of France to that
of Spitzbergen. The temperature of the sun cannot be
kept up by the mere combustion of its materials. If the
sun were solid carbon, and if a constant and adequate supply
of oxygen were also present, it has been shown that, at the
present rate of radiation, the heat arising from the com-
bustion of the mass would not last more than 6000 years.
An explanation of the solar heat and light has been suggested,
which depends upon the fact that great amounts of heat and light
are produced by the collision of two rapidly moving heavy bodies,
or even by the passage of a heavy body like a meteorite through the
earth's atmosphere. In fact, if we had a certain mass available with
which to produce heat in the sun, and if this mass were of the best
possible materials to produce heat by burning, it can be shown that,
by burning it at the surface of the sun, we should produce vastly
less heat than if we simply allowed it to fall into the sun. In the
last case, if it fell from the earth's distance, it would give 6000 times
more heat by its fall than by its burning.
The least velocity with which a body from space could fall upon
the sun's surface is in the neighborhood of 280 miles in a second of
ASTRONOMY.
time, and the velocity may be as great as 350 miles. The meteoric
theory of solar heat is in effect that the heat of the sun is kept up by
the impact of meteors upon its surface.
No doubt immense numbers of meteorites fall into the sun daily
and hourly, and to each one of them a certain considerable portion
of heat is due. It is found that, to account for the present amount of
radiation, meteorites equal in mass to the whole earth would have to
fall into the sun every century. It is extremely improbable that a
mass one tenth as large as this is added to the sun in this way per
century, if for no other reason because the earth itself and every
planet would receive far more than its present share of meteorites,
and would become quite hot from this cause alone.
There is still another way of accounting for the sun's constant
supply of energy, and this has the advantage of appealing to no cause
outside of the sun itself in the explanation. It is by supposing the
heat, light, etc., to be generated by a constant and gradual contrac-
tion of the dimensions of the solar sphere. As the globe cools by
radiation into space, it must contract. In so contracting its ultimate
constituent parts are drawn nearer together by their mutual attrac-
tion, whereby a form of energy is developed which can be trans-
formed into heat, ligh*. electricity, or other physical forces.
This theory is in complete agreement with the known laws of
force. It also admits of precise comparison with facts, since the
laws of heat enable us, from the known amount of heat radiated, to
infer the exact amount of contraction in inches which the linear
dimensions of the sun must undergo in order that this supply of heat
may be kept unchanged, as it is practically found to be. With the
present size of the sun, it is found that it is only necessary t<> sup-
pose that its diameter is diminishing at the rate of about 220 feet per
year, or 4 miles per century, in order that the supply of heat radiated
shall be constant. It is plain that such a change us this may be
taking place, since we possess no instruments sufficiently delicate to
have detected a change of even ten times this amount since the in-
vention of the telescope.
It may seem a paradoxical conclusion that the cooling of a body
may cause it to become hotter. This indeed is true only when we
suppose the interior to be gaseous, and not solid or liquid. It is,
however, proved by theory that this law holds for gaseous masses.
We cannot say whether the sun has yet begun to liquefy
in his interior parts, and hence it is impossible to predict
at present the duration of his constant radiation. Theory
THE SVtf. 219
shows us that after about 5,000,000 years, the sun radiat-
ing heat as at present, and still remaining gaseous, will be
reduced to one half of his present volume. It seems prob-
able that somewhere about this time the solidification will
have begun, and it is roughly estimated, from this line of
argument, that the present conditions of heat radiation
cannot last greatly over 10,000,000 years.
The future of the sun (and hence of the earth) cannot,
as we see, be traced with great exactitude. The past can
be more closely followed if we assume (which is tolerably
safe) that the sun up to the present has been a gaseous and
not a solid or liquid mass. Four hundred years ago, then,
the sun was about 16 miles greater in diameter than now;
and if we suppose this process of contraction to have regu-
larly gone on at the same rate (an uncertain supposition),
we can fix a date when the sun filled any given space, out
even to the orbit of Neptune; that is, to the time when
the solar system consisted of but one body, and that a gas-
eous or nebulous one. It will subsequently be seen that
the ideas here reached a posteriori have a striking analogy
to the a priori ideas of KANT and LA PLACE.
It is not to be taken for granted, however, that the
amount of heat to be derived from the contraction of the
sun's dimensions is infinite, no matter how large the prim-
itive dimensions may have been. A body falling from any
distance to the sun can only have a certain finite velocity
depending on this distance and the mass of the sun itself,
which, even if the fall be from an infinite distance, cannot
exceed, for the sun, 350 miles per second. In the same
way the amount of heat generated by the contraction of the
sun's volume from any size to any other is finite and not
infinite.
220 ASTRONOMY.
It has been shown that if the sun has always been radi-
ating heat at its present rate, and if it had originally filled
all space, it has required 18,000,000 years to contract to its
present volume. In other words, assuming the present
rate of radiation, and taking the most favorable case, the
age of the sun does not exceed 18,000,000 years. The
earth is, of course, less aged. The supposition lying at
the base of this estimate is that the radiation of the sun
has been constant throughout the whole period. This is
quite unlikely, and any changes in this datum affect greatly
the final number of years which we have assigned. While
this number may be greatly in error, yet the method of
obtaining it seems, in the present state of science, to be
satisfactory, and the main conclusion remains that the past
of the sun is finite, and that in all probability its future is
a limited one. The exact number of centuries that it is to
last are of no moment even were the data at hand to obtain
them: the essential point is that, so far as we can see, the
sun, and incidentally the solar system, has a finite past and
a limited future, and that, like other natural objects, it
passes through its regular stages of birth, vigor, decay, and
death, in one order of progress.
CHAPTER III.
THE INFERIOR PLANETS.
MOTIONS AND ASPECTS.
THE inferior planets are those whose orbits lie between the sun
and the orbit of the earth. Commencing with the more distant ones,
they comprise Venus and Mercury.
The real and apparent motions of these planets have already been
briefly described in Part I., Chapter V. It will be remembered that,
in accordance with KEPLER'S third law, their periods of revolution
around the sun are less than that of the earth. Consequently they
overtake the latter between successive inferior conjunctions.
The interval between these
conjunctions is about four
months in the case of Mer-
cury, and between nineteen
and twenty months in that of
Venus. At the end of this
period each repeats the same
series of motions relative to
the sun. What these motions
are can be readily seen by
studying Fig. 65. In the first
place, suppose the earth at
any point, E, of its orbit, and
if we draw a line, E L or
EM, from E, tangent to the
P IG
orbit of either of these planets,
it is evident that the angle
which this line makes with that drawn to the sun is the greatest
elongation of the planet from the sun. The orbits being eccentric,
this elongation varies with the position of the earth. In the case
of Mercury it ranges from 16 to 29, while in the case of Venus, the
orbit of which is nearly circular, it varies very little from 45. These
planets, therefore, seem to have an oscillating motion, first swinging
ABTRONOMT.
toward the east of the sun, and then toward the west of it, as already
explained. Since, owing to the annual revolution of the earth, the
sun has a constant eastward motion among the stars, these planets
must have, on the whole, a corresponding though intermittent motion
in the same direction. Therefore the ancient astronomers supposed
their period of revolution to be one year, the same as that of the
sun.
If, again, we draw a line E S C from the earth through the sun, the
point /, in which this line cuts the orbit of the planet, or the point
of inferior conjunction, will be the least distance of the planet from
the earth, while the second point C,
or the point of superior conjunction,
on the opposite side of the sun, will
be the irreatc-t di>laiirc. Owing to
the difference of ihe>e distances the
apparent magnitude, of these planets,
as seen from the earih, is subject to
Fio. 66. APPARENT MAGNITUDES great variations.
OF THE DIS* OF MEBCURT. j,^ ,.,. ^^ j,,^ variut ionS ill tllO
case of Mercury, A representing its apparent magnitude when at its
greatest distance, B when at its mean distance, and C when at its
least distance. In the case of Venus (Fig. C7) the variations are much
greater than in that of Mercury, the greatest distance, 1.72, being
more than six times the least distance, which is only 0.28. The
variations of apparent magnitude are therefore great in the same
proportion.
In thus representing the apparent angular magnitude of these
planets, we suppose their whole disks to be visible, as they would be
if they shone by their own light. But since they can be seen only by
the reflected light of the sun, only those portions of the disk can be
seen which are at the same time visible from the sun and from the
earth. A very little consideration will show that the proportion of
the disk which can be seen constantly diminishes as the planet ap-
proaches the earth, and looks larger.
When the planet is at its greatest distance, or in superior conjunction
(C, Fig. 65), its whole illuminated hemisphere can be seen from the
earth. As it moves around and approaches the earth, the illuminated
hemisphere is gradually turned from us. At the point of greatest
elongation, M or L, one half the hemisphere is visible, and the
planet has the form of the moon at first or second quarter. As it
approaches inferior conjunction, the apparent visible disk assumes
the form of a crescent, which becomes thinner and thinner as the
planet approaches the sun.
THE INFERIOR PLANETS.
223
Fi?. 68 shows the apparent disk of Mercury at various times during
its synodic revolution. The planet will appear brightest when this
disk has the greatest surface. This occurs about half way between
greatest elongation and inferior conjunction.
In consequence of the changes in the brilliancy of these planets
produced by the variations of distance, and those produced by the
FIG. 67. APPARENT MAGNITUDES OF THE DISK OF VENUS.
variations in the proportion of illuminated disk visible from the
earth, partially compensating each other, their actual brilliancy is
not subject to such great variations as might have been expected.
As a general rule, Mercury shines with a light exceeding that of a
star of the first magnitude. But owing to its proximity to the sun,
A
> >
< cc
FIG. 68. APPEARANCE OP MERCURY AT DIFFERENT POINTS OF ITS ORBIT.
it can never be seen by the naked eye except in the west a short time
after sunset, and in the east a little before sunrise. It is then of
necessity near the horizon, and therefore does not seem so bright as
if it were at a greater altitude. In our latitudes we might almost
say that it is never visible except in the morning or evening twilight
224 ASTRONOMY.
On the other hand, the planet Venn* is, next to the sun and moon,
the most brilliant object in the heavens. It is so much brighter
than any fixed star that there can seldom be any difficulty in identi-
fying it. The unpractised observer might under some circumstances
find a difficulty in distinguishing between Venus and Jupiter, but
the different motions of the two planets will enable him to distin-
guish them if they are watched from night to night during several
weeks.
ATMOSPHERE AND ROTATION OF MERCURY.
The various phases of Mercury, as dependent upon its various
positions relative to the sun. have already 1> n shown. If the planet
were an opaque sphere, without inequalities and without an atmos-
phere, the apparent disk would always be bounded by a circle on
one side and an ellipse on the other, as represented in the figure.
Whether any variation from this simple and perfect form has ever
been detected is an open question, the balance of evidence being very
strongly in the negative. Since no spots are visible upon it, it would
follow that unless variations of form due to inequalities on its sur-
face, such as mountains, can be detected, it is impossible to deter-
mine whether the planet rotates on its axis.
We may regard it as doubtful whether any evidence of an atmos-
phere of Mercury has been obtained, and it is certain that we know
nothing definite respecting its physical constitution.
ATMOSPHERE AND ROTATION OF VENUS.
As Venus sometimes comes nearer the earth than any other pri-
mary planet, astronomers have examined its surface with great at-
tention ever since the invention of the telescope. But no conclusive
evidence respecting the rotation of the planet and no proof of any
changes or any inequalities on its surface have ever been obtained.
Atmosphere of Venus. The evidence of an atmosphere of Venus is
perhaps more conclusive than in the case of any other planet.
When Venus is observed very near its inferior conjunction, and
when it therefore presents the view of a very thin crescent, it is
found that this crescent extends over more than 180. This would
be evidently impossible unless the sun illuminated more than one
half the planet. We therefore conclude that Venus has an atmos-
phere which exercises so powerful a refraction upon the light of the
sun that the latter illuminates several degrees more than one half the
globe. A phenomenon which must be attributed to the same cause
has several times been observed during transits of Venus. During
THE INFERIOR PLANETS. 225
the transit of December 8th, 1874, most of the observers who enjoyed
a fine steady atmosphere saw that when Venus was partially pro-
jected on the sun, the outline of that part of its disk outside the sun
could be distinguished by a delicate line of light. From these
several observations it would seem that the refractive power of the
atmosphere of Venus is greater than that of the earth.
TRANSITS OF MERCURY AND VENUS.
When Mercury or Venus passes between the earth and sun, so as
to appear projected on the sun's disk, the phenomenon is called a
transit. If these planets moved around the sun in the plane of the
ecliptic, it is evident that there would be a transit at every inferior
conjunction.
The longitude of the descending node of Mercury at the present
time is 227, and therefore that of the ascending node 47. The
earth has these longitudes on May 7th and November 9th. Since a
transit can occur only within a few degrees of a node, Mercury can
transit only within a few days of these epochs.
The longitude of the descending node of Venus is now about 256*
and therefore that of the ascending node is 76. The earth has these
longitudes on June 6th and December 7th of each year. Transits of
Venus can therefore occur only within two or three days of these
times.
Recurrence of Transits of Mercury. The following table shows the
dates of occurrence of transits of Mercury during the present cen-
tury. They are separated into May transits, which occur near the
descending node, and November ones, which occur near the ascend-
ing node. November transits are the most numerous, because
Mercury is then nearer the sun, and the transit limits are wider.
1799, May 6. 1802, Nov. 9.
1832, May 5. 1815, Nov. 11.
1845, May 8. 1822, Nov. 5.
1878, May 6. 1835, Nov. 7.
1891, May 9. 1848, Nov. 10.
1861, Nov. 12.
1868, Nov. 5.
1881, Nov. 7.
1894, Nov. 10.
Recurrence of Transits of Venus. For many centuries past and to
come, transits of Venus occur in a cycle more exact tlian those of
ASTRONOMY.
Mercury. It happens that Venut makes 13 revolutions around the
sun in nearly the same lime that the earth makes 8 revolutions; that
is, in eight years. During this period tiiere will be 5 inferior con-
junctions of Venus, because the latter has made 5 revolutions more
than the earth. Consequently, if we wait eight years from an inferior
conjunction of Venus, we shall, at the end of that time, have another
inferior conjunction, the fifth in regular order, at nearly the same
point of the two orbits. It will, therefore, occur at the same time
of the year, ami in nearly the same position relative to the node of
Venus.
After a pair of transits 8 years apart, an interval of over 100 years
must elapse before the occurrence of another pair as is shown in the
following table. The dates and intervals of the transits for three
cycles nearest to the present time are as follows:
1518, June 2.
1761, June 5.
2004, June 8
Intervals.
8 years.
1526, June 1.
1769, June 3.
2012, June 6.
105* '
1631, Dec. 7.
1874, Dec. 9.
2117, Dec. 11.
8 "
163V, Dec. 4.
1882, Dec. 6.
2125, Dec. 8
121i "
SUPPOSED INTEAMERCUEIAL PLANETS.
Some astronomers are of opinion that there is a small planet or
a group of planets revolving around the sun inside the orbit of
Mercury. To this supposed planet the name Vulcan has been given;
but astronomers generally discredit the existence of any such planet
of considerable size.
The evidence in favor of the existence of such planets may be
divided into three classes, as follows, which will be considered in
their order:
(1) A motion of the perihelion of the orbit of Mercury, supposed
to be due to the attraction of such a planet or group of plunets.
(2) Transits of dark bodies across the disk of the sun which have
been supposed to be seen by various observers during the past cen-
tury.
(3) The observation of certain unidentified objects by Professor
WATSON and Mr. LEWIS SWIFT during the total eclipse of the sun,
July 29th, 1878.
(1) In 1858 LE VERRIER made a careful collection of all the obser-
vations on the transits of Mercury which had been recorded since the
invention of the telescope. The result of that investigation was
THE INFERIOR PLANETS. 227
that the observed times of transit could not be reconciled with the
calculated motion of the planet, as due to the gravitation of the
other bodies of the solar system. He found, however, that if, in
addition to the changes of the orbit due to the attraction of the
known planets, he supposed a motion of the perihelion amounting to
36" in a century, the observations could all be satisfied. Such a
motion might be produced by the attraction of an unknown planet
inside the orbit of Mercury. Since, however, a single planet, in
order to produce this effect, would have to be of considerable size,
and since no such object had ever been observed during a total
eclipse of the sun, he concluded that there was probably a group of
planets much too small to be separately distinguished.
(2) It is to be noted that if such planets existed they would fre-
quently pass over the disk of the sun. During the past fifty years
the sun has been observed almost every day with the greatest $
assiduity by eminent observers, armed with powerful instruments,
who have made the study of the sun's surface and spots the principal
work of their lives. None of these observers has ever recorded the
transit of an unknown planet. This evidence, though negative in
form, is, under the circumstances, conclusive against the existence
of such a planet of such magnitude as to be visible in transit with
ordinary instruments.
(3) The observations of Professor WATSON during the total eclipse
above mentioned seem to afford the strongest evidence yet obtained
in favor of the real existence of the planet. His mode of proceeding
was briefly this: Sweeping to the west of the sun during the eclipse,
he saw two objects in positions where, supposing the pointing of his
telescope accurately known, no fixed star existed. There is, how-
ever, a pair of known stars, one of which is about a degree distant
from one of the unknown objects, and the other about the same
distance and direction from the second. It is probable that Professor
WATSON'S supposed planets were this pair of stars.
Since the above was written Prof. WATSON'S observations have
been repeated under exceptionally favorable circumstances at the
eclipse of May 6, 1883, and no trace of his supposed planets was seen,
while much smaller stars were observed.
CHAPTER IV.
THE MOON.
WHEN it became clearly understood that the earth and
moon were to be regarded as bodies of one class, and that
the old notion of an impassable gulf between the character
of bodies celestial and bodies terrestrial was unfounded,
the question whether the moon was like the earth in all its
details became one of great interest. The point of most
especial interest was whether the moon could, like the
earth, be peopled by intelligent inhabitants. Accordingly,
when the telescope was invented by GALILEO, one of the
first objects examined was the moon. With every im-
provement of the instrument the examination became
more thorough, so that at present the topography of the
moon is much better known than that of the State of
Arkansas, for example.
With every improvement in the means of research, it
has become more and more evident that the surface of the
moon is totally unlike that of our earth. There are no
oceans, seas, rivers, air, clouds, or vapor. We can hardly
suppose that animal or vegetable life exists under such cir-
cumstances, the fundamental conditions of such existence
on our earth being entirely wanting. We might almost as
well suppose a piece of granite or lava to be the abode of
life as the surface of the moon.
The length of one mile on the moon would. t as seen from
THE MOON. 229
the earth, subtend an angle of about Y of arc. More
exactly, the angle subtended would range between O ff .8 and
0*.9, according to the varying distance of the moon. In
order that an object may be plainly visible to the naked
eye, it must subtend an angle of nearly 1'. Consequently
a magnifying power of 60 is required to render a round
object one mile in diameter on the surface of the moon
plainly visible. Starting from this fact, we may readily
form the following table, showing the diameters of the
smallest objects that can be seen with different magnifying
powers, always assuming that vision with these powers is
perfect:
Power 60; diameter of object 1 mile.
Power 150; diameter 2000 feet.
Power 500; diameter 600 feet.
Power 1000; diameter 300 feet.
Power 2000; diameter 150 feet.
If telescopic power could be increased indefinitely, there
would of course be no limit to the minuteness of an object
visible on the moon's surface. But the necessary imper-
fections of all telescopes are such that only in extraordinary
cases can anything be gained by increasing the magnifying
power beyond 1000. The influence of warm and cold cur-
rents in our atmosphere will forever prevent the advan-
tageous use of high magnifying powers. After a certain
limit we see nothing more by increasing the power, vision
becoming indistinct in proportion as the power is increased.
It is hardly likely that an object less than 600 feet in extent
can ever be seen on the moon by any telescope whatever,
unless it becomes possible to mount the instrument above
the atmosphere of the earth. It is therefore only the great
features on the surface of the moon, and not the minute
ones, which can be made out with the telescope.
230
ASTRONOMY.
FIG. 69. ASPECT OF THB MOON'S SURFACE.
Character of the Moon's Surface. The most striking point of
ference between the earth and moon is seen in the total absence *
the latter of anything that looks like an undulating surface.
MOON.
formations similar to our valleys and mountain-chains have been
detected. The lowest surface of the moon which can be seen with
the telescope appears to be nearly smooth and flat, or, to speak
more exactly, spherical (because the moon is a sphere). This sur-
face has different shades of color in different regions. Some por-
tions are of a bright silvery tint, while others have a dark gray ap-
pearance. These differences of tint seem to arise from differences of
material.
Upon this surface as a foundation are built numerous formations
of various sizes, but all of a very simple character. Their general
form can be made out by the aid of Fig. 69, and their dimensions by
the scale of miles at the bottom of it. The largest and most promi-
nent features are known as craters. They have a typical form con-
sisting of a round or oval rugged wall rising from the plane in the
manner of a circular fortification. These walls are frequently from
three to six thousand metres in height, very rough and broken. In
their interior we see the plane surface of the moon already described.
It is, however, generally covered with fragments or broken up by
small 'inequalities so as not to be easily made out. In the centre of
the craters we frequently find a conical formation rising up to a con-
siderable height, and much larger than the inequalities just described.
In the craters we have a vague resemblance to volcanic formations
upon the earth, the principal difference being that their magnitude is
very much greater than anything known here. The diameter of the
larger ones ranges from 50 to 200 kilometres, while the smallest are
so minute as to be hardly visible with the telescope.
When the moon is only a few days old, the sun's rays strike very
obliquely upon the lunar mountains, and they cast long shadows.
'from the known position of the sun, moon, and earth, and from the
measured length of these shadows, the heights of the mountains can
be calculated. It is thus found that some of the mountains near the
south pole rise to a height of 8000 or 9000 metres (from 25,000 or 30,000
. feet) above the general surface of the moon. Heights of from 3000
to 7000 metres are very common over almost the whole lunar surface.
; The question of the origin of the lunar features has a bearing on
theories of terrestrial geology as well as upon various questions re-
specting the past history of the moon itself. It has been considered
'"\ this aspect by various geologists.
"unar Atmosphere. The question whether the moon has an atmos-
are has been much discussed. The only conclusion which has yet
n reached is that no positive evidence of an atmosphere has ever
an obtained, and that if one exists it is certainly several hundred
A )S rarer than the atmosphere of our earth.
232 ASTRONOMY.
Light and Heat of the Moon. Many attempts have been made to
measure the ratio of the light of the full moon and that of the sun.
The results have been very discordant, but all have agreed in show-
ing that the sun emits several hundred thousand times as much light
as the full moon. The last and most careful determination is that of
ZOLLNER, who finds the sun to be 618,000 times as bright as the full
moon.
The moon must reflect the heat as well as the light of the sun, and
must also radiate a small amount of its own heat. The latest re-
searches indicate that the amount received by the earth is inappre-
ciable.
Is there any Change on the Surface of the Moon t When the sur-
face of the moon was first found to be covered by craters having the
appearance of volcanoes at the surface of the earth, it was very
naturally thought that these supposed volcanoes might be still in
activity, and exhibit themselves to our telescopes by I heir flamei.
Not the slightest sound evidence of any incandescent eruption at the
moon's surface has been found, however.
Several instances of supposed changes of shape of features on the
moon's surface have been described in recent times.
The question whether these changes are proven is one on which
the opinions of astronomers differ. The difficulty of reaching a cer-
tain conclusion arises from the fact that each feature necessarily
varies in appearance, owing to the different directions in which the
sun's light falls upon it. Sometimes the changes arc very difficult
to account for, even when it is certain that they do not arise from
any change on the moon itself. Hence while some regard the appa-
rent changes as real, others regard them as due only to differences in
the mode of illumination.
The Moon only Shows one Face to the Earth. The moon rotates on
her axis from west to east, and the time required for one rotation is
the same as that required for one revolution in her orbit. If a line
be drawn from the earth to the moon, this line will always touch the
same hemisphere of the moon : and the moon does not rotate at all
with reference to this line. But if any line be drawn through the
sun parallel to the moon's axis, the moon sometimes turns one face
and sometimes another to this line. An observer on the earth, how-
ever, sees but one hemisphere of the moon.
CHAPTER V.
THE PLANET MARS.
DESCRIPTION OF THE PLANET.
Mars is the next planet beyond the earth in the order of
distance from the sun, being about half as far again as the
earth. It has a decided red color, by which it may be
readily distinguished from all the other planets. Owing to
the considerable eccentricity of its orbit, its distance, both
from the sun and from the earth, varies in a larger propor-
tion than does that of the other outer planets.
At the most favorable oppositions, its distance from the
earth is about, 0.38 of the astronomical unit, or, in round
numbers, 57,000,000 kilometres (35,000,000 of miles).
This is greater than the least distance of Venus, but*we
can nevertheless obtain a better view of Mars under these
circumstances than of Venus, because when the latter is
nearest to us its dark hemisphere is turned toward us,
while in the case of Mars and of the outer planets the
hemisphere turned toward us at opposition is fully illumi-
nated by the sun.
The period of revolution of Mars around the sun is a
little less than two years, or, more exactly, 687 days. The
successive oppositions occur at intervals of two years and
one or two months, the earth having made during this in-
terval a little more than two revolutions around the sun,
and the planet Mars a little more than one. The dates of
234 ASTRONOMY.
several past and future oppositions are shown in the fol-
lowing table:
1881 December 26th.
1884 January 31st.
1886 March 6th.
Owing to the unequal motion of the planet, arising from
the eccentricity of its orbit, the intervals between succes-
sive oppositions vary from two years and one month to two
years and two and a half months.
Mars necessarily exhibits phases, but they are not so well
marked as in the case of Venus, because the hemisphere
which it presents to the observer on the earth is always
more than half illuminated. The greatest phase occurs
when its direction is 90 from that of the sun, and even
then six sevenths of its disk is illuminated, like that of the
moon, three days before or after full moon. The phases
of Mars were observed by GALILEO in 1610.
notation of Mars. The early telescopic observers noticed that the
disk of Mars did not appear uniform in color and brightness, but
had a variegated aspect. In 1666 Dr. ROIJEHT HOOKE found that
the markings on Mart were permanent and moved around in such a
way as to show that the planet revolved on its axis. The markings
given in his drawings can be traced at the present day, and are
made use of to determine the exact period of rotation of the planet.
So well is the rotation fixed by them that the astronomer can now
determine the exact number of times the planet has rotated on its
axis since these old drawings were made. The period has been
found to be 24 h 37 m 22 s -7, a result which appears certain to one or
two tenths of a second. It is therefore less than an hour greater
than the period of rotation of the earth.
Surface of Mars. The most interesting result of these markings
on Mart is the probability that its surface is diversified by land and
water, covered by an atmosphere, and altogether very similar to the
surface of the earth. Some portions of the surface are of a decided
red color, and thus give rise to the well-known fiery aspect of the
planet. Other parts are of a greenish hue, and are therefore sup-
posed to be seas. The most striking features are two brilliant white
THE PLANET MARS. 235
regions, one lying around each pole of the planet. It has been sup-
posed that this appearance is due to immense masses of snow and
ice surrounding the poles. If this were so, it would indicate that
the processes of evaporation, cloud formation, and condensation of
vapor into rain and snow go on at the surface of Mars as at the sur-
face of the earth. A certain amount of color is given to this theory
by supposed changes in the magnitude of these ice-caps. But the
problem of establishing such changes is one of extreme difficulty.
The only way in which an adequate idea of this difficulty can be
formed is by the student himself looking at Man through a telescope.
If he will then note how hard it is to make out the different
shades of light and darkness on the planet, and how they must vary in
aspect under different conditions of clearness in our own atmosphere,
he will readily perceive that much evidence is necessary to establish
great changes. All we can say, therefore, is that the formation of
the ice-caps in winter and their melting in summer has some evi-
dence in its favor, but is not yet completely proven.
SATELLITES OF MAES.
Until the year 1877 Mars was supposed to have no satellites, none
having ever been seen in the most powerful telescopes. But in
August of that year Professor HALL, of the Naval Observatory,
instituted a systematic search with the great equatorial, which
resulted in the discovery of two such objects.
These satellites are by far the smallest celestial bodies known. It is
of course impossible to measure their diameters, as they appear in
the telescope only as points of light. The outer satellite is probably
about six miles and the inner one about seven miles in diameter.
The outer one was seen with the telescope at a distance from the
earth of 7,000,000 times this diameter. The proportion would be
that of a ball two inches in diameter viewed at a distance equal to
that between the cities of Boston and New York. Such a feat of
telescopic seeing is well fitted to give an idea of the power of modern
optical instruments.
Professor HALL found that the outer satellite, which he called
Deimos, revolves around the planet in 30 h 16 m , and the inner one,
called Phobos, in 7 h 38 m . The latter is o;nly 5800 miles from the
centre of Mars, and less than 4000 miles from its surface. It would
therefore be almost possible with one of our telescopes on the sur-
face of Mars to see an object the size of a large animal on the
satellite.
This short distance and rapid revolution make the inner satellite
236
ASTRONOMY.
of Mars one of the most interesting bodies with which we are ac-
quainted. It performs a revolution in its orbit in less than half the
time that Mars revolves on its axis. In consequence, to the inhab-
itants of Mars it would seem to rise in the west and set in the east.
It will be remembered that the revolution of the moon around the
earth and of the earth on its axis are both from west to east ; but the
FIG. 70. TELESCOPIC VIEW OP MARS.
latter revolution being the more rapid, the apparent diurnal motion
of the moon is from east to west. In the case of the inner satellite
of Mars, however, this is reversed, and it therefore appears to move
in the actual direction of its orbital motion. The rapidity of its
phases is also equally remarkable. It is less than two hours from
new moon to first quarter, and so on. Thus the inhabitants of Mars
may see their inner moon pass through all its phases from new to
full and again to new in a single night.
CHAPTER VI.
THE MINOR PLANETS.
the solar system was first mapped out in its true
proportions by COPERNICUS and KEPLER, only six primary
planets were known; namely, Mercury, Venus, the Earth,
Mars, Jupiter, and Saturn. These succeeded each other
according to a nearly regular law, as we have shown in
Chapter L, except that between Mars and Jupiter a gap
was left where an additional planet might be inserted,
and the order of distances be thus made complete. It was
therefore supposed by the astronomers of the seventeenth
and eighteenth centuries that a planet might be found in
this region. A search for this object was instituted to-
ward the end of the last century, but before it had made
much progress a planet in the place of the one so long
expected was found by PIAZZI, of Palermo. The discov-
ery was made on the first day of the present century, 1801,
January 1st.
In the course of the following seven years the astronom-
ical world was surprised by the discovery of three other
planets, all in the same region, though not revolving in
the same orbits. Seeing four small planets where one
large one ought to be, OLBERS was led to his celebrated
hypothesis that these bodies were the fragments of a large
planet which had been broken to pieces by the action of
some unknown force.
238 - ASTRONOMY.
A generation of astronomers now passed away without
the discovery of more than these four. In 1845 a fifth
planet of the group was found. In 1847 three more were
discovered, and discoveries have since been made at a rate
which thus far shows no signs of diminution. The num-
ber has now reached 225, and the discovery of additional
ones seems to be going on as fast as ever. The frequent
announcements of the discovery of planets which appear
in the public prints all refer to bodies of this group.
The minor planets are distinguished from the major
ones by many characteristics. Among these we may men-
tion their small size; their positions, all being situated be-
tween the orbits of Mars and Jupiter; the great eccentrici-
ties and inclinations of their orbits.
Number of Small Planets. It would be interesting to know how
many of these planets there are in all, but it is as yet impossible even
to guess at the number. As already stated, fully 200 are now
known, and the number of new ones found every year ranges from
7 or 8 to 10 or 12. If ten additional ones are found every year dur-
ing the remainder of the century, 400 will then have been dis-
covered.
A minor planet presents no sensible disk, and therefore looks ex-
actly like a small star. It can be detected only by its motion among
the surrounding stars, which is so slow that hours must elapse before
it can be noticed.
Magnitudes. It is impossible to make any precise measurement of
the diameters of the minor planets. These can, however, be esti
mated by the amount of light which the planet reflects. Supposing
the proportion of light reflected about the same as in the case of the
larger planets, it is estimated that the diameters of the three or four
largest, which are those first discovered, range between 300 and 600
kilometres, while the smallest are probably from 20 to 50 kilometres
in diameter. The average diameter of all that are known is perhaps
less than 150 kilometres; that is, scarcely more than one hundredth
that of the earth. The volumes of solid bodies vary as the cubes of
their diameters; it might therefore take a million of these planets to
make one of the size of the earth.
THE MINOR PLANETS.
Form of Orbits. The orbits of the minor planets are much more
eccentric than those of the larger ones; their distance from the sun
therefore varies very widely.
Origin of the Minor Planets. The question of the origin of these
bodies was long one of great interest. The features which we have
described associate themselves very naturally with the hypothesis
of OLBERS, that we here have the fragments of a single large planet
which in the beginning revolved in its proper place between the
orbits of Mars and Jupiter. No support has been given to OLBERS'
hypothesis by subsequent investigations, and it is no longer consid-
ered by astronomers to have any foundation. So far as can be judged,
these bodies have been revolving around the sun as separate planets
ever since the solar system itself was formed.
CHAPTER VII.
JUPITER AND HIS SATELLITES.
THE PLANET JUPITER.
Jupiter is much the largest planet in the system. His
mean distance is nearly 800,000,000 kilometres (480,000,-
000 miles). His diameter is 140,000 kilometres, corre-
sponding to a mean apparent diameter, as seen from the
sun, of 36*. 5. His linear diameter is about -fa, his surface
is r j T) and his volume y^ that of the sun. His mass is
Y^I-J, and his density is thus nearly the same as the sun's;
viz., 0.24 of the earth's. He rotates on his axis in
9 h 55 m 20".
He is attended by four satellites, which were discovered
by GALILEO on January 7th, 1610. He named them, in
honor of the MEDICIS, the Medicean stars. They are
now known as Satellites I, II, III, and IV, I being the
nearest.
The surface of Jupiter has been carefully studied with
the telescope, particularly within the past twenty years.
Although further from us than Mars, the details of his
disk are much easier to recognize. The most characteristic
features are given in the drawings appended. These
features are, first, the dark bands of the equatorial
regions, and, secondly, the cloud-like forms spread over
nearly the whole surface. At the limb all these details
become indistinct, and finally vanish, thus indicating a
JUPITER AND HIS SATELLITES. 241
highly absorptive atmosphere. The light from the centre
of the disk is twice as bright as that from the poles. The
bands can be seen with instruments no more powerful
than those used by GALILEO, yet he makes no mention of
them.
The color of the bands is reddish. The position of the
bands varies in latitude, and the shapes of the limiting
curves also change from day to day; but in the main they
remain as permanent features of the region to which they
belong. Two such bands are usually visible, but often
FIG. 71. TELESCOPIC VIEW OF JUPITER AND HIS SATELLITES.
more are seen. HERSCHEL, in the year 1793, attributed
the aspects of the bands to zones of the planet's atmos-
phere more tranquil and less filled with clouds than the re-
maining portions, so as to permit the true surface of the
planet to be seen through these zones, while the prevailing
clouds in the other regions give a brighter tint to these
latter. The color of the bands seems to vary from time to
time, and their bordering lines sometimes alter with such
rapidity as to show that these borders are formed of some-
thing like clouds.
The clouds themselves can easily be seen at times, and
242 ASTRONOMY.
they have every variety of shape, sometimes appearing as
brilliant circular white masses, but oftener they are similar
in form to a series of white cumulus clouds such as are
frequently seen piled up near the horizon on a summer's
day. The bands themselves seem frequently to be veiled
over with something like the thin cirrus clouds of our at-
mosphere.
FIG. 72. TELESCOPIC VIEW OF JUPITER. WITH A SATELLITE AND ITS SHADOW
SEEN ON THE DISK.
Such clouds can be tolerably accurately observed, and may be used
to determine the rotation-time of the planet. These observations
show that the clouds have often a motion of their own, which is also
evident from other considerations.
The following results of observation of spots situated in various
regions of the planet will illustrate this;
JUPITER AND HIS SATELLITES.
243
h. m. 8.
CASSINI 1665, rotation-time = 9 56 00
= 9 55 40
= 9 50 48
= 9 56 56
= 9 55 26
HERSCHEL 1778,
HERSCHEL 1779,
SCHROETER 1785,
BEER and MADLER . 1835,
AIRY 1835,
SCHMIDT 1862,
= 9 55 21
= 9 55 29
Fro. 73.
THE SATELLITES OF JUPITER.
Motions of the Satellites. The four satellites move about Jupiter
from west to east in nearly circular orbits. When one of these
satellites passes between the sun and Jupiter, it casts a shadow upon
Jupiter's disk (see Fig. 73) precisely as the shadow of our moon is
244 ASTRONOMY.
thrown upon the earth in a solar eclipse. If the satellite passes
through Jupiter's own shadow in its revolution, an eclipse of this
satellite takes place. If it passes between the earth and Jupiter, it
is projected upon Jupiter' 8 disk, and we have a transit; if Jupiter is
between the earth and the satellite, an occultation of the latter oc-
curs. All these phenomena can be seen with a common telescope,
and the times of observation are all found predicted in the Nautical
Almanac. These shadows being seen black upon Jupiter's surface,
show that this planet shines by reflecting the light of the sun.
Telescopic Appearance of the Satellites. Under ordinary circum-
stances, the satellites of Jupiter are seen to have disks; that is, not
to be mere points of light. Under very favorable conditions, mark-
ings have been seen on these disks.
The satellites completely disappear from telescopic view when
they enter the shadow of the planet. This seems to show that
neither planet nor satellite is self luminous to any great extent. If
the satellite were self-luminous, it would be seen by its own light;
and if the planet were luminous, the satellite might be seen by the re-
flected light of the planet.
The motions of these objects are connected by two curious and
important relations discovered by LA PLACE, and expressed as fol-
lows:
I. The mean motion of t7ie first satellite added to twice the mean mo-
tion of the third is exactly equal to three times the mean motion of the
second.
II. If to the mean longitude of the first satellite we add twice tJt# mean
longitude of the third, and subtract three times the mean longitude of the
second, the difference is always 180.
The first of these relations is shown in the following table of the
mean daily motions of the satellites:
Satellite I in one day moves 203. 4890
" II " " 101 .3748
" III " " 50. 3177
" IV " " 21.5711
Motion of Satellite 1 203.4890
Twice that of Satellite III. . 100. 6354
Sum 304. 1 244
Three times motion of Satellite II 304. 1244
Observations showed that this condition was fulfilled as exactly as
possible, but the discovery of LA PLACE consisted in showing that if
the approximate coincidence of the mean motions was once estab-
JUPITER AND HIS SATELLITES.
lished, they could never deviate from exact coincidence with the
law. The case is analogous to that of the moon, which always
presents the same face to us and which always will, since the rela-
tion being once approximately true, it will become exact and ever
remain so.
The discovery of the gradual propagation of light by means of
these satellites has already been described, and it has also been ex-
plained that they are of use in the rough determination of longi-
tudes. To facilitate their observation, the Nautical Almanac gives
complete ephemerides of their phenomena. A specimen of a portion
of such an ephemeris for 1865, March 7th, 8th, and 9th, is added.
The times are Washington mean times.
1865 MARCH.
d. h. m. s.
I
Eclipse
Disapp.
7 18 27 38.5
I
Occult.
Reapp.
7 21 56
III
Shadow
Ingress
8 7 27
III
Shadow
Egress
8 9 58
III
Transit
Ingress
8 12 31
~ II
Eclipse
Disapp.
8 13 1 22.7
1 III
Transit
Egress
8 15 6
II
Eclipse
Reapp.
8 15 24 11.1
II
Occult.
Disapp.
8 15 27
I
Shadow
Ingress
8 15 43
I
Transit
Ingress
8 16 58
I
Shadow
Egress
8 17 57
II
Occult.
Reapp.
8 17 59
I
Transit
Egress
8 19 13
I
Eclipse
Disapp.
9 12 55 59.4
I
Occult.
Reapp.
9 16 25
Suppose an observer near New York City to have determined his
local time accurately. This is about 13 m faster than "Washington
time. On 1865. March 8th, he would look for the reappearance of
II at about 15 h 34 m of his local time. Suppose he observed it at
15 h 36 m 22 s . 7 of his time: then his meridian is 12 m 11 8 .6 east of
Washington. The difficulty of observing these eclipses with accu-
racy, and the fact that the aperture of the telescope employed has an
important effect on the appeararcns seen, have kept this method
from a wide utility, which it at first seemed to promise.
CHAPTER VIII.
SATURN AND ITS SYSTEM.
GENERAL DESCRIPTION.
Saturn is the most distant of the major planets known
to the ancients. It revolves around the sun in 29 years,
at a mean distance of about 1,400,000,000 kilometres
(883,000,000 miles). The angular diameter of the ball of
the planet is about 16*. 2, correspond ing- to a true diameter
of about 110,000 kilometres (70,500 miles). Its diameter
is therefore nearly nine times and its volume about 700
times that of the earth. It is remarkable for its small
density, which, so far as known, is less than that of any
other heavenly body, and even less than that of water. It
revolves on its axis in 10 h 14 m 24 s , or less than half a day.
Saturn is perhaps the most remarkable planet in the
solar system, being itself the centre of a system of its
own, altogether unlike anything else in the heavens. Its
most noteworthy feature is a pair of rings which surround
it at a considerable distance from the planet itself. Out-
side of these rings revolve no less than eight satellites,
or twice the greatest number known to surround any other
planet. The planetj rings, and satellites are altogether
called the Saturnian system. The general appearance of
this system, as seen in a small telescope, is shown in Fig. 74,
SATURN AND ITS SYSTEM. 247
To the naked eye Saturn is of a dull yellowish color,
shining with about the brilliancy of a star of the first mag-
nitude. It varies in brightness, however, with the way in
which its ring is seen, being brighter the wider the ring
appears. It comes into opposition at intervals of one year
and from twelve to fourteen days. The following are the
FIG. 74. TELESCOPIC VIEW OP THE SATURNIAN SYSTEM
times of some of these oppositions, by studying which one
will be enabled to recognize the planet:
1885 December 25th.
1887 January 8th.
1888 January 22d.
During these years it will be best seen in the autumn
and winter.
When viewed with a telescope, the physical appearance
of the ball of Saturn is quite similar to that of Jupiter,
248 ASTRONOMY.
having light and dark belts parallel to the direction of its
rotation.
THE RINGS OF SATURN.
The rings arc the most remarkable and characteristic feature of
the Saturnian system. Fig. 75 gives two views of the ball and rings.
The upper one shows one of their aspects as actually presented in
the telescope, and the lower one shows what the appearance would
be if the planet were viewed from ft direction at right angles to the
plane of the ring (which it never can be from the earth).
The first telescopic observers of &itnrn were unable to see the
rings in their true form, and were greatly perplexed to account
for the appearance which the planet presented. GALILEO described
the planet as " tri-corporate," the two ends of the ring having, in his
imperfect telescope, the appearance of a pair of small planets at-
tached to the central one. "On each side of old Sitnm were ser-
vitors who aided him on his way." This supposed discovery was
announced to his friend KEPLEH in this logogriph:
"smaismrmilmepoetalevmibimenugttaviras," which, being trans-
posed, becomes
" Altissimum planetam tergeminum observavi" (I have observed
the most distant planet to be tri-form).
The phenomenon constantly remained a mystery to its first ob-
server. In 1610 he had seen the planet accompanied, as he supposed,
by two lateral stars; in 1612 the latter hail vanished and the central
body alone remained. After that GALILEO ceased to observe Saturn.
The appearances of the ring were also incomprehensible to HE-
VELIUS, GASSENDI, and others. It was not until 1655 (after seven
years of observation) that the celebrated HUYQIIENS discovered the
true explanation of the remarkable and recurring series of phenom-
ena present by the tri-corporate planet.
He announced his conclusions in the following logogriph:
"aaaaaa ccccc d eeeee g h iiiiiii 1111 mm.nnnnnnnnn oooo pp q rr s
ttttt uuuuu," which, when arranged, read
" Annulo cingitur, tcnui, piano, nusquam coherente, ad eclipticam
inclinato" (it is girdled by a thin plane ring, nowhere touching, in-
clined to the ecliptic).
This description is complete and accurate.
In 1675 it was found by CASSTNT, that what HUYGHENS had seen
as a single ring was really two. A division extended all the way
around neai the outer edge This division is shown in the figures.
In 1850 the Messrs BOND of ILirv;inl College Observatory, found
SATURN AND ITS SYSTEM. 249
FIG. 75. RING" OF SATURH,
250 ASTRONOMY.
that there was a third ring, of a dusky and nebulous aspect, inside the
other two, or rather attached to the inner edge of the inner ring. It
is therefore known as Bond's dusky ring. It had not been before fully
described owing to its darkness of color, which made it a difficult
object to see except witli a good telescope. It is not separated from
the bright ring, but seems as if attached to it. The latter shades off
toward its inner edge, and merges gradually into the dusky ring.
The latter extends about half way from the inner edge of the bright
ring to the ball of the planet.
Aspect of the Rings. As Saturn revolves around the sun, the
plane of the rings remains parallel to itself. That is, if we consider
a straight line passing through the centre of the planet, perpendic-
ular to the plane of the ring, as the axis of the latter, this axis will
always point in the same direction. In this respect the motion is
similar to that of the earth around the sun. The ring of Hiturn is
inclined about 27 to the plane of its orbit. Consequently, as the
planet revolves around the sun, there is a change in the direction in
which the sun, shines upon it similar to that which produces the
change of seasons upon the earth, as shown in Fig. 32.
The corresponding changes for Saturn are shown in Fig 76. Dur-
ing each revolution of Saturn the plane of the ring passes through
the sun twice. This occurred in the years 1862 and 1878, at two
opposite points of the orbit, as shown in the figure. At two other
points, midway between these, the sun shines upon the plane of the
ring at its greatest inclination, about 27. Since the earth is little
more than one tenth as far from the sun as Saturn is, an observer
always sees Saturn nearly, but not quite, as if he were upon the sun.
Hence at certain times the rings of Saturn are seen edgeways; while
at other times they are at an inclination of 27, the aspect depending
upon the position of the planet in its orbit. The following are the
times of some of the phases:
1878, February 7th. The edge of the ring was turned toward the
sun. It could then be seen only as a thin line of light.
1885. The planet having moved forward 90, the south side of the
rings may be seen at an inclination of 27.
1891, December. The planet having moved 90 further, the edge
of the ring is again turned toward the sun.
1899. The north side of the ring is inclined toward the sun, and
is seen at its greatest inclination.
The rings are extremely thin in proportion to their extent. Con-
sequently, when their edges are turned toward the earth, they appear
as a thin line of light, which can be seen only with powerful tele-
scopes. With such telescopes, the planet appears as if it were
SATURN AND ITS SYSTEM.
251
pierced through by a piece of very fine wire, the ends of which pro-
ject on each side more than the diameter of the planet. It has fre-
quently been remarked that this appearance is seen on one side of
the planet, when no trace of the ring can be seen on the other.
There is sometimes a period of a few weeks during which the
plane of the ring, extended outward, passes between the sun and the
earth. That is, the sun shines on one side of the ring, while the
other or dark side is turned toward the earth. In this case it seems
to be established that only the edge of the ring is visible. If this be
Fio. 76. DIFFERENT ASPECTS OF THE RING OF SATURN AS SEEN FROM THE
EARTH.
so, the substance of the rings cannot be transparent to the sun's rays,
else it would be seen by the light which passes through it.
Constitution of the Rings of Saturn. The nature of these objects
has been a subject both of wonder and of investigation by mathema-
ticians and astronomers ever since they were discovered. They were
at first supposed to be solid bodies; indeed, from their appearance it
was difficult to conceive of them as anything else. The question
then arose: What keeps them from falling on the planet? It was
shown by LA PLACE that a homogeneous and solid ring surrounding
the planet could not remain in a state of equilibrium, but must be
precipitated upon the central ball by I lie smallest disturbing force.
252
A8THONOMT.
It is now established beyond reasonable doubt that the rings do not
form a couliuuous mass, but are really a countless multitude of small
separate particles, each of which revolves on its own account. These
satellites are individually far too small to be seen in any telescope, but
so numerous that when viewed from the distance of the earth they
appear as a continuous mass, like particles of dust floating in a
sunbeam.
SATELLITES OF SATURN.
Outside the rings of Saturn revolve its eight satellites, the order
and discovery of which are shown in the following table:
No.
NAME
Distance
from
Planet.
Discoverer.
Date of Discovery.
1
2
3
4
5
6
7
8
Mimas
Enceladus
Tethys
Dione
Rhea
Titan
Hyperion
Japetus
3-3
4-3
5-3
6-8
9-5
20-7
26-8
64-4
Herschel
Herschel
Cassini
Cassini
Cassini
Huyghens
Bond
Cassini
1789, September 17.
1789, August 28.
1G84. March.
1684, March.
1672, December 23.
1655, March 25.
1848, September 16.
1671, October.
The distances from the planet are given in radii of the latter. The
satellites Mimas and Hyperion are visible only in the most powerful
telescopes. The brightest of all is Titan, which can be seen in a
telescope of the smallest ordinary size. Japetus has the remarkable
peculiarity of appearing nearly as bright as Titan when seen west' of
the planet, and so faint as to be visible only in large telescopes when
on the other side. This appearance is explained by supposing that,
like our moon, it always presents the same face to the planet, and
that one side of it is dark and the other side light. When west of
the planet, the bright side is turned toward the earth and the satel-
lite is visible. On the other side of the planet, the dark side is turned
toward us, and it is nearly invisible. Most of the remaining five
satellites can ordinarily be seen with telescopes of moderate power.
CHAPTER IX.
THE PLANET URANUS.
Uranus was discovered on March 13th, 1781, by Sir
WILLIAM HERSCHEL (then an amateur observer) with a
ten-foot reflector made by himself. He was examining a
portion of the sky near H Geminorum, when one of the
stars in the field of view attracted his notice by its peculiar
appearance. On further scrutiny, it proved to have a
planetary disk, and a motion of over 2" per hour. HERSCHEL
at first supposed it to be a comet in a distant part of its
orbit, and under this impression parabolic orbits were com-
puted for it by various mathematicians. None of these,
however, satisfied subsequent observations, and it was
finally determined that the new body was a planet revolv-
ing in a nearly circular orbit. We can scarcely compre-
hend now the enthusiasm with which this discovery was
received. No new body (save comets) had been added to
the solar system since the discovery of the third satellite
of Saturn in 1684, and all the major planets of the heavens
had been known for thousands of years.
Uranus revolves about the sun in 84 years. Its apparent
diameter as seen from the earth varies little, being about
3". 9. Its true diameter is about 50,000 kilometres, and its
figure is spheroidal.
In physical appearance it is a small greenish disk with-
254 ASTZONOMY.
out markings. It is possible that the centre of the disk is
slightly brighter than the edges. At its nearest approach
to the earth, it shines as a star of the sixth magnitude,
and is just visible to an acute eye when the attention is
directed to its place. In small telescopes with low powers,
its appearance is not markedly different from that of stars
of about its own brilliancy.
Sir WILLIAM HERSCHEL suspected that Uranus was ac-
companied by six satellites.
Of the existence of two of these satellites there has never
been any doubt. No one of the other four satellites de-
scribed by HERSCHEL has ever been seen, and he was
undoubtedly mistaken in supposing them to exist. Two
additional ones were discovered by LASSELL in 1847, and
they are, with the satellites of Mars, the faintest objects in
the solar system. Neither of them is identical with any of
the missing ones of HERSCHEL. As Sir WILLIAM HER-
SCHEL had suspected six satellites, the following names for
the true satellites are generally adopted to avoid confusion:
DAYS.
I. Aritl Period = 2.520383
II. Umltriel " = 4.144181
III. Titania, HERSCHKL'S (II.) " = 8.705897
IV. Oberon, HERSCHEL'S (IV.) " = 13.463269
It is likely that Ariel varies in brightness on different
sides of the planet, and the same phenomenon has also
been suspected for Titania.
The most remarkable feature of the satellites of Uranus is that
their orbits are nearly perpendicular to the ecliptic instead of
having a small inclination to that plane, like those of all the orbits
of both planets and satellites previously known. To form a correct
idea of the position of tne orbits, we must imagine them tipped over
until their north pole is nearly 8 below the ecliptic, instead of 90
THE PLANET URANUS. 255
above it. The pole of the orbit which should be considered as the
north one is that from which, if an observer look down upon a re-
volving body, the latter would seem to turn in a direction opposite
that of the hands of a watch. When the orbit is tipped over more
than a right angle, the motion from a point in the direction of the
north pole of the ecliptic will seem to be the reverse of this; it is
therefore sometimes considered to be retrograde. This term is fre-
quently applied to the motion of the satellites of Uranus, but is
rather misleading, since the motion, being nearly perpendicular to
the ecliptic, is not exactly expressed by the term.
The four satellites move in the same plane. This fact renders it
highly probable that the planet Uranus revolves on its axis in the
same plane with the orbits of the satellites, and is therefore an oblate
spheroid like the earth. This conclusion is founded on the consid-
eration that if the planes of the satellites were not kept together by
some cause, they would gradually deviate from each other owing to
the attractive force of the sun upon the planet. The different satel-
lites would deviate by different amounts, and it would be extremely
improbable that all the orbits would at any time be found in the
same plane. Since we see them in the same plane, we conclude that
some force keeps them there, and the oblateness of the planet would
cause such a force.
CHAPTER X.
THE PLANET NEPTUNE.
AFTER the planet Uranus had been observed for some
thirty years, tables of its motion were prepared by Bou-
VARD. He had as data available for this purpose not only
the observations since 1781, but also observations extend-
ing back as far as 1695, in which the planet was observed
and supposed to be a fixed star. As one of the chief diffi-
culties in the way of obtaining a theory of the planet's
motion was the short period of time during which it had
been regularly observed, it was to be supposed that these
ancient observations would materially aid in obtaining
jxact accordance between the theory and observation. But
it was found that, after allowing for all perturbations pro-
duced by the known planets, the ancient and modern
observations, though undoubtedly referring to the same
object, were yet not to be reconciled with each other, but
differed systematically. BOUVARD was forced to omit the
older observations in his tables, which were published in
1820, and to found his theory upon the modern observa-
tions alone. By so doing, he obtained a good agreement
between theory and the observations of the few years
immediately succeeding 1820.
BOUVARD seems to have formulated the idea that a pos-
sible cause for the discrepancies noted might be the exist-
ence of an unknown planet, but the meagre data at his
disposal forced him to leave the subject untouched. In
THE PLANET NEPTUNE. 257
1830 it was found that the tables which represented the
motion of the planet well in 1820-25 were 20" in error, in
1840 the error was 90*, and in 1845 it was over 120".
These progressive and systematic changes attracted the
attention of astronomers to the subject of the theory of
the motion of Uranus. The actual discrepancy (120*) in
1845 was not a quantity large in itself. Two stars of the
magnitude of Uranus, and separated by only 120*, would
be seen as one to the unaided eye. It was on account of
its systematic and progressive increase that suspicion was
excited. Several astronomers attacked the problem in
various ways. The elder STRUVE, at Pulkova, prosecuted
a search for a new planet along with his double-star obser-
vations; BESS EL, at Koenigsberg, set a student of his own,
FLEMING, at a new comparison of observation with theory,
in order to furnish data for a new determination; ARAGO,
then Director of the Observatory at Paris, suggested this
subject in 1845 as an interesting field of research to LE
VERRIER, then a rising mathematician and astronomer.
Mr. J. C. ADAMS, a student in Cambridge University,
England, had become aware of the problems presented by
the anomalies in the motion of Uranus, and had attacked
this question as early as 1843. In October, 1845, ADAMS
communicated to the Astronomer Koyal of England ele-
ments of a new planet so situated as to produce the per-
turbations of the motion of Uranus which had actually
been observed. Such a prediction from an entirely un-
known student, as ADAMS then was, did not carry entire
conviction with it. A series of accidents prevented the
unknown planet being looked for by one of the largest
telescopes in England, and so the matter apparently
dropped. It may be noted, however, that we now know
258 ASTRONOMY.
ADAMS' elements of the new planet to have been so near
the truth that if it had been really looked for by the power-
ful telescope which afterward discovered its satellite, it
could scarcely have failed of detection.
BESSEL'S pupil FLEMING died before his work was done,
and BESSEL'S researches were temporarily brought to an
end. STRUVE'S search was unsuccessful. Only LE VER-
RIER continued his investigations, and in the most
thorough manner. He first computed anew the pertur-
bation of Uranus produced by the action of Jupiter and
Saturn. Then he examined the nature of the irregulari-
ties observed. These showed that if they were caused by
an unknown planet, it could not be between Sot urn and
Uranus, or else Saturn would have been more affected
than was the case.
The new planet was outside of Uranus if it existed at
all, and as a rough guide BODE'S law was invoked, which
indicated a distance about twice that of Uranus. In the
summer of 1846 LE VERRIER obtained complete elements
of a new planet, which would account for the observed
irregularities in the motion of Uranus, and these were
published in France. They were very similar to those of
ADAMS, which had been communicated to Professor CHAL-
LIS, the Director of the Observatory of Cambridge, Eng-
land.
A search was immediately begun by CHALLIS for such
an object, and as no star-maps were at hand for this region
of the sky, he began mapping the surrounding stars. In
so doing the new planet was actually observed, both on
August 4th and 12th, 1846, but the observations remain-
ing unreduced, and so the planetary nature of the object
was not recognized.
THE PLANET NEPTUNE. 259
In September of the same year LE VEBKIER wrote to
Dr. GALLE, then Assistant at the Observatory of Berlin,
asking him to search for the new planet, and directing
him to the place where it should be found. By the aid
of an excellent star-chart of this region, which had just
been completed, the planet was found September 23d, 1846.
The strict rights of discovery lay with LE VEKRIEK,
but the common consent of mankind has always credited
Fio. 77.
ADAMS with an equal share in the honor attached to this
most brilliant achievement. Indeed, it was only by the
most unfortunate succession of accidents that the discovery
did not attach to ADAMS' researches. One thing must in
fairness be said, and that is that the results of LE VER-
RIER, which were reached after a most thorough investi-
gation of the whole ground, were announced with an en-
tire confidence which, perhaps, was lacking in the other
260 ASTRONOMY.
This brilliant discovery created more enthusiasm than
even the discovery of Uranus, as it was by an exercise of
far higher qualities that it was achieved. It appeared to
savor of the marvellous that a mathematician could say
to a working astronomer that by pointing his telescope to
a certain small area, within it should be found a new
major planet. Yet so it was.
The general nature of the disturbing force which re-
vealed the new planet may be seen by Fig. 77, whicli
shows the orbits of the two planets, and their respective
motions between 1781 and 1840. The inner orbit is that
of Uranus, the outer one that of Neptune. The arrows
passing from the former to the latter show the directions
of the attractive force of Neptune. It will be seen that
the two planets were in conjunction in the year 1822.
Since that time Uranus has, by its more rapid motion,
passed more than 90 beyond Neptune, and will continue
to increase its distance from the latter until the begin-
ning of the next century.
Our knowledge regarding Neptune is mostly confined to
a few numbers representing the elements of its motion.
Its mean distance is more than 4,000,000,000 kilometres
(2,775,000,000 miles); its periodic time is 164.78 years;
its apparent diameter is 2.6 seconds, corresponding to a
true diameter of 55,000 kilometres. Gravity at its surface
is about nine tenths of the corresponding terrestrial surface
gravity. Of its rotation and physical condition nothing
is known. Its color is a pale greenish blue. It is attended
by one satellite, which was discovered by Mr. LASSELL, of
England, in 1847. The satellite requires a telescope of
twelve inches' aperture or upward to be well seen.
CHAPTER XL
THE PHYSICAL CONSTITUTION OF THE PLANETS.
IT is remarkable that the eight large planets of the solar
system, considered with respect to their physical constitu-
tion as revealed by the telescope and the spectroscope, may
be divided into four pairs, the planets of each pair having
a great similarity, and being quite different from the ad-
joining pair.
Mercury and Venus. Passing outward from the sun, the
first pair we encounter will be Mercury and Venus. The
most remarkable feature of these two planets is a negative
rather than a positive one, being the entire absence of any
certain evidence of change on their surfaces. We have al-
ready shown that Venus has a considerable atmosphere,
while there is no evidence of any such atmosphere around
Mercury. They have therefore not been proved alike in
this respect, yet, on the other hand, they have not been
proved different. In every other respect than this the
similarity appears perfect. No permanent markings have
ever been certainly seen on the disk of either. If, as is
possible, the atmosphere of both planets is filled with clouds
and vapor, no change, no openings, and no formations
among these cloud masses are visible from the earth. When-
ever either of these planets is in a certain position relative
to the earth and the sun, it seemingly presents the same
appearance, and not the slightest change occurs in that
262 ASTRONOMY.
appearance from the rotation of the planet on its axis,
which every analogy of the solar system leads us to believe
must take place.
When studied with the spectroscope, the spectra of Mer-
cury and Venus do not differ strikingly from that of the
sun. This would seem to indicate that the atmospheres of
these planets do not exert any decided absorption upon the
rays of light which pass through them ; or, at least, they
absorb only the same rays which are absorbed by the at-
mosphere of the sun and by that of the earth. The one
point of difference is that the lines of the spectrum pro-
duced by the absorption of our own atmosphere appear
darker in the spectrum of Venus. If this were so, it
would indicate that the atmosphere of Venus is similar in
constitution to that of our earth, because it absorbs the
same rays. But the means of measuring the darkness of
the lines are as yet so imperfect that it is impossible to
speak with certainty on a point like this.
The Earth and Mars. These planets are distinguished
from all the others in that their visible surfaces are mark-
ed by permanent features, which show them to be solid,
and which can be seen from the other heavenly bodies. It
is true that we cannot study the earth from any other
body, but we can form a very correct idea how it would
look if seen in this way (from the moon, for instance).
Wherever the atmosphere was clear, the outlines of the
continents and oceans would be visible, while they would
be invisible where the air was cloudy.
Now, so far as we can judge from observations made at
so great a distance, never much less than forty millions of
miles, the planet Mars presents to our telescopes very
much the same general appearance that the earth would if
PHYSICAL CONSTITUTION Of 1 THE PLANETS. 263
observed from an equally great distance. The only ex-
ception is that ihe visible surface of Mars is seemingly much
less obscured by clouds than that of the earth would be. In
other words, that planet has a more sunny sky than ours.
It is, of course, impossible to say what conditions we might
find could we take a much closer view of Mars : all we can
assert is, that so far as we can judge from this distance,
its surface is like that of the earth.
This supposed similarity is strengthened by the spectro-
scopic observations.
Jupiter and Saturn. The next pair of planets is Jupi-
ter and Saturn. Their peculiarity is that no solid crust
or surface is visible from without. In this respect they
differ from the earth and Mars, and resemble Mercury
and Venus. But they differ from the latter in the very
important point that constant changes can be seen going
on at their surfaces. The preponderance of evidence is
in favor of the view that these planets have no solid
crusts whatever, but consist of masses of molten matter,
surrounded by envelopes of vapor constantly rising from
the interior.
This view is further strengthened by their very small
specific gravity, which can be accounted for by supposing
that the liquid interior is nothing more than a compara-
tively small central core, and that the greater part of the
bulk of each planet is composed of vapor of small density.
That the visible surfaces of Jupiter and Saturn are cov-
ered by some kind of an atmosphere follows not only from
the motion of the cloud forms seen there, but from the
spectroscopic observations.
Uranus and Neptune, These planets have a strikingly
similar aspect when seen through a telescope. They differ
264 ASTRONOMY.
from Jupiter and Saturn in that no changes or variations
of color or aspect can be made out upon their surfaces;
and from the earth and Mars in the absence of any perma-
nent features. Telescopically, therefore, we might classify
them with Mercury and Venus, but the spectroscope re-
veals a constitution entirely different from that of any
other planets. The most marked features of their spectra
are very dark bands, evidently produced by the absorption
of dense atmospheres. Owing to the extreme faintness of
the light which reaches us from these distant bodies, the
regular lines of the solar spectrum are entirely invisible in
their spectra, yet these dark bands which are peculiar to
them have been seen by several astronomers.
This classification of the eight planets into pairs is ren-
dered yet more striking by the fact that it applies to what
we have been ableto discover respecting the rotations of
these bodies. The rotation of the inner pair, Mercury
and Venus, has eluded detection, notwithstanding their
comparative proximity to us. The next pair, the earth
and Mars, have perfectly definite times of rotation,
because their outer surfaces consist of solid crusts, every
part of which must rotate in the same time. The next
pair, Jupiter and Saturn, have well-established times
of rotation, but these times are not perfectly definite,
because the surfaces of these planets are not solid, and dif-
ferent portions of their mass may rotate in slightly different
times. Jupiter and Saturn have also in common a very
rapid rate of rotation. Finally, the outer pair. Uranus
and Neptune, seem to be surrounded by atmospheres of
such density that no evidence of rotation can be gathered.
Thus it seems that of the eight planets only the central
four have yet certainly indicated a rotation on their axes.
CHAPTER XII.
METEORS.
PHENOMENA AND CAUSES OF METEORS.
DURING the present century evidence has been collected
that countless masses of matter, far too small to be seen
with the most powerful telescopes, are moving through
the planetary spaces. This evidence is afforded by the
phenomena of "aerolites," "meteors," and "shooting-
stars." Although these several phenomena have been ob-
served and noted from time to time since the earliest his-
toric era, it is only recently that a complete explanation
has been reaehed.
Aerolites. Reports of the falling of large masses of
stone or iron to the earth have been familiar to antiqua-
rian students for many centuries. The problem where
such a body could come from, or how it could get into the
atmosphere to fall down again, formerly seemed so nearly
incapable of solution that it required some credulity to
admit the facts. When the evidence became so strong as
to be indisputable, theories of their origin began to be
propounded. One theory quite fashionable in the early
part of this century was that they were thrown from
volcanoes in the moon. This theory has little to sup-
port it.
The proof that aerolites did really fall to the ground first became
conclusive by the fall being connected with other more familiar
phenomena. Nearly every one who is at all observant of the
266 ASTRONOMY.
heavens is familiar with bolides, or fire-balls brilliant objects having
the appearance of rockets, which are occasionally seen moving with
great velocity through the upper regions of the atmosphere.
Scarcely a year passes in which such a body of extraordinary bril-
liancy is not seen. Generally these bodies, bright though they may
be, vanish without leaving any trace, or making themselves evident
to any sense but that of sight. But on rare occasions their appearance
is followed at an interval of several minutes by loud explosions like
the discharge of a battery of artillery. The fall of these aerolites is
always accompanied by light and sound, though the light may be
invisible in the daytime.
When chemical analysis was applied to aerolites, they were proved
to be of extramundane origin, because they contained chemical
combinations not found in terrestrial substances. It is true that they
contained no new chemical elements, but only a combination of the
elements which are found on the earth. These combinations are
now so familiar to mineralogists that they can distinguish an aerolite
from a mineral of terrestrial origin by a careful examination. One
of the most frequent components of these bodies is iron.
Meteors. Although the meteors we have described are of dazzling
brilliancy, yet they run by insensible 'gradations into phenomena,
which any one can see on any clear night. The most brilliant
meteors of all are likely to be seen by one person only two or three
times in his life. Meteors having the appearance and brightness of
a distant rocket may be seen several times a year. Smaller ones
occur more frequently; and if a careful watch be kept, it will be
found that several of the faintest class of all, familiarly known as
shooting-stars, can be seen on every clear night. We can draw no
distinction between the most brilliant meteor illuminating the whole
sky, and perhaps making a noise like thunder, and the faintest
shooting-star, except one of degree. There seems to be every grada-
tion between these extremes, so that all should be traced to some
common cause.
Cause of Meteors. There is now no doubt that all these phenomena
have a common origin, and that they are due to the earth encounter-
ing innumerable small bodies in its annual course around the sun.
The great difficulty in connecting meteors with these invisible bodies
arises from the brilliancy and rapid disappearance of the meteors.
The question may be asked, Why do they burn with so great an evolu-
tion of light on reaching our atmosphere? To answer this question
we must have recourse to the mechanical theory of heat. Heat is a
vibratory motion in the particles of solid bodies and a progressive
motion in those of gases. By making this motion more rapid we
^
METEORS. Xs[> * 267
make the body warmer. By simply blowing air against any com-
bustible body with sufficient velocity it can be set on fire, and, if
incombustible, the body will be made red-hot and finally melted.
Experiments to determine the degree of temperature thus produced
have been made which show that a velocity of about 50 metres per
second corresponds to a rise of temperature of one degree Centi-
grade. From this the temperature due to any velocity can be readily
calculated on the principle that the increase of temperature is pro-
portional to the "energy" of the particles, which again is propor-
tional to the square of the velocity. Hence a velocity of 500 metres
per second would correspond to a rise of 100 above the actual tem-
perature of the air, so that if the latter was at the freezing-point the
body would be raised to the temperature of boiling water. A velocity
of 1500 metres per second would produce a red heat.
The earth moves around the sun with a velocity of about 30,000
metres per second; consequently if it met a body at rest the concus-
sion between the latter and the atmosphere would correspond to a
temperature of more than 300,000. This would instantly dissolve
any known substance.
It must be remembered that when we speak of these enormous
temperatures, we are to consider them as potential, not actual, tem-
peratures. We do not mean that the body is actually raised to a
temperature of 300,000, but only that the air acts upon it as if it
were put into a furnace heated to this temperature; that is, it is
rapidly destroyed by the intensity of the heat.
This potential temperature is independent of the density of the
medium, being the same in the rarest as in the densest atmosphere.
But the actual effect on the body is not so great in a rare as in a
dense atmosphere. Every one knows that he can hold his hand
for some time in air at the temperature of boiling water. The rarer
the air the higher the temperature the hand would bear without
injury. In an atmosphere as rare as ours at the height of 50 miles,
it is probable that the hand could be held for an indefinite period,
though its temperature should be that of red-hot iron; hence the
meteor is not consumed so rapidly as if it struck a dense atmosphere
with planetary velocity. In the latter case it would probably dis-
appear like a flash of lightning.
The amount of heat evolved is measured not by that which
would result from the combustion of the body, but by the vis viva
(energy of motion) which the body loses in the atmosphere. The
student of physics knows that motion, when lost, is changed into a
definite amount of heat. If we calculate the amount of heat which
is equivalent to the energy of motion of a pebble having a velocity
268 ASTRONOMY.
of 20 miles a second, we shall find it sufficient to raise about 1300
times the pebble's weight of water from the free/.ing to the boiling
point. This is many times as much heat as could result from burn-
ing even the most combustible body.
The detonation which sometimes accompanies the passage of
very brilliant meteors is not caused by an explosion of the meteor,
but by the concussion produced by its rapid motion tli rough our at-
mosphere. This concussion is of much the same nature as that pro-
duced by a flash of lightning. The air is suddenly condensed in
front of the meteor, while a vacuum is left behind it.
The invisible bodies which produce meteors in the way just de-
scribed have been called meteoroids. Meteoric phenomena depend
very largely upon the nature of the meteoroids. and the direction and
velocity with which they are moving relatively to the earth. With
very rare exceptions, they are so small and fusible as to be entirely
dissipated in the upper regions of the atmosphere. Even of those
so hard and solid as to produce a brilliant light and the loudest deto-
nation, only a small proportion reach the earth. On rare occasions
the body is so hard and massive as to reach the earth without being
entirely consumed. The potential heat produced by its passage
through the atmosphere is then all expended in melting and destroy-
ing its outer layers, the inner nucleus remaining unchanged. When
such a body first strikes the denser portion of the atmosphere, the
resistance becomes so great that the body is generally broken to
pieces Hence we very often find not simply a single aerolite, but a
small shower of them.
Heights of Meteors. Many observations have been made to deter-
mine the height at which meteors are seen. This is effected by two
observers stationing themselves several miles apart and mapping out
the courses of such meteors as they can observe. In the case of very
brilliant meteors, the path is often determined with considerable pre-
cision by the direction in which it is seen by accidental observers in
various regions of the country over which it passes This observa-
tion is nothing but a simultaneous determination of the parallax of a
meteor as seen from two stations. See Fig. 17.
Meteors and shooting-stars commonly commence to be visible at a
height of about 160 kilometres, or 100 statute miles. The separate
results vary widely, but this is a rough mean of them. They
are generally dissipated at about half this height, and therefore
above the highest atmosphere which reflects the rays of the sun.
From this it may be inferred that the earth's atmosphere rises to a
height of at least 160 kilometres. This is a much greater height than
it was formerly supposed to have.
METEORS. 269
METEORIC SHOWERS.
As already stated, the phenomena of shooting-stars may
be seen by a careful observer on almost any clear night.
In general, not more than three or four of them will be
seen in an hour, and these will be so minute as hardly to
attract notice. But they sometimes fall in such numbers
as to present the appearance of a meteoric shower. On
rare occasions the shower has been so striking as to fill the
beholders with terror. The ancient and mediaeval records
contain many accounts of these phenomena which have been
brought to light through the researches of antiquarians.
It has long been known that some showers of this class
occur at an interval of about a third of a century. One
was observed by HUMBOLDT, on the Andes, on the night of
November 12th, 1799, lasting from two o'clock until day-
light. A great shower was seen in this country in 1833,
and is well known to have struck the negroes of the
Southern States with terror. The theory that the showers
occur at intervals of 34 years was propounded by OLBERS,
who predicted a return of the shower in 1867. This pre-
diction was completely fulfilled, but instead of appearing
in the year 1867 only, it was first noticed in 1866. On the
night of November 13th of that year a remarkable shower
was seen in Europe, while on the corresponding night of
the year following it was again seen in this country, and,
in fact, was repeated for two or three years, gradually dy-
ing away.
The occurrence of a shower of meteors evidently shows
that the earth encounters a swarm of meteoroids. The re-
currence at the same time of the year, when the earth is
in the same point of its orbit, shows that the earth meets
270 ASTRONOMY.
the swarm at the same point in successive years. All the
meteoroids of the swarm must of course be moving in the
same direction, else they would soon be widely scattered.
This motion is connected with the radiant point, a well-
marked feature of a meteoric shower.
Kadiant Point. Suppose that, during a meteoric shower, we mark
the path of each meteor on a star-map, as in the figure. If we con-
tinue the paths backward in a straight line, we shall find that they
all meet near one and the same point of the celestial sphere; that is,
they move as if they all radiated from this point. The latter is,
therefore, called the radiant point. In the figure the lines do not all
pass accurately through t lie same point. This is owing to the un-
avoidable errors made in marking out the path.
It is found that the radiant point is always in the same position
among the stars, wherever the observer may be situated, and that
as the utars apparently move toward the west, tfie radiant point moves
with them.
The radiant point is due to the fact that the meteoroids which
strike the earth during a shower are all moving in the same direc-
tion. Their motions will all be parallel; hence when the bodies
strike our atmosphere the paths described by them in their passage
will all be parallel straight lines. A straight line seen by an ob-
server at any point is projected as a great circle of the celestial
sphere, of which the observer supposes himself to be the centre. If
we draw a line from the observer parallel to the paths of the meteors,
the direction of that line will represent a point of the sphere through
which all the paths will seem to pass; this will, therefore, be the
radiant point in a meteoric shower.
Orbits of Meteoric Showers. From what has just been said it will
be seen that the position of the radiant point indicates the direction
in which the meteoroids move relatively to the earth. If we also
knew the velocity with which they arc really moving in space, we
could make allowance for the motion of the earth, and thus deter-
mine the direction of their actual motion in space. If we know this,
it is possible to calculate the actual direction and velocity of the
meteoric swarm in space. Having this direction and velocity, the
orbit of the swarm around the sun admits of being calculated.
Kelations of Meteors and Comets, The velocity of the
meteoroids does not admit of being determined from obser-
METEORS. 271
yation. One element necessary for determining the orbits
of these bodies is, therefore, wanting. In the case of the
FIG. 78. RADIANT POINT OF METEORIC SH
showers of 1799, 1833, and 1866, commonly called the
November showers, this element is given by the time of
272 ASTRONOMY.
revolution around the sun. Since the showers occur at
intervals of about a third of a century, it is highly proba-
ble this is the periodic time of the swarm around th esun.
The periodic time being known, the velocity at any dis-
tance from the sun admits of calculation from the theory
of gravitation. Thus we have all the data for determining
the real orbits of the group of meteors around the sun.
The calculations necessary for this purpose were made
by LE VERRIER and other astronomers shortly after the
great shower of 1866. The following was the orbit as
given by LE VERRIER:
Period of revolution 33.25 years.
Eccentricity of orbit 0.9044.
Least distance from the sun 0.9890.
Inclination of orbit 165 19'.
Longitude of the node 51 18'.
Position of the perihelion (near the node).
The publication of this orbit brought to the attention of
the world an extraordinary coincidence which had never
before been suspected. In December, 1865, a faint tele-
scopic comet was discovered. Its orbit was calculated as
follows :
Period of revolution 33.18 years.
Eccentricity of orbit 9054.
Least distance from the sun 0.9765.
Inclination of orbit 162 42'.
Longitude of the node 51 26'.
Longitude of the perihelion 42 24'.
The publication of the cometary orbit and that of the
orbit of the meteoric group were made independently with-
in a few days of each other by two astronomers, neither of
whom had any knowledge of the work of the other. Corn-
Daring them, the result is evident. The swarms of meteor-
METEORS. 273
oids which cause the November showers move in the same
orbit with this comet.
The comet passed its perihelion in January, 1866. The
most striking meteoric shower commenced in the following
November, and was repeated during several years. It
seems, therefore, that the meteoroids which produce these
showers follow after TEMPEL'S comet, moving in the same
orbit with it. This shows a curious relation between
comets and meteors, of which we shall speak more fully in
the next chapter. When this fact was brought out, the
question naturally arose whether the same thing might not
be true of other meteoric showers.
Other Showers of Meteors. Although the November
showers (which occur about November 14) are the only
ones so brilliant as to strike the ordinary eye, it has long
been known that there are other nights of the year (nota-
bly August 10) in which more shooting-stars than usual
are seen, and in which the large majority radiate from one
point of the heavens. This shows conclusively that they
arise from swarms of meteoroids moving together around
the sun.
The Zodiacal Light. If we observe the western sky during the
winter or spring months, about the end of the evening twilight, we
shall see a stream of faint light, a little like the Milky Way, rising
obliquely from the west, and directed along the ecliptic toward a
point south-west from the zenith. This is called the zodiacal light.
It may also be seen in the east before daylight in the morning during
the autumn months, and has sometimes been traced all the way
across the heavens. Its origin is still involved in obscurity, but it
seems probable that it arises from an extremely thin cloud either of
meteoroids or of semi-gaseous matter like that composing the tail of
a comet, spread all around the sun inside the earth's orbit. Its
spectrum is probably that of reflected sunlight, a result which gives
color to the theory that it arises from a cloud of meteoroids revolv-
ing round the sun.
CHAPTER XIII.
COMETS.
ASPECT OF COMETS.
COMETS are distinguished from the planets botli by their
aspects and their motions. They come into view without
anything to herald their approach, continue in sight for a
few weeks or months, and then gradually vanish in the
distance. They are commonly considered us composed of
three parts: the nucleus, the coma (or hair), and the tail.
The nucleus of a comet is, to the naked eye, a point of
light resembling a star or planet. Viewed in a telescope,
it generally has a small disk, but shades off so gradually
that it is difficult to estimate its magnitude. In large
comets it is sometimes several hundred miles in diameter.
The nucleus is always surrounded by a mass of foggy
light, which is called the coma. To the naked eye the
nucleus and coma together look like a star seen through a
mass of thin fog, which surrounds it with a sort of halo.
The nucleus and coma together are generally called the
head of the comet.
The tail of the comet is simply a continuation of the
coma extending out to a great distance, and always di-
rected away from the sun. It has the appearance of a
stream of milky light, which grows fainter and broader
as it recedes from the head. Like the coma it shades off
so gradually that it is impossible to fix any boundaries to
it. The length of the tail varies from 2 or 3 to 90 or
COMETS. 275
more. Generally the more brilliant the head of the comet,
the longer and brighter is the tail.
The above description applies to comets which can be
plainly seen by the naked eye. Half a dozen telescopic
comets may be discovered in a single year, while one of the
brighter class may not be seen for ten years or more.
When comets are studied with a telescope, it is found
that they are subject to extraordinary changes of structure.
FIG. 79. TELESCOPIC COMET WITHOUT FIG. 80. TELESCOPIC COMET WITH
A NUCLEUS. A NUCLEUS.
To understand these changes, we must begin by saying that
comets do not, like the planets, revolve around the sun in
nearly circular orbits, but always in orbits so elongated
that the comet is visible in only a very small part of its
course. See page 278, Fig. 82.)
THE VAPOROUS ENVELOPES.
If a comet is very small, it may undergo no changes of aspect
during its entire course. If it is an unusually bright one. a bow
surrounding the nucleus on the side toward the sun will develop
as the comet approaches the sun. This bow will gradually rise up
and spread out on all sides, finally assuming the form of a semi-
circle having the nucleus in its centre, or, to speak with more pre-
cision, the form of a parabola having the nucleus near its focus.
The two ends of this parabola will extend out further and further
so as to form a part of the tail, and finally be lost in it. Other bows
276 ASTRONOMY.
will successively form around the nucleus, all slowly rising from it
like clouds of vapor. These distinct vaporous masses are called the
envelopes : they shade off gradually into the coma so as to be with
difficulty distinguished from it, and indeed maybe considered as part
of it. These appearances are apparently caused by masses of vapor
streaming up from that side of the nucleus nearest the sun, and grad-
ually spreading around the comet on each side. The form of a bow
is not the real form of the envelopes, but only the apparent one in
which we see them projected against the background of the sky.
Perhaps their forms can be best imagined by supposing the sun to
be directly above the comet, and a fountain, throwing a liquid hori-
zontally on all sides, to be built upon that part of the comet which
is uppermost. Such a fountain would throw its water in the form
of a sheet, falling on all sides of the cometic nucleus, but not touch-
Fio. 81. FORMATION OF ENVELOPES.
ing it. Two or three vapor surfaces of this kind are sometimes seen
around the comet, the outer one enclosing each of the inner ones,
but no two touching each other.
THE PHYSICAL CONSTITUTION OF COMETS.
To tell exactly what a comet is, we should be able to show how all
the phenomena it presents would follow from the properties of mat-
ter, as we learn them at the surface of the earth. This, however, no
one has been able to do, many of the phenomena being such as we
should not expect from the known constitution of matter. All we
can do, therefore, is to present the principal characteristics of comets,
as shown by observation, and to explain what is wanting to reconcile
these characteristics with the known properties of matter.
In the first place, all comets which have been examined with the
spectroscope show a spectrum composed, in part at least, of bright
lines or bands. The positions and characters of these bands leave no
COMETS. 277
doubt that carbon, hydrogen, and nitrogen, and probably oxygen are
present in the cometary matter. More than twenty comets have been
examined since the invention of the spectroscope and all agree in
giving the same evidence. In some recent comets sodium has also
been discovered.
In the last chapter it was shown that swarms of minute particles
called meteoroids follow certain comets in their orbits. This is no
doubt true of all comets. We can only regard these meteoroids as
fragments or debris of the comet. On this theory a telescopic comet
which has no nucleus is simply a cloud of these minute bodies. The
nucleus of the brighter comets may either be a more condensed mass
of such bodies or it may be a solid or liquid body itself.
If the reader has any difficulty in reconciling this theory of de-
tached particles with the view already presented, that the envelopes
from which the tail of the comet is formed consist of layers of vapor,
he must remember that vaporous masses, such as clouds, fog, and
smoke, are really composed of minute separate particles of water or
carbon.
Formation of the Comet's Tail. The tail of the comet is not a per-
manent appendage, but is composed of the masses of vapor which
we have already described as ascending from the nucleus, and after-
ward moving away from the sun. The tail which we see on one
evening is not absolutely the same we saw the evening before, a por-
tion of the latter having been dissipated, while new matter has taken
its place, as with the stream of smoke from a steamship. The
motion of the vaporous matter which forms the tail being always
away from the sun, there seems to be a repulsive force exerted by
the sun upon it. The form of the comet's tail, on the supposition
that it is composed of matter driven away from the sun with a uni-
formly accelerated velocity, has been several times investigated, and
found to represent the observed form of the tail so nearly as to
leave little doubt of its correctness. We may, therefore, regard it as
an observed fact that the vapor which rises from the nucleus of the
comet is repelled by the sun instead of being attracted toward it, as
larger masses of matter are.
No adequate explanation of this repulsive force has ever been
given.
MOTIONS OF COMETS.
Previous to the time of NEWTON, no certain knowledge respecting
the actual motions of comets in the heavens had been acquired, ex-
cept that they did not move around the sun in ellipses like the planets.
278 ASTRONOMY.
When NEWTON investigated the mathematical results of the theory
of gravitation, he found that a body moviug under the attraction of
the sun might describe either of the three conic sections, the ellipse,
parabola, or hyperbola. Bodies moving in an ellipse, as the planets,
would complete their orbits at regular intervals of time, according
to laws already laid down. But if the body moved in a parabola or
an hyperbola, it would never return to the sun after once passing it,
but would move off to infinity. It was, therefore, very natural to
conclude that comets might be bodies which resemble the planets in
moving under the sun's attraction, but which, instead of describing
FIG. 82. ELLIPTIC AND PARABOLIC ORBITS.
an ellipse in regular periods, like the planets, move in parabolic or
hyperbolic orbits, and therefore only approach the sun a single time
during their whole existence.
This theory is now known to be essentially true for most of the
observed comets. A few are indeed found to be revolving around
the sun in elliptic orbits, which differ from those of the planets only
in being much more eccentric. But the greater number which have
been observed have receded from the sun in orbits which we are un-
able to distinguish from parabolas, though it is possible they ma} 7 be
extremely elongated ellipses. Comets are therefore divided with re-
COMETS.
sped to their motions into two classes: (Aperiodic comets, which are
known to move in elliptic orbits, and to return to the sun at fixed in-
tervals; and (2) parabolic comets, apparently moving in parabolas,
never to return.
The first discovery of the periodicity of a comet was made by HAL-
LEY in connection with the great comet of 1682. Examining the records
of past observations, he found that a comet moving in nearly the
same orbit with that of 1682 had been seen in 1607, and still another
in 1531. He was therefore led to the conclusion that these three
comets were really one and the same object, returning to the sun at
intervals of about 75 or 76 years. He therefore predicted that it
would appear again about the year 1758. The coinet was first seen
FIG. 83. ORBIT OF HALLEY'S COMET.
on Christmas-day, 1758, and passed its perihelion March 12th, 1759,
only one month before the predicted time. At present it is possible
to predict the places of some of the best known periodic comets
almost as accurately as the positions of the planets.
We give a figure showing the position of the orbit of HALLEY'S
comet relative to the orbits of the four outer planets. It attained its
greatest distance from the sun, far beyond the orbit of Neptune,
about the year 1873, and then commenced its return journey. The
figure shows the position of the comet in 1874. It was then far be-
yond the reach of the most powerful telescope, but its distance and
direction admit of being calculated with so much precision that a
telescope could be pointed at it at any required moment.
280 ASTRONOMY.
REMARKABLE COMETS.
It is familiarly known that bright comets were in former
years objects of great terror, being supposed to presage
the fall of empires, the death of monarchs, the approach
of earthquakes, wars, pestilence, and every other calamity
which could afflict mankind. In showing the entire
groundlessness of such fears, science has rendered one of
its greatest benefits to mankind.
In 1456 the comet known as HALLEY'S, appearing
when the Turks were making war on Christendom, caused
D
STERN DJROKT
ROESE SACHBN
TRAV.
GOTT
WlRDsWoL
Fio. 84. MEDAL OF THE GREAT COMET OP 1680-81.
such terror that Pope CALIXTUS ordered prayers to be
offered in the churches for protection against it. This
is supposed to be the origin of the popular myth that the
Pope once issued a bull against the comet.
The number of comets visible to the naked eye, so far as
recorded, has generally ranged from twenty to forty in a
century. Only a small portion of these, however, have
been so bright as to excite universal notice.
Comet of 1680. One of the most remarkable of these
brilliant comets is that of 1680. It inspired such terror
that a medal, of which we present a figure, was struck
upon the Continent of Europe to quiet apprehension. A
free translation of the inscription is : "The star threatens
COMETS. 281
evil things ; trust only ! God will turn them to good." *
What makes this comet especially remarkable in history
is that NEWTON calculated its orbit, and showed that it
moved around the sun in a conic section, in obedience to
the law of gravitation.
Great Comet of 1811. It has a period of over 3000
years, and its aphelion distance is about 40,000,000,000
miles.
Great Comet of 1843. One of the most brilliant comets
which have appeared during the present century was that
of February, 1843. It was visible in full daylight close to
the sun. Considerable terror was caused in some quar-
ters lest it might presage the end of the world, which had
been predicted for that year by MILLER. At perihelion it
passed nearer the sun than any other body has ever been
known to pass, the least distance being only about one
fifth of the sun's semi diameter. With a very slight
change of its original motion, it would have actually fallen
into the sun.
Great Comet of 1858. Another comet remarkable for
the length of time it remained visible was that of 1858.
It is frequently called after the name of DON ATI, its first
discoverer. No comet visiting our neighborhood in recent
times has afforded so favorable an opportunity for study-
ing its physical constitution. Its greatest brilliancy
occurred about the beginning of October, when its tail was
40 in length and 10 in breadth at its outer end. Its period
is 1950 years.
* The student should notice the care which the author of the in-
scription has taken to make it consolatory, to make it rhymo, and
to give implicitly the year of the comet by writing certain Roman
numerals larger than the other letters.
FIG. 85. Dwuii'i OOMBT OP 1868.
COMETS. 283
Great Comet of 1882. It is yet too soon to speak of the
results of the observations on this magnificent object. Its
splendor will not soon be forgotten by those who have
seen it.
Encke's Comet and the Eesisting Medium. Of telescopic comets,
that which has been most investigated by astronomers is known as
ENCKK'S comet. Its period is between three and four years. Viewed
with a telescope, it is not different in any respect from other tele-
scopic comets, appearing simply as a mass of foggy light, somewhat
brighter near one side. .Under the most favorable circumstances, it
is just visible to the naked eye. The circumstance which has lent
most interest to this comet is that the observations which have been
made upon it seem to indicate that it is gradually approaching the
sun. ENCKE attributed this change in its orbit to the existence in
space of a resisting medium, so rare as to have no appreciable effect
upon the motion of the planets, and to be felt only by bodies of ex-
treme tenuity, like the telescopic comets. The approach of the
comet to the sun is shown, not by direct observation, but only by a
gradual diminution of the period of revolution. It will be many
centuries before thif period would be so far diminished that the
comet would actually touch the sun.
If the change in the period of this comet were actually due to the
cause which ENCKE supposed, then other faint comets of the same
kind ought to be subject to a similar influence. But the investiga-
tions which have been made in recent times on these bodies show no
deviation of the kind. It might, therefore, be concluded that the
change in the period of ENCKE'S comet must be due to some other
cause. There is, however, one circumstance which leaves us in
doubt. ENCKE'S comet passes nearer the sun than any other comet
of short period which has been observed with sufficient care to de-
cide the question. It may, therefore, be supposed that the resisting
medium, whatever it may be, is densest near the sun, and does not
extend out far enough for the other comets to meet it. The question
is one very difficult to settle. The fact is that all comets exhibit
slight anomalies in their motions which prevent us from deducing
conclusions from them with the same certainty that we should from
those of the planets. One of the chief difficulties in investigating
the orbits of comets with all rigor is due to the difficulty of obtaining
accurate positions of the centre of so ill-defined an object as the
nucleus.
PART III.
THE UNIVERSE AT LARGE.
INTRODUCTION.
IN our studies of the heavenly bodies, we have hitherto
been occupied almost entirely with those of the solar sys-
tem. Although this system comprises the bodies which
are most important to us, yet they form only an insignifi-
cant part of creation. Besides the earth on which we
dwell, only seven of the bodies of the solar system are
plainly visible to the naked eye, whereas some 2000 stars
or more can be seen on any clear night.
The material universe, as revealed by the telescope, con-
sists principally of shining bodies, many millions in num-
ber, a few of the nearest and brightest of which are visible
to the naked eye as stars. They extend out as far as the
most powerful telescope can penetrate, and no one knows
how much farther. Our sun is simply one of these stars,
and does not, so far as we know, differ from its fellows in any
essential characteristic. From the most careful estimates,
it is rather less bright than the average of the nearer stars,
and overpowers them by its brilliancy only because it is so
much nearer to us.
The distance of the stars from each other, and therefore
from the sun, is immensely greater than any of the dis-
tances which we have hitherto had to consider in the solar
286 ASTRONOMY.
system. In fact, the nearest known star is about seven
thousand times as far as the planet Neptune. If we sup-
pose the orbit of this planet to be represented by a child's
hoop, the nearest star would be three or four miles away.
We have no reason to suppose that contiguous stars are, on
the average, nearer than this, except in special cases where
they are collected together in clusters.
The total number of the stars is estimated by millions, and
they are probably separated by these wide intervals. It
follows that, in going from the sun to the nearest star, we
would be simply taking one step in the universe. The
most distant stars visible in great telescopes are probably
several thousand times more distant than the nearest one,
and we do not know what may lie beyond.
The point we wish principally to impress on the reader
in this connection is that, although the stars and planets pre-
sent to the naked eye so great a similarity in appearance,
there is the greatest possible diversity in their distances
and characters. The planets, though many millions of
miles away, are comparatively near us, and form a little
family by themselves, which is called the solar system.
The fixed stars are at distances incomparably greater the
nearest star being thousands of times more distant than
the farthest planet. The planets are, so far as we can see,
worlds somewhat like this on which we live, while the stars
are suns, generally larger and brighter than our own.
Each star may, for aught we know, have planets revolving
around it, but their distance is so immense that the largest
planets will remain invisible with the most powerful tele-
scopes man can ever hope to construct.
The classification of the heavenly bodies thus leads us to
this curious conclusion. Our sun is one of the family of
THE UNIVERSE AT LARGE. 287
stars, the other members of which stud the heavens at
night, or, in other words, the stars are suns like that which
makes the day. The planets, though they look like stars,
are not such, but bodies more like the earth.
The great universe of stars, including the creation in its
largest extent, is called the stellar system) or stellar
universe. We have first to consider how it looks to the
naked eye.
CHAPTER I.
CONSTELLATIONa
GENERAL ASPECT OF THE HEAVENS.
WHEN we view the heavens with the unassisted eye, the
stars appear to be scattered nearly at random over the
surface of the celestial vault. The only deviation from an
entirely random distribution which can be noticed is a cer-
tain grouping of the brighter ones into constellations.
A few stars are comparatively much brighter than the rest,
and there is every gradation of brilliancy, from that of
the brightest to those which are barely visible. We also
notice at a glance that the fainter stars outnumber the
bright ones; so that if we divide the stars into classes ac-
cording to their brilliancy, the fainter classes will contain
the most stars.
The total number one can see will depend very largely
upon the clearness of the atmosphere and the keenness of
the eye. There are in the whole celestial sphere about
6000 stars visible to an ordinarily good eye. Of these,
however, we can never see more than a fraction at any
one time, because one half of the sphere is always below the
horizon. If we could see a star in the horizon as easily as
in the zenith, one half of the whole number, or 3000, would
be visible on any clear night. But stars near the horizon
are seen through so great a thickness of atmosphere as
greatly to obscure their light ; consequently only the
CONSTELLATIONS. 289
brightest ones can there be seen. As a result of this ob-
scuration, it is not likely that more than 2000 stars can
ever be taken in at a single yiew by any ordinary eye.
About 2000 other stars are so near the south pole
that they never rise in our latitudes. Hence out of the
6000 supposed to be visible, only 4000 ever come within
the range of our vision, unless we make a journey toward
the equator.
The Galaxy. Another feature of the heavens, which is
less striking than the stars, but has been noticed from
the earliest times, is the Galaxy, or Milky Way. This
object consists of a magnificent stream or belt of white
milky light 10 or 15 in breadth, extending obliquely
around the celestial sphere. During the spring months it
nearly coincides with our horizon in the early evening,
but it can readily be seen at all other times of the year
spanning the heavens like an arch. It is for a portion of
its length split longitudinally into two parts, which remain
separate through many degrees, and are finally united
again. The student will obtain a better idea of it by
actual examination than from any description. He will
see that its irregularities of form and lustre are such that
in some places it looks like a mass of brilliant clouds.
Lucid and Telescopic Stars. When we view the heavens
with a telescope, we find that there are innumerable stars
too small to be seen by the naked eye. We may there-
fore divide the stars, with respect to brightness, into two
great classes.
Lucid Stars are those which are visible without a tele-
scope.
Telescopic Stars are those which are not so visible.
When GALILEO first directed his telescope to the heav-
290 ASTRONOMY.
ens, about the year 1610, he perceived that the Milky
Way was composed of stars too faint to be individually
seen by the unaided eye. We thus have the interesting
fact that although telescopic stars cannot be seen one by
one, yet in the region of the Milky Way they are so numer-
ous that they shine in masses like brilliant clouds. HUY-
GHENS in 1656 resolved a large portion of the Galaxy into
stars, and concluded that it was composed entirely of them.
KEPLEK considered it to be a vast ring of stars surround
ing the solar system, and remarked that the sun must be
situated near the centre of the ring. This view ngrecs
very well with the one now received, only that the stars
which form the Milky Way, instead of lying around the
solar system, are at a distance so vast as to elude all our
powers of calculation.
Such are in brief the more salient phenomena which
are presented to an observer of the starry heavens. We
shall now consider how these phenomena have been clas-
sified by an arrangement of the stars according to their
brilliancy and their situation.
MAGNITUDES OF THE STARS.
In ancient times the stars were arbitrarily classified into six
orders of magnitude. The fourteen brightest visible in our lati-
tude were designated as of the first magnitude, while those which
were barely visible to the naked eye were said to be of the sixth
magnitude. This classification, it will be noticed, is entirely arbi-
trary, since there are no two stars which are absolutely of the same
brightness; that is, if all the stars were arranged in the order of
their actual brilliancy, we should find a regular gradation from the
brightest to the faintest, no two being precisely the same. There-
fore the brightest star of any one magnitude is about of the same
brilliancy with the faintest one of the next higher magnitude. Be-
tween the north pole and 35 south declination there are:
CONSTELLATIONS. 291
14 stars of the first magnitude. -
48 " " second "
152 " " third "
313 " " fourth "
854 " " fifth "
3974 " " sixth "
5355 of the first six magnitudes.
Of these, however, nearly 2000 of the sixth magnitude are so faint
that they can be seen only by an eye of extraordinary keenness. A
star of the second magnitude is four tenths as bright as one of the
first; one of the third is four tenths as bright as one of the second,
and so on.
THE CONSTELLATIONS AND NAMES OF THE STABS.
The earliest astronomers divided the stars into groups,
called constellations, and gave special proper names both
to these groups and to many of the more conspicuous
stars.
We have evidence that more than 3000 years before the commence-
ment of the Christian chronology the star Sinus, the brightest in the
heavens, was known to the Egyptians under the name of Sothis.
The seven stars of the Great Bear, so conspicuous in our northern
sky, were known under that name to HOMER and HESIOD, as well as
the group of the Pleiades, or Seven Stars, and the constellation of
Orion. Indeed, it would seem that all the earlier civilized nations,
Egyptians, Chinese, Greeks, and Hindoos, had some arbitrary divi-
sion of the surface of the heavens into irregular and often fantastic
shapes, which were distinguished by names.
In early times the names of heroes and animals were given to the
constellations, and these designations have come down to the present
day. Each object was supposed to be painted on the surface of the
heavens, and the stars were designated by their position upon some
portion of the object. The ancient and mediaeval astronomers would
speak of "the bright star in the left foot of Orion," " the eye of the
Bull," "the heart of the Lion," "the head of Perseus," etc. These
figures are still retained upon some star-charts, and are useful where
it is desired to compare the older descriptions of the constellations
with our modern maps. Otherwise they have ceased to serve any
292 ASTRONOMY.
purpose, and are not generally found on maps designed for purely
astronomical uses.
The Arabians, who used this clumsy way of designating stars,
gave special names to a large number of the brighter ones. Some of
these names are iu common use at the present time, as Aldebaran,
Fomalhaut, etc.
In 1654 BAYER, of Germany, mapped down the constellations
upon charts, designating the brighter stars of each constellation by
the letters of the Greek alphabet. When this alphabet was exhaust-
ed he introduced the letters of the Roman alphabet. In general, the
brightest star was designated by the first letter of the alphabet, a,
the next by the following letter, ft, etc.
On this system, a star is designated by a certain Greek letter, fol-
lowed by the genitive of the Latin name of the constellation to which
it belongs. For example, a Canis flfajoris, or, in English, a of the
Great Dog, is the designation of Sinus, the brightest star in the
heavens. The seven stars of the Great Bear are called a Ursa Ma-
joris, ft Ursce Majorin, etc. Arcturus is a Bootis. The reader will
here see a resemblance to our way of designating individuals by a
Christian name followed by the family name. The Greek letters
furnish the Christian names of the separate stars, while the name of
the constellation is that of the family. As there are only fifty letters
in the two alphabets used by BAYER, it will be seen that only the
fifty brightest stars in each constellation could be designated by this
method.
When by the aid of the telescope many more stars than these were
laid down, some other method of denoting them became necessary.
FLAMSTEED, who observed before and after 1700, prepared an ex-
tensive catalogue of stars, in which those of each constellation were
designated by numbers in the order of right ascension. These num-
bers were entirely independent of the designations of BAYER that
is, he did not omit the BAYER stars from his system of numbers, but
numbered them as if they had no Greek letter. Hence those stars to
which BAYER applied letters have two designations, the number and
the letter. The fainter stars are designated either by their R.A. and
d, or by their numbers in some catalogue of stars.
NUMBERING AND CATALOGUING THE STABS.
As telescopic power is increased, we still find stars of fainter and
fainter light. But the number cannot go on increasing forever in
the same ratio as with the brighter magnitudes, because, if it did,
the whole sky would be a blaze of starlight,
CON STELLA TTON8.
293
If telescopes with powers far exceeding our present ones were
made, they would no doubt show new stars of the 20th and 21st
magnitudes. But it is highly probable that the number of such suc-
cessive orders of stars would not increase in the same ratio as is ob-
served in the 8th, 9th, and 10th magnitudes, for example. The
enormous labor of estimating the number of stars of such classes will
long prevent the accumulation of statistics on this question ; but this
much is certain, that in special regions of the sky, which have been
searchingly examined by various telescopes of successively increas-
ing apertures, the number of new stars found is by no means in pro-
portion to the increased instrumental power. If this is found to be
true elsewhere, the conclusion may be that, after all, the stellar sys-
tem can be experimentally shown to be of finite extent, or to con-
tain only a finite number of stars, rather.
We have already stated that in the whole sky an eye of average
power will see about 6000 stars. With a telescope this number is
greatly increased, and the most powerful telescopes of modern times
will probably show more than 60,000,000 stars. As no trustworthy
estimate has ever been made, there is great uncertainty upon this
point, and the actual number may range anywhere between
40.000.000 to 100,000.000. Of this number, not one out of twenty
has ever been catalogued at all.
The southern sky has many more stars of the first seven magni-
tudes than the northern, and the zones immediately north and south
of the equator, although greater in surface than any others of the
same width in declination, are absolutely poorer in such stars.
This will be much better understood by consulting the grnphical
representation on page 294. On this chart are laid down all the stars
of the British Association Catalogue (a dot for each star), and beside
these the Milky Way is represented. The relative richness of the
various zones can be at once seen.
The distribution and number of the brighter stars (1st to 7th magni-
tude) can be well understood from this chart.
In ARGELANDER'S Durchmuxterung of the stars of the northern
heavens there are recorded as belonging to the northern hemisphere:
37
128
310
1,016
4,328
13,593
57,960
237,544
10 stars between the 1.0 magnitude and the 1.9 magnitude.
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
2.9
3.9
4.9
5.9
6.9
7.9
8.9
9.5
294
ASTRONOMY.
CONSTELLATIONS.
295
In all 314,926 stars from the first to the 9.5 magnitudes are enu-
merated in the northern sky, so that there are about 600,000 in the
whole heavens.
We may readily compute the amount of light received by the earth
on a clear but moonless night from these stars. Let us assume that
the brightness of an average star of the first magnitude is about 0.5
of that of a LyroB. A star of the 2d magnitude will shine with a
light expressed by 0.5 X 0.4 = 0.20, and so on. (See p. 291.)
The total brightness of
10
37
128
310
1,016
4,328
13,593
57,960
1st magi
2d
3d
4th
5th
6th
7th
8th
litude st
ars is 5.0
7.4
102
9.9
13.0
22.1
27.8
47.4
Sum = 142.8
It thus appears that from the stars to the 8th magnitude, inclusive,
we receive 143 times as much light as from a Lyres, a Lyres has
been determined by ZOLLNER to be about 44,000,000,000 times fainter
than the sun, so that the proportion of starlight to sunlight can be
computed. It also appears that the stars of magnitudes too high to
allow them to be individually visible to the naked eye are yet so
numerous as to affect the general brightness of the sky more than
the so-called lucid stars (1st to 6th magnitude). The sum of the last
two numbers of the table is greater than the sum of all the others.
NOTE. At the end of this book two Star Maps (with
explanations) are given, by means of which the constella-
tions and principal stars can be identified. The larger
map is copied from BRUHNS' excellent "Atlas der Astron-
omic" (BROCKHAUS, Leipzig, 1872).
CHAPTER II.
VARIABLE AND TEMPORARY STARS.
STABS REGULARLY VAKIABLE.
ALL stars do not shine with a constant light. Since the
middle of the seventeenth century, stars variable in bril-
liancy have been known. The period of a variable star
means the interval of time in which it goes through all its
changes, and returns to its original brilliancy.
The most noted variable stars are Mir a Ceti (o Ceti) and
Algol (ft Persei). Mir a appears about twelve times in
eleven years, and remains at its greatest brightness (some-
times as high as the 2d magnitude, sometimes not above
the 4th) for some time, then gradually decreases for about
74 days, until it becomes invisible to the naked eye, and so
remains for about five or six months. From the time of
its reappearance as a lucid star till the time of its maximum
is about 43 days. The mean period, or the interval from
minimum to minimum, is about 333 days, but this period
varies greatly. The brilliancy of the star at the maxima
also varies.
Algol has been known as a variable star since 1667.
This star is commonly of the 2d magnitude; after remain-
ing so about 2| days, it falls to 4 m in the short time of
4| hours, and remains of 4 ra for 20 minutes. It then com-
VARIABLE AND TEMPORARY STARS. 297
mences to increase in brilliancy, and in another 3$ hours it
is again of the 2d magnitude, at which point it remains for
the rest of its period, about 3 d 12 h .
These two examples of the class of variable stars give a
rough idea of the extraordinary nature of the phenomena
they present. A closer examination of others discloses
minor variations of great complexity and apparently with-
out law.
About 90 variable stars are well known, and as many
more are suspected to vary. In nearly all cases the mean
period can be fairly well determined, though anomalies of
various kinds frequently appear. The principal anomalies
are:
First. The period is seldom constant. For some stars
the changes of the period seem to follow a regular law; for
others no law can be fixed.
Second. The time from a minimum to the next maxi-
mum is usually shorter than from this maximum to the
next minimum.
Third. Some stars (us ft Lyrce) have not only one maxi-
mum between two consecutive principal minima, but two
such maxima. For fi Lyrce, according to ARGELANDER,
3 d 2 h after the principal minimum comes the first maxi-
mum; then, 3 d 7 h after this, a secondary minimum in.which
the star is by no means so faint as in the principal mini-
mum, and finally 3 d 3 h afterward comes the principal maxi-
mum, the whole period being 12 d 21 h 47 m .
The course of one period is illustrated in the following table,
supposing the period to begin at O 4 O h . Opposite each phase is
given the intensity of light in terms of y Lyr = 1.
Phases of ft Lyrae.
Relative
Intensity.
Principal Minimum
0*
O 11
040
First Maximum
3 d
083
Second Minimum
6 d
9 h
058
Principal Maximum
9*
12 h
089
Principal Minimum
22 m
040
The periods of 94 well-determined variable stars being tabulated,
it appears that they are as follows:
Period between
No. of Stars.
Period
between
No. of Star*
Id.
and 20 d.
13
350 d. ;
ind 400 d.
13
20
50
1
400
450
8
50
100
4
450
500
3
100
150
4
500
550
150
200
5
550
600
200
250
9
600
650
1
250
300
14
650
700
300
350
18
700
750
1
2=94
It is natural that there should be few known variables of periods
of 500 days and over, but it is not a little remarkable that the periods
of over half of these variables should fall between 250 aud 450 days.
The color of over 80 per cent of the variable stars is red or orange.
Red stars (of which 600 to 700 arc known) are now receiving close
attention, as there is a strong likelihood of finding among them many
new variables.
The spectra of variable stars show changes which appear to be
connected with the variations in their light.
TEMPORARY OR NEW STARS.
There are a few cases known of apparently new stars which have
suddenly appeared, attained more or less brightness, and slowly de-
creased in magnitude, either disappearing totally, or finally remain-
ing as comparatively faint objects.
The most famous one was that of 1572, which attained a brightness
VARIABLE AND TEMPORARY STARS.
greater than that of Sirius or Jupiter and approached to Venus, being
even visible to the eye in daylight. TYCHO BRAHE first observed this
star in November, 1572, and watched its gradual increase in light
until its maximum in December. It then began to diminish in bright-
ness, and in January, 1573, it was fainter than Jupiter. In February
it was of the 1st magnitude, in April of the 2d, in July of the 3d, and
in October of the 4th. It continued to diminish until March, 1574,
when it became invisible, as the telescope was not then in use. Its
color, at first intense white, decreased through yellow and red.
When it arrived at the 5th magnitude its color again became white,
and so remained till its disappearance. TYCHO measured its distance
carefully from nine stars near it, and near its place there is now a star
of the 10th or llth magnitude, which is possibty the same star.
The history of temporary stars is in general similar to that of the
star of 1572, except that none have attained so great a degree of bril-
liancy. More than a score of such objects are known to have ap-
peared, many of them before the making of accurate observations,
and the conclusion is probable that many have appeared without
recognition. Among telescopic stars there is but a small chance of
detecting a new or temporary star.
Several supposed cases of the disappearance of stars exist, but here
there are so many possible sources of error that great caution is neces-
sary in admitting them.
Two temporary stars have appeared since the invention of the spec-
troscope (1859), and the conclusions drawn from a study of their spec-
tra are most important as throwing light upon the phenomena of
variable stars in general.
The general theory of variable stars which has now the most evi-
dence in its favor is this: These bodies are, from some general cause
not fully understood, subject to eruptions of glowing hydrogen gas
from their interior, and to the formation of dark spots on their sur-
faces. These eruptions and formations have in most cases a greater
or less tendency to a regular period.
In the case of our sun (which is a variable star) the period is 11
years, but in the case of many of the stars it is much shorter. Ordi-
narily, as in the case of the sun and of a large majority of the stars,
the variations are too slight to affect the total quantity of light to any
visible extent. But in the case of the variable stars this spot-producing
power and the liability to eruptions are very much greater, and thus
we have changes of light which can be readily perceived by the eye.
Some additional strength is given to this theory by the fact just men-
tioned, that so large a proportion of the variable stars are red. It is well
known that glowing bodies emit a larger proportion of red rays and
300 ASTRONOMY.
a smaller proportion of blue ones the cooler they become. It is there-
fore probable that the red stars have the least heat. This being the
case, it is more easy to produce spots on their surface; and if their
outside surface is so cool as to become solid, the glowing hydrogen
from the interior when it did burst through would do so with more
power than if the surrounding shell were liquid or gaseous.
There is, however, at least one star of which the variations may be
due to an entirely different cause; namely, Algol. The extreme regu-
larity with which the light of this object fades away and disappears
suggest* the possibility that a dark body may be revolving around it,
and partially eclipsing it at every revolution. The law of variation
of its light is so different from that of the light of other variable stars
as to suggest a different cause. Most others are near their maximum
for only a small part of their period, while Algol is at its maximum
for nine tenths of it. Others are subject to nearly continuous changes,
while the light of Algol remains constant during nine tenths of its
period.
CHAPTER III.
MULTIPLE STARS.
CHAEACTEE OF DOUBLE AND MULTIPLE STAES.
we examine the heavens with telescopes, we find
many cases in which two or more stars are extremely close
together, so as to form a pair, a triplet, or a group. It is
evident that there are two ways to account for this appear-
ance.
1. We may suppose that the stars happen to lie nearly
in the same straight line from us, but have no connection
with each other. It is evident that in this case a pair of
stars might appear double, although the one was hundreds
or thousands of times farther off than the other. It is,
moreover, impossible, from mere inspection, to determine
which is the farther off.
2. We may suppose that the stars are really near together,
as they appear, and are to be considered as forming a con-
nected pair or group.
A couple of stars in the first case is said to be optically
double.
Stars which are really physically connected are said to be
physically double.
If the lucid stars are equally distributed over the celestial sphere,
the chances are 80 to 1 against any two being within three minutes
of each other, and the chances are 500,000 to 1 against the six visible
stars of the Pleiades being accidentally associated as we see them.
When the millions of telescopic stars are considered, there is a greater
302 ASTSONOMY.
i
probability of such accidental juxtaposition. But the probability of
many such cases occurring is so extremely small that astronomers
regard all the closest pairs as physically connected. Of the 600,000
stars of the first ten magnitudes, about 10,000, or one out of every
60, has a companion within a distance of 30" of arc. This proportion
is many times greater than could possi-
bly be the result of chance distribution.
There are several cases of stars which
appear double to the naked eye. e Lyra
is such a star and is an interesting ob-
ject, from the fact that each of the two
stars which compose it is itself double.
This minute pair of points, capable of
being distinguished as double only by
the most perfect eye (without the tele-
scope), is really composed of two pairs
Fio. 86. THK QrADRtjpLK STAR of stars wide apart, with a group of
LYR*L smaller stars between and around
them. The figure shows the appearance in a telescope of consider-
able power.
Bevolutions of Double Stars Binary Systems. It is evident that if
double stars are endowed with the property of mutual gravitation,
they must be revolving around
each other, as the earth and
planets revolve around the sun,
else they would be 'drawn to-
gether as a single star.
The method of determining
the period of revolution of a
binary star is illustrated by the
figure, which is supposed to rep-
resent the field of view of an in-
verting telescope pointed toward
the south. The arrow shows the
direction of the apparent diur-
nal motion. The telescope is
supposed to be so pointed that
the brighter star may be in the
centre of the field. The num-
bers around the surrounding Flo> 87 -~" POSITIOKKA^QLE OP A DOUBLE
circle then show the angle of
position, supposing the smaller star to be in the direction of the
number.
MULTIPLE STARS. 303
Fig. 87 is a a example of a pair of stars in which the position-
angle is about 44.
If, by measures of this sort extending through a series of years, the
distance or position-angle of a pair of stars is found to change peri-
odically, it shows that one star is revolving around the other. Such
a pair is called a binary star or binary system. The only distinction
which we can make between binary systems and ordinary double
stars is founded on the presence or absence of this observed motion.
It is probable that nearly all the very close double stars are really
binary systems, but that many hundreds of years are required to per-
form a revolution in some instances, so that the motion has not yet
been detected.
The discovery of binary systems is one of great scientific interest,
because from them we learn that the law of gravitation includes the
stars as well as the solar system in its scope, and may thus be regarded
as truly universal.
When the parallax of a binary star is known, as well as the orbit,
it is possible to compute the mass of the binary system in terms of
the sun's mass. It is an important fact that such binary systems as
have been investigated do not differ greatly in mass from our sun.
CHAPTER IV.
NEBULA AND CLUSTERS.
DISCOVERY OF NEBTJLE.
IN the star-catalogues of PTOLEMY, HEVELIUS, and the
earlier writers, there was included a class of nebulous or
cloudy stars, which were in reality star-clusters. They ap-
peared to the naked eye as masses of soft diffused light of
greater or less extent. In this respect they were quite
analogous to the Milky Way. In the telescope, the nebu-
lous appearance of these spots vanishes, and they are seen
to consist of clusters of stars.
As the telescope was improved, great numbers of such
patches of light were found, some of which could be re-
solved into stars, while others could not. The latter were
called nebuldB and the former star-clusters.
About 1656 HUYGHENS described the great nebula of
Orion, one of the most remarkable and brilliant of these
objects. During the last century MESSIER, of Paris, made
a list of 103 northern nebulae, and LACAILLE noted a few
of those of the southern sky. Sir WILLIAM HERSCHEL
with his great telescopes first gave proof of the enormous
number of these masses. In 1 786 he published a, catalogue
of one thousand new nebulae and clusters. This was fol-
lowed in 1789 by a catalogue of a second thousand, and in
1802 by a third catalogue of five hundred new objects of
this class. Sir JOHN HERSCHEL added about two thou-
NEBULA AND CLUSTERS. 305
sand more nebulae. The general catalogue of nebulae and
clusters of stars of the latter astronomer, published in
1864, contains 5079 nebulae. Over two thirds of these
were first discovered by the HERSCHELS.
CLASSIFICATION OF NEBULA AND CLUSTEBS.
In studying these objects, the first question we meet is this: Are
all these bodies clusters of stars which look diffused only because
they are so distant that our telescopes cannot distinguish them sepa-
rately? or are some of them in reality what they seem to be; namely,
diffused masses of matter?
In his early memoirs of 1784 and 1785, Sir WILLIAM HEKSCHEL
took the first view. He considered the Milky Way as nothing but a
congeries of stars, and all nebulae naturally seemed 1o him to be but
stellar clusters, so distant as to cause the individual stars to disap-
pear in a general milkiness or nebulosity.
In 1791, however, his views underwent a change. He had dis-
covered a nebulous star (properly so called), or a star which was un-
doubtedly similar to the surrounding stars, and which was encom-
passed by a halo of nebulous light.
He says: "Nebulae can be selected so that an insensible gradation
shall take place from a coarse cluster like the Pleiades down to a
milky nebulosity like that in Orion, every intermediate step being
represented. This tends to confirm the hypothesis that all are com-
posed of stars more or less remote.
" A comparison of the two extremes of the series, as a coarse cluster
and a nebulous star, indicates, however, that the nebulosity about the
star is not of a starry nature.
"Considering a typical nebulous star, and supposing the nucleus
and chevelure to be connected, we may, first, suppose the whole
to be of stars, in which case either the nucleus is enormously
larger than other stars of its stellar magnitude, or the envelope is
composed of stars indefinitely small; or, second, we must admit that
the star is involved in a shining fluid of a nature totally unknown to
us.
"The shining fluid might exist independently of stars. The
light of this fluid is no kind of reflection from the star in the
centre. If this matter is self-luminous, it seems more fit to pro-
duce a star by its condensation than to depend on the star for its
existence.
306
ASTRONOMY.
"Both diffused nebulosities and planetary nebulae are better ac-
counted for by the hypothesis of a shining fluid than by supposing
them to be distant stars."
This was the first exact statement of the idea that, beside stars
and star-clusters, we have in the universe a totally distinct series of
objects, probably much more simple in their constitution. Observa-
tions on the spectra of these bodies have entirely confirmed the con-
clusions of HERSCIIEL.
Nebulae and clusters were divided by HERSCHEL into classes. He
FIG. 88. SPIRAL NEBULA.
applied the name planetary nebulae, to certain circular or elliptic
nebulae which in his telescope presented disks like the planets.
Spiral nebula are those whose convolutions have a spiral shape. This
class is quite numerous.
The different kinds of nebulae and clusters will be better under-
stood from the cuts and descriptions which follow than by formal
definitions. It must be remembered that there is an almost infinite
variety of such shapes.
NEBULAE AND CLUSTERS.
307
FIG. 89. THE OMEGA OR HORSESHOK
308
ASTRONOMY.
STAB-CLTTSTEBS.
The most noted of all the clusters is the Pleiades, which may be
seen during the winter months to the northwest of the constellation
Taurus. The average naked eye can easily distinguish six stars
within it, but under favorable conditions ten, eleven, twelve, or more
stars can be counted. With the telescope, over a hundred stars are
seen.
The clusters represented in Figs. 90 and 91 are good examples of
their classes. The first is globular and contains several thousand
small stars. The second is a cluster of about 200 stars, of magni-
tudes varying from the ninth to the thirteenth and fourteenth, in
which the brighter stars are scattered.
Fia. 90 GLOBULAR CLUSTER.
FIG. 01 COMPRESSED CLUSTER.
Clusters are probably subject to central powers or forces. This was
seen by Sir WILLIAM HERSCHEL in 1789. He says :
"Not only were round nebulae and clusters formed by central
powers, but likewise every cluster of stars or nebula that shows a
gradual condensation or increasing brightness toward a centre.
This theory of central power is fully established on grounds of ob-
servation which cannot be overturned.
"Clusters can be found of 10'diameter with a certain degree of
compression and stars of a certain magnitude, and smaller clusters
of 4', 3', or 2' in diameter, with smaller stars and greater compression,
and so on through resolvable nebulas by imperceptible steps, to the
NEBULAE AND CLUSTERS. 309
smallest and faintest [and most distant] nebulae. Other clusters there
are, which lead to the belief that either they are more compressed or
are composed of larger stars. Spherical clusters are probably not
more different in size among themselves than different individuals of
plants of the same species. As it has been shown that the spherical
figure of a cluster of stars is owing to central powers, it follows that
those clusters which, cceterit paribus, are the most complete in this
figure must have been the longest exposed to the action of these
causes.
"The maturity of a sidereal system may thus be judged from the
disposition of the component parts.
" Though we cannot see any individual nebula pass through all
its stages of life, we can select particular ones in each peculiar
stage," and thus obtain a single view of their entire course of de-
velopment.
SPECTRA OF NEBUUE AND CLUSTERS, AND FIXED STARS,
In 1864, five years after the invention of the spectroscope, the
examination of the spectra of the nebulae led to the discovery that
while the spectra of stars were invariably continuous and crossed with
dark lines similar to those of the solar spectrum, those of many ne-
bulae were discontinuous, showing these bodies to be composed of
glowing gas.
The spectrum of most clusters is continuous, indicating that the
individual stars are truly stellar in their nature. In a few cases,
however, clusters are composed of a mixture of nebulosity (usually
near their centre) and of stars, and the spectrum in such cases is
compound in its nature, so as to indicate radiation both by gaseous
and solid matter.
SPECTRA OF FIXED STARS.
Stellar spectra are found to be, in the main, similar to the solar
spectrum; i.e., composed of a continuous band of the prismatic col-
ors, across which dark lines or bands were laid, the latter being fixed
in position. These results show the fixed stars to resemble our own
sun in general constitution, and to be composed of an incandescent
nucleus surrounded by a gaseous and absorptive atmosphere of
lower temperature. This atmosphere around many stars is different
in constitution from that of the sun, as is shown by the different posi-
tion and intensity of the various black lines and bands which are due
to the absorptive action of th,e atmospheres of the stars,
310 ASTRONOMY.
It is probable that the hotter a star is the more simple a spectrum
it has; for the brightest, and therefore probably the hottest stars,
such as Sirius, give spectra showing only very thick hydrogen lines
and a few very thin metallic lines, while the cooler stars, such as
our sun, are shown by their spectra to contain ;i much larger num-
ber of metallic elements than stars of the type of Sinus, but no
non-metallic elements (oxygen possibly exccptcd). The coolest
stars give band spectra characteristic of compounds of metallic
with non-metallic elements, and of the non metallic elements uu-
combined.
MOTION OF STARS IN THE LINE OF SIGHT.
Spectroscopic observations of stars not only give information in
regard to their chemical and physical constitution, but have been
applied so as to determine approximately the velocity in kilometres
per second with which the stars are approaching to or receding from
the earth along the line joining earth and star. The theory of such a
determination is briefly as follows:
In the solar spectrum we find a group of dark lines, as a, b, c,
which always maintain their relative position. From laboratory
experiments, we can show that the three bright lines of incandescent
hydrogen (for example) have always the same relative position as
the solar dark lines a, b, c. From this it is inferred that the solar
dark lines are due to the presence of hydrogen in its absorptive
atmosphere.
Now, suppose that in a stellar spectrum we find three dark lines
a', b', c'. whose relative position is exactly the same as that of the
solar lines a, b, c. Not only is their relative position the same, but
the characters of the lines themselves, so far as the fainter spectrum
of the star will allow us to determine them, are also similar; that is,
a' and , b' and b, c' and c are alike as to thickness, blackness, nebu-
losity of edges, etc. etc. From this it is inferred that the star really
contains in its atmosphere the substance whose existence has been
shown in the sun.
If we contrive an apparatus by which the stellar spectrum is seen
in the lower half, say, of the eye-piece of the spectroscope, while
the spectrum of hydrogen is seen just ab<-ve it, we find in some
cases this remarkable phenomenon. The three dark stellar lines,
a', b f , c', instead of being exactly coincident with the three hydrogen
lines a, b, c, are seen to be all thrown to one side or the other by a
like amount; that is, the whole group a', b 1 ', c' , while preserving its
relative distances the same as those of the comparison group a, b c,
NEBULA AND CLUSTERS.
311
is shifted toward either the violet or red end of the spectrum by a
small yet measurable amount. Repeated experiments by different
instruments and observers show always a shifting in the same direc-
tion and of like amount. The figure shows the shifting of the P
line in the spectrum of Sirius, compared with one fixed line of
hydrogen.
This displacement of the
spectral lines is to be ac-
counted for by a motion of
the star toward or from the
earth. It is shown in Phy-
sics that if the source of
the light which gives the
spectrum a, b', c' is mov-
ing away from the earth,
this group will be shifted
toward the red end of the
spectrum ; if toward the
earth, then the whole group
will be shifted toward the
blue end. The amount of
this shifting is a function of
the velocity of recession or
approach, and this velocity
in miles per second can be calculated from the measured displace-
ment. This has been done for many stars. The results agree well,
when the difficult nature of the research is considered. The rates of
motion vary from insensible amounts to 100 kilometres per second;
and in some cases agree remarkably with the velocities computed
from the proper motions and probable parallaxes.
FIG. 92. F LINE IN SPECTRUM OP SIRIUS.
CHAPTER V.
MOTIONS AND DISTANCES OF THE STARS.
PROPER MOTIONS.
WE have already stated that, to the unaided vision, the
fixed stars appear to preserve the same relative position in
the heavens through many centuries, so that if the an-
cient astronomers could again see them, they could hardly
detect the slightest change in their arningement. But
accurate measurements have shown that there are slow
changes in the positions of the brighter stars, consisting in
a motion forward in a straight line and with uniform
velocity. These motions are, for the most part, so slow
that it would require thousands of years for the change of
position to be perceptible to the unaided eye. They are
called proper motions, since they are peculiar to the star
itself.
In general, the proper motions even of the brightest
stars are only a fraction of a second in a year, so that
thousands of years would be required for them to
change their place in any striking degree, and hundreds
of thousands to make a complete revolution around the
heavens.
PROPER MOTION OF THE SUN.
It is a priori evident that stars, in general, must have
proper motions, when once we admit the universality of
MOTIONS AND DISTANCES OF THE STARS. 313
gravitation. That any fixed star should be entirely at
rest would require that the attractions on all sides of it
should be exactly balanced. Any change in the position
of this star would break up this balance, and thus, in gen-
eral, it follows that stars must be in motion, since all of
them cannot occupy such a critical position as has to be
assumed.
If but one fixed star is in motion, this affects all the
rest, and we cannot doubt but that every star, our sun
included, is in motion by amounts which vary from small
to great. If the sun alone had a motion, and the other
stars were at rest, the consequence of this would be that
all the fixed stars would appear to be retreating en masse
from that point in the sky toward which we were moving.
Those nearest us would move more rapidly, those more
distant less so. And in the same way, the stars from
which the solar system was receding would seem to be
approaching each other. If the stars, instead of being
quite at rest, as just supposed, had motions proper to
themselves, then we should have a double complexity.
They would still appear to an observer in the solar system
to have motions. One part of these motions would be
truly proper to the stars, and one part would be due to the
advance of the sun itself in space.
Observations can show us only the resultant of these
two motions. It is for reasoning to separate this resultant
into its two components. At first the question is to deter-
mine whether the results of observation indicate any solar
motion at all. If there is none, the proper motions of
stars will be directed along all possible lines. If the sun
does truly move, then there will be a general agreement in
the resultant motions of the stars near the ends of the line
314 ASTRONOMY.
along which it moves, while those at the sides, so to speak,
will show comparatively less systematic effect. It is as if
one were riding in the rear of a railway train and watching
the rails over which it has just passed. As we recede from
any point, the rails at that point seem to come nearer and
nearer together.
If we were passing through a forest, we should see the
trunks of the trees from which we were going apparently
come nearer and nearer together, while those on the sides
of us would remain at their constant distance, and those in
front would grow further and further apart.
These phenomena, which occur in a case where we are
sensible of our own motion, serve to show how we may
deduce a motion, otherwise unknown, from the appear-
ances which are presented by the stars in space.
In this way, acting upon suggestions which had been
thrown out previously to his own time, HERSCHEL demon-
started that the sun, together with all its system, was mov-
ing through space in an unknown and majestic orbit of its
own. The centre round which this motion is directed
cannot yet be assigned. We can only determine the point
in the heavens toward which our course is directed " the
apex of solar motion."
A number of astronomers have since investigated this
motion with a view of determining the exact point in the
heavens toward which the sun is moving. Their results
differ slightly, but the points toward which the sun is
moving all fall in the constellation Hercules. The amount
of the motion is such that if the sun were viewed at right
angles to the direction of motion from an average star
of the first magnitude, it would appear to move about one
third of a second per year.
MOTIONS AND DISTANCES OF T.
DISTANCES OF THE FIXED STARS.
The ancient astronomers supposed all the fixed stars to
be situated at a short distance outside of the orbit of the
planet Saturn, then the outermost known planet. The
idea was prevalent that Nature would not waste space by
leaving a great region beyond Saturn entirely empty.
When COPERKICUS announced the theory that the sun
was at rest and the earth in motion around it, the problem
of the distance of the stars acquired a new interest. It was
evident that if the earth described an annual orbit, then
the stars would appear in the course of a year to oscillate
back and forth in' Corresponding orbits, unless they were
so immensely distant that these oscillations were too small
to be seen. The apparent oscillation of Saturn pro-
duced in this way was described in Part I. It amounts to
some 6 on each side of the mean position. These oscilla-
tions were, in fact, those which the ancients represented
by the motion of the planet around a small epicycle. But
no such oscillation had ever been detected in a fixed star.
This fact seemed to present an almost insuperable difficulty
in the reception of the Copernican system. Very natural-
ly, therefore, as the instruments of observation were from
time to time improved, this apparent annual oscillation of
the stars was ardently sought for.
The problem is identical with that of the annual parallax
of the fixed stars, which has been already described. This
parallax of a heavenly body is the angle which the mean
distance of the earth from the sun subtends when seen
from the body. The distance of the body from the sun is
inversely as the parallax (nearly). Thus the mean distance
of Saturn being 9.5, its annual parallax exceeds 6, while
316 ASTliONOMY.
that of Neptune, which is three times as far, is about 2.
It was very evident, without telescopic observation, that
the stars could not have a parallax of one half a degree.
They must therefore be at least twelve times as far as
Saturn if the Copernican system were true.
When the telescope was applied to measurement, a con-
tinually increasing accuracy began to be gained by the
improvement of the instruments. Yet for several genera-
tions the parallax of the fixed stars eluded measurement.
Very often indeed did observers think they had detected
a parallax in some of the brighter stars, but their succes-
sors, on repeating their measures with better instruments,
and investigating their methods anew, found their conclu-
sions erroneous. Early in the present century it became
certain that even the brighter stars had not, in general, a
parallax as great as 1*, and thus it became certain that they
must lie at a greater distance than 200,000 times that
which separates the earth from the sun.
Success in actually measuring the parallax of the stars
was at length obtained almost simultaneously by two as-
tronomers, BESSEL of Konigsberg and STRUVE of Dorpat.
BESSEL selected 61 Gygni for observation, in August, 1837.
The result of two or three years of observation was that
this star had a parallax of 0*.35, or about one third of a
second. This would make its distance from the sun nearly
600,000 astronomical units. The reality of this parallax
has been well-established by subsequent investigators, only
it has been shown to be a little larger, and therefore the
star a little nearer than BESSEL supposed. The most prob-
able parallax is now found to be 0" . 51, corresponding to a
distance of 400,000 radii of the earth's orbit.
The distances of the stars arc sometimes expressed by
MOTIONS AND DISTANCES OF THE STARS. 317
the time required for light to pass from them to our sys-
tem. The velocity of light is, it will be remembered, about
300,000 kilometres per second, or such as to pass from the
sun to the earth in 8 minutes 18 seconds.
The time required for light to reach the earth from some
of the stars, of which the parallax has been measured, is as
follows :
STAR.
Years.
STAR.
Years.
(x. Ocntaui'i
3-5
70 Ophiuclii
19-1
61 Cygni
6-7
z UTSCB MQJOTIS
24-3
21 185 Lelande
6-3
Al'CtUTUS . ...
25-4
ft Centduri
6-9
Y Di'dconis
35-1
H CassiopeioB
9-4
1830 Groombridge. .
35-9
34 Groombrid tv e
10-5
Polaris
42-4
21 258 Lelande
11 -9
3077 Bradley
46-1
17 415 Oeltzen
13-1
85 Pegasi
64-5
Sirius .
16-7
ct AUTIOCB
70-1
cc LyTffi
17-9
d Dvciconis
129-1
CHAPTER VI.
CONSTRUCTION OF THE HEAVENS.
THE visible universe, as revealed to us by the telescope, is
a collection of many millions of stars and of several thou-
sand nebulae. It is sometimes called the stellar or sidereal
system, and sometimes, as already remarked, the stellar
universe. The most far-reaching question with which
astronomy has to deal is that of the form and magnitude
of this system, and the arrangement of the stars which
compose it.
It was once supposed that the stars were arranged on the
same general plan as the bodies of the solar system, being
divided up into great numbers of groups or clusters, while
all the stars of each group revolved in regular orbits round
the centre of the group. All the groups were supposed to
revolve around some great common centre, which was
therefore the centre of the visible universe.
But there is no proof that this view is correct. We have
already seen that a great many stars are collected into clus-
ters, but there is no evidence that the stars of these
clusters revolve in regular orbits, or that the clusters them-
selves have any regular motion around a common centre.
The first astronomer to make a careful study of the arrangement
of the stars with a view to learn the structure of the heavens was Sir
WILLIAM HERSCHEL.
HERSCHEL'S method of study was founded on a mode of observa-
CONSTRUCTION OF THE HEAVENS.
319
tion which he called star-gauging. It consisted in pointing a power-
ful telescope toward various parts of the heavens and ascertaining by
actual count how thick the stars were in each region. His 20-foot
reflector was provided with such an eye piece that, in looking into
it, he would see a portion of the heavens about 15' in diameter. A
circle of this size on the celestial sphere has about one quarter the
apparent surface of the sun, or of the full moon. On pointing the
telescope in any direction, a greater or less number of stars were
nearly always visible. These were counted, and the direction in
which the telescope pointed was noted. Gauges of this kind were
made in all parts of the sky at which he could point his instrument,
and the results were tabulated in the order of right ascension.
The following is an extract from the gauges, and gives the average
number of stars in each tield at the points noted in right ascension
and north-polar distance :
N. P. D.
N. P. D.
R.
A.
92 to 94.
R.A.
78 to 80.
No. of Stars.
No. of Stars.
h.
m.
h.] m.]
15
10
9.4
11 6
3.1
15
47
10.6
12 44
4.6
16
25
13.6
12 49
3.9
16
37
18.6
14 30
3.6
In this small table, it is plain that a different law of clustering or
of distribution obtains in the two regions.
The number of these stars in certain portions is very great. For
example, in the Milky Way this number was as great as 116, 000 stars
in a quarter of an hour in some cases.
HERSCHEL supposed at first that he completely resolved the whole
Milky Way into small stars. This conclusion he subsequently modi-
fied. He says:
" It is very probable that the great stratum called the Milky Way is
that in which the sun is placed, though perhaps not in the very cen-
tre of its thickness.
" We gather this from the appearance of the Galaxy, which seems
to encompass the whole heavens, as it certainly must do if the sun is
within it. For, suppose a number of stars arranged between two
parallel planes, indefinitely extended every way, but at a given con-
siderable distance from each other, and calling this a sidereal stratum,
an eye placed somewhere within it will see all the stars in the direc-
320
ASTRONOMY.
lion of the planes of the stratum projected into a great circle, which
will appear lucid on account of the accumulation of the stars, while
* * ~-r"& p x>^ * *
B s&f' * . ^^
x * *d$f*l, * * * * * ^ * *
:- ; - ; ::%xW * *'* ; -Xv
FIG. 93. HERSCHKL'S THEORY OF THE STELLAR SYSTEM.
the rest of the heavens, at the sides, will only seem to be scattered
over with constellations, more or less crowded, according to the dis,-
CONSTRUCTION OF THE HEAVENS. 321
tance of the planes, or number of stars contained in the thickness or
sides of the stratum."
Thus in HERSCHEL'S figure an eye at S within the stratum a b will
see the stars in the direction of its length a b, or height c d, with all
those in the intermediate situations, projected into the lucid circle
A CBD, while those in the sides mv, nw, will be seen scattered over
the remaining part of the heavens MV NW.
" If the eye were placed somewhere without the stratum, at no
very great distance, the appearance of the stars within it would
assume the form of one of the smaller circles of the sphere, which
would be more or less contracted according to the distance of the
eye; and if this distance were exceedingly increased, the whole
stratum might at last be drawn together into a lucid spot of any
shape, according to the length, breadth, and height of the stratum.
" Suppose that a smaller stratum pq should branch out from the
former in a certain direction, and that it also is contained between
two parallel planes, so that the eye is contained within the great
stratum somewhere before the separation, and not far from the place
where the strata are still united. Then this second stratum will not
be projected into a bright circle like the former, but it will be seen
as a lucid branch proceeding from the first, and returning into it
again at a distance less than a semicircle.
" In the figure the stars in the small stratum p q will be projected
into a bright arc PR It P, which, after its separation from the circle
CBD, unites with it again at P.
"If the bounding surfaces are not parallel planes, but irregularly
curved surfaces, analogous appearances must result."
The Milky Way, as we see it with the naked eye, presents the
aspect which has been just accounted for. in its general appearance
of a girdle around the heavens and in its bifurcation at a certain
point, and HERSCHEL'S explanation of this appearance, as just given,
has never been seriously questioned. One doubtful point remains:
are the stars in Fig. 93 scattered all through the space 8 abpdl
or are they near its bounding planes, or clustered in any way within
this space so as to produce the same result to the eye as if uniformly
distributed ?
HERSCHEL assumed that they were nearly equably arranged all
through the space in question. He only examined one other arrange-
ment viz., that of a ring of stars surrounding the sun and he pro-
nounced against such an arrangement, for the reason that there is
absolutely nothing in the size or brilliancy of the sun to cause us to
suppose it to be the centre of such a gigantic system. No reason ex-
cept its importance to us personally can be alleged for such a sup-
322 ASTRONOMY.
position. By the assumptions of Fig. 93, each star will have its
own appearance of a galaxy or milky way, which will vary accord-
ing to the situation of the star.
Such an explanation will account for the general appearances of
the Milky Way and of the rest of the sky, supposing the stars equally or
nearly equally distributed in space. On this supposition, the system
must be deeper where the stars appear more numerous.
I
CHAPTER VIL
COSMOGONY.
A THEORY of the operations by which the universe re-
ceived its present form and arrangement is called Cosmog-
ony. This subject does not treat of the origin of matter,
but only of its transformations.
Three systems of Cosmogony have prevailed among
thinking men at different times:
(1) That the universe had no origin, but existed from
eternity in the form in which we now see it. This was the
view of the ancient philosophers.
(2) That it was created in its present shape in a mo-
ment, out of nothing. This view is based on the literal
sense of the words of the Old Testament.
(3) That it came into its present form through an ar-
rangement of materials which were before " without form
and void." This may be called the evolution theory. It
is to be noticed that no attempt is made to explain the
origin of the primitive matter.
The last is the idea which has prevailed, and it receives
many striking confirmations from the scientific discoveries
of modern times. The latter seem to show beyond all rea-
sonable doubt that the universe could not always have
existed in its present form and under its present condi-
tions ; that there was a time when the materials composing
it were masses of glowing vapor, and that there will be a
324 ASTRONOMY.
time when the present state of things will cease. The ex-
planation of the processes through which this occurs is
sometimes called the nebular hypothesis. It was first pro-
pounded by the philosophers SWEDEXBORG, KAXT, and
LAPLACE, and, although since greatly modified in detail,
their views have in the main been retained until the
present time.
We shall begin its consideration by a statement of the
various facts which appear to show that the earth and
planets, as well as the sun, were once a fiery mass.
The first of these facts is the gradual but uniform in-
crease of temperature as we descend into the interior of
the earth. Wherever mines have been dug or wells sunk
to a great depth, the temperature increases as we go down-
ward at the rate of about one degree centigrade to every 30
metres, or one degree Fahrenheit to every 50 feet. The
rate differs in different places, but the general average ie
near this. The conclusion which we draw from this may
not at first sight be obvious, because it may seem that the
earth might always have shown this same increase of tem-
perature. But there are several results which a little
thought will make clear, although their complete establish-
ment requires the use of the higher mathematics.
The first result is that the increase of temperature can-
not be merely superficial, but must extend to a great
depth, probably even to the centre of the earth. If it did
not so extend, the heat would have all been lost long ages
ago by conduction to the interior and by radiation from
the surface. It is certain that the earth has not received
any great supply of heat from outside since the earliest
geological ages, because such an accession of heat at the
earth's surface would have destroyed all life, and even
COSMOGONY. 325
melted all the rocks. Therefore, whatever heat there is
in the interior of the earth must have been there from be-
fore the commencement of life on the globe, and remained
through all geological ages.
The interior of the earth being hotter than its surface,
and hotter than the space around it, must be losing heat,
We know by the most familiar observation that if any ob-
ject is hot inside, the heat will work its way through to the
surface by the process of conduction. Therefore, since the
earth is a great deal hotter at the depth of 30 metres than
it is at the surface, heat must be continually coming to the
surface. On reaching the surface, it must be radiated off
into space, else the surface would have long ago become
as hot as the interior. Moreover, this loss of heat must
have been going on since the beginning, or at least since
a time when the surface was as hot as the interior. Thus, if
we reckon backward in time, we find that there must have
been more and more heat in the earth the further back
we go, so that we must finally reach back to a time when
it was so hot as to be molten, and then again to a time
when it was so hot as to be a mass of fiery vapor.
The second fact is that we find the sun to be cooling off
like the earth, only at an incomparably more rapid rate.
The sun is constantly radiating heat into space, and, so far
as we can ascertain, receiving none back again. A small
portion of this heat reaches the earth, and on this portion
depends the existence of life and motion on the earth's sur-
face. The quantity of heat which strikes the earth is only
about OTFinsWiroT of that which the sun radiates. This
fraction expresses the ratio of the apparent surface of the
earth, as seen from the sun, to that of the whole celestial
sphere.
326 ASTRONOMY.
Since the sun is losing heat at this rate, it must have had
more heat yesterday than it has to-day ; more two days ago
than it had yesterday, and so on. Thus calculating back-
ward, we find that the further we go back into time the
hotter the sun must have been. Since we know that heat
expands all bodies, it follows that the sun must have been
larger in past ages than it is now, and we can trace back
this increase in size without limit. Thus we are led to the
conclusion that there must have been a time when the sun
filled up the space now occupied by the planets, and must
have been a very rare mass of glowing vapor. The plan-
ets could not then have existed separately, but must have
formed a part of this mass of vapor. The latter was there-
fore the material out of Avhich the solar system was
formed.
The same process may be continued into the future.
Since the sun by its radiation is constantly losing heat, it
must grow cooler and cooler as ages advance, and must
finally radiate so little heat that life and motion can no
longer exist on our globe.
The third fact is that the revolutions of all the planets
around the sun take place in the same direction and in
nearly the same plane. We have here a similarity amongst
the different bodies of the solar system, which must have
had an adequate cause, and the only cause which lias ever
been assigned is found in the nebular hypothesis. This
hypothesis supposes that the sun and planets were once
a great mass of vapor, as large as or larger than the present
solar system, revolving on its axis in the same plane in
which the planets now revolve.
The fourth fact is seen in the existence of nebulae. The
spectroscope shows these bodies to be masses of glowing
COSMOGONY.
vapor. We thus actually see matter in the celestial spaces
under the very form in which the nebular hypothesis sup-
poses the matter of our solar system to have once existed.
Since these masses of vapor are so hot as to radiate light
and heat through the immense distance which separates us
from them, they must be gradually cooling off. This cool-
ing must at length reach a point when they will cease to
be vaporous and condense into objects like stars and
planets. We know that every star in the heavens radiates
heat as our sun does. In the case of the brighter stars the
heat radiated has been made sensible in the foci of our
telescopes by means of the thermo-multiplier. All the
stars must, like the sun, be radiating heat into space.
A fifth fact is afforded by the physical constitution of
the planets Jupiter and Saturn. The telescopic examina-
tion of these planets shows that changes on their surfaces
are constantly going on with a rapidity and violence to
which nothing on the surface of our earth can compare.
Such operations can be kept up only through the agency of
heat or some equivalent form of energy. But at the dis-
tance of Jupiter and Saturn the rays of the sun are entirely
insufficient to produce changes so violent. We are there-
fore led to infer that Jupiter and Saturn must be hot
bodies, and must therefore be cooling off like the sun,
stars, and earth.
We are thus led to the general conclusion that, so far
as our knowledge extends, nearly all the bodies of the
universe are hot, and are cooling off by radiating their
heat into space.
The idea that the heat radiated by the sun and stars may
in some way be collected and returned to them by the
operation of known natural laws is equally untenable. It
328 ASTRONOMY.
is a fundamental principle of the laws of heat that " the
latter can never pass from a cooler to a warmer body/' and
that a body can never grow warm or acquire heat in a space
that is cooler than the body is itself. All differences of
temperature tend to equalize themselves, and the only
state of things to which the universe can tend, under its
present laws, is one in which all space and all the bodies con-
tained in space are at a uniform temperature, and then all
motion and change of temperature, and hence the condi-
tions of vitality, must cease. And then all such life as ours
must cease also unless sustained by entirely new methods.
The general result drawn from all these laws and facts
is, that there was once a time when all the bodies of the
universe formed either a single mass or a number of masses
of fiery vapor, having slight motions in various parts, and
different degrees of density in different regions. A grad-
ual condensation around the centres of greatest density then
went on in consequence of the cooling and the mutual at-
traction of the parts, and thus arose a great number of
nebulous masses. One of these masses formed the ma-
terial out of which the sun and planets are supposed to
have been formed. It was probably at first nearly glob-
ular, of nearly equal density throughout, and endowed
with a very slow rotation in the direction in which the
planets now move. As it cooled oC, it grew smaller and
smaller, and its velocity of rotation increased in rapidity.
The rotating mass we have described must have had an axis
around which it rotated, and therefore an equator defined
as being everywhere 90 from this axis. In consequence
of the increase in the velocity of rotation, the centrifugal
force would also be increased as the mass grew smaller.
This force varies as the radius of the circle described by
COSMOGONY. 329
any particle multiplied by the square of its angular velocity.
Hence when the masses, being reduced to half the radius,
rotated four times as fast, the centrifugal force at the equa-
tor would be increased -Jx4 a , or eight times. The gravi-
tation of the mass at the surface, being inversely as the
square of the distance from the centre, or of the radius,
would be increased four times. Therefore as the masses
continue to contract, the centrifugal force increases at a
more rapid rate than the central attraction. A time would
therefore come when they would balance each other at the
equator of the mass. The mass would then cease to con-
tract at the equator, but at the poles there would be no
centrifugal force, and the gravitation of the mass would
grower stronger and stronger. In consequence the mass
would at length assume the form of a lens or disk very thin
in proportion to its extent. The denser portions of this
lens would gradually be drawn toward the centre, and there
more or less solidified by the process of cooling. A point
would at length be reached, when solid particles would begin
to be formed throughout the whole disk. These would grad-
ually condense around each other and form a single planet, or
they might break up into small masses and form a group of
planets. As the motion of rotation would not be altered
by these processes of condensation, these planets would all
be rotating around the central part of the mass, which is
supposed to have condensed into the sun.
It is supposed that at first these planetary masses, being
very hot, were composed of a central mass of those sub-
stances which condensed at a very high temperature, sur-
rounded by the vapors of those substances which were
more volatile. We know, for instance, that it takes a much
higher temperature to reduce lime and platinum to vapor
330 ASTRONOMY.
than it does to reduce iron, zinc, or magnesium. There-
fore, in the original planets, the limes and earths would
condense first, while many other metals would still be in
a state of vapor. The planetary masses would each be
affected by a rotation increasing in rapidity as they grew
smaller, and would at length form masses of melted metals
and vapors in the same way as the larger mass out of which
the sun and planets were formed. These masses would
then condense into a planet, with satellites revolving
around it, just as the original mass condensed into sun and
planets.
At first the planets would be so hot as to be in a molten
condition, each of them probably shining like the sun.
They would, however, slowly cool off by the radiation of
heat from their surfaces. So long as they remained liquid,
the surface, as fast as it grew cool, would sink into the in-
terior on account of its greater specific gravity, and its
place would be taken by hotter material rising from the
interior to the surface, there to cool off in its turn. There
would, in fact, be a motion something like that which
occurs when a pot of cold water is set upon the fire to boil.
Whenever a mass of wator at the bottom of the pot is
heated, it rises to the surface, and the cool water moves
down to take its place. Thus, on the whole, so long as
the planet remained liquid, it would cool off equally
throughout its whole mass, owing to the constant motion
from the centre to the circumference and back again. A
time would at length arrive when many of the earths and
metals would begin to solidify. At first the solid particles
would be carried up and down with the liquid. A time
would finally arrive when they would become so large
and numerous, and the liquid part of the general mass
COSMOGONY. 331
become so viscid, that the motion would be obstructed.
The planet would then begin to solidify. Two views
have been entertained respecting the process of solidifica-
tion.
According to one view, the whole surface of the planet
would solidify into a continuous crust, as ice forms over a
pond in cold weather, while the interior was still in a
molten state. The interior liquid could then no longer
come to the surface to cool off, and could lose no heat
except what was conducted through this crust. Hence
the subsequent cooling would be much slower, and the
globe would long remain a mass of lava, covered over by
a comparatively thin solid crust like that on which we
live.
The other view is that, when the cooling attained a cer-
tain stage, the central portion of the globe would be
solidified by the enormous pressure of the superincumbent
portions, while the exterior was still fluid, and that thus
the solidification would take place from the centre out-
ward.
It is still an unsettled question whether the earth is now
solid to its centre, or whether it is a great globe of molten
matter with a comparatively thin crust. Astronomers and
physicists incline to the former view ; geologists to the lat-
ter one. Whichever view may be correct, it appears cer-
tain that there are great lakes of lava in the interior from
which volcanoes are fed.
It must be understood that the nebular hypothesis, as we
have explained it, is not a perfectly established scientific
theory, but only a philosophical conclusion founded on the
widest study of nature, and pointed to by many otherwise
disconnected facts. The widest generalization associated
332 ASTRONOMY.
with it is that, so far as we can see, the universe is not self-
sustaining, but is a kind of organism which, like all other
organisms we know of, must come to an end in consequence
of those very laws of action which keep it going. It must
have had a beginning within a certain number of years
which we cannot yet calculate with certainty, but which
cannot much exceed 20,000,000, and it must end in a chaos
of cold, dead globes at a calculable time in the future,
when the sun and stars shall have radiated away all their
heat, unless it is re-created by the action of forces of which
we at present know nothing.
APPENDIX.
SPECTRUM ANALYSIS.
ALTHOUGH the subject of Spectrum Analysis belongs
properly to physics, a brief account of its relations to astron-
omy may be useful here,
To understand the instruments and methods of Spectrum
Analysis it will be necessary to recall the optical properties
of a prism, which are demonstrated in all treatises on phy-
sics.
The Prism. When parallel rays of homogeneous light,
FIG. 94.
red for example, fall on a face of a prism they are bent out
of their course, and when they emerge from the prism they
334 APPENDIX.
are again bent, but they still remain parallel; thus the rays
r r, r"r" , are bent into the final direction r V. This is true
for parallel rays of every color. They remain parallel after
deviation by the prism. This can be shown by experiment.
If the incident rays r r, in Fig. 94, are red, they will come
to the screen at r'r'. If they are violet rays, they will
come to v'v' on the screen, after having been bent more
from their original course than the red rays. The violet
rays, with the shortest wave-length, are the most refrangi-
ble. The red, with the longest wave-length, are the least
refrangible.
The experiments of Sir ISAAC NEWTON (1704) proved
that white light (as sunlight, moonlight, starlight) was
not simple but compound. That is, white light is made up
of light of different wave-lengths. Difference of wave-length
shows itself to the eye as difference of color. Seven colors were
distinguished by NEWTON; viz., violet, indigo, blue, green,
yellow, orange, red. (Memorize these in order. It is the
order of the colors in the rainbow.) If parallel rays of
white light, as sunlight, r r, fall on a prism, the red rays of
this beam will still fall at r'r', and the violet rays will fall
at v'v'. Between v' and r' the other rays will fall, in the
order just given; that is, in the order of their refrangibility.
The rainbow-colored streak on the screen is called the
spectrum; it is a solar, a lunar, or a stellar spectrum ac-
cording as the source of the rays is the sun, moon, or a star.
The solar spectrum is very bright; the lunar spectrum is
much fainter; and the spectrum of a star is far fainter than
either.
If we let parallel rays, rr, of red light come through a
circular hole at Q, they will form a circular image of the
hole at r'r'. If the hole is square or triangular, a square or
APPENDIX. 335
a triangular image will be formed. If it is a narrow slit, a
narrow streak of red light will be projected at r'r'.
When white light is passed through a circular hole at Q,
circular images of the hole are formed all along the line
r V to ?;V: the red images at r'r', the orange, yellow,
green, blue images in succession, and the violet image at
v'v'. If the hole is of any size these imnges will overlap,
so that the colors are not pure. If white light falls through
a narrow slit at Q, placed parallel to the edge A of the
prism, the purest spectrum is obtained. The different
spectra do not overlap.
FRAUNHOFER tried this experiment in 1804, and he
found that the spectrum of the sun was interrupted by certain
dark lines, fixed in relative position. These are the Fraun-
hofer lines, so called. He made a map of the solar spec-
trum, and on the map he placed the various lines in their
proper places, These lines appear in the same relative
position no matter whether a slit or a very small circular
hole is used, and they belong to the incident light and are
not produced by the apparatus. This simply renders them
visible. They are not seen when the light comes through
wide apertures, on account of the overlapping of the vari-
ous images.
The Spectroscope. A spectroscope consists essentially of
one or more prisms (or any other device, as a diffraction
grating) by means of which a spectrum is produced; of
a means to make the spectrum pure (a slit and collimator),
and of a means to see it well (a small telescope).
Fig. 95 shows the arrangement of a one-prism spectro-
scope. The light enters the slit S, which is exactly in
the focus of the objective A of the collimator. The rays
therefore emerge from A in parallel lines. They are de-
336
APPENDIX,
viated by the prism P, and enter the objective B, forming
an image of the spectrum at 0, which is viewed by the eye
Fro. 95.
The Solar Spectrum. Part of this image (of the solar
spectrum) is shown in Fig. 96, except as to color. The
A a B C
E b
FIG. 96.
various colors extend in succession from end to end of the
spectrum. In each color are certain dark lines which have
a definite position. The most conspicuous of these lines
are called the Fraunhofer lines, and a^e lettered A, B, C,
D, J2, F, G, H. A is below the easily visible red, B is at
its lower edge, G is near the middle of the red, D is a double
APPEKD1X 337
line in the orange, Eis in the green, F is in the blue, G in the
indigo, and Hm the violet. There are at least 500 lines
besides which can be seen with spectroscopes of moderate
power. Each and every one of these has a definite position.
When the instrument drawn in Fig. 95 is pointed toward
the sun (so that the sun's rafs fall on S), the spectrum
seen is that of the whole sun. If we wish to examine the
spectrum of & part of the sun, as of a spot for example, we
must attach the whole instrument (Fig. 95) to a telescope,
so that S is in the principal focal plane of the telescope-
objective (page 62). An image of the sun will then be
formed by the telescope-objective on the slit plate 8, and
the light from any part of that image can be examined at
will. The spectroscope is used in the same way to examine
faint stars. We employ a telescope in this case so that its
objective may collect more light and present it at the slit
of the spectroscope.
Spectra of Solids and Gases. A solid body, heated so
intensely as to give off light, has a continuous spectrum.
That is, there are no Fraunhofer lines in it, but prismatic
colors only. A gaseous body, heated so intensely as to give
off light, has a discontinuous spectrum.* That is, the colors
red to violet are no longer seen, but on a dark background
the spectrum shows one or more bright lines.
These lines have a definite relative position and are
characteristic of the particular gas. The vapor of sodium,
for example, gives two bright lines, whose relative position
is fixed. These facts can be shown by laboratory experi-
ments. Another experiment must be cited. If the source
of light is a solid body, intensely heated, the spectroscope
will show a continuous spectrum, without lines, as has been
* Unless under great pressure, when the spectrum is continuous as in the case
of our sun, and of stars of similar constitution,
338 APPENDIX.
said. If between the solid body and the slit of the spec-
troscope we place a glass vessel containing the vapor of
sodium, the spectrum will no longer be without lines. Two
dark lines will appear in the orange. If we remove the
vapor of sodium, the lines will go also. They are produced
by the absorptive action of this vapor on the incident light.
If we register exactly the spot in the field of view of the
spectroscope where each of these dark lines appears, and if
we then remove the sodium vapor and replace the solid
body (the source of light) by intensely heated sodium
vapor, we shall find the new spectrum to be composed of
two bright lines, as has been said; but these two bright
lines will occupy exactly the same places in the field of view
that the two dark lines formerly occupied.
The two dark lines are a sign of the kind of light that is
absorbed by sodium vapor; the two bright lines are a sign
of the kind of light that is emitted^ sodium vapor. These
two kinds are the snme. What is true of sodium vapor is
true of every gas. It absorbs light of the same kind (wave-
length) as that which it emits.
If a spectroscopist had to determine what kind of gas
was in a certain jar, he might do it in two ways. He might
heat it intensely, and measure the positions of the bright
lines of its spectrum; or he might place the gas between the
slit of his spectroscope and a highly heated solid body, and
agjiin measure the positions of the dark lines of its
absorption-spectrum. The measures and thus the positions
of the lines will be the same in both cases. By comparing
the measures with previous measures for known gases, the
name of the particular gas in question would become known
to him. New chemical elements have been discovered in
this way.
A PPENDIX. 339
Comparison of the Spectra of Incandescent Gases with
the Solar Spectrum. Laboratory experiments show the posi-
tions of the spectral lines characteristic of each gas or vapor.
The positions of the dark lines in the solar spectrum are
also known with accuracy. It is found that nearly every
one of the thousands of dark lines of the solar spectrum
has a position corresponding exactly to that of some one
of the lines of some gas or of the vapor of some metal. For
example, the vapor of iron has over 400 lines, whose posi-
tions are accurately known. In the solar spectrum there
are 400 lines whose positions precisely correspond to the
lines of iron vapor. The same is true of many other
substances, hydrogen, sodium, potassium, magnesium,
nickel, copper, etc. etc.
From this it is inferred that the sun's atmosphere con-
tains the metal iron in an incandescent state, as well as the
vapors of the other substances named.
Let us see the process of reasoning which led KIRCHHOFF
and BTOSEN (1859) to this interpretation of the observation.
We have seen (Part II., Chap. II.) that the sun is com-
posed of a luminous surface, the photosphere, surrounded
by a gaseous envelope. The photosphere alone would give a
continuous spectrum (with no dark lines). The gaseous
envelope will absorb the kind of light that it would itself
emit. The absorption is only selective, and it is character-
istic. If a solid incandescent body were placed in a labo-
ratory and surrounded by the vapors of iron, hydrogen,
sodium, etc., we should see the same spectrum that we
do see when we examine the sun.
The kind of evidence is easily understood from the fore-
going. Only the spectroscopist can fully appreciate the
amount of it. The resulting inference that the sun's
340 APPENDIX.
atmosphere contains the vapors of the metals named is
certain. These vapors exist uncombined in the sun's at-
mosphere. The temperature is too high to allow their
chemical combination.
RESULTS OF SPECTROSCOPIC OBSERVATIONS.
The Sun. The rays which come from the edges of the
sun give lines more marked and definite than those from
the centre.
This shows that rays from the limb traverse a greater
thickness of the absorbing layer. In Fig. 36, suppose SE
to be the sun's radius, and SMto be the radius of his at-
mosphere. A person stationed at E' and looking at the
sun along the lines E'S and E'E would see the centre of
the sun's disk by means of a ray which had traversed the
distance S M SE only; while the ray from the edge
E would have traversed a greater distance and would have
suffered a greater absorption. The sun's absorbing atmos-
phere ("reversing layer") is very thin, about 2000 kilometres
only. This layer is seen for an instant only, at the begin-
ning and end of a solar eclipse. The spectroscopic ex-
amination of sun-spots confirms what has already been said
of them. (Part II., Chapter II.)
The solar protuberances are now daily studied by the
spectroscope at various observatories. An explanation of
the method of viewing them, etc., is given on pp. 215, 216.
The Stars. The spectroscopic examination of stars (ana
star clusters) shows the fixed stars to be bodies of the same
general nature as our sun (see pp. 309, 310). Not only
have the elements composing many of the fixed stars been
determined by the spectroscope, but the velocity of the
motion of stars towards or from the earth has been fixed.
(See pp. 310, 31U
APPENDIX. 341
Comets and Nebulae. The spectra of comets and nebulae
are also studied, and the principal results of observation
are given on pp. 276, 277, and 309.
The Planets. The physical constitution of the planets as
revealed by the spectroscope is treated in Part II., Chapter
XL, pp. 261 to 264.
The Moon. The spectrum of the moon is simply an en-
feebled solar spectrum without any lines of selective ab-
sorption, which is one proof that the moon has no atmos-
phere.
Meteors. The gases shut up in the cavities of meteoric
stones have been spectroscopically examined, and they show
the characteristic comet spectrum. This gives a new proof
of the connection between comets and meteors.
DESCRIPTION AND MAPS OF THE CONSTELLA-
TIONS.
Every intelligent person desires to possess some know-
ledge of the names and forms of the principal constella-
tions. We therefore present a brief description of the
more striking ones, illustrated by figures, so that the
reader may be able to recognize them when he sees them.
We begin with the constellations near the pole, because
they can be seen on any clear night, while the southern
ones can, for the most part, only be seen during certain
seasons, or at certain hours of the night. Figure 97 shows
all the stars within 50 of the pole down to the fourth
magnitude inclusive. The Roman numerals around the
margin show the meridians of right ascension, one for
every hour. In order to have the map represent the
northern constellations exactly as they are, it must be
held so that the hour of sidereal time at which the observer
is looking at the heavens shall be at the top of the map.
Supposing the observer to look at nine o'clock (mean solar
time) in the evening, the months around the margin of
the map show the regions near the zenith. He has there-
fore only to hold the map with the month upward and face
the north, when he will have the northern heavens as they
appear, except that the stars near the bottom of the map
will be cut off by the horizon.
The first constellation to be looked for is Ursa Major,
APPENDIX.
343
Fio. 97. MAP OF THE NORTHERN CONSTELLATIONS.
344 APPENDIX.
the Great Bear, familiarly known as "the Dipper." The
two extreme stars in this constellation point toward the
pole-star, as already explained in the opening chapter.
Ursa Minor, sometimes called " the Little Dipper/' is
the constellation to which the pole-star belongs. About
15 from the pole, in right ascension XV hours, is a star
of the second magnitude, ft Ursce Minoris, about as bright
as the pole-star. A curved row of three small stars lies
between these two bright ones, and forms the handle of
the supposed dipper.
Cassiopeia, or " the Lady in the Chair," is near hour I
of right ascension, on the opposite side of the pole-star
from Ursa Major, and at nearly the same distance. The
six brighter stars are supposed to bear a rude resemblance
to a chair.
Jn hour III of right ascension is situated the constella-
tion Perseus, about 10 further from the pole than Cas-
siopeia. The Milky Way passes through these two con-
stellations.
Draco, the Dragon, is formed principally of a long row
of stars lying between Ursa Major and Ursa Minor. The
hcud of the monster is formed of the northernmost three
of four bright stars arranged at the corners of a lozenge
between XVII and XVIII hours of right ascension.
Cepheus is on the opposite side of Cassiopeia from Per-
seus, lying in the Milky Way, about XXII hours of right
ascension. It is not a brilliant constellation.
Other constellations near the pole are Camelopardalis,
Lynx, and Lacerta (the Lizard), but they contain only
small stars.
Figure 98 shows the equatorial stars situated between 30
north and 30 south declination. The forms of the con-
m
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(Henry Jfolt <
APPENDIX.
stellations are indicated by dotted lines,
men and animals with which the ancients covered the sky
are omitted. The Latin name within each boundary is the
name of the constellation. The Greek letters serve to
name the brightest stars (p. 292). The parallels of decli-
nation (for every 15) and the hour-circles (every hour) are
laid down.
The magnitudes of the stars are indicated by the sizes
of the dots. To use these maps it must be remembered
that as you face the south greater right ascensions are on
your left hand, less on your right. The right ascensions
of the stars immediately to the south between 6 and 7 P.M.
are :
For January 1, 1 hour;
" February 1, 3 "
" March 1, 5 "
" April 1, 7 "
" May 1, 9 "
" June 1, 11 "
For July 1, 13 hours;
" August 1, 15 "
" September 1, 17 "
" October 1, 19
" November 1, 21 "
" December 1, 23 "
By remembering these precepts, and by tracing the
alignments of the brighter stars, the map can be used to
identify every constellation marked on it.
INDEX.
THIS index is intended to point out the subjects treated in the
work, and further, to give references to the pages where technical
terms are denned or explained.
Aberration-constant, value of,
178.
Aberration of light, 174.
Achromatic telescope described,
63.
ADAMS'S work on perturbations
of Uranus, 256.
AIRY'S determination of the den-
sity of the earth, 148.
Algol (variable star), 296.
Altitude of a star defined, 18.
Angles, 3.
Annular eclipses of the sun, 135.
Apparent place of a star, 16.
Apparent time, 45.
ARISTARCHUS determines the so-
lar parallax, 165.
Asteroids defined, 191.
Asteroids, number of, 225 in
1882, 238.
Astronomical instruments (in
general), 60.
Astronomy (defined), 1.
Atmosphere of the moon, 231.
Atmospheres of the planets. See
Mercury, Venus, etc.
Axis of the earth defined, 21.
Azimuth defined, 19.
BESSEL'S parallax of 61 Cygni
(1837), 315.
Binary stars, 302.
BODE'S law stated, 193.
BOND'S discovery of the dusky
ring of Saturn, 1850, 250.
BOUVARD on Uranus, 256.
BRADLEY discovers aberration in
1729, 176.
BUNSEN, 339.
Calendars, how formed, 182.
CASSINI discovers four satellites
of Saturn (1684-1671), 852.
Catalogues of stars, general ac-
count, 79.
Celestial sphere, 14.
Centre of gravity of the solar
system, 194.
Chronology, 180.
Chronometers, 68.
CLARKE'S elements of the earth,
152.
Clocks, 68.
Clusters of stars, 308.
Comets, general account, 274.
Comets' orbits, 277.
Comets' tails, repulsive force,
277.
348
INDEX.
Comets, their physical constitu-
tion, 276.
Comets, their spectra, 277.
Conjunction (of a planet with
the sun) defined, 97.
Constellations, 288, 342.
Construction of the heavens, 317.
Co-ordinates of a star, 19, 37.
COPERNICUS, 103.
Correction of a clock defined, 69.
Cosmogony, 322.
Corona, its spectrum, 216.
Day, how subdivided into hours,
etc., 187.
Days, mean solar and solar, 46.
Declination of a star defined, 41.
Distance of the fixed stars, 314.
Distribution of the stars, 318.
Diurnal motion, 21, 22.
Dominical letter, 186.
DONATI'S comet (1858), 281.
Double (and multiple) stars, 301.
Earth, general account of, 142.
Earth's density, 142.
Earth's dimensions, 151.
Earth's mass, 142.
Eclipses of the moon, 131.
Eclipses of sun and moon, 129.
Eclipses of the sun, explanation,
132.
Eclipses of the sun, physical
phenomena, 212.
Eclipses, their recurrence, 136.
Ecliptic defined, 84.
Elements of the orbits of the ma-
jor planets, 198.
Elongation (of a planet) defined,
97.
ENCKE'S comet, 283.
ENCKE'S value of the solar paral-
lax, 8". 578, 166.
Epicycles, their theory, 102.
Equation of time, 188.
Equator (celestial) defined, 21.
Equatorial stars, 344.
Equatorial telescope, 74.
Equinoxes, 87.
Eye-pieces of telescopes, 62.
FABRITIUS observes solar spots
(1611), 207.
Figure of the earth, 148.
FRAUENHOFER'S Experiments
with the Prism, 335; Lines,
335, 337.
Future of the solar system, 332.
Galaxy, or milky way, 319.
GALILEO observes solar spots
(1611), 207.
GALILEO'S discovery of satellites
of Jupiter (1610), 240.
GALLE observes Neptune (1846),
259.
Gases, spectra of incandescent,
338; in meteoric stones, 341.
Geodetic surveys, 150.
Golden number, 184.
Gravitation extends to stars, 303.
Gravitation resides in each par-
ticle of matter, 119.
Gravitation, terrestrial, 146.
Greek alphabet, 11.
Gregorian calendar, 185.
HALLEY predicts the return of a
comet (1682), 279.
JELALi/s discovery of satellites of
Mars, 235.
HANSEN'S value of the solar par-
allax, 8". 92, 166.
HERSCHEL (W.) discovers two
satellites of Saturn (1789), 252.
HERSCHEL (W.) discovers two
satellites of Uranus (1787), 254.
INDEX.
849
HERSCHEL (W.) discovers Uranus
(1781), 253.
HERSCHEL'S catalogues of nebu-
lae, 305.
HERSCHEL'S star-gauges, 318.
HERSCHEL (W.) states that the
solar system is in motion (1783),
312.
HERSCHEL'S (W.) views on the
nature of nebulae, 305.
HIPPARCHUS discovers preces-
sion, 153.
HOOKE'S drawings of Mars
(1666), 234.
HORIZON (celestial sensible) of
an observer defined, 17, 20.
Hour-angle of a star defined, 39.
HUGGINS' determination of mo-
tion of stars in line of sight,
310.
HUGGINS first observes the spec-
tra of nebulae (1864). 309.
HUYGHENS discovers a satellite
of Saturn (1655), 252.
HUYGHENS discovers laws of
central forces, 116.
HUYGHENS' explanation of the
appearances of Saturn's rings
(1655), 248.
Inferior planets defined, 99.
lutramercurial planets, 226.
JANSSEN first observes solar pro-
minences in daylight, 213.
Julian year, 184.
Jupiter, general account, 240; ro-
tation-time, 242; satellites, 243.
KANT'S nebular hypothesis, 323.
KEPLER'S laws enunciated, 109.
KIRCHHOFF, 339.
LAPLACE'S nebular hypothesis,
323.
LAPLACE'S investigation of the
constitution of Saturn's rings,
252.
LAPLACE'S relations between the
mean motions of Jupiter's satel-
lites, 243.
LASSELL discovers Neptune's sat-
ellite (1847), 260.
LASSELL discovers two satellites
of Uranus (1847), 254.
Latitude (geocentric geogra-
phic) of a place on the earth de-
fined, 8, 31, 41, 152.
Latitude of a point on the earth
is measured by the elevation of
the pole, 31.
Latitudes and longitudes (celes-
tial) defined, 95.
Latitudes (terrestrial), how deter-
mined, 53.
LE VERRIER computes the orbit
of metoric shower, 271.
LE VERRIER'S researches on the
theory of Mercury, 226.
LE VERRIER'S work on perturba-
tions of Uranus, 257.
Light-gathering power of an ob-
ject-glass, 63.
Light-ratio (of stars) is about 2.5,
295.
Line of collimation of a telescope,
71.
Local time, 47.
LOCKYER'S discovery of a spec-
troscopic method, 216.
Longitude of a place, 9, 10.
Longitude of a place on the
earth (how determined), 50, 52.
Longitudes (celestial) defined,
95
Lucid stars defined, 289.
350
INDEX.
Lunar phases, nodes, etc. See
Moon's phases, nodes, etc.
Magnifying power of an eye-
piece, 65.
Major planets defined, 191.
Mars, physical description, 233.
Mars, rotation, 234.
Mars's satellites discovered by
HALL (1877), 235.
MASKKLYNE determines the den-
sity of the earth, 145.
Mass of the sun in relation to
masses of planets, 167.
Mean solar time defined, 45.
Mercury's atmosphere, 244.
Mercury, its apparent motions,
221.
Meridian (celestial) defined, 27.
Meridian circle, 72.
Meridians (terrestrial) defiued,27,
Melon ic cycle, 183.
Meteoric showers, 269.
Meteoric stones, gases in, 341.
Meteors and comets, their re-
lation, 271.
Meteors, their cause, 265.
Milky Way, 289.
Milky Way, its general shape ac-
cording to HERSCHEL, 319.
Minor planets defined, 191.
Minor planets, general account,
237.
Mira Ceti (variable star), 296.
Months, different kinds, 182.
Moon, general account, 228.
Moon's light <ig 1 000 of suns, 232.
Moon's phases, 123.
Moon's parallax, 161.
Moon, spectrum of the, 341.
Moon's surface, does it change?
232.
Motion of stars in the line of
sight, 310.
Nadir of an observer defined, 18.
Nautical almanac described, 79.
Nebulae and clusters in general,
304.
Nebulae, their spectra, 309.
Nebular hypothesis stated, 322.
Neptune, discovery of, by LE
VEUKIER and ADAMS (1846),
256.
Neptune, general account, 256.
Neptune's satellite, 260.
New stars, 298.
NEWTON (I.) Laws of Force, 115;
calculates orbit of comet of
1680, 280; Spectrum Analysis
experiments, 334.
Objectives, or object-glasses, 60.
Obliquity of the ecliptic, 91.
Occultations of stars by the moon
(or planets), 140.
OLBERS'S hypothesis of the ori-
gin of asteroids, 239.
OLBERS predicts the return of a
meteoric shower, 269.
Old style (in dates), 185.
Opposition (of a planet to the
sun) defined, 85.
Parallax (annual) defined, 58.
Parallax (horizontal) defined, 56.
Parallax (in general) defined, 50.
Parallax of the sun, 161.
Parallax of the stars, general ac-
count, 314.
Parallel sphere defined, 28.
Penumbra of the earth's or moon's
shadow, 131.
Photosphere of the sun, 201.
PIAZZI discovers the first asteroid
(1801), 237.
INDEX.
351
Planets, their relative size exhib-
ited, 191.
Planetary nebulae denned, 306.
Planets; seven bodies so called
by the ancients, 81.
Planets, their apparent and real
motions, 96.
Planets, their physical constitu-
tion, 261.
Poles of the celestial sphere de-
fined, 21.
POUILLET'S measures of solar ra-
diation, 205.
Practical astronomy (defined), 78.
Precession of the equinoxes, 153.
Prime vertical of an observer de-
fined, 19.
Prism, The, 333.
Problem of three bodies, 119.
Proper motions of stars. 312.
Proper motion of the sun, 312.
PTOLEMY determines the solar
parallax, 166.
Radiant point of meteors, 270.
Radius vector, 107.
Reflecting telescopes, 66.
Refracting telescopes, 60.
Refraction of light in the atmos-
phere, 169.
Resisting medium in space, 281.
Reticle of a transit instrument,
71.
Retrogradations of the planets
explained, 100.
Right ascension of a star defined,
40.
Right ascensions of stars, how
determined by observation, 72.
Right sphere defined, 29.
ROEMER discovers that light
moves progressively, 175.
ROSSE'S measure of the moon's
heat, 232.
Saros (the), 140.
Saturn, general account, 246.
Saturn's rings, 248.
Saturn's satellites, 252.
Seasons (the), 92.
SECCHI, on solar temperature,
206.
Semidiameters (apparent) of ce-
lestial objects, 59.
Sextant, 76.
Sidereal time explained, 43.
Sidereal year, 153.
Signs of the Zodiac, 90.
Solar corona, etc. See Sun,
Solar corona, extent of, 213.
Solar cycle, 185.
Solar heat, its amount, 204.
Solar motion in space, 312.
Solar parallax, history of attempts
to determine it, 165.
Solar parallax probably about
8" -81, 168.
Solar prominences gaseous, 213.
Solar system, description, 190.
Solar system, its future, 220.
Solar temperature. 206.
Solstices, 94.
Spectroscope, The, 335.
Spectroscopic observations, 340.
Spectrum Analysis, 333.
Spectrum of Solar prominences,
214; Solar corona, 216; Lunar,
341; Mercury and Venus, 262;
Nebulae and Clusters, 309;
fixed Stars, 309; as indicating
motions of stars, 310; Solids
and Gases, 336; Solar, 336.
Star-clusters, 308.
352
INDEX.
Star-gauges of HERSCHEL, 318.
Stars had special names 3000
B.C., 291 ; magnitudes, 290, 345;
various magnitudes, how dis-
tributed, 294; parallax and dis-
tance, 314; about 2000 seen by
the naked eye, 291; proper
motions, 312; spectra, 310,
340; map of the northern, 343;
map of the equatorial, 844.
STRUVE'S (W.) parallax of alpha
Lyras (1838), 315.
Summer solstice, 88.
Sun's apparent path, 86.
Sun's Atmosphere, 339, 340.
Sun's constitution, 217.
*H3un'8 (the) existence cannot be
indefinitely long, 220, 325.
Sun's mass over 700 times that
of the planets, 194.
Sun, physical description, 200.
Sun's proper motion, 312.
Sun's rotation-time about 25
days, 200.
Sun, Speclroscopic observations
of the, 340.
Sun-spots and faculae, 200, 206.
Sun-spots are confined to certain
parts of the disk, 208.
Sun-spots, their nature, 209, 340.
Sun-spots, their periodicity, 211.
Superior planets (defined), 99.
SWEDENBORG'S nebular hypothe-
sis, 323.
SWIFT'S supposed discovery of
Vulcan, 226.
Symbols used in astronomy, 11.
Telescopes, 66, 337.
Telescopes (reflecting), 66.
Telescopes (refracting), 60.
TEMPEL'S comet, its relation to
November meteors, 272.
Temporary stars, 298.
Tides, 126.
Total solar eclipses, description
of, 212.
Transit instrument, 70.
Transits of Mercury and Venus
225.
Transits of Venus, 163.
Triaofulation, 150.
Tropical year, 154.
Twilight, 172.
TYCHO BRAHE observes new star
of 1572, 299.
Universal gravitation discovered
by NEWTON, 121.
Universal gravitation treated,
113.
Uranus, general account, 253.
Variable and temporary stars.
general account, 296.
Variable stars, theories of, 299.
Velocity of light, 179.
Venus's atmosphere, 224.
Venus, its apparent motions, 221.
Vernal equinox, 87.
Vulcan, 226.
WATSON'S supposed discovery ol
Vulcan, 226.
Weight of a body defined, 143.
WILSON'S theory of sun-spots,
210.
Winter solstice, 89.
Years, different kinds, 183.
Zeniih defined, 17.
Zodiac, 90.
Zodiacal light 272.
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