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AMERICAN SCIENCE SERIES, ELEMENTARY COURSE
ELEMENTARY ASTRONOMY
BEGINNER'S TEXT-BOOK
BY
EDWARD S. HOLDEN, M.A., Sc.D., LL.D.
Sometime Director of the Lick Observatory
NEW YORK
HENRY HOLT AND COMPANY
1899
Copyright, 1899,
BY
HENRY HOLT & CO.
ROBERT DRUMMOND. PKINTER, NHW YORK.
INTRODUCTION.
THE first notions of Astronomy are acquired in the
study of Geography. Geography lays special stress on the
fact that the surface of the Earth is in a state of constant
change. Its oceans and its atmosphere are subject to
tides ; its surface is leveled for the sites of cities and
towns ; its mines and quarries are explored for substances
useful to mankind. Men navigate its seas and use its soils
to produce the food that supports them. Its ceaseless
changes, natural and artificial, give to it a kind of life
for the sign of life is change.
Geography teaches, also, that the Earth is one of the
planets, but in this larger relation says little or nothing of
changes taking place in the solar system. The youcg
student is very apt to conclude that the other planets of
whose existence he knows Venus and Jupiter for ex-
ample are changeless, immutable; that they are bright
points of light without a history. This was the view of
the ancients.
The special business of Astronomy is to develop the ideas
of the student so that he may understand that all the
bodies of the Solar system the Sun and all the planets
are themselves subject to ceaseless changes and are thus
endowed with a kind of life. Not only this; the bodies
throughout the whole universe Sun and stars alike are
perpetually altering both their places and the arrangement
of their separate parts. Our life on the Earth, for instance,
would quickly cease were it not for changes in the Sun.
There are many stellar systems in which such changes have
iii
701040
iv INTRODUCTION.
already ceased and which are themselves now dead as the
Moon is dead. Others again are in their prime of youth,
and still others are in their ripe maturity. The Cosmos is,
as it were, alive; and it is still in a state of uncompleted
development.
The study of Astronomy should lead the student to com-
prehensive ideas of the universe at large. He will gradually
become possessed of at least a part of the vast body of re-
sults that has been slowly amassed, and, what is even more
important, of the methods that have been invented by the
great men of past times for the discovery of results. A
part of the lesson of the science will have been missed if it
does not teach a sympathetic admiration for great names
like those of Galileo, Kepler, and Newton. Its history is
intimately connected with the history of the intellectual
development of mankind.
As Astronomy is one of the oldest of the sciences its
methods have been perfected to a very high degree, and
have served as models for the methods of the other sciences.
It is chiefly for this reason that it is so well fitted to be the
science first studied by the young student.
In teaching Astronomy every endeavor should be made
to have the student realize what he learns. What is al-
ready known about the Earth will serve as a stepping-stone
to a knowledge of the planets. When something is learned
of the planets, the knowledge will throw light upon the
past (or the future) condition of the earth. Jupiter rep-
resents, in many respects, the past condition of the Earth,
just as the Moon, in all likelihood, represents its state in a
very remote future. The Sun is like the bright stars
strewn by thousands over the celestial vault not unlike
them. Everything that can be learned regarding the Sun
helps us to comprehend physical conditions in the stars,
therefore; and the converse is true.
The nebulae are not exceptional bodies of unique nature,
INTRODUCTION. V
but they are examples of what our own solar system
was iii ages long past. Though we cannot see any indi-
vidual nebula pass through all the stages of its life from its
birth to its maturity, we can select from the vast numbers
of such bodies particular nebulas in each especial stage. As
Sir William Herschel wrote in 1789, "This method of
viewing the heavens seems to throw them into a new kind
of light. They are now seen to resemble a luxuriant gar-
den which contains the greatest variety of productions in
different flourishing beds; and we can, as it were, extend the
range of our experience to an immense duration. For is it
not the same thing whether we live to witness successively
the germination, blooming, foliage, fecundity, fading,
withering, and corruption of a plant, or whether a vast
number of specimens selected from every stage through
which the plant passes in the course of its existence be
brought at once to our view ? "
It should be the aim of the text-book and of the teacher
to so marshal the most significant of the results of observa-
tion that the student may acquire such wide and general
views. If he at the same time gains a luminous idea of
the most important of the methods by which such results
are reached, his teaching has been successful. It is neces-
sary to recollect, on the other hand, that it is not the
province of an elementary text-book to present all the
latest interpretations of observation, or to give more than
the principles of the methods employed. Details of the
sort cannot be thoroughly understood by the beginner.
Questions that are still in debate, like the nature of the
planet Mars or the constitution of comets, cannot be pre-
sented with fulness because the student is not yet sufficiently
equipped to judge the points at issue. At the same time
the materials for such a judgment should be, so far as
possible, laid before him in such a way as to stimulate his
thought and his imagination.
vi INTRODUCTION.
In all the natural sciences one of the very first matters
is to make an orderly inventory of the visible universe.
Things must then be grouped into classes, in order that
the relations of the various classes may afterwards be
studied. In Astronomy the classes are few; there are the
Sun and the stars, the planets, the comets, the nebulae.
The next step is to study typical members of each class
with the telescope. All that the text-book can do is to
give descriptions of the appearances presented by tele-
scopes. These must, in most cases, be taken on faith.
The Moon can be studied to advantage by opera-glasses
or by such small telescopes as are available for use in
schools. Something can be learned, by like means, of the
spots on the Sun, etc. The existence of the brighter
satellites of Jupiter and of Saturn can be verified. But for
all the more significant facts the pupil must accept the
verbal descriptions of the book. The apparent motions of
the stars and planets can perfectly well be observed, out of
doors, by the student who has time and opportunity. But
here again there are difficulties. Dwellers in city streets,
seldom have an uninterrupted view of the sky; and even
those who live in the country rarely have time enough to
give to actual observation. It is entirely impossible in a
few weeks to even verify what it has taken centuries to
disclose.
All the actual observing of the heavens that can be ar-
ranged for should be done. Its chief use will be to illus-
trate by actual examples the methods laid down in the
text-book. Conviction will come to the pupil because he
has learned hoiv to prove or to disprove its theorems; not
because he has actually made the proofs for himself. He
knows that if he has sufficient time they can be proved or
disproved by following a certain method. He thoroughly
understands the method and he has applied it in a few
cases. He is satisfied that the method itself is adequate
INTRODUCTION. vii
and he accepts the conclusions even those that he has not
himself tested. If the student will take the time and the
pains to actually make the observations suggested, he will
learn much. Enough is here given to start him on his
way and to make it easy for him to go on by himself.
The present book endeavors to place the pupil in this
independent position by suggesting tests that he can him-
self apply. Quite as much stress is laid on the spirit of the
methods of the science as on the results to which those
methods have led. And the separate results of observation
are prized mainly because each one bears on an explanation
of the whole universe. .
This book is condensed from two volumes previously
written by Professor SIMOIST NEWCOMB and myself for the
American Science Series. I have to express my sincere
thanks to him for permission to print the condensation in
its present form, and to the Astronomical Society of the
Pacific, to Professor CHARLES A. YOUNG, and to Dr. J, E.
KEELEE, Director of the Lick Observatory, for permission
to use some of the cuts here printed.
The book is addressed especially to pupils who are study-
ing Astronomy for the first time. The chief difficulties of
such students are not due to the intrinsic complexity of the
separate problems that they meet, but rather to their appar-
ent want of connection one with another, and above all to the
unfamiliarity 01 the student with the methods of reasoning
employed. It is therefore necessary to treat each new topic
with great clearness, and not to dismiss it until its relation
to other topics has been at least partially apprehended.
The important point is to present the subject in a way to
convince and to enlighten the pupil, and this object can
only be attained in a text-book by some repetitions and by
avoiding undue brevity. This volume contains more
pages than one of its predecessors in the American Science
Series. The increased space is given to very full explana-
viii INTRODUCTION.
tions of difficult points, to lists of test-questions, and to
pictures and diagrams. Where the mathematical equip-
ment of the pupil is not yet adequate as in the case of
NEWTON'S discoveries in Celestial Mechanics, for example
an historical treatment must be adopted.
It is probable that most of the students who will read
this book will not pursue the subject further in the way of
formal studies. Their ideas of the measurement of time,
of the apparent and real motions of the planets, of
the cause of the seasons, and of other fundamental and
practical matters of the sort, will be derived from this one
course of study. Especial stress is therefore laid on such
topics, and many interesting subjects of less importance are
passed by with a mere mention, or are omitted altogether.
The prescribed limits of space do not permit a treatment
of. all the parts of a vast science like Astronomy.
It may sometimes be useful to the teacher, and it will
always be so to the student, to refer to the questions printed
in Part I, which will suggest new ways of testing the
knowledge gained by the reading of each lesson. It is not
here attempted to set down all, or any great part, of the
questions which each topic may suggest, but only to give
such as are most essential and important.
If the student finds that he has an answer in clear and
definite English for each of the questions given here, he
may be sure that he has comprehended the explanations of
the text. And he should not finally leave any topic until
he does so.
The second part of the book is mainly devoted to a de-
scription of the bodies of the solar system, one by one, and
to some account of nebulae, stars, and comets. It is to be
expected that the formal studies of the pupil will have
created a living interest in such information, and that he
will, for his own pleasure, read some of the many admira-
ble popular works on Astronomy that we owe to Mr. PROG-
INTRODUCTION. IX
TOR, Sir EOBEKT BALL, and others. The text-book will
have performed its part if such an interest has been awak-
ened, and if at the same time a solid foundation for the
student's future reading has been laid. For this reason
Parts II and III of this book have been somewhat ab-
breviated.
If the class has sufficient time it is desirable that the
teacher should supplement his instruction by reading, with
the students, certain chapters from the books of the
school library named in Chapter XXIX. Chapters bearing
on a certain subject can be selected by the teacher from
the books referred to, after the students have studied the
corresponding chapter in the present volume. If such
books cannot be had articles from encyclopaedias will serve
in their stead.
It will not be out of place to give a few practical hints
based on experience. Excellent training in observation
can be had from tracing the areas and the boundaries of
the constellations. The positions of the brighter stars of
each constellation should first be fixed in the memory.
There are ten stars of the first magnitude and about thirty
of the second magnitude in the northern sky. After these,
or most of them, have been identified, the constellation
figures may be taken up one by one and their boundaries
traced. The six small star-maps of this book can be
used for this purpose in connection with the Map of the
Equatorial Stars. A celestial globe is even more con-
venient and satisfactory, and every school should own one
if it is practicable. It should be constantly used to illus-
trate or to prove the theorems of the text-book.
The globe will be a material aid in planning any
series of observations, and it should be always at hand to
explain the results of observations already made.
The course of one of the bright planets among the stars
x INTRODUCTION.
should be mapped from night to night. The path of the
Moon, also, should be followed whenever it is practicable.
The place of a planet can be fixed with considerable pre-
cision by noting its allineations with two or more stars. In
these observations it will be found useful to employ a
straight ruler three or four feet long. The phases of the
Moon can be studied with the eye, or better, with a com-
mon opera-glass. A watch regulated to sidereal time
should form a part of the equipment of the school.
If a small telescope on a firm stand is available much
may be done by its aid. Many of the surface-features of
the bright planets (Mars, Jupiter) can be made out. The
existence of the larger satellites of Jupiter and Saturn can
be proved. The ring of Saturn can be seen. Some of the
double stars can be separated. The brighter nebulas can
be shown. Some of the principal star groups or clusters
can be studied. The changes in brightness of a short-
period variable star can be observed. The spots on the
Sun can be shown by projecting the Sun's image on a
screen.
In these observations it is important to do the work
thoroughly and systematically. If the satellites of Jupiter
are in the field every student in the class should see all of
the bright satellites that are then visible. If a double star
is viewed it should be looked at until both its components
are plainly seen, and so with other cases. No one should
leave the telescope unconvinced. The object of such
observations is to make an ocular demonstration of facts
that have heretofore been received on faith, not to make
additions to science. For this reason the instructor should
select the objects to be examined, with care. They should
be typical, but not difficult to make out. Each student
should be required to keep neat, accurate, and concise
notes of his own observations, and whenever a drawing or
a diagram will explain the observation he should be
INTRODUCTION. xi
required to make it. All observations should be dated and
authenticated with the pupil's signature. He should be
taught to feel a responsibility for the records that he
makes.
The student should be practised in pointing out in the
sky the principal lines and points of the celestial sphere
the meridian, the equator, the ecliptic, the vernal equinox,
the poles of the two last-named circles, and so forth. There
is no mystery in these plain geometric figures. A little
practice will serve to make them quite familiar.
The school should own a small collection of works on
popular and descriptive astronomy, which can be loaned
to the students for reading at home. These can be selected
by the teacher and added to the equipment of the school
from time to time, as fast as circumstances permit.
Simple models to illustrate the motions of the different
instruments of astronomy are easy to make, and they are of
great practical utility in the class-room. Most of them
can be made by the pupils. If practicable, models of the
sextant, the transit instrument, the meridian circle and the
equatorial should be provided. Directions for making
such models are given in the text.
Finally it is of the first importance that difficulties
should not be shirked. To be useful, the student's work
should be thorough so far as it goes. An instructor (or a
writer of text-books) is often tempted to smooth away ob-
stacles, forgetting that one great use of the study of
science is to train the mind to resolutely meet and to con-
quer difficulties. The advantage of scientific problems is
that they are capable of a definite solution, and that the
student himself cannot fail to know whether he has or has
not accomplished that which he set out to do. If our
nation is to take and hold a foremost place in the world,
it will do so through the predominance of certain qualities
xii INTRODUCTION.
in its citizens that scientific education can foster to a very
important degree. We cannot afford to neglect any means
of developing thoroughness and faithfulness in the per-
formance of duty in those who will soon be the responsible
governors of our country. E. S. H.
NEW YORK, June 17, 1899.
TABLE OF CONTENTS.
(Consult the index at the end of the book also.)
PART I. INTRODUCTION.
CHAPTER PAGE
I. INTRODUCTORY HISTORICAL 1
II. SPACE THE CELESTIAL SPHERE DEFINITIONS 15
III. DIURNAL MOTION OF THE SUN, MOON, AND STARS.. 41
IV. THE DIURNAL MOTION TO OBSERVERS IN DIFFER-
ENT LATITUDES, ETC 59
V. CO-ORDINATES SIDEREAL AND SOLAR TIME 77
VI. TIME LONGITUDE 94
VII. ASTRONOMICAL INSTRUMENTS . ... 112
VIII. APPARENT MOTION OF THE SUN TO AN OBSERVER
ON THE EARTH THE SEASONS 154
IX. THE APPARENT AND REAL MOTIONS OF THE PLAN-
ETS KEPLER'S LAWS 179
X. UNIVERSAL GRAVITATION 203
XI. THE MOTIONS AND PHASES OF THE MOON 216
XII. ECLIPSES OF THE SUN AND MOON 222
XIII. THE EARTH 232
XIV. CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. 260
PART II. THE SOLAR SYSTEM.
XV. THE SOLAR SYSTEM 269
XVI. THE SUN 280
XVII. THE PLANETS MERCURY, VENUS, MARS 299
xiii
xiv TABLE OF CONTENTS. ,
CHAPTER PAGE
XVI11. THE MOON THE MINOR PLANETS 315
XIX. THE PLANETS JUPITER, SATURN, URANUS, AND
NEPTUNE 325
XX. METEORS 347
XXI. COMETS 357
PART III. THE UNIVERSE AT LARGE.
XXII. INTRODUCTION 369
XXIII. MOTIONS AND DISTANCES OF THE STARS. 379
XXIV. VARIABLE AND TEMPORARY STARS 386
XXV. DOUBLE, MULTIPLE, AND BINARY STARS 390
XXVI. NEBULAE AND CLUSTERS , 393
XXVII. SPECTRA OF FIXED STARS 400
XXVIII. COSMOGONY 407
XXIX. PRACTICAL HINTS ON MAKING OBSERVATIONS LISTS
OF INTERESTING CELESTIAL OBJECTS MAPS OF
THE STARS 414
APPENDIX SPECTRUM ANALYSIS 433
INDEX. . . 441
SYMBOLS AND ABBREVIATIONS.
SIGNS OF THE PLANETS, ETC.
9 or
The San.
The Moon.
Mercury.
Venus.
The Earth.
Mars.
Jupiter.
Saturn.
Uranus.
Neptune.
The asteroids are distinguished by a circle enclosing a number,
which number indicates the order of "discovery, or by their names, or
by both, as (TOO) ; Hecate.
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 :
Names.
Alpha
Beta
Gamma
Letters.
A a
B ft
r y
A 8
E e
Delta
Epsilon
Z C Zeta
77 77 Eta
Theta
/ i Iota
K K Kappa
A A Lambda
M ju Mu
THE METRIC SYSTEM.
MEASURES OF LENGTH.
1 kilometre = 1000 metres = 0.62137 mile.
1 metre = the unit = 39.370 inches.
1 millimetre = W^ of a metre = 03937 Inch.
Letters.
Names.
N r
Nu
(3
Xi
Omicron
n it it
Pi
P p
Rho
2 a S
Sigma
T r
Tau
r v
Upsilon
, c, #, h, I, m) are
from the Sun.
15
16 ASTRONOMY.
Try to conceive this arrangement of stars clearly. They
are scattered everywhere in Space. There are millions
upon millions of them. Each one of them is as distant
from its nearest neighbor as the stars nearest to the Sun are
distant from the Sun. Now how far is the nearest star
from the Sun? We shall see by and by that it is at least
20,000,000,000,000 miles; that is, twenty millions of mil-
lions of miles. Every other star in the sky is as distant
from its nearest neighbor as this. And there are millions
of such stars in succession one to another as we go out-
* * 3
/ g Sun
lc I in n o
FIG. 2.
The stars are arranged in Space somewhat as in the picture, only not in
a plane, but throughout a solid.
wards through Space. Space contains them all, and there
is room for countless millions more. The spaces between
them are empty.
Let us try to realize this in another way. Think first
of the Sun it is 870,000 miles in diameter. Then think
of the nearest star. It is 20,000,000,000,000 miles from
the Sun. Then imagine a whole universe of countless
millions of stars no one nearer to another than twenty
billion miles. All these stars may be thought of as a
great cluster in the shape of a globe. Imagine this cluster
to shrink and shrink, to get smaller and smaller. The
stars will come nearer and nearer to each other, and the
globe of the Sun (870,000 miles in diameter, remember)
SPACE- THE CELESTIAL SPHERE DEFINITIONS. 17
will also grow smaller at the same time and in the same
proportion. Let the shrinking go on till the universe is
2,300,000,000 times smaller than at first till the Sun's
globe is only two feet in diameter,* and then stop the
shrinking.
We shall have a model of the universe with everything
in its true proportions, only the Sun will be two feet
in diameter instead of 870,000 miles. Now how far
off will the nearest star to the Sun be, in this shrunken
model of the universe? It will be as far from the San as
the city of Peking is from the city of New York ! The
nearest star will be so far off. The other stars will be ar-
ranged in order out beyond this one, and none of them
will be any nearer, in this model, to its neighbors than the
distance from China to New York. And the model mus~t
contain millions of stars. Even this model will be incon-
ceivably large. The real universes-Space is inconceiva-
bly larger than the model. An. illustration like this en-
tirely fails to give a measure of the size of Space, but it
certainly does give some conception of its immense exten-
sion. In thinking of the universe of stars you must try
to realize it in this way. The Sun and all the stars lie in
space, none of them near together, with immense empty
regions between the different bodies. Each star is incon-
ceivably far from its nearest neighbors, and there are mil-
lions upon millions of stars. It is not at all easy to have
clear ideas of an infinite extension ; but it is absolutely
necessary in beginning the study of Astronomy to have
some idea of the space in which the Sun, all the planets,
and all the stars exist.
Why do we call Space "empty"? How far away is the Moon
from the Earth ? The diameter of the globe of the Sun is how much
larger than this distance ? Is the Sun a star ? Space contains mil-
* Two feet is OTnrt s ffTnnnj tk part of 870,000 miles.
18 ASTRONOMY.
lions upon millions of stars. Each star is at least twenty millions of
millions of miles from its nearest neighbors. Are the spaces be-
tween them empty of large bodies? Suppose you could make an
exact model of Space with each star in its right place, and suppose
you could make this model shrink until the 870,000 miles of the
Sun's diameter had shrunk to two feet how far off would the star
nearest to the Sun be from the Sun itself ? Would these words do
for a definition of Space Space is indefinite extension ? If you have
a dictionary, look up the word and see how it is defined there.
8. The Celestial Sphere. In what has just heen said
about Space we have spoken of the universe as it really is.
The stars are scattered all about through Space at enormous
distances one from another. That is the way the universe
really is. Now we have to ask how does it appear to be to
us ? If you look at the heavens on a clear night what do
you see ?* In the first place you see hundreds of stars, some
very bright, some less bright. They all seem to be at the
same distance from you. They look as if they were bright
points fastened to the inside surface of a great hollow globe
the celestial sphere hung over the Earth. You see the
bright points. The surface on which you imagine them
to lie is called the celestial sphere. There is, in fact, no
such surface, but there seems to be one. Let us make a
formal definition of it which is to be learned by heart.
The Celestial Sphere is that surface to which the stars seem
to he fastened. No one ever thinks of the stars as if they
were outside of the celestial sphere and shining through it.
In Fig. 3 the black square is a part of Space.* There
are a few stars in it, namely p, q, r, s, , , , u, v. In
respect to the immense distances of the stars, the Earth, 0,
may be considered as a mere point. The configurations of
the stars are the same whether you are at Lisbon or at
* The student must remember here and throughout the book that
the drawings have to be on a small scale. All the Universe has to
be drawn on a few square inches.
SPACE THE CELESTIAL SPHERE DEFINITIONS. 19
New York. No change of place on the Earth alters the
grouping of the stars. You are on the Earth looking out
at the sky at night and you see all these stars. If you look
at the star which is really at q you are looking along the
line Oq and see it as if it were on the surface of the celes-
tial sphere at Q. If you look at r and s, you see them at
FIG. '6. THE CELESTIAL SPHERE.
The Earth is supposed to be at O, a few of the stars at p, q, 7% s, t, t, t, w, v.
These stars are seen by us as if they were all on the surface of the celes-
tial sphere at P, Q, R, S, T, 17, V.
R and S. If you look at u and v you see them at U and
V. All of them appear to be at one and the same distance
from you, though they really are at very different dis-
tances. The point Q is in the line Oq prolonged; the
points R, 8, U, V are in the lines Or, Os, On, Ov pro-
longed. Now suppose there happened to be three stars, t,
20 ASTRONOMY.
t, t, in a line. They would all three appear on the celes-
tial sphere at T. You would never know there were three
separate stars, because yon could only see one bright point
at T. You do not see the other stars r, s, v, etc.,
where they really are, but at places on the celestial sphere
at R, 8, F.
F IG> 4. THE EARTH (n, q, *) IN THE CENTRE OF THE CELESTIAL
SPHERE.
On the surface of the celestial sphere meridians and parallels are sup-
posed to be drawn corresponding to meridians and parallels on the Earth.
What you see in a dark night is stars apparently studded
over the inner surface of the celestial sphere. It is only
by reasoning about it that you know they are not on this
surface but scattered about inside of the sphere. The an-
SPACE THE CELESTIAL SPHERE-DEFINITIONS. 21
cient astronomers thought that the sphere actually existed
and that the stars were really fastened to it. Although it
does not exist, the idea can be made to serve a useful pur-
pose. For instance, if we want to know the angle be-
tween the two lines Or and Os (the angle between the two
lines joining the Earth and two distant stars) all we have
to do is to measure the arc RS on the celestial sphere.
The arc RS is the measure of the angle rOs in space.
The sphere has other uses, too. Just as there is a ter-
restrial equator on the globe of the Earth (and terrestrial
meridians, etc.), so there is a celestial equator (and celes-
tial meridians, etc.) on the celestial sphere. The simplest
part of astronomy deals with the apparent places of stars
as they seem to be on the celestial sphere it is called
Spherical Astronomy for that reason. It is only after we
have learned about the apparent places and motions of
stars and planets that we can go on to study their real
motions. So that the idea of a celestial sphere will be use-
fnl. Whenever you go out at night you will see it it is
the dark sphere on which the bright stars seem to rest.
Imagine that the stars are not there ; yet the sphere will
remain. Every one imagines the blue vault of the sky in
the daytime as if it were a hollow sphere hanging over us.
The Sun seems to be on its inner surface. When you see
the Moon in the daytime it, too, seems to lie on the celes-
tial sphere.
The stars really are at very different distances from us ; all are
very far away, but some are much further away than others do
they seem to be at different distances when you look at them at
night ? Do they seem to lie on the inner surface of a sphere ? What
is the celestial sphere ? Is it a sphere that really exists, or only one
that appears to exist ? Does the celestial sphere seem to exist in the
daytime as well as at night?
9. Some Mathematical Terms used in Astronomy. It
22 ASTRONOMY.
is convenient to use a few mathematical terms in speaking
about the geometrical parts of Astronomy. All of the
mathematical ideas here introduced are simple, but it may
be well to set them down in order. If they are under-
stood by the student he will have no difficulty in compre-
hending the astronomical matters that are to be spoken of.
If they are not thoroughly understood some points will not
be as clear as they should be.
ANGLES: THEIR MEASUREMENT. An angle is the
amount of divergence of two lines. For example, the
angle between the two lines S 1 E
and S*E is the amount of diver-
gence of these lines. The angle
S*ES* is the amount of divergence
of the two lines S*E and S'E.
The eye sees at once that the
angle S*ES* in the figure is
greater than the angle /S' 1 ^ 2 ,
FIG. 5. -ANGLES: THEIR and that the an g le S'W is
MEASUREMENT. greater than either of them.
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 circumference 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, SES* is about 12, S*ES* is about
22, S*ES* is about 30, and &ES* is about 64. The vertex of the
angle is at the centre E ; the measure of the angle is on the circum-
ference S ] S*S S S*, or on any circumference drawn from E &s 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 the
degree has been subdivided into minutes and seconds.
One circumference = 360 = 21600' = 1296000"
1 = 60' = 360"
V = 60"
SPACE-THE CELESTIAL SPHERE-DEFINITIONS. 23
Smaller angles than seconds are expressed by 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 one
circumference = 2 nR, where n = 3.1416. That is,
2 nR - 360 = 21600' = 1296000"
or R = 57.3 = 3437'.7 = 206264".8.
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 subtend an angle of a min-
ute? 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 distance from us. If it
07. o
subtends an angle of 1", ita 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 can determine
their distance 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 diam-
24 ASTRONOMY.
eter at this distance is 1922". What is the diameter of the
sun in miles? (1" is about 451 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 immedi-
ately 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 com-
pute it.
It is convenient to remember that the angular distance
between the two "Pointers" in the Great Bear (see Fig. 1)
is about 5.
PLANE TRIANGLES. The angles of which we have spoken are
angles in a plane. In any plane triangle there are three angles A, B, G
and three sides a, b, c six parts. If any three of the parts are given
(except the three angles) we can construct the triangle. For in-
FIG. 6. A PLANE FIG. 7. Two SIMILAR PLANE
TRIANGLE. TRIANGLES.
stance, if you know the three sides a, b, c, you can make one triangle,
and only one, with these sides. If you only know the three angles
you can make any number of triangles with three such angles. All
of them will have the same shape, but they will have different sizes.
(See Fig. 7.)
THE SPHERE : ITS PLANES AND CIRCLES. In Fig.
8, is the centre of the sphere. Suppose any plane
SPACE THE CELESTIAL SPHERE DEFINITIONS. 25
as AB to pass through the centre of the sphere. It will
cut 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' in which it
intersects the surface of the sphere are every where 90 from
the circle AEBF. They are the poles of that circle. The
poles of the great circle CEDF are Q and Q'. It is
proved in geometry that the following relations exist be-
tween the angles made in the figure :
FIG. 8. THE SPHERE ; ITS GHEAT CIRCLES ; THEIR POLES.
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 circles
intersect each other, are the poles of the great circle
26 ASTRONOMY.
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 trian-
gle 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 has a school globe, let him mark on it the triangle
whose sides are
a = 10, 6 = 7, e = 4.
Its angles will be (A is opposite to a, B to b, C to e) :
A = 128 44' 45". I
B= 83 11' 12'
C- 1815'31".l
LATITUDE AND LONGITUDE OF A PLACE ON THE
EAKTH'S SURFACE. According to geography, the latitude
of a place on the Earth's surface is its angular distance
north or south of the Earth's equator.
Tfie longitude of a place on the Earth's surface is its an-
gular distance east or west of a given first meridian (the
meridian of Greenwich, for example).
If P in Fig. 9 is the north pole of the earth, the lat-
itude of the point B is 60 north; of Z it is 30 north; of
/ it is 27 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.
SPACE THE CELESTIAL SPHERE- DEFINITIONS. 27
All places having the same longitude are situated on the
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 astronom-
Fio. 9. LATITUDE AND LONGITUDE OP PLACES ON THE EARTH'S
SURFACE.
ical purposes it is found more convenient to count the
longitude of a place from the first meridian 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 a day
of 24 hours every point on the Earth's surface moves
once round a circle (its parallel of latitude). Every point
28 ASTRONOMT.
moves 360 in 24 hoars, or at the rate of 15 every hour
(360 divided by 24 is 15).
Hence we can measure the longitude of a place in de-
grees or in hours, just as we choose. Washington is 5 h 8 m
west of Greenwich (77) and Sydney is 13 h 56 m west of
Greenwich (209). In the figure suppose F to be west of
the first meridian. All the places on the meridian PQ
have a longitude of 15 or 1 hour ; all those on the merid-
ian P5 h Q have a longitude of 75 or 5 hours ; and so on.
What is an angle? What is a degree? What is a minute of
arc? a second? The radius of a circle, if wrapped around the cir-
cumference of a circle, would cover an arc of how many degrees?
What is the angular diameter of the Moon ? of the Sun ? How far
apart in arc are the two " pointers " of the Great Bear? What is the
difference between a plane triangle and a spherical triangle? Give
an example of a plane triangle ; of a spherical triangle. Define the
latitude of a place on the Earth's surface. Define the longitude of
a place on the Earth's surface.
10. The Points and Circles of the Celestial Sphere.
THE HORIZOK. We only see
one half of the celestial sphere;
namely, the half above our
heads. If we are at sea, or in
a large open country on land,
the concave vault of the day-
time sky seems to rest on a flat
plain, and this plain seems to
be bounded by a circle. The
flat plain is called the plane of
Fio. IO.-HAT,* OF THE CK- the horizon (pronounced hor-I'-
LESTIAT, SPHERE, STUDDED Z on). Its bounding circle is the
WITH STARS. circle of the horizon. A point
The sphere seems to rest on the , ,
plane of the horizon. The horizon on the celestial sphere directly
seems to be bounded by the circle . , . ,
NHS. N is the north point, s is overhead is called the zenitn-
the south point of the horizon. Z . . a .>
is the zenith-point or the point point, or more briefly the
directly overhead.
SPACE THE CELESTIAL SPHERE DEFINITIONS. 29
zenith. A line joining the observer and the zenith-point
is perpendicular to the plane of the horizon. If you wish
to describe the situation of a star you can say that its
zenith-distance is so many degrees 50 for example. The
star 8 in the figure is distant from the zenith Z by an arc
ZS. Its zenith-distance is 50. The arc from the zenith
to the horizon is 90. That is, the zenith-distance of the
horizon is everywhere 90. The altitude of a star is its
angular distance above the horizon. The altitude of the
star 8 in the figure is HS = 40.
The zenith-distance and the altitude of a star are meas-
ured on a vertical circle, i.e., on a circle passing through
the star and perpendicular to the horizon.
The zenith-distance of any star + the altitude of the star = 90.
FIG. 11. THE EAKTH'S Axis AND THE PLANE OF ITS
EQUATOR EQ.
NP is the earth's north pole ; SP is the south pole ; eq is the earth's
equator ; EQ is the plane of the celestial equator.
30 ASTRONOMY.
THE CELESTIAL EQUATOR. In the figure there is a pic-
ture of the Earth. NP is its north pole, SP is its south
pole, and the line joining them is the Earth's axis, eq is
the Earth's equator. It is a circle round the Earth. If
we imagine the plane of that circle to continue out beyond
the Earth on all sides till it reaches the celestial sphere the
shaded surface EQ (a circle) will represent it. This sur-
face is the plane of the equator of the celestial sphere or
more briefly, it is the plane of the celestial equator. If we
imagine the axis of the earth prolonged both ways till it
meets the celestial sphere the prolonged line is the axis of
the celestial sphere.
If we imagine the planes of the meridians and parallels
on the Earth to be prolonged outwards to meet the celes-
tial sphere, they will meet it in circles that are the merid-
ians and parallels of that sphere. They are not drawn in
the last figure, so as to avoid confusing it ; but some of
them are drawn in the next figure. In this n is the north
pole of the Earth, NP the north pole of the celestial
sphere; eq is the equator of the Earth, EQ the equator of
the celestial sphere the celestial equator; the plaues of the
meridians of the Earth are prolonged and make the merid-
ians of the celestial sphere ; the plaues of the parallels on
the Earth make the parallels ML, EQ (for the equator is
a parallel of latitude), and SO.
Z is the zenith-point of the observer it is the point of
the celestial sphere directly over his head. JVis the nadir-
point of the observer it is the point of the celestial sphere
directly beneath his feet. HR is a plane through the cen-
tre of the Earth and perpendicular to the line ZN. We
shall now define the plane of the horizon to be that plane
passing through the centre of the Earth which is perpen-
dicular to the line joining the observer's zenith- and nadir-
points. On page 28 the horizon was described as the flat
plain on which the observer stands and on which the up-
SPACE THE CELESTIAL SPHERE DEFINITIONS. 31
per half of the celestial sphere rests. Such a plane is
called the plane of the sensible horizon (i.e., of the horizon
evident to the senses). HR through the centre of the
Earth divides the celestial sphere into two equal parts. It
is called the rational horizon. The sensible and the ra-
tional horizons are parallel to each other.
FIG. 12. THE EARTH (n, q, s, e) SURROUNDED BY THE CELESTIAL
SPHERE (N, Q, S, E).
The meridians and parallels on the celestial sphere serve
the same purpose as the meridians and parallels on the
Earth. The latitude of a place on the Earth is its angular
distance north or south of the terrestrial equator. The
longitude of a place on the Earth is the angular distance
of that place west of the first meridian. If we know the
32 ASTRONOMY.
latitude and longitude of a place on the surface of the
Earth we know all that can be known of its situation.
Just in the same way we describe the situations of stars
on the surface of the celestial sphere. The declination (like
latitude) of a star is its angular distance north or south of
the celestial equator. The right-ascension (like longi-
tude) of a star is its angular distance east of the first me-
ridian. Declinations in the sky are like latitudes on the
Earth. Eight-ascensions in the sky are like longitudes on
the Earth. The names are different, but the principle of
measurement is the same.
DECLINATION OF A STAR. The declination of a star is
its angular distance north or south of the celestial equator.
FIG. 13. DECLINATION AND RIGHT- ASCENSION OF A STAR.
In the figure EVQ is the equator of the celestial sphere the celes-
tial equator. The Earth is not shown in the picture. If it were
shown it would be a dot at the centre of the sphere. PAa is a merid.
ian of the celestial sphere passing through the star A. The angular
distance of the star A north of the celestial equator is Aa. Aa is
the north declination of that star. PbB is a meridian of the celestial
sphere passing through the star B. This star is south of the celes-
tial equator by an angular distance measured by bB. bB is the south
declination of the star B.
SPACE THE CELESTIAL SPHERE DEFINITIONS. 33
If for a moment we should take the sphere PEQ to represent the
Earth and EQ the equator of the Earth, then the terrestrial north
latitude of A would be measured by aA and the south latitude of B
by bB. The declination of a point on the surface of the celestial
sphere corresponds to the latitude of a point on the surface of the
Earth. PA is the north polar-distance of A ; P'B is the south polar-
distance of B
The polar-distance of a star + the star's decimation =90*.
EIGHT-ASCENSION OF A STAR. The right-ascension of ,1
star is its angular distance east of a first meridian.
FIG. 13 Ms.
In the figure P V is the first meridian. PAa is the meridian
through the star A. This meridian is east of the first meridian by
the angle VPa, which is measured by the arc Va. Va is the right-
ascension of the star A. PbB is the meridian through the star B.
This meridian is east of the first meridian by the angle VPb, which
is measured by the arc Vb. Vb is the right-ascension of the star B.
If for a moment we should take the sphere PEQ to represent the
Earth, and EQ the equator of the Earth, and PV the meridian of
Greenwich, (east) terrestrial longitude of a place A would be Va;
the longitude of a place B would be bB. The right- ascension of a
point on the surface of the celestial sphere corresponds to the longi-
tude of a point on the surface of the Earth.
It is very important to understand these matters at the beginning,
34 ASTRONOMY.
and it is necessary for the student to memorize the following defini-
tions:
The plane of the horizon is a plane through the centre of the Earth
perpendicular to the line joining the zenith and the nadir of the ob-
server. The zenith of an observer is the point of the celestial sphere
directly over his Lead. Therefore each person has a different zenith-
point. The nadir of an observer is the point of the celestial sphere
directly beneath his feet. The zenith and nadir are points on the
surface of the celestial sphere not points on the Earth. Tliezenii/t-
distance of a star is its angular distance from the zenith. The alti-
tude of a star is its angular distance above the horizon. A vertical
circle is a great circle of the sphere whose plane is perpendicular to
the plane of the horizon. The axis of the celestial sphere is the line
of the Earth's axis prolonged. The equator of the celestial sphere
the celestial equator is that great circle cut from the celestial sphere
by the plane or the Earth's equator extended. The declination of a
star is its angular distance north or south of the celestial equator.
The right- ascension of a star is its angular distance east (not west) of
the first meridian of the celestial sphere. (This first meridian has
nothing to do with the meridian of Greenwich on the Earth, as we
shall soon see. )
The terrestrial meridian of an observer is that great cir-
cle of the Earth that passes through the observer and
through the Earth's axis. All terrestrial meridians pass
through the north and south poles of the Earth.
The celestial meridian of an observer is that great circle
of the celestial sphere that passes through the zenith of
the observer and through the axis of the celestial sphere.
All celestial meridians pass through the north and south
poles of the celestial sphere.
In figure 14 n, e, q, 8 is the earth, and some terrestrial meridians are
drawn upon it. Some celestial meridians are drawn on the celestial
sphere NP, E, Q, SP. Z is the zenith of the observer. Where must
he be in the figure ? He must be on the surface of n, e, q, s, where
aline ZN (zenith to nadir) intersects it. Make a pin-prick at this
point. His terrestrial meridian is the little circle n, e, q, s (because
it passes through the observer's place and through n and s). His
celestial meridian is NP, Z, SP (because it contains his zenith and
the two celestial poles).
SPACE THE CELESTIAL SPHERE DEFINITIONS. 35
FIG. 14. CORRESPONDENCE OF THE TERRESTRIAL AND CELESTIAL
MERIDIANS OP AN OBSERVER.
FIG. 15. THE CELESTIAL SPHERE.
36 ASTRONOMY.
It is so important for the student to understand the foregoing
definitions clearly that the following exercises are added. The fig-
ures have been purposely drawn unlike each other.
In figure 15 P is the north pole of the celestial sphere ; Z is the
observer's zenith ; HE his horizon ; is the position of the Earth.
What is the zenith-distance of ? What is the altitude of S?
What is the altitude of Z? What is the altitude of P? What is the
altitude of M ? (Answers : Z8, TS, 90, RP, HM.) Notice that an
observer at looks along a horizontal line OT ; he sees the star S
along the line OS ; the angle TOS is the altitude of S, and it is meas-
ured by the arc TS. RH is the observer's north and south line, EW
is his east and west line. His points of the compass are R = north,
E = east, // south, W = west.
FIG. 16. THE CELESTIAL SPHERE.
In figure 16 P is the north pole of the celestial sphere, ECWD
is the celestial equator ; P V is the first meridian of the celestial
sphere. What is the right-ascension of the point F? of B ? of (7? of
Et of D1 of Wt (Answers : 0, VB, VG, VCE, VCED, VCEDW.)
What are the right ascension and declination of the point A 't (An-
swer : VB and north BA). What is the altitude of A ? (Answer :
GA.)
SPACE THE CELESTIAL &PSERE DEFINITIONS. 37
What is the horizon of an observer ? Can you conceive a hori-
zon without specifying an observer's place? What is a vertical line?
If you had a string and a bunch of keys, how could you use them to
show the vertical direction at your station ? Is this direction the
same with respect to each observer, no matter where he is situ-
ated ? Do you suppose this direction is absolutely the same in space
for two observers 1000 miles apart ?
What is the zenith of an observer ? His nadir ? Have the words
zenith and nadir any meaning if no observer or station is supposed ?
When you assume a point on the celestial sphere as the zenith of an
observer, is his place on the earth fixed? When you assume the
FIG. 17. PART OF A CELESTIAL GLOBE:
Showing the principal circles of the celestial sphere.
place of an observer on the earth, is his zenith a determinate point
on the celestial sphere ? Or may it be two points ? What is a star's
altitude? its zenith distance? In an swering these two questions,
did you say its angular distance from, etc. ?
In figure 17 Z is the zenith of the observer and NWS his hori-
38 ASTRONOMY.
zon. P is the north celestial pole. PZ8 is the observer's celestial
meridan. XXI, XXII . . . 0, I, II ... is the celestial equator,
and is the vernal equinox the origin of right-ascensions. Paral-
lels of declination are shown (circles parallel to the celestial equator)
every 10 both north and south of the equator. Meridians of the
celestial sphere (hour-circles) are drawn every 15; every hour. They
pass from pole to pole across the celestial sphere and cross the equa-
tor at the points marked XXI, XXII, . . . I, II . . . Every star on
the hour-circle I has a right ascension of 15, or 1 hour ; on // of
30, or 2 h ; on XXII of 330, or 22 hours ; and so on.
All stars on the parallel of declination marked A have a north
declination of 40 (+ 40) ; on the parallel C, of + 30 ; on the equa-
tor, of ; on the parallel Sof 30. The student should mark the
following places on the figure :
R. A. = 22 h and Decl. = + 80 ; R. A. = O h and Decl. = - 40 ;
= 23 h " = - 30 ; = l h " = + 60 ;
= 24" " =0; = 2 = + 40;
= o h " = + 40 ; = 2* " = - 30'.
CHAPTER III
DIURNAL MOTION OF THE SUN, MOON, AND STARS.
11. The Diurnal Motion of the Sun, Moon, and Stars.
It is a familiar fact to all of us that the Sun rises and sets
every day. The Moon rises and sets. Stars also rise above
the eastern horizon; they appear to move across the sky
and to come to their greatest altitude on the meridian ;
FIG. 18. THE APPARENT MOTION OF THE SUN FROM RISING TO
SETTING.
and then they appear to decline to the west and set below
the western horizon. Every one is familiar with the Sun's
rising and setting. It is too splendid a spectacle to be
overlooked. We are all more or less familiar with the mo-
tion of the Moon from rising to setting. We may know
39
40 ASTRONOMY.
the fact that groups of stars also rise and set. But to thor-
oughly understand their motions we must actually observe
some particular stars carefully. The student should him-
self make the observations that are described here so far as
his time and opportunities will allow.
DIURNAL MOTIONS OF SOUTHERN STARS. Let the
student go out into a field or park at night where he can
see the sky from his zenith towards the southern horizon,
III
IV
FIG. 19. DIURNAL MOTION OF A GROUP OF SOUTHERN STARS.
The right hand of this picture is west : the left hand is east.
and where he can command an unobstructed view of the
eastern and western horizon. Let him select a group of
bright stars that are not very far apart, and that are not
very far above the eastern horizon. He must learn the
group so well that he can always recognize it in the sky no
matter where it may be. Let him stand with his back
toward the north. The group is rising, let us say (the
lower left-hand circle in Fig. 19) when he begins to
DIURNAL MOTION: SUN, MOON, AND STARS. 41
observe it. If he watches the group looking at it every
half hour or so he will see that it is continually rising
above the eastern horizon and getting higher in the heav-
ens.
About three hours after the rising of this group it
will be towards the southeast (the second circle counting
from the left of Fig. 19). About six hours after rising,
the group will be just south of him and at its highest
at its greatest altitude. The point in the sky where a
star (or a group of stars) has its greatest altitude is called
its point of culmination. It is due south of the observer
at culmination (the uppermost circle, S 9 in the last figure).
It requires about six hours for a group of southern stars to
move from the eastern horizon, where it rises, to the point
due south, where it culminates. Six hours of watching is
quite as long as can be given by the student. But if he
should watch longer than this, he would see the group of
stars decline to the west and finally set (as in the two right-
hand circles of the last figure).
Hunters, sailors, shepherds, as well as astronomers, have
observed facts like these thousands and thousands of times.
Any one who wishes can observe them whenever he likes on
any clear night. So that the student can prove them for
himself if he chooses; and we may take them as proved
facts. The picture shows what actually does happen for a
group of southern stars. When it is due south it looks
like the upper circle, marked S. It is at its culmination.
It is at its greatest altitude. Three hours before the time
of culmination the group was as in the circle next S, to
the left. Six hours before this time it was as in the lower
left-hand circle. Three hours after the time of culmina-
tion the group has declined towards the west (see the
figure), and six hours after this time it is setting in the
west, as in number V.
It is not to be expected that a schoolboy will have the
42 ASTRONOMY.
leisure to watch throughout a whole night. If he were to
do so he would see the group move as in the figure if he
used a long winter's night for his observation and began
his watch as soon as the sky grew dark. There is a sim-
ple experiment that he can try, however, which will make
the diurnal motion of the southern stars quite easy to un-
derstand. Let him provide himself with a hammer and
with a bundle of common laths, and let him sharpen one
end of each lath so that it can be easily driven into the
ground. Let him choose a spot of ground to stand on that
is soft, so that the laths can be set in place without too
much trouble. Let him select some one bright star that
is near the eastern horizon, and remember it well so as
not to mistake it for any other star.
Now he should kneel down, set the sharp end of a lath
on the ground, and sight along the lath until it points ex-
actly to the star. The lath is to be sighted at the star just
as a rifle is pointed at a deer. The lath is now to be driv-
en into the ground firmly; and after this is done it is well
to take another sight along the lath at the star to be sure
that it still points correctly. When all is right the ob-
server should look at his watch and note the time and
write it down, like this:
First lath set at 8 h O m P.M.
Things will look as in Fig. 20. The lath 01 will
point to the star at 8 h O m .
The observer need pay no more attention to the star for
a couple of hours. A little before ten o'clock he should
take another lath and make the same observation on the
same star. He will find that the star has moved towards
the west and upwards. Leaving the first lath in place, he
must now fix a second one so as to point at the star at 10
o'clock. Its point will have to be set a few inches away
DIURNAL MOTION: SUN, MOON, AND STARS. 43
East
West
The
Ground
FIG. 20. A POINTER DIRECTED AT A STAR.
East
West
The
Ground
FIG. 21. A POINTER DIRECTED AT A STAB.
III
East
The
West
Ground
FIG. 22. A POINTER DIRECTED AT A STAR.
44 ASTRONOMY.
from the point of the first one, so as not to interfere with
it. It will appear as in Fig. 21.
He should make a second record, thus :
Second lath set at 10 h O ra P.M.
Now the observer can go to sleep if he likes, setting
his alarm-clock to wake him about quarter before twelve.
At 12 h he should set a third lath to point at the same star.
It will be like Fig. 22.
His note-book will read :
Third lath set at 12 h O m P.M.
He should do the same thing at 2 o'clock in the morning,
and the fourth lath will point as in the next figure.
Fourth lath set at 2 A.M.
East / West
The [_ Ground
O
FIG. 23. A POINTER DIRECTED AT A STAR.
These four observations will be enough, though the more
that are made the clearer the motion of the star will be.
The chief practical trouble will be that the points of the
laths cannot be set very close together without interfering
with each other. If they could be set just right and if a
great number of them were so set, things would look like
the group of laths, B, in the next figure, where the flat
DIURNAL MOTION: SUN, MOON, AND STARS. 45
table represents the ground, and the lines in the circle B
represent a number of laths accurately set at the point 0.
This figure makes everything clear. The laths have
been set at equal intervals of time and they are at equal
angles apart. This proves that the apparent motion of the
star B is such that it moves through equal angles in equal
times. Its motion is uniform.
If the observer had chosen to select a star very far south
(A, for example) and had set laths for it, also, the group
FIG. 24 A MODEL TO SHOW HOW STARS SEEM TO MOVE FROM
RISING TO SETTING IN THEIR DIURNAL PATHS.
of pointers for this star would look like the cone of rays
marked A in the figure. All the laths would lie in the
surface of a cone, and the vertex of this cone would
be at 0. If he had chosen a star nearer to his zenith
((7, for example) and had set the laths for it, just as
before, they would also lie in the surface of a cone (7, as
in the figure. Finally, if he had chosen a star much fur-
ther north (Z>, for example) the pointers to that star would
all lie in the cone D. The line OP is the axis of all these
cones, and it points to the north pole of the heavens.
46
ASTRONOMY.
The north pole of the heavens is that point ivhere the axis
of the Earth, prolonged, meets the celestial sphere.
DIURNAL MOTIONS OF NORTHERN STARS. After the
motions of southern stars, from their rising to their setting,
have been carefully observed and are thoroughly under-
FIG. 25. THE NORTHERN HEAVENS;
as they appear to an observer in the United States in the early evening
during August. The right-hand side of the picture is east.
stood, the motions of northern stars must be observed.
They can be studied in the same way as before. The
drawings of the cones C and D in the last figure show ex-
actly what would be observed. In every one of these
cones, for any and every star in the sky, experiments will
DIURNAL MOTION: SUN, MOON, AND STARS. 47
prove that the star moves through equal angles in equal
times. The diurnal motions of all the stars are uniform.
The time required for the star D to go completely round
its cone once and to come back to the starting-point again
is 24 hours, one day; and the same is true for any and
every star.
In Fig. 25 the stars of the northern sky are shown
as they appear to an observer in the middle regions of the
United States in the early evening in August. The same
stars are visible all the year round, but they will not always
be at the same altitudes above the horizon at the same hour
of the night. No matter what hour of the night, or what
time of the year you read this paragraph, you can see the
stars of this picture (if the night is clear) by going now
out-of-doors and looking towards the north. In order to
make the picture look right you may have to turn the page
of the book round somewhat (in the direction of the arrows)
so as to put a different part of the page uppermost. But
by taking a little pains you can hold the picture in such a
position that it will agree with the configuration of the
stars in the sky.
The first set of stars to find in the sky is the Great Bear
Ursa Major the Great Dipper, as it is often called. It
is made up of seven stars arranged somewhat as in the
next figure:
j # Polaris.
* *
FIG. 26. URSA MAJOR AND POLARIS.
48 ASTRONOMY.
They are called by these names : a (Alpha) Ursae ma-
joris; ft (Beta) Ursae majoris; y (Gamma) Ursae majoris;
6 (Delta) Ursae majoris; e (Epsiloti) Ursae majoris ; TI
(Eta) Ursae majoris; C (Zetd) Ursae majoris. The letters
a, /3, y, d, e, rj, C are the first seven letters of the Greek
alphabet. The stars themselves are a part of the constel-
lation or group of stars named Ursa Major the Great Bear
by the ancients (see Fig. 25). After you have found
them you must notice that two of them a and ft (they are
called "the pointers") point to another star, not so
bright, which is itself called Polaris the pole-star the
star near the north pole of the celestial sphere.
It is well to form the habit of glancing up at the north-
FIG. 27. THE STABS OF THE DIPPER;
as they appear in the early hours of the evening in the month of May.
ern heavens every time you go out of doors on a clear
night, so as to be able to find Ursa Major, Polaris, and
Cassiopea quickly and easily.
If yon study the motions of the northern stars you will
find that Polaris the polar star seems to be almost sta-
tionary. If it were exactly at the north pole of the heav-
ens (which it is not) it would be absolutely stationary; but
it is very nearly so. All the other northern stars seem to
DIURNAL MOTION: SUN, MOON, AND STARS. 49
move ronud Polaris in circles. They move from the east,
then upwards, then to the west, then downwards, then to
the east again (in the direction of the arrows in Fig. 25),
and so on forever. It takes 24 hoars for each and every
star to move once completely round the pole. Its motion
has a period of one day hence the name diurnal motion.
The diurnal motions of all the stars can be described in
three theorems (following) , and you should learn these the-
orems by heart, because that is the quickest way to get a
perfectly definite and correct statement of the appearances
in the sky. Recollect that the north-polar- distance
(N.P.D.) of a star is its angular distance from the north
The following are the laws of the diurnal motion:
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 period of time, which is the time required for the earth
to turn once on its axis (twenty-four hours).
These laws are true of the thousands of stars visible to
the naked eye, and of the millions upon millions seen by
the telescope.
The circle which a star appears to describe in the sky in
consequence of the diurnal motion of the earth is called
the diurnal orbit of that star (an orbit is a path in the
sky).
These laws are proved by observation. The student can
satisfy himself of their correctness on 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
50 ASTRONOMY.
revelation round the pole. Such stars are shown in
Fig. 25. The apparent diurnal motion of the stars is in
the direction shown by the arrows in the cut. Below the
north 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. Within it the
FIG. 28. THE STARS OF THE DIPPER;
as they appear at different times during their daily revolution round
the pole.
stars perpetually appear are visible. 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.
When a photographic camera is directed to the north
pole of the heavens at night and an exposure of about 12
hours is given the developed plate will look like Fig. 29.
DIURNAL MOTION: SUN, MOON. AND STARS. 51
The plate has remained stationary; the stars have in 12
hours moved one-half round their diurnal orbits. In
moving they have left " trails" on the plate. Each trail
is an arc of a circle, and the centre of all these circles is
FIG. 29.
From a photograph of the motion of the stars near the north p6le of the
heavens. The exposure-time was 12 hours. The bright trail nearest the
pole was made by Polaris.
the same. It is the north celestial pole. If the camera
had been directed to the equator the trails of the stars
passing across the plate would have been straight lines.
52 ASTRONOMY.
If the student is a photographer, he should try these ex-
periments for himself, using the longest-focus lens that he
can obtain.
We have now to inquire why do the stars rise and set ac-
cording to these laws. What explanations can be given of
their motions ? Of all the possible explanations, which is
FIG. 30.
From a photograph of the trails of stars near the celestial equator.
the right one ? It is possible to explain the rising and set-
ting of the stars in several ways. Let us give three such
ways.
(A.) The Earth and the observer are at rest and each and
every star has a particular motion of its own, each star
DIURNAL MOTION: SUN, MOON, AND STARS. 53
moving at just such a rate as actually to move completely
round the Earth back to its starting-point in 24 hours.
There are at least a hundred million stars, in all possible
situations. It is incredible that each one of them has a
special rate of motion of its own just as a railway train
has its own rate of motion and that the 100,000,000 mo-
tions are so nicely regulated as to obey the laws of the di-
urnal motion exactly. This explanation is too complicated.
It must be rejected.
(J9.) All the stars are set in a huge sphere above us ; all
of them are at the same distance from us; the sphere itself
turns round the Earth once in 24 hours, while the Earth
and the observer remain at rest. This was the explanation
given by the ancients and it was a perfectly good explana-
tion so long as it was not known that the stars were sit-
uated at very different distances from us; so long as it was
not known that some stars were comparatively near and
some much further off. As soon as we know this one fact
it is impossible to suppose the stars to be set all in one
sphere. There would need to be a sphere for each star
(since no two stars are at exactly the same distance from
us). Moreover the planets ( Venus, Jupiter, etc.) and the
comets, are sometimes at one distance from us and some-
times at another. So that the explanation adopted by the
ancients must also be given up, since the planets and comets
rise and set like the stars.
(0.) The simplest explanation possible is that the stars
are fixed and do not move at all ; that the whole Earth
with the observer on its surface revolves round an axis once
every 24 hours; so that the actual turning of the Earth
from west to east makes the stars (and the planets and
comets) appear to move from east to west from rising to
setting. This is the true explanation. It is not true be-
cause it is the simplest ; nor is there any one simple and
conclusive proof of its truth. It is true because it com-
54: ASTRONOMY.
pletely and thoroughly explains every single one of millions
and millions of cases some of them very different from
others. There are some rather complicated proofs of it,
but no simple ones suitable to be given here. We must
accept it as. true because it explains completely and thor-
oughly every case that has arisen in the past and because
there are millions and millions of such cases. Or, let us
say that we will accept it as true until we come to some
case which is not explained by it.
FIG. 31.
The real motion of the horizon of an observer among the stars makes
them appear to rise and set.
The 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 were
on a steamer which was turning round, and as if he saw the
harbor-shores, the ships, and the houses apparently turn-
ing in an opposite direction.
DIURNAL MOTION: SUN, MOON, AND STARS. 55
Fig. 31 is intended to explain the apparent diurnal motion of
the stars which is caused by the real rotation of the Earth on its axis.
The little circle N is the Earth, seen as it would be by a spectator
very far away. The circle WZEis one of the circles of the celestial
sphere. W is towards the west and E towards the east. The Earth
revolves from west to east in the direction of the arrow. Suppose a
to be the situation of an observer on the Earth. Z will be his zenith
in the heavens. HH will be his horizon (since it is a plane through
tha cemtre of the Earth perpendicular to the line joining his zenith
and nadir). After a while the observer will have been carried on-
wards by the rotation of the Earth and his zenith will be at Zl '. His
horizon will have moved to HH f , It will have moved below all the
stars in the space HEH', and these stars will have " risen "
they will have come above his horizon. His horizon will have
moved above all the stars in the space HWH' and these stars
will have " set "they wilt have sunk below his horizon.
It is really the horizon that moves and the stars that are at
rest ; but in common language we say that one group of stars
has risen above his horizon, and that the second group has set. A
little later the observer on the rotating Earth will be at the point b ;
his zenith will be at Z' and his horizon at H"H". His horizon will
have sunk below a new group of stars in the east (and these stars will
have "risen"); and his horizon will have moved above a group of
stars in the west (and this group will have " set ").
The zenith of an observer moves once round the celestial sphere
each day. His horizon (which is perpendicular to the line joining
his zenith and nadir) moves once round the celestial sphere each
day, likewise. Therefore, stars in the east rise, culminate (come to
their greatest altitude), and set daily. This is the apparent diurnal
motion of the stars, and it is explained by the actual motion of the
Earth on its axis.
Before leaving this figure one important thing must be noticed.
Suppose there are two observers on the Earth, one at a and one at b.
Their zeniths would be at Z and at Z" on the celestial sphere at
some ^instant. Their horizons would be, at this instant, HH and
H''H". The observer to the eastward (b) would see a whole group of
stars that are yet invisible to the other observer further west (a).
That is, an observer at Greenwich at ten o'clock at night (for ex-
ample) will see groups of stars then invisible to an observer at
Washington. The horizon of the Washington observer has not yet
moved below them ; they have not yet risen to him. If the Wash-
ington observer waits for several hours these groups will, by and by,
56 ASTRONOMY.
rise. But the Greenwich observer always sees stars rise before they
have risen at Washington.
What is the diurnal motion of the stars ? Describe the course of
a southern star from its rising to its setting. At what point does such
a star attain its greatest altitude above the horizon ? What number
will express the altitude (in degrees, for instance) of a star when it
is rising? What is the point of culmination of a star? The word
culmination is often used to express a time as well as a definite point
in the sky what time ? How can stakes set in the ground be used
to demonstrate the diurnal motion of the stars? Is the motion of the
stars from rising to setting uniform? How do you know? The
southern stars all rise and set. What stars do not rise and set?
What stars, then, are always above the observer's horizon ? The
north-polar-distance of every star that never sets must be less than
the altitude of what point ? Make a sketch of the seven stars of
the Great Bear. Which two are the pointers ? Where would Polaris
be in this sketch ? Hold the paper on which the sketch is made be-
tween the thumb and finger of your left hand with Polaris covered
by your thumb. Now turn the paper round slowly, taking hold of
the outer edges of it. If you face the north while doing this you
will see that you are imitating, by a model, the actual diurnal mo-
tions of the northern stars. Define the north pole of the heavens. In
which direction (west to east, or east to west) do such stars move
when they are above the pole? When they are below below the pole ?
How do they move (up or down ?) when they are furthest east ? Fur-
thest west ?
Define in a brief and accurate phrase the north-polar-distance in
stars?
Give the three laws of the diurnal motion. I. Every star in the
heavens . II. The greater the star's N.P.D. III. All
the stars describe their diurnal orbits in the same , which is the
? What is the diurnal orbit of a star? How can you know that
these laws are true? What is the circle of perpetual apparition?
Why is it so called?
The foregoing laws, I, II, III, are true, as we know from observa-
tion. These are the appearances. What is the real cause of these
appearances? How do we know that the stars are not actually set in
a huge sphere above our heads, and that this sphere does not turn
around the fixed Earth once every day ? (motions of planets, comets,
etc.) The Earth turns on its axis once in 24 hours do you feel it
turning ? If the Earth turns, and the observer stays at one place (say
in New York) on its surface, does he move in space ? If the observer
DIURNAL MOTION: SUN, MOON, AND STARS. 57
moves round a circle every day, will liis zenith move on the surface
of the celestial sphere? his nadir? Will his horizon move among the
stars? When his horizon moves below a group of stars in the east,
those stars will ? When his horizon moves above a group of
stars in the west those stars will ?
FIG. 32. PART OF A CELESTIAL GLOBE:
Showing the principal circles of the celestial sphere.
In this figure Z is the zenith of the observer, and .ZVWS'his horizon.
P is the north celestial pole, and XX, XXI . . . 0, I . . . the celes-
tial equator. is the vernal equinox. All stars on the hour circle
of II hours are on the celestial meridian of the observer (PZS). The
star C (whose R.A.= 22 h ) is 4 hours west of the meridian ; the star
D (R. A. = 20 h ) is 6 h west nearly to the western horizon.
In Fig. 33 Z, P, NWS, etc., have the same meaning as in Fig.
32. In fact, the picture represents the same globe after it has
been turned one hour towards the west. The stars C and D are
in the same places on the celestial sphere as before, but C is now 5 h
58 ASTRONOMY.
west of the meridian, and D is just setting 7 h west of the meridian.
In Fig. 32 A and B (whose right ascensions are 2 h ) were on the
celestial meridian of the observer ; here they are l h west of the
meridian.
N FIG. 33. PART OP A GLOBE:
Showing the principal circles of the celestial sphere.
CHAPTER IV.
THE DIURNAL MOTION TO OBSERVERS IN DIFFERENT
LATITUDES, ETC.
12. The Latitude of an Observer on the Earth. The al-
titude of the celestial pole above the horizon of any place on
the Earth's surface is equal to the latitude of that place.
Let L be a place on the Earth PEpQ, Pp being the
Earth's axis and EQ its equator. Z is the zenith of the
place, and HR its sensible horizon. Its celestial or rational
FIG. 34.
horizon would be represented by a line through parallel
to HR. LOQ is the latitude of L according to ordi-
nary geographical definitions ; i.e., it is the angular
distance of L from the Earth's equator. Prolong OP in-
definitely to P' and draw LP" parallel to it. P' and P"
60 ASTRONOMY.
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 radins
of the celestial sphere.* "We have then to prove that
LOQ = P"LH.
POQ and ZLH are right angles, and therefore equal.
ZLP" = ZOP' by construction. Hence ZLH- ZLP"
= P"LH= POQ - ZOP' = LOQ, or the latitude of the
point L is measured by either of the equal angles LOQ or
P"LH.
In Geography, which deals only with the Earth, it is
convenient to define the latitude of an observer anywhere
on the surface to be the angular distance of the point
where he stands from the terrestrial equator. The lati-
tude of an observer at L is LOQ .
In Astronomy, which deals chiefly with the heavens, it
is convenient to define the latitude of an observer anywhere
on the Earth's surface to be the altitude of his celestial pole
above his horizon. The latitude of an observer at L is
P"LH = the altitude of the pole ; or we might say, the lat-
itude of an observer is the N.P.D. of tho north point of
his horizon (if he is in the northern hemisphere). The
latitude of an observer at L is P"LH in Fig. 34.
It is often more convenient, in Astronomy, to define the
latitude of an observer by describing the place of his zenith
on the celestial sphere and to say, the latitude of an ob-
server anywhere on the Earth's surface is the declination
of his zenith.
Fig. 35 represents the celestial sphere HZEN. The
Earth is a point at the centre of the circle. Some ob-
server on the Earth has a zenith Z, a nadir N, a horizon
HR. P is 'the pole of the heavens and E a point of the
celestial equator.
* Two lines drawn from the star Polaris to the points L and
make an angle with each other of less than
LATITUDE. 61
In the figure PH measures the latitude of the observer,
because PH is the north-polar-distance of the north-point
of his horizon. Z is his zenith, EZ is the declination of
his zenith (it is the angular distance of Z from the celestial
equator).
Now the arc PH = the arc EZ because the arc ZH is
90, and PH = 90 - PZ; moreover, the arc PE is 90,
and EZ = 90 PZ. Therefore PH (the observer's lati-
tude) is measured by EZ (the decimation of his zenith).
FIG. 35.
The latitude of an observer is measured by the declination of his Zenith.
In Fig. 12 the latitude of the observer is measured either by
(NP) H or by QZ.
In Fig. 16 the latitude of the observer is measured either by the
angle PON or by the angle COZ (or by the arcs PJVand 6 Y Z).
In Fig. 36 the latitude of the observer whose zenith is Z is
the elevation of the north pole of the heavens (P) above his
horizon (NWS) = 40 ; it is measured by the declination of his zenith
(Z) = 40.
Define the latitude of an observer on the Earth according to
Geography. Define the latitude of an observer on the Earth ac-
cording to Astronomy in three ways : I. The altitude of the North
Pole above the observer's horizon is the of the observer, II.
62
ASTRONOMY.
The N.P.D. of the north point of an observer's horizon is the
of the observer. III. The declination of an observer's zenith
is the of that observer.
FIG. 36.
So far we have only spoken of observers in the northern
hemisphere of the Earth. The northern hemisphere is
the most important to ns, because all the more intelligent
nations of the globe lived in it for centuries and all astron-
omy was perfected there. Later on, our definitions will
be extended to cover all cases.
13. The Horizon of an Observer Changes as He Moves
from Place to place on the Earth. The theorem that has
just been written is easily proved. As the observer travels
from place to place on the Earth his zenith moves on the
celestial sphere. It is the point directly over his head.
DIURNAL MOTION IN 34 NORTH LATITUDE. 63
His horizon is the plane always perpendicular to the line
joining his zenith and nadir. As this line moves with the
motion of the observer his horizon must move.
It is so important to understand just how the horizon of
an observer moves and just how the appearances of his sky
are changed, that it is well worth while to take space to
consider several cases.
FIG. 87.
The circles of a celestial sphere for an observer in north latitude PJVor CZ.
The student must pay particular attention to this figure.
When he understands just what it means he has mas-
tered all the more important theorems of spherical astron-
omy. The large circle stands for the celestial sphere.
The Earth is a point at 0. P is the north pole of the
heavens (and p the south pole), and hence D WCE must be
the celestial equator (since its plane is perpendicular to the
line joining the poles). The celestial sphere is full of stars.
64 ASTRONOMY.
Now let us suppose there is an observer on the Earth ( 0)
at some point in the northern hemisphere. If he is in the
northern hemisphere his zenith must be somewhere be-
tween C and P. Let us suppose that the observer is on
the parallel of 34 north latitude, say on the parallel of Wil-
mington, N. C., or of Los Angeles, California. His lati-
tude is 34 then, and his zenith must be at Z, just 34
north of C. His nadir must beat n; his horizon must
be N8. Suppose that we are looking at the celestial
sphere, as drawn in the figure, from a point outside of it
and west of it. W will be his west point; ^his east point;
the line EW\& drawn so that it looks (in perspective) per-
pendicular to NS, the observer's north and south line.
The Earth will turn round once a day on the axis joining
the poles P and p. The stars in the celestial sphere will
appear to rise above his eastern horizon NES ; they will
culminate on his meridian NZS ; they will set below his
western horizon NWS. A star which rises at E will cul-
minate at C and set at W. If he could see below his hori-
zon this star would seem to him to move from W to D
and then from D to E again. The interval of time be-
tween two successive risings would be 24 hours. Some
stars in the north would never set. All of them would lie
within the circle of perpetual apparition KN. Im is the
diurnal orbit of a circumpolar star. Some stars would
never rise to this observer. His horizon would hide them.
All the stars further south than the circle SR, (the circle of
perpetual occultation) would never be seen. A star near
the south pole would have a diurnal orbit like or.
The student should notice that a part of this drawing is
quite independent of the situation of the observer. We
can draw the celestial sphere, the celestial poles, the equa-
tor, the earth, and they will be the same for any and every
observer; they will be the same whether any observer exists
or not. But the instant we imagine an observer on the
DIURNAL MOTIONS AT THE NORTH POLE. 65
earth anywhere on the earth his zenith is fixed. It
must be at a point on the celestial sphere distant from the
celestial equator by an arc equal to the observer's latitude.
So soon as the zenith is fixed a horizon is fixed. As soon
as the horizon is fixed we know that some stars will never
rise above it, and that some stars will never set below it.
If we draw the celestial sphere as it is for any particular
observer we shall be able to say just how the stars will ap-
pear to move for him; just what stars he can see, and just
what others he can never see.
The student should exercise himself in making diagrams of the
celestial sphere for observers in different latitudes. Let him make
such a diagram, placing the observer's zenith (Z) at K in the last
figure, and another placing the observer's zenith at I.
FIG.
The circles of the celestial sphere and the diurnal motions of the stars
as they appear to an observer at the north pole of the earth.
The Diurnal Motion of Stars as Seen by an Observer at
the North Pole of the Earth. An observer at the north
pole of the Earth is in terrestrial latitude 90 ; the altitude
of the north celestial pole above his horizon will be 90.
66 ASTRONOMY.
His zenith and the north celestial pole will coincide. The
star Polaris will be neatly at his zenith.
Fig. 38 shows the celestial sphere as it would appear
to an observer at the north pole of the Earth. The zenith
of the observer will be exactly overhead, of course, and
the pole will coincide with his zenith. His horizon and
the celestial equator will coincide, therefore. As all the
stars perform their diurnal revolutions in circles parallel
to the celestial equator, no matter what the latitude, in this
particular latitude they will revolve parallel to the horizon.
None of the stars of the southern half of the celestial
sphere will be visible at all. All the stars of the northern
hemisphere will be constantly visible. They will not rise
and set, but they will revolve in diurnal orbits parallel to
the horizon.
Arctic explorers who travel from temperate regions to-
wards the north find the north celestial pole constantly
higher and higher above their horizon. When they are in
latitude 50, the altitude of the pole (of the star Polaris)
will be 50; when they are in latitude 70, the altitude of
Polaris will be 70; if they reach the pole of the Earth,
the altitude of Polaris will be 90.
The student may know that from March to September of every
year the Sun is north of the celestial equator (in north declination) ;
and that from September to March the Sun is south of the celestial
equator (in south declination). From March to September, then,
the Sun is a star of the northern hemisphere ; from September to
March the Sun is a southern star. An observer at the north pole
of the Earth sees all the northern stars revolve in diurnal orbits par-
allel to his horizon, and he will thus have the Sun above the horizon
for six entire months, and for the next six months he will not see
the Sun at all. An observer at the south pole of the Earth will
have the Sun constantly above his horizon from September to
March; constantly below it from March to September. The Fig. 39
will illustrate the diurnal orbit of the Sun to an observer at the
north pole of the Earth. The Sun is at the point (near W) on
March 22, and from March to June travels every day about 1 along
DIURNAL MOTIONS AT THE EQUATOR.
67
the lowest broken line of the figure. The Sun is on the
hour circle 7 on April 6, on 77 on April 22, on 777 (near E) on May
8, on 7 Fon May 23 (and always on the dotted curve). The student
should trace out in the picture the diurnal orbits of the Sun on the
dates just given.
The Diurnal Motion of Stars as Seen by an Observer at
the Earth's Equator. If the observer is at any point on
FIG. 39.
A globe so set as to show the circles of the celestial sphere for an observer
at the north pole of the earth.
the Earth's equator his terrestrial latitude will be ; the
elevation of the north celestial pole above his horizon will
be ; the star Polaris will be in his horizon.
Fig. 40 shows the celestial sphere as it appears to an
68 A8TRONOMT.
observer on the Earth's equator. The zenith of the ob-
server is in the celestial equator. The latitude of the ob-
server is and hence the altitude of the north celestial
pole (of Polaris) is 0; that is, the north and south celes-
tial poles are in his horizon. All the stars appear to move
in their diurnal orbits parallel to the celestial equator, no
matter what may be the observer's latitude. In this case
they will all appear to revolve in circles perpendicular to
the horizon. All the stars of the sky, those in both halves
FIG. 40.
The circles of the celestial sphere and the diurnal motions of the stars as
they appear to an observer on the earth's equator.
of the celestial sphere, will be visible, for all of them will
rise, every day, above the eastern horizon and will pass
across the sky and set below the western horizon. Every
star will be above the horizon exactly half a day 12 hours.
In Fig. 41 the diurnal paths of all stars are perpendicular to the
horizon, and every star is 12 h above and 12 h below it. Stars whose
right-ascension is 6 h are on the meridian in the picture The star E
is 3 h , the stars A, B, are 4 h west of the meridian. The vernal equi-
nox (0) is 6 h west.
The ecliptic (the path of the Sun) is marked on the northern celes-
tial hemisphere by a broken line from towards E,
DIURNAL MOTION OF TUB SUN. 69
etc. The Sun is at on March 22 ; on the hour-circle I, April 6 ;
on II, April 22 ; on III, May 8; on IV, May 23 (and always on the
dotted curve). The student should trace out the diurnal orbits of the
Sun for the dates just given. It is clear that the Sun will cross the
celestial meridian of an observer at the Earth's equator north of his
zenith when the Sun is in north declination (March to September),
and south of it whenever the Sun is in south declination In our
latitudes the Sun is never seen north of the zenith, as may be seen by
inspecting Fig. 33, where the dotted line is the Sun's path.
FIG. 41.
A globe so set as to show the circles of the celestial sphere for an ob-
server at the earth's equator. Z is his zenith ; P the north celestial pole :
NWS his horizon.
If now the observer travels southward from the equator,
the south pole will, in its turn, become elevated above his
horizon, and in the southern hemisphere appearances will
be reproduced that have been already described for the
northern, except that the direction of the motion will, in
70 ASTRONOMY.
one respect, be different. The heavenly bodies will still
rise in the east and set in the west, but those near the
celestial equator will pass north of the zenith of the ob-
server instead of south of it, as in our latitudes. The sun,
instead of moving from left to right, there moves from
right to left. In the northern hemisphere of the Earth
we have to face to the south to see the sun ; while in the
southern hemisphere we have to face to the north to see it.
If the observer travels west or east on a parallel of lati-
tude of the Earth's surface, his zenith will still remain at
the same angular distance from the north pole as before
(since his terrestrial latitude remains unchanged), and as
the phenomena caused by the 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.
FIG. 42.
The risings of the stars to an observer on the earth are earlier the
farther east he is. East is in the direction of the arrow, since the earth
revolves from west to east.
DIURNAL MOTIONS IN DIFFERENT LATITUDES. Tl
A star that 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 constant angular
distance from the pole), but later in time, since it has to
pass through the zenith of every place between the two sta-
tions. 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 suc-
cessively, and in the same order, at both. An observer at
b (east of a) will see the same stars rise earlier than an ob-
server at a. (See Fig. 42.)
Change of the Position of the Zenith of an Observer by
the Diurnal Motion. If the student has mastered what
has gone before he can solve any questions relating to the
diurnal motion. The following presentation of these ques-
tions will be found useful in relation to problems of longi-
tude and time, that are to be considered shortly.
In Figure 43 nesq is the Earth ; NESQ, is the celestial sphere. An
observer at n will have his zenith at NP, and his horizon will coin-
cide with the celestial equator. The stars will appear to revolve
parallel to his horizon (the celestial equator), as we have seen. If
the observer is at s, his zenith is at SP. If the observer is in 45
north latitude (the latitude of Minneapolis), his zenith will be at Z in
the figure. The Earth revolves on its axis once daily, and the ob-
server will be carried round a circle. His zenith (Z) will move round
a circle of the celestial sphere (ML) corresponding to the parallel of
45 on the Earth. If the observer is on the earth's equator at q, his
zenitli will be at Q, and it will move round the circle EQ of the celes-
tial sphere once daily. If the observer is at 45 south latitude on
the Earth, his zenith will be at S, and the zenith will move round a
circle of the celestial sphere (SO) once daily, and so on. Thus, for
each parallel of latitude on the Earth we have a corresponding circle
on the celestial sphere (a parallel of declination), and each of these
latter circles lias its poles at the celestial poles.
Not only are there circles of the celestial sphere that correspond
to parallels of latitude on the Earth, but there are also celestial
meridians which correspond to the various terrestrial meridians. The
plane of the meridian of any place contains the zenith of that place
72 ASTRONOMY.
and the two celestial poles. It cuts from the earth's surface the ter-
restrial 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
FIG. 43.
The change of the position of the observer's zenith on the celestial sphere
due to the diurnal motion.
cuts from the celestial sphere the celestial meridian. As the Earth
rotates on its axis his zenith moves round the celestial sphere in a par-
allel, as ZL in the last figure.
Suppose that the east point is in front of the picture, the west
point being behind it. Then as the Earth rotates the zenith Z will
move along the line ZL from Z towards L. The celestial meridian
always contains the celestial poles and the point Z, wherever it may
tilUHNAL MOTIONS IN DIFFERENT LATITUDES. 73
be. Hence, the arcs of great circles joining N.P. and S. P. in the fig-
ure are representatives of the celestial meridian of this observer,
at different times during 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-revolution of the Earth.
In this time Z moves from Z to L. In the next semi-revolution
Z moves from L to Z t along the other half of the parallel ZL. In 24
ho irs 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, S.P., through every inter-
mediate position to JV.P., L, E, 0, S.P , and from this last position
back to N.P., Z, Q, S, S.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 pass-
age 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 terres-
trial meridians is 15 (see page 28). From what we have just learned
it follows that their celestial meridians are also 15 apart. When B's
meridian is N.P., Z, Q, K, 8.P., A's will be the first one (in the fig-
lire) beyond it ; when B's meridian has moved to this first position,
A's will be in the second, and so on, always 15 (one hour) in advance.
A group of stars that has just come to A's meridian will not pass B's
for an hour. When they are on B's meridian they will be one hour
west of A's, and so on. A's zenith is always one hour west of B's.
The same stars successively rise, culminate, and set to each observer
(A and B), but the phenomena will be presented earlier to the eastern
observer.
If the student has access to a celestial globe all the prob-
74 ASTRONOMY.
lems that have been considered in this chapter can be
quickly solved by its use.
In Figure 44 Z is the zenith, .ZVthe nadir, and W the west point
of the observer. Pis the north celestial pole, X, XI, . . . XIV, XV,
. . . the celestial equator. The dotted line from P through XII to
the south celestial pole is the hour-circle of 12 hours. The dotted
line inclined to the equator by an angle of 23 is the sun's path the
ecliptic. Stars whose right-ascension are 17 h are on the observer's
celestial meridian.
The star K (K.A. = 13 b , Decl. = + 20) is 4 h west of the merid-
ian ; the star R (R.A. = 10 h , Decl. = -f 30) is just setting ; the
stars north of Decl. -(- 50 are circumpolar they never set.
Prove that as an observer moves from place to place his hori-
zon must change. If an observer is in the northern hemisphere of
the Earth his zenith is in the northern half of the celestial sphere.
Prove it by a diagram. What is a circumpolar star ? Draw a dia-
gram representing the celestial sphere with its poles, its equator.
Now, suppose an observer on the Earth in 30 north latitude ;
where will his zenith be on the diagram ? Draw a circle to show
what stars will always be above his horizon. Suppose an observer
in 86 north latitude (the highest latitude reached by NANSEN in
1895); where will his zenith be? Draw circles to show how the
stars appeared to move in their diurnal orbits to NANSEN. The hori-
zon of an observer in some latitude is the same as the celestial equa-
tor in what latitude? An observer at the north pole of the Earth
would have the Sun constantly above his horizon for six months
prove it. All the stars are successively visible to an observer on the
Earth's*equator prove it.
The Celestial Globe. A celestial globe is a globe marked
with the lines and circles of the celestial sphere the celes-
tial poles, the celestial equator, the celestial meridians and
parallels, etc., and with the principal stars, each one in its
proper right-ascension and declination. The Figs. 32, 33,
39, 41, and 44 represent such a globe with the stars omit-
ted. Every school should own a celestial globe, because all
the problems of spherical astronomy can be simply ex-
plained or illustrated by its use. In text-books we are
obliged to use diagrams. They are necessarily drawn on a
THE CELESTIAL GLOBE.
FIG. 44.
View of a globe showing the circles of the celestial sphere for an
observer in 40 north latitude (the latitude of Philadelphia, Columbus, O.,
Quincy, 111., Denver, etc.).
76 ASTRONOMY.
flat surface, and the student has to imagine the spherical
surface. The school-globe shows the surface as it really is.
The celestial globe must be set so that the elevation of
the north celestial pole (if the observer lives in the north-
ern hemisphere) above the horizon is the same as the lati-
tude of the observer. (His latitude can be taken from any
good map.) Then the celestial globe will represent his ce-
lestial sphere just as it really is, when the line N8 is placed
north and south, N to the north. Any one of the problems
of this chapter can be illustrated by turning the celestial
globe about the axis. For instance, let the student point
out the circumpolar stars, those that never rise and set
to him. Let him take a star a little further south and
turn the globe till the star is at the eastern horizon just
rising. By turning the globe slowly he will see exactly how
this particular star moves in its apparent diurnal orbit from
rising to culmination, and from ccilmination to setting.
Let him particularly notice how its altitude increases from
zero at rising to a maximum at culmination; and how it
decreases from culmination to zero at setting.
After he has studied the diurnal motion of one star, let
him choose another one and trace its course from rising to
setting. He should study, in this way, the diurnal mo-
tions of stars in all parts of the sky. If he has his globe
by him while he is observing the real stars in the sky, the
globe will help him to understand quickly, in a few min-
utes, motions that the real stars require 24 hours to make.
Other problems can be, and should be, studied in the same
way.
CHAPTER V.
CO-ORDINATES -SIDEREAL AND SOLAR TIME.
14. Systems of Co-ordinates to define the Place of a Star
in the Celestial Sphere. Let us now briefly consider some
of the ways in which the position of a star in the celestial
sphere may be described. Many of them are already fa-
miliar.
FIG. 45. SYSTEMS OP CO-ORDINATES ON THE CELESTIAL SPHERE.
Any 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.
77
78 ASTRONOMY.
The hour-circle of any particular star is that one which
passes through the star at the time. As the Earth re-
volves, different hour-circles, or celestial meridians, come
to the star, pass over it, and move away towards the east.
In Fig. 45 let be tlie position of the Earth in the centre of the
celestial sphere NZSD. Let Z be the zenith of the observer at a
given instant, and P, p, the celestial poles. By definition PZSpnNP
is his celestial meridian. NS is the horizon of the observer at the
instant chosen. PON is his latitude. If P is the north pole, he is
in latitude 34 north, because the angle PON 34.
ECWD is the celestial equator ; E and W are the east and west
points. The Earth is turning from TFto E. The celestial meridian,
which at the instant chosen in the picture contains PZp, was in the
position PV about three hours earlier.
PC, PB, PV, PD are parts of hour-circles. If A is a star, PB is
the hour-circle passing through that star. As the Earth turns PB
turns with it (towards the east), and directly PB will have moved
away from A towards the top of the picture, and soon the hour-circle
PV will pass through the star A. When it does so, PV will be the
hour-circle of the star A. At the instant chosen for making the
picture PB is its hour-circle.
We are now seeking for ways of defining the position of
a star, of any star, on the celestial sphere. We define the
position of a place on the Earth by giving its latitude and
longitude. These two angles are called the co-ordinates of
this place. Co-ordinates are angles which, taken together,
determine the position of a point. If we say that the
longitude of a city is 77 and that its latitude is 38 53' N.,
we know that this city is Washington. These two num-
bers determine its position. The place of this city is de-
scribed by them and no other city can be meant.
To describe and determine the place of a star on the
celestial sphere we may employ several different pairs of
co-ordinates. Those spoken of here will all be needed in
what is to follow.
North-polar-distance and Hour-angle. The north-
polar-distance (N.P.D.) of the star A is PA. The hour-
CELESTIAL CO-ORDINATES.
79
angle of a star is the angular distance between the celes-
tial meridian of the observer and the hour-circle passing
through that star. The honr-angle is connted from the
meridian toivards the icest from to 360 (or from O h to
24 b ). The hoar-angle of a star at A at the instant chosen
for making the picture is ZPB. The hour-angle of a star
at /iTis 0. The hour-angle of a star at Fis ZPV\ of a
star at D is ZPD = 180 = 12 h ; and so on.
The hour-angle is measured by the arc of the celestial
45 bis.
equator between the celestial meridian of the observer and
the foot of the hour-circle through the star. The arc CB
is the measure of the angle ZPB. Knowing the two co-
ordinates PA and CB the place of the star A is described
and determined.
North-polar-distance and Right-ascension. The north-
polar-distance of the star A is PA, measured along the
hour-circle PB. Let us choose some fixed point F on the
80 ASTRONOMY.
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, <7,
E, D, TF, successively.
VB 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 the
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
(K.A. and N.P.D.) of a star, we can point it out. Thus
VB and PA define the position of A.
The right-ascension of the star A" is VC. Of a star at
E it is VCE; of a star at D it is VCED ; of a star at W it
is VCEDWfwbdi so on.
Right-ascension and Declination. It is sometimes con-
venient to use in place of the north-polar-distance of a star
its declination.
The declination of a star is its angular distance north or
south of the celestial equator.
The declination of A is BA, which is 90 minus PA.
The relation between N.P.D. and 6 is
N.P.D. = 90 - tf; d = 90 - N.P.D.
North declinations are + ; south declinations are ,
just as geographical latitudes are -f (north) and (south).
Altitude and Azimuth. A vertical plane with respect to any ob-
server is a plane that 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.
* It is, in fact, that point at which the Sun passes the celestial
equator in moving from the southern half of the heavens to the
northern half. The Sun is south of the celestial equator from Sep-
tember 22 to March 21 and north of it from March 21 to September 22.
CELESTIAL CO-ORDINATES.
81
FIG. 46.
As soon as we imagine an observer to beat any point on the Earth's
surface his horizon is at once fixed ; his zenith and nadir are also
fixed. From his zenith radiate a
number of vertical circles that
cut the celestial horizon perpen-
dicularly, and unite again at his
nadir.
Some one of these vertical cir-
cles will pass through any and
every star visible to this observer.
The altitude of a heavenly body
is its angular 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, ZS is the zenith distance (C) of 8, and HS (a) is its
altitude. ZSH is an arc of a vertical circle.
ZSH = a + C = 90; C = 90 - a ; a = 90 -.
The azimuth of a star is the angular distance from the point where
the vertical circle through the star meets the horizon from the north (or
south) point of the horizon. NHor SH is the azimuth of S in Fig.
46. The prime-vertical of an observer is that one of his verti-
cal circles that passes through his east and west points. The azi-
muth of a star on the prime- vertical is 90.
Co-ordinates of a Star. In what has gone before we
have described 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 declina-
tion) of the star. The apparent position of the star on the
celestial sphere is fixed by these two co-ordinates just as
the position of a place on the Earth is fixed by its two co-
ordinates, latitude and longitude.
If the student has a celestial globe he can set it so as to make the
preceding definitions very clear. The north pole of the globe must
be above the horizon of the globe by an angle equal to the latitude,
82 ASTRONOMY.
In the figure Z is the observer's zenith, as before. The star A has
the following co-ordinates : R.A. = 2 h , hour-angle l h west, Decl. =
+ 40, N.P.D. = 50, zenith distance = the arc ZA, altitude = 90
ZA, azimuth, the arc measured on the horizon SWN from S
through W to to the foot of a vertical circle from Z through A ;
the azimuth of A is something more than 90. The student should
point out the corresponding co-ordinates for the stars B, G, and D.
FIG. 47.
A globe showing the circles of the celestial sphere as they appear to an
observer in 40 north latitude.
Students mast try to realize the circles that have been
described in the book as they actually exist in the sky.
They are in the sky first; and in the book only to explain
the appearances in the sky. On a starlit night let him
first find the north celestial pole (near the star Polaris).
All hour-circles pass through this point. Next he must
CELESTIAL CO-ORDINATES. 83
find his zenith. All vertical circles pass through this
point. The great circle in the sky that passes through the
north pole of the heavens and his own zenith is his own
celestial meridian. Let him trace it out in the sky from
the north point of his horizon to the south point; and
imagine it extending completely round the earth as a great
circle. Let him choose a star a little to the west of his
meridian and decide : 1st. What is the N.P.D. of this
star? 2d. What is its hour-angle? Next he should select a
star far to the west, and decide what its N.P.D. and hour-
angle are. Then he should take a star a little to the east
of his meridian and decide the same points for this star.
A little practice of this sort will make all the circles of the
sky quite familiar.
Define hour-circles of the celestial sphere. What is the hour-
circle of a star ? Does a star have different hour-circles at different
instants ? What are the two co-ordinates that determine the position
of a point on the surface of the Earth ? What pairs of co-ordinates
may be used to determine and describe the position of a star on the
celestial sphere ? Define the hour-angle of a star. What is the
measure of the hour-angle on the celestial equator ? Define the
right- ascension of a star. Hour-angles are counted from the celestial
meridian of a place towards the ? The right- ascension of a star
is counted, on the celestial equator, towards the ?
15. Measurement of Time ; Sidereal Time ; Solar Time;
Mean Solar Time SIDEREAL TIME. The Earth rotates
uniformly on its axis and it makes one complete revolution
in a sidereal day.
A sidereal day is the interval of time required for the
Earth to make one complete revolution on its axis, or, what
is the same thing, it is the interval between two successive
transits of the same star over the celestial meridian of a
place on the Earth. A sidereal day = 24 sidereal hours.
A sidereal hour = 60 sidereal minutes, A sidereal minute
84: ASTRONOMY.
= 60 sidereal seconds. In a sidereal day the earth turns
through 360, so that
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 (seepage 79). 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.
48, where ECWD 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 conven-
ient to select that point in the sky from which the right
ascensions of stars are counted the vernal equinox the
point V in Fig. 48. The sidereal time at any instant is
measured ly the hour-angle of the vernal equinox. The
fundamental theorem of sidereal time is: TJie hour-angle
of the vernal equinox, or the sidereal time, is equal to the
right-ascension of the meridian; that is, CV VC.
To avoid continual reference to the stars, we set a clock
so that its hands shall mark hours minutes seconds
SIDEREAL TIME. 85
at the instant the vernal equinox is on the celestial merid-
ian of the place; and the clock is regulated so that exactly
24 hours of its time elapses during one revolution of the
Earth on its axis.
In this figure PZCS is the celestial meridian of the observer whose
zenith is Z. V is the vernal equinox. It is that point on the celes-
tial sphere from which right-ascensions are counted. We shall soon
see how to determine it.
PIG. 48. MEASUREMENT OF SIDEREAL TIME.
Suppose that there were a very bright star exactly at V. (There is
no star exactly at the vernal equinox.) Such a star would rise (at E);
culminate (at C); and set (at W). When it is on the celestial merid-
ian of the observer its hour-angle is O h O m s (at C). Two hours
later the star V will have moved 30 to the westward, towards set-
ting. Its hour-angle ZPB will then be 2 h . The sidereal time of the
observer whose zenith is Z will then be 2 h . Six hours after its cul-
mination (at C) the star "Fwill have moved to TFand its hour-angle
will be 6 h . The sidereal time of the particular observer whose zenith
86 ASTRONOMY.
is Z will then be 6 h . When Fhas moved to Z>, the sidereal time will
be 12 h . When F has moved to E, the sidereal time will be 18 h .
When V has moved to C the sidereal time will be 24 1 ' (or O' 1 again)
and a new sidereal day will begin ; and so on forever.
When the hour-angle of V is 2 h and the vernal equinox
is at It, the right-ascension of the celestial meridian (of the
FIG. 49.
The hour-angle of the vernal equinox, O, in this figure is 2 hours west.
The sidereal time is therefore 2 hours. The R.A. of the observer's merid-
ian is 2 hours.
point (7) is 2 h . The right-ascension of any star on the
meridian at that instant must be 2 hours. Speaking gen-
erally, when the vernal equinox is anywhere (as at F in
Fig. 48) the right-ascension of the celestial meridian (of the
point C) in the figure will be VC. The sidereal time is
the angle ZP V measured by the arc CV. The right-ascen-
SIDEREAL TIME. 87
sion of the meridian is VC. The right-ascension of any
star on the meridian at that instant will be VC.
Conversely if a star C is on the celestial meridian of a
place at any instant the right-ascension of that star is ex-
pressed by the same number of degrees (or of hours) as the
hour-angle of the vernal equinox or as the sidereal time.
FIG. 50.
The hour-angle of the vernal equinox, O, in this figure is 3 hours west.
The sidereal time is therefore 3 hours. The R. A. of the observer's merid-
ian is 3 hours.
Suppose then that we had a catalogue of the right-ascensions of
stars like this and we have such catalogues. See Table V for a
specimen of the sort :
The R. A. of the star Aldebaran is 4 h 30"'
" " "" " " Siriusis 6 h 41 m
" " " " " " Regulm\s 10 h 3 m
" " " " " " Spica is 13 h 20 m
*' " " " " " Arcturus is 14 h ll m
" " " " " " Vega is 18 h 34 m
" " " " " " Fomalhaut is 22 b 52 m
88 ASTRONOMY.
Suppose further that we Lad a way of knowing when a star was
on our celestial meridian, that is, exactly south of us (and we have
such a way, as will soon be seen), then if an observer noticed that
Sirius was on his celestial meridian at a certain instant he would know
that the sidereal time at that instant must be 6 h 41 1 * 1 . (For the R.A.
of Sirius is 6' 1 41 ra and this is the R.A. of the meridian, and this is
equal to the hour-angle of the vernal equinox; and, finally, this is
FIG. 51.
The hour-angle of the vernal equinox, O, in this figure is 6 hours west.
The sidereal time is therefore 6 hours. The R.A of the observer's merid-
ian is 6 hours.
the sidereal time at that instant). If the star FomalJiavt is on the
celestial meridian of an observer at another instant, the sidereal time
at that instant must be 22 h 52 m , and so on. The sidereal clock must
show on its dial 6 1 ' 41 ni when Sirius is on the meridian ; and it must
show 22 h 52 m when Fomalhaut is on the meridian, and so on. As
soon as we know the right-ascension of one star we can set the hands
of the sidereal clock correctly. When Sirius is on the meridian on
8IDERIAL TIME.
89
FIG. 52.
The hour-angle of the vernal equinox in this figure is 17 hours. The
sidereal time is therefore 17 hours. The R.A. of the observer's meridian
is 17 hours.
90 ASTRONOMY.
Monday they must point to 6 h 41 m . When Sinus comes to the merid-
ian on Tuesday they must again mark 6 1 ' 41 m . And it is just the
same for other stars. Any star whose right-ascension is known will
enable us to set the hands of the sidereal clock correctly as soon as
we know the direction of our meridian in space. The hour-hand of
the clock must move over 24 h every day, from one transit of the star
till the next succeeding transit.
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 celestial meridian. The instant
of the transit of the Sun over the meridian of any place is
the apparent noon of that place, or local apparent noon.
When the Sun's hour-angle is 12 hours or 180, it is lo-
cal apparent midnight.
The ordinary sun-dial marks apparent solar time. As a
matter of fact, apparent solar days are not equal. In in-
tervals of time that are really equal the hour-angle of the
true Sun changes by quantities that are not quite equal.
The reason for this will be fully explained later. Hence
our clocks are not made to keep this kind of 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, because it regulates our civil affairs.
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. We have tables that give us the position
of this imaginary body at any and every instant, just as cat-
alogues of stars give us the right-ascensions of stars. We
may therefore speak of the transit of the mean Sun as if
it were a bright shining point in the sky. A mean solar
day is the interval of time between two consecutive transits
of the mean Sun over the celestial meridian. Mean noon at
any place is the instant when the mean Sun is on the ce-
MEAN SOLAR TIME. 91
lestial meridian of that place (at C in Fig. 48). Twelve
hours after local mean noon is local mean midnight. The
mean sun is then at D in Fig. 48. The mean solar day is
divided into 24 hours of 60 minutes each.
Astronomers begin the mean solar day at noon and count
round to 24 hours. It happens to be convenient for them
to do so. In ordinary life the civil day is supposed to be-
gin at midnight, and is divided into two periods of 12
hours each. When the mean Sun is at Z), in Fig.
48, it is midnight (12 h ) of Sunday Monday begins.
When the mean Sun is at 6", it is mean noon (12 h ) of Mon-
day. When the mean Sun has again reached D it is mid-
night (12 h ) Tuesday begins, and so on. It is more con-
venient, in ordinary life, to change the date the day at
midnight, when most persons are asleep.
Everything that is here said about the measurement of time can be
clearly illustrated by the use of a celestial globe. Set the globe to
correspond to the observer's latitude. The vernal equinox is marked
on every globe. Place the vernal equinox on the meridian of the ob-
server. It is now sidereal O h . Rotate the globe slowly to the west.
The hour angle of the vernal equinox measures the sidereal time.
Trace the course of the equinox throughout a whole revolution ; that
is, throughout a sidereal day.
Again, suppose the sun to be in north declination 15, and in R. A. 2 h
3i m (its approximate position on May 1 of each year). Find this point
on the globe (see Fig. 50), and trace the sun's course from rising to
setting, and to rising again ; that is, throughout 24 h . You will see
that the sun rises north of the east point on May 1 and reaches a high
altitude at noon for observers in the northern hemisphere of the
Earth.
Again, suppose the Sun to be in south declination 15, and in R. A.
14 h 34 m , its approximate position on November 3 of each year (see
Fig. 52). Find this point on the globe, and trace the Sun's
course from rising to setting, and to rising again. You will see that
the Sun rises south of the east point on November 3, and that its alti-
tude at noon is considerably less in November than in May.
The student should also try to realize all these explana-
92 ASTRONOMY.
tions regarding time by conceiving the appearances in the
sky. On a starlit night he should face southwards and he
will see some star on his celestial meridian. If the right
ascension of that star is 3 h 24 m 16.93 s then, at that instant,
the sidereal time is 3 h 24 m 16.93 s ; a second later it is 3 h
24 m 17.93 s ; an hour later still it is 4 h 24 m 17.93% and so
on. Let him trace out in the sky the position of the ce-
lestial equator. The vernal equinox must be west of his
meridian by an arc of 3 b 24 m , etc., or of 51. Let him
fix in his mind a point of the equator 51 west of the me-
ridian. The vernal equinox is there. In an hour it will
be 15 further to the west; in two hours it will be 30 far-
ther, and so on. In 24 hours it will have made the circuit
of the sky and have returned to its former place once more.
The same kind of exercises should be gone through with
in the daytime, so as to realize the motions of the mean
Sun. The mean Sun is never very far away from the true
Sun. At noon the Sun is due south, on the celestial me-
ridian. At 2 P.M. the hour-angle of the mean Sun is 2 1 ' ;
at 3 P.M. it is 3 h ; at midnight it is 12 h .
Define a sidereal day. What is the measure of the sidereal time
at any instant? When the vernal equinox is on the celestial merid-
ian of a place, what is the sidereal time at that instant ? What is the
relation between the sidereal time at any instant and the right ascen-
sion of the meridian at that instant ? Draw a diagram that will show
that relation. If a star whose R.A. is 6 h 41 m is on the celestial merid-
ian of a place at a certain instant, what is the sidereal time of that
place at that instant ? If you knew that the R A. of Siriiis was 6 1 '
4 l m , how could you set the hands of a clock so as to mark the correct
sidereal time? What is true solar time? What kind of time is marked
by a sun-dial? How is mean solar time measured? Is the mean
Sun a body that really exists ? Is there any objection to imagining
such a body to exist in the sky, and to supposing that it has motions
from rising and setting like the stars? What is a mean solar day?
Define the instant of mean noon. How many hours in a mean solar
day ? In civil life we divide a mean solar day into groups of
hours each. If you have a celestial globe use it so as to illus-
TIME. 93
trate what you have learned about different kinds of time. Stand up
and imagine yourself out of doors on a starlit night. Point at your
zenith (Z). Point out your horizon. Point out the north celestial
pole (P) (it is at an altitude equal to your latitude). Point out
the celestial equator. Choose some point of the equator to be the
vernal equinox V. What is the hour-angle of F ? (Answer : It is
ZP V point out this angle.) lu an hour from now where will Fbe?
in two hours? in 24 hours ? Why does F have different positions
in the sky at different instants ? In speaking of sidereal time we
refer everything to V= the vernal equinox. Now, suppose that in-
stead of considering the motions of Fjou think of the motions of the
true Sun. Describe those motions as well as you know them, and say
what the apparent solar time is. Do the same things for the mean
Sun. Do you now thoroughly understand that the hour-angle of the
mean Sun is measured by the motion of the hour-hand of your watch?
The hands of your watch point to 4 P.M. What event took place 4
hours ago (supposing your watcu to be keeping local mean solar
time)?
CHAPTER VI.
TIME LONGITITUDE.
16. Time Terrestrial Longitudes. We have seen that
time may be reckoned in at least three ways. The natural
unit of time is the day.
A sidereal day is the time required for the Earth to turn
once on its axis; it is measured by the interval between
two successive transits of the same star (sidereus is the
Latin for a star or a group of stars) over the same celestial
meridian.
A solar day is the interval of time between two succes-
sive transits of the true Sun over the same celestial merid-
ian. It is longer than a sidereal day, because -the Sun ap-
pears to be constantly moving eastwards among the stars
(as we shall soon see), so that if the Sun has the same
right-ascension as the star Sirius on Monday noon, by
-o -o
East West
# *
Monday Tuesday
Tuesday noon it will have moved about a degree to the
east of Sirius. Therefore Sirius will come to the celes-
tial meridian on Tuesday a little earlier than the Sun, and
hence the solar day will be a little longer than the sidereal
day. The eastward motion of the true Sun in right-
ascension is not uniform, so that intervals of time that are
really equal are not measured by equal angular motions of
the true Sun. The true Sun moves in the ecliptic not
in the celestial equator. Hence a " mean Sun " has been
94
TIME. 95
invented, as it were. The mean Sun is an imaginary
point like a star moving uniformly along the celestial
equator so as to make one complete circuit of the heavens in
a year.
A mean solar day is the interval of time between two
successive transits of the mean Sun over the same celestial
meridian. As the mean Sun moves eastwards among the
stars, a mean solar day is longer than a sidereal day. The
exact relation is:
1 sidereal day = 0.997 mean solar day, #
24 sidereal hours = 23 h 56 m 4". 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 celestial
meridian of any place, as Boston, it is mean noon at Bos-
ton. When the mean Sun is on the celestial 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 earlier than the local noon
at St. Louis. 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 can be calculated before-
hand (as we shall see) and is given in the astronomical
ephemeris (the Nautical Almanac, so called) for every day
of the year. We can thus determine the local mean solar
time when we know the sidereal time. In what precedes
we have shown (page 84) how to set and regulate a sidereal
clock. A mean-solar clock can be regulated by comparing
it with a sidereal time-piece as well as by direct observa-
tion of the Sun. After the student understands the con-
struction and use of astronomical instruments we shall re-
96 ASTRONOMY.
turn to this matter of time and show exactly how the mean
solar time of our clocks and watches is determined.
Terrestrial Longitudes. Owing to the rotation of the
Earth, there is no such fixed correspondence between merid-
ians on the Earth and meridians on the celestial sphere as
there is between latitude on the Earth and declination in
the heavens. The observer can always determine his lati-
tude by finding the declination of his zenith, but he can-
not find his longitude from the right-ascension of his
zenith with the same facility, because that right-ascension
is constantly changing.
Consider 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 celestial
sphere so as to make an angle of about forty-five degrees
with each other in this case.
Let the observer imagine himself at San Francisco. His
celestial meridian is over his head, at rest with reference to
him, though it is moving among the stars. Let him con-
ceive the meridian of Washington to be visible on the
celestial sphere, and to extend from the pole over toward
his southeast horizon so as to pass 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 Wash-
ington are moving in consequence of the Earth's rotation.
The stars in their courses will first pass the meridian of
Washington, and about three hours later they will pass his
own meridian. Kow it is evident that if he can determine
the interval which a star requires to pass from the merid-
ian of Washington to that of his own place, he will at
once have the difference of longitude of the two places by
turning the interval of time into degrees, at the rate of 35
to each hour.
LONGITUDE.
97
The difference of longitude between any two places depends upon
tlie angular distance of the terrestrial (or celestial) 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 thejongitude
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 Gfreenwich is 5 h 8 ra or 77, and this is in fact the ratio of the
angular distance of the meridian of Washington from that of Green-
wich, to 24 hours or 360. The angle between the two meridians is
of 24 hours, or of a whole circumference.
FIG. 53. RELATION BETWEEN TERRESTRIAL MERIDIANS AND
CELESTIAL MERIDIANS.
Every observer on the earth has a terrestrial meridian on which he
stands and a celestial meridian over his head. The latter passes through
the celestial poles and the observer's zenith.
The difference of longitude of any two places on the Earth
is measured ly the difference of their simultaneous local
times,
98 ASTRONOMY.
If two stations on the Earth (say Greenwich and Wash-
ington) have sidereal time-pieces set and regulated properly
to the two local times, we shall know the difference of
longitude of the two places as soon as we can compare the
two time-pieces. The dials will differ by the difference of
longitude.
One way to determine the longitude is actually to carry
the Washington time-piece over to Greenwich and to com-
pare its dial with that of the Greenwich time-piece. When
the Greenwich time-piece marks 5 h 8 m P.M. the Washing-
ton time-piece will mark O h (noon). We cannot transport
pendulum clocks by sea and keep them running, so that
the Washington time-piece referred to must be a chro-
nometer, which is nothing but a large and perfect watch
kept going by the motive power of a coiled spring.
A much better way of comparing the two time-pieces is
to send the beats of a clock by telegraph from one station
to the other. It is possible to arrange things so that an
observer at Greenwich can make a signal that can be ob-
served at Washington. If Greenwich sends a signal at
5 h 8 m P.M., Washington will note the face of the standard
clock when it is received, and the Washington local time
will be O h (noon). A Greenwich signal sent at 6 h 8 m local
Greenwich time, will be received at Washington at l h , and
so on. This is the theory of the method now universally
employed for exact determinations of longitude. It was
first employed by oar Coast and Geodetic Survey between
Baltimore and Washington in 1844, and it was called " the
American method."
It is of vital importance to seamen to be able to deter-
mine the longitude of their vessels. The voyage between
Liverpool and 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 latitude of his vessel upon the chart.
LONGITUDES AT SEA. 99
The method used by a sailor is this: with a sextant (see
Chapter VII) the local time of the ship's position is de-
termined by an observation of the Sun. That is, on a
given day he can set his watch so that its hands point to
twelve at local mean noon. He carries on his ship a
chronometer which is regulated to Greenwich mean time.
Its hands always point to the Greenwich hour, minute, and
second. Suppose that when the ship's time is O h (noon)
the Greenwich time is 3 h 20 m . The ship is west of Green-
wich 3 h 20 m 50. The difference of simultaneous local
times measures the difference of longitude. ' Hence the
ship is somewhere on the terrestrial meridian of 50 west of
Greenwich. If the altitude of the pole-star is measured,
the latitude of the ship is also known. Suppose the alti-
tude of the pole-star above the horizon to be 45. The
ship is then in the regular track of vessels bound for Liver-
pool. Observations like this are made every day.
When the steamer Faraday was laying the direct cable from
Europe to America she obtained her longitude every day by compar-
ing her ship's time (found by observation on board) with the Green-
wich time telegraphed along the cable and received at the end of it
which she had on her deck.
From the National Observatory at Washington the beats of a clock
are sent out by telegraph along the lines of railway every day at
Washington noon ; 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 (by making
observations of the sun at his own station), and who can compare it
with the signals of the Washington clock, can determine for himself
the difference of the simultaneous local times of Washington and of
his station, and thus his own longitude east or west from Wash-
ington.
Standard Time in the United States. In a country of
small area, it is practicable to use the local time of its cap-
ital city all over the country. Greenwich time (nearly the
same as London time) is the standard time of the whole of
100 ASTRONOMY.
England. The case is not quite the same in a country of
wide extent in longitude. San Francisco is about 3 h west
of Washington, and it would be inconvenient to use Wash-
ington local time in San Francisco.
The matter was regulated in 1883 by the railways of the
United States and Canada, which adopted the system now
in use. By this system the continent was divided into
four sections, each 15 (one hour) of longitude in width
(from east to west). Each section extended south from
the Arctic Ocean to Central America and the Gulf. In
each section a central meridian was chosen, and the local
time of that meridian was taken for the standard time of
all the cities and towns of that section. The meridians
chosen as central were:
I. The meridian of 75 W. from Greenwich (it passes
west of Albany and east of Philadelphia).
II. The meridian of 90 W. from Greenwich (it passes
east of St. Louis and nearly through New Orleans).
III. The meridian of 105 W. from Greenwich (it passes
a little to the west of Denver).
IV. The meridian of 120 W. from Greenwich (it passes
a little west of Virginia City and of Santa Barbara).
The local time of the 75th meridian was called Eastern Time ;
" " " " " 90th " " " Central Time;
" " " "105th " " " Mountain Time ;
" " " 120th " " " Pacific Time.
Greenwich time is 5 hours later than Eastern time ;
" " " 6 " " " Central time ;
" " " 7 " " " Mountain time;
" g Pacific time.
Eastern lime is used throughout the New England States, Pennsyl-
vania, New Jersey, Delaware, the Virginias, and in the greater por-
tion of the Carolinas east of the Blue Ridge.
Central time is used in Florida and Georgia and in the Central
States, including Texas, most of Kansas and Nebraska, and in the
half of the two
STANDARD TIME. ' 101"
Mountain time is used in the group of States about the Rocky
Mountains, including most of Arizona, Utah, Idaho, and Montana.
Pacific time is used in the Pacific States.
Throughout the United States and Canada every watch
and clock running on standard time should show the same
minute and second. The hour hands alone should differ.
Standard time is Greenwich time, so far as the minutes
and seconds are concerned, with an arbitrary change of
whole hours in the different sections. All time-pieces in
England show Greenwich time. The chronometers of most
ships on the Atlantic run on Greenwich time. All time-
pieces in the United States run on Greenwich time so far
as the minutes and seconds are concerned ; the only differ-
ence is a difference in the whole hour. The chronometers
of most ships in the Pacific Ocean run on Greenwich time,
with no change in the hour.
The standard time of the Hawaiian Islands will probably be that
of the 150th meridian west of Greenwich (10 hours slower than
Greenwich time); that of the Philippine Islands will probably be the
local time of the 120th meridian east of Greenwich (8 hours faster
than Greenwich time). Cape Colony (Cape of Good Hope) time is
l h 30 fast of Greenwich time, and Natal time is 2 h fast The time
of West Australia is 8 h , of Japan and South Australia 9 h , of Victoria
and Queensland 10 h , and of New Zealand ll h 30 m fast of Greenwich
time. On the Continent of Europe, Belgium and Holland use Green-
wich time unchanged, while Norway, Sweden, Denmark, Austria,
and Italy employ a standard time l h fast of Greenwich time. France
still holds to the meridian of Paris as standard, and French time is
9 m 21 8 faster than Greenwich time. The system of standard time is
so convenient that it will eventually be extended to all civilized
countries, in all likelihood.
Change of the Day to an Observer travelling round
the Earth. Suppose an observer to be at Greenwich.
When the mean Sun crosses his celestial meridian it is
noon. Let us say it is Monday noon. When the mean
Sun next crosses his celestial meridian it is Tuesday noon,
102 ASTRONOMY.
and so on. Whenever the mean Sun crosses the meridian
of any observer anywhere on the Earth it is noon for him.
If he is east of Greenwich the San crosses his celestial
meridian before it reaches the Greenwich meridian, and his
time is later than the Greenwich time. If he is west of
Greenwich the -Sun does not cross his celestial meridian
until after it has crossed that of Greenwich, and the Green-
wich time is later.
Suppose a traveller to set out from Greenwich carrying a watcli
with him that shows not only the Greenwich hour and minute, but
also the day. It would be easy to have a watch made with a day-
hand that went forward one number (of days) every time the hour-
hand marked another 24 hours elapsed. Suppose this observer to
carry a card also, on which he makes a mark, thus | every time Hie
Sun crosses his celestial meridian. He makes a mark for every one
of his noons. Suppose him to travel eastwards round the globe.
When he comes to Sicily (15 = 1 hour of longitude east of Green-
wich) the local time will be 1 P.M. of Monday, when his watch shows
noon of Monday. At Alexandria in Egypt (30 = 2 hours of longi-
tude east of Greenwich) the local time will be 2 P.M. when his watch
shows noon, and the day will be the same as the Greenwich day.
If he goes to the Fiji Islands (180 = 12 hours of longitude east of
Greenwich) he will find the date later there than the date he carries
with him in his watch. The local time at Fiji will be 12 hours later
than his. It will be Monday midnight (and thus the beginning of
Tuesday) when his watch marks Monday noon. This is natural
enougn. He is travelling eastwards and the Sun crosses these east-
ern meridians before it crosses that of Greenwich. When he reaches
St. Louis (270 = 18 hours of longitude east of Greenwich) the date
there would be, on the same principle, 18 hours later than the Green-
wich date. When his watch marks Monday noon the people there
might call the time 18 hours later ; that is, Tuesday 6 A.M. (12 h (noon)
f 18 h - 30 h , and 30 h - 24 h = 6 h ). But in fact they call the day Mon-
day instead of Tuesday, though they call the hour corresponding to
Greenwich noon 6 A.M. Instead of reckoning their time to be 18
hours more (later) than Greenwich time, they reckon it to be 6 hours
less (earlier). The 18 hours more that they fail to count at all and
the 6 hours less make up 24 hours = 1 day. The traveller has thus
gained a day on his journey.
When he finally arrives at Greenwich again his watch agrees
GRANGE OF THE DAT. 103
with the Greenwich reckoning as to hours and minutes. The day-
hand of the watch shows that he has been away for 100 days (let us
say), but his card shows 101 marks on it. The Sun has somehow
passed his celestial meridian once more than the number of days
elapsed. To make the name of his day agree with the name of the
day used in Hawaii, the United States, and England he has to drop
one day. How is it that he has gained a whole day in travelling
eastwards round the Earth?
When the Sun crosses the celestial meridian of an observer it is
noon for him. If the observer stays at one spot on the Earth the
Earth itself, in turning on its axis eastwardly, brings his celestial
meridian to and past the Sun daily. If the observer travels round
the Earth towards the east to meet the Sun his own travels will move
his celestial meridian eastward a little every day. The Sun will pass
his meridian 101 times if he has himself gone round the Earth in 100
days. One hundred of the transits of the Sun will be due to the
rotation of the Earth on its axis. One of them will be due to his own
circumnavigation of the globe.
If instead of going eastwards the observer (with his watch and his
card) should travel westwards round the globe he would find the
local time at Washington five hours less (earlier) than the Greenwich
time. At St. Louis the local time would be six hours less (earlier).
At San Francisco it would be eight hours less (earlier). When his
watch marks Greenwich noon of Monday the people of San Francisco
will call the date 4 A.M. of Monday eight hours less (earlier) than
Greenwich.
When he reaches India or Germany he will find his Monday is not
called Monday but Tuesday. When he returns to Greenwich he will
find that his reckoning agrees with the Greenwich reckoning in every
respect but one. His watch will show the Greenwich hour and minute
exactly. His watch shows that he has been absent for 100 days, let
us say. But his card shows that he has had only 99 noons. In going
round the world to the westward, away from the Sun, he has lost one
whole day. If he had remained in Greenwich the Earth's rotation
would have brought his celestial meridian to the Sun and past it 100
times. But in his journey westward he has carried his celestial
meridian with him and moved it away from the Sun. The Earth has
turned round 100 times during his absence, but the Sun has only
crossed his (travelling) meridian 99 times. Thus he has lost a day
by travelling completely round the Earth westwards away from
sunrise. If he had travelled towards sunrise eastwards he would
have gained a day, as we have just seen.
104 ASTRONOMY.
The Earth turns round just 100 times in a certain inter-
val of time, and there is never any trouble in keeping the
account. Those persons who stay in one place (as at
Greenwich) have simply to count the number of transits of
the Sun over their celestial meridian. Those persons who
travel westwards must add a day when they cross the
meridian of Fiji (180 from Greenwich). Those persons
who travel eastivards must subtract a day at this meridian,
which is called the international date-line (meaning change-
of-date line).
When Alaska was transferred from Russia to the United
States it was found that one day had to be dropped. The
Russian settlers had brought their Asiatic date with them,
while we were using a reckoning less by one day because
our count was brought from Europe.
Ships in the Pacific Ocean passing the meridian of 180
add a day going westwards and subtract a day going east-
wards.
It is to be noted that the place where the change of date is made
depends upon civil convenience and not upon astronomical necessity.
The traveller must necessarily change his date somewhere on his
journey round the world. It is convenient for trade that two adja-
cent countries should have the same day-names; so that the date-line
in actual use deflects slightly from the 180th meridian. All Asia is
to the west of this line ; all America, including the Aleutian Islands,
is east of it. Samoa is east of it, but the Tonga group and Chatham
Island are west of it.
Define a sidereal day, a so^r day, a mean-solar day. Which
of the three is the shorter ? Why is a sidereal day shorter than a
mean solar day ? What is local time ? What measures the difference
of longitude between two places on the Earth ? Describe how to de-
termine the difference of longitude between Boston and San Fran-
cisco by the transportation of chronometers by the comparison of
clocks by telegraph. How does a sailor determine his longitude from
Greenwich at sea ? Give an account of standard time as employed in
the United States. Into how many sections is the country divided ?
Name the four kinds of time employed. Four watches keeping the
LATITUDE. 105
standard time of San Francisco, Denver, St. Louis, and Philadel-
phia are laid side by side : How will their standard times differ?
How will their minutes and seconds compare with Greenwich time?
What time is used by most ships? Change of the Day. When is it
noon to any observer? If the observer is E. of Greenwich does his
noon occur earlier or later than the noon of Gieenwich? Explain
why it is that an observer travelling completely round the Earth to
the eastwards towards sunrise gains a day ; and why an observer
travelling completely round the Earth westwards away from sunrise
loses a day.
17. METHODS OF DETERMINING THE LATITUDE OF A
PLACE ON THE EARTH. Latitude from Circumpolar
Stars. In the figure suppose Z to be the zenith of the
observer, HZRN his meridian, P the north pole, HR his
horizon. Suppose 8 and S' to be the two points where
a circumpolar star crosses the meridian, as it moves around
FIG. 54.
The latitude of a place on the earth can be determined by measuring
the zenith distances of a circumpolar star at its two culminatic
ions.
the pole in its apparent diurnal orbit. PS = PS' in the
star's north-polar-distance, and PH = = the latitude
of the observer.
106 ASTRONOMY.
Therefore
y measuring the meridian altitude *O re KHOWn, 1 P Ato -
of the sun (or of a star). _ fl S Q$ j g t ]j e declina-
tion of the Sun (or of a star), and QS is given in the
Nautical Almanac.
ZS -f QS = QZ = the declination of the observer's zenith,
or
-[- = = the latitude of the observer.
If the star (or Sun) S' culminates north of the zenith
'
QS' - ZS'= QZ,
or
d - C = 0.
This is the method uniformly used at sea, where the
PARALLAX. 107
meridian altitude of the Sun is measured every day with
the sextant. The meridian altitudes of stars are often
measured at sea, by night, to determine the latitude.
Explain how to determine the latitude of a place on the Earth
by measuring the zenith distances of a circumpolar star at its upper
and at its lower culmination. Draw a diagram to illustrate the
method. Explain how to determine the latitude of a place on the
Earth by measuring the meridian altitude of the Sun.
18. Parallaxes of the Heavenly Bodies. The apparent
position of a body (a planet, for instance) on the celestial
sphere remains the same as long as the observer is fixed. If
the observer changes his place and the planet remains in
the same position, the apparent position of the planet will
change. The change in the apparent position of a planet
due to a change in the position of the observer is called the
FIG. 56. PARALLAX.
Change in the apparent position of a star due to a change in the place of
the observer.
parallax of the planet. To show how this is let CH' be
the Earth, C being its centre. S' and S" are the places
of two observers on the surface. Z' and Z" are their
zeniths in the celestial sphere H l P". P is a planet. (P is
drawn near to the Earth to save space in the figure. If
it were drawn at its proper proportional distance for the
108 ASTRONOMY.
Moon, which is the nearest celestial body to the Earth
(240,000 miles distant), the drawing would show P more
than two feet distant from (7.)
8' will see P in the apparent position P'. 8" will see
P in the apparent position P". That is, two different
observers will see the same object in two different appar-
ent positions. If the observer 8 ' moves along the surface
directly to $", the apparent position of P on the celestial
sphere will appear to move from P ' to P ". This change
is due to the parallax of P.
If the observers S' and S" could go to the centre of the
Earth (C) they would both see the planet P in the posi-
tion P,.
Astronomical observations made by observers at points
on the Earth's surface (as at Greenwich and Washington)
are corrected, therefore, by calculation, so as to reduce
them to what they would have been had the observers been
situated at the centre of the Earth, from which point the
planet would be seen always in one position on the celestial
sphere.
The student can try an experiment in the classroom that will illus-
strate what parallax is (See Fig. 57). Let him set up a pointer some-
where in the middle of the room and look at it from a point near the
south-west corner of the room I. The line joining his eye and the
pointer will meet the opposite wall in a point 1. One of his class-
mates under his direction should mark the point 1. Now let the
observer go to another station, II. He will see the pointer projected
against the opposite wall at 2, and this point should be marked also.
If he goes to III the pointer will be seen projected at 3, and so on.
The change in the apparent position of the pointer on the opposite
wall due to the change in the observer's place is the parallax of the
pointer. The real position of the pointer has not changed at all.
While the observer has moved from I to III the apparent posi-
tion of the pointer has moved from 1 to 3. Any one who is making
a railway journey can find many examples of parallactic changes of
apparent position by fixing his eye on points in the landscape They
will appear to move relatively to each other as the observer moves.
PARALLAX.
109
In Fig. 58 suppose that C represents the Sun, around which the
Earth 8' moves in the nearly circular orbit 8' 8" H'. S'C is no
longer 4000 miles as in the last example, but it is 93,000,000 miles.
Suppose P to be a star. When the Earth is in the position 8' the
1V.E. ,S.E.
N.W. -
1
1
III
t
2
n
Pointer
1
1
3
I
s.w.
FIG. 57.
To illustrate the parallax of a body.
star will be projected on the celestial sphere at P' ; when the Earth
has moved to 8", the star will be projected on the celestial sphere at
P". While the Earth is moving from S' to 8" the star P will appear
to move from P' to P". It will not really move iu space at all, but
FIG. 58. THE ANNUAL PARALLAX OF A STAR.
its apparent position on the celestial sphere will appear to move be-
cause the observer moves. If the observer were at the Sun (C) in-
stead of on the Earth (at 8') he would see the star at P, ; if the ob-
server 8" were a,t the Sun (C) he, also, would see the star at P^
110 ASTRONOMY.
Observations made at different points of the Earth's orbit (at dif-
ferent times of the year, that is) are reduced, by calculation, to what
they would have been if the observer had made them from the Sun
instead of from the Earth.
One important point should be especially noted here. If the dis-
tance of Pfrom C, in the last figure, increases the changes in its posi-
tions P f , P" due to changes in the position of the observer (/S' t S" etc.)
will be .less and less. The student can prove this by drawing the
figure three times, making the small circle and the points S', S" the
same in each figure. In the first drawing let him make CP 1 inch,
in the second make CP 2 inches, in the third make CP 3 inches.
The greater the distance of a body from the observer, the less the
change in the body's apparent position due to a given change in the
observer's place.
The Moon is 240,000 miles away from the Earth. An
observer at Greenwich will see the Moon projected on the
celestial sphere in a place quite different from the Moon's
place as seen from the Cape of Good Hope. Jupiter is
over 400,000,000 miles away from the Earth. Observers
at Greenwich and at the Cape of Good Hope will see it at
different apparent positions on the celestial sphere, but
these positions will not be very far apart. Sirius is over
200,000,000,000,000 miles away from the Earth. Observers
at Greenwich and at the Cape of Good Hope will see it in
the same position. That is, we have no telescopes that
will measure its exceedingly small change of place. An
observer at Greenwich looking at Sirius in January will
see it in a position on the celestial sphere only a very
little different from the place in which the same observer
will see it in July. Yet the observer has travelled half
round the Earth's orbit meanwhile, and his place in July
is about 186,000,000 miles distant from his place in
January. (The distance from the Earth to the Sun is
about 93,000,000, and twice that is 186,000,000.) It is
clear that if we can measure the amount of displacement
of the Moon, of Jupiter, of Sirius, due to a known change
in the observer's place, there must be a way to calculate
PAKALLAX. Ill
how far off these bodies are to suffer the observed changes
in their apparent positions.
What is the parallax of a star (or of the Sun, or of a planet)?
To what point of the Earth are observations made on its surface re-
duced? Why are they so reduced? Describe a simple experiment
to illustrate parallactic changes. Is there a change in the apparent
position of stars due to the revolution of the Earth round its orbit ?
Draw a figure to illustrate this. To what point within the Earth's
orbit are observations reduced to avoid such parallactic changes?
Prove by three drawings that the further a star is from the observer
the less are its parallactic changes due to a given change in the
observer's place.
CHAPTER VII.
ASTRONOMICAL INSTRUMENTS.
19. Astronomical Instruments Telescopes. Celestial
Photography The Nautical Almanac. The instruments
of astronomy are telescopes that enable us to see faint
stars which otherwise we should not see at all ; or telescopes
and circles combined, that enable us to measure angles;
or timepieces (chronometers and clocks) that enable us to
measure intervals of time with exactness; spectroscopes,
that enable us to analyze the light from a heavenly body
and to say what chemical substances it is made of, etc.
All these instruments have been gradually perfected until
most of them are now extremely accurate, but many of
them had very humble beginnings.
Clocks. The first timepieces were sun-dials,* water-
clocks, etc. The ancients noticed that the shadow of an
obelisk moved during the day. When the Sun was rising
in the east the shadow of an obelisk lay opposite to the
Sun towards the west. As the Sun rose higher in the sky
and moved towards the meridian the shadow moved towards
the north and grew shorter. When the Sun was exactly
south of the obelisk (on the meridian due south of the ob-
server and at its greatest altitude) the shadow lay exactly
to the north and it was the shortest. As the Sun drew
towards the west the shadow moved towards the east and
* We know that a Sun-dial was set up in Rome B.C. 263. PLAU-
TUS speaks of a slave who complained of Sun-dials and the new-
fangled hours. In old time, he says, he used to eat when he was
hungry ; now the time when he gets his rnea.ls depends on the Sun !
FIG. 59. GALILEO.
Born 1564; died 1642.
113
114 ASTRONOMY.
grew longer; and as the Sun was setting in the west the
shadow pointed towards the east. A circle was traced on
the ground round the obelisk
and the north point of the circle
was marked. When the shadow
fell at this point the San was
due south at noon and the day
was half over. This was the
first timepiece. By dividing
the circle into smaller parts the
day was likewise divided into
parts. Some of the churches
in Italy have sun-dials laid out
on their floors so that a spot of
sunlight admitted through the
south wall traverses an arc
divided into hours and minutes.
The student should set up a verti-
cal pole and trace a circle around it
and divide the circle into parts, using
his watch to get the hour marks. The
circular dial of Fig. 60 is horizontal
FIG. 60. A SUN DIAL. an d XII is towards the north.
It was not easy, in ancient times, to mark the places on
the dial that corresponded to the hours and to the smaller
divisions of time. These were often counted by water-
clocks or sand-clocks, in which water or sand poured from
a box through a hole in the bottom. The lowering of the
upper surface of the water or sand marked the passage of
time. The common hour-glass is a sand-clock. Candles
were marked by lines at equal intervals and equal intervals
of time were counted by the burning of equal lengths of
wax. The student can construct timepieces in this way
and he can test their accuracy by a watch or clock.
GALILEO noticed about the year 1600 that a given
pendulum always made its swings in equal times no matter
ASTRONOMICAL INSTRUMENTS. 115
whether it swung through large arcs or small ones. A
long pendulum swung slowly; a short pendulum swung
faster; but each pendulum had its own time of swinging
and it always swung in that time. A pendulum about
inches long made a swing in one
second (from its lowest point to its ^^7-^
lowest point again in one second).
It made 86,400 vibrations in a
mean solar day.* Intervals of time
could now be accurately divided.
The student should make a pendulum
for himself. A very good method is
described in Allen's Laboratory Physics
as follows :
Near !S, which may be the edge of a
table or shelf, is screwed a spool S'.
The screw is "set up" until the spool
turns with considerable friction. A
string is wound around the spool and is
held in place by passing through the slot
of another screw, R, inserted horizontally
in the edge of the support. The lower
end of the string passes through a hole
in a ball B, which forms the pendulum- {&)
boh. The length of the pendulum may jp
be varied by turning the spool so as to FIG. 61. A HOME-MADE
wind or unwind the string. Small PENDULUM WHOSE
adjustments are best made by gently LENGTH CAN BE
turning the spool. READILY VARIED.
Many improvements have been made in pendulum-clocks
since they were first invented by HUYGHENS (pronounced
hi'genz) in 1657, and they are now extraordinarily accu-
rate. Chronometers are merely very perfect watches.
Their motive force is a coiled spring, and they can be
transported by sea or land while they are running, which
is not true of clocks, of course.
* 00 X 60 X 24 = 86,400,
116 ASTRONOMY.
Circles. Angles can be measured by circles divided to
degrees, etc. If the arc S'S* is so divided and if it has a
radial bar ES' that can be moved around a pin at the
centre of the circle at E, the angle between any two stars
can be measured in the following way :
1st. Place the circle so that its
plane passes through the two stars
S' and $ 2 when the eye is at E.
2d. Point the bar at S' and
read the divisions on the circle
as 10 5', for example. The eye
will still be at E, of course.
3d. Point the bar at S* and read
FIG. 62. -MEASUREMENT the circle " as 22 n/ -
OP ANGLES BY A CIRCLE The angle between the two stars
(OR BY A PART OF A s , m * ig 12 o g, the difference of
v/IRCLEJ.
the two readings. In the figure
the angle S'ES* is about 12; S*ES* isabout 22; S*S 3
is about 30; S'ES 4 is about 64.
Before the telescope was invented the bar ES' was pro-
vided with sights like the sights on a rifle. One sight was
at E (the place of the eye), the other at the further end of
the bar. The unavoidable error of directing such a bar to
a star is about 1' of arc, so that the positions of stars before
the telescope was invented were liable to errors of 1' or so.
The eye cannot detect a change of direction less than about
one minute of arc. The bar and its sights are nowadays
replaced by a telescope, and the positions of stars deter-
mined by such a combination of a circle and a telescope are
affected by errors of less than 1". The precision is more
than 60 times greater.
The student will do well to make a half-circle in the following
way: Cut a half-circle 8 inches in diameter out of a piece of thick
hard pasteboard, leaving a knob or projection about 1 inch square at
(7. Through this knob bore a hole with an awl at the exact centre of
ASTRONOMICAL INSTRUMENTS. 117
the circle. Order from Keuffel & Esser, opticians, No. 127 Fulton
street, New York city, a paper circle, 8 inches in diameter, divided
to 30'. It is No. 1296 of their cata-
logue. It can be sent by mail and
will cost 20 cents. Cut the paper-
circle in two along a diameter and
fasten it to the pasteboard, making
the centre of the paper-circle coin-
cide with the centre of the paste-
board circle. Make a narrow flat
light wooden arm for the index-arm, FIG. 63. A HALF CIRCLE.
like Fig. 64 : A is the centre of the
circle. The arm must revolve about a pin (or a rivet) at A. B and
C are the sights. Two common pins will do. D is an index mark, or
pointer, drawn on the arm. All angles are read from this mark, a,
b, c, d, are four divisions of the paper circle. If a = 17, b = 18,
c = 19, d = 20, then the reading of the pointer is 18 degrees. In
using the circle the eye must be at A ; the observer looks along the
A B
FIG. 64. INDEX ARM FOR A DIVIDED CIRCLE.
sights EC and moves the arm till the sights and the star are in the
same line. To measure the angle between two stars the plane of the
circle must be put in the plane of the eye and of the two stars and
kept there. To measure the altitude of the celestial pole (the latitude
of the observer) the plane of the circle must be vertical. Two read-
ings'must be made: 1st, when the index arm is horizontal (a level
will show this) and 2d, when the arm points to Polaris. A light
plumb line suspended from the centre of the circle will mark the
vertical direction, so that zenith distances can be measured.
Invention of the Telescope. The first telescope used in
astronomy was invented by GALILEO in 1609.* It was like
a long single-barreled opera-glass. The best of GALILEO'S
telescopes magnified only about 30 times; but this was
* Eleven years before the Pilgrims landed at Plymouth. Prob-
ably no one of them had even heard of this invention.
118 ASTRONOMY.
enough to explain many things that had heen mysteries
for two thousand years. The Moon's face was very well
shown in GALILEO'S instruments and the mountains of the
Moon were then discovered. The Milky Way was shown
to consist of closely crowded stars. If the student will
look at the Moon's face and at the Milky Way with a com-
mon opera-glass (which magnifies about 3 times) he will
see far more than with the eye. The true shapes of the
planets Venus and Mercury were made out for the first
time. It was seen that they had phases like the Moon
(they were sometimes crescent, sometimes full, etc.), and
this discovery, more than any other, helped to overthrow
the theory of PTOLEMY that the Earth was the centre of
the universe, and to establish the theory of COPERNICUS,
that the centre of our system was the Sun, not the Earth.
GALILEO discovered four satellites of Jupiter also and
showed, in this way, that " the seven planets" (Sun,
Moon, Mercury, Venus, Mars, Jupiter, Saturn) were
seven in number, not because of some mystic law, but
simply because the other bodies of the system happened
to be too faint to be seen with the unassisted eye.
^ Seven had been a mystical number since
the times of PYTHAGORAS. There were
seven planets, seven days of the week,
seven wise men of Greece, seven cardinal
virtues, seven deadly sins, seven notes of
music in the octave, etc. Men regarded
this number as if it were sacred in itself;
and they were not willing to believe their
own eyes when more than seven heavenly
J BLE - CONVEX U " bodies were shown to them. The greatest
LENS OP GLASS, value of GALILEO'S discovery was precisely
its demonstration that men must accept a scientific fact
when it is proved.; and that Nature was governed by
laws of a different kind from the fanciful analogies of the
ASTRONOMICAL INSTRUMENTS. 119
imagination. From the time of GALILEO men began to
think about Nature in a new way and the discoveries of his
telescope are, for that reason, the most important scientific
discoveries ever made.
Construction of the Telescope. Long before the time of
GALILEO glass lenses had been used for spectacles. The
Emperor Nero (died A.D. 68) is said to have employed
such a lens. It was found that a double-convex lens made
out of glass not only collected light, but that if it was held
in a proper position it magnified the object looked at.
The ordinary hand reading-glass is a familiar example of
this fact.
Figure 66 shows the way in which the reading-glass
FIG. 66.
The reading-glass C magnifies an object AB to the size ab.
magnifies. AMB is an object viewed by a reading-glass
C. From every point of the object AB rays of light issue,
and they go in every direction. (The proof of this fact is
that no matter where you stand you can still see AB\ and
if you see it there must be rays that come from AB and
reach your eye.) The bundle of rays that comes from the
point A and falls on the reading-glass C is c Ad. No other
rays from A fall on the glass. These pass through the
glass and come to a focus at a; a is the image of the point
A of the object. The point B of the object is sending out
rays in every direction. Some of them fall on the glass
120 ASTRONOMY.
namely the bundle cBd. This bundle of rays passes
through the glass and comes to a focus at Z>; b is the
image of the point B of the object. The point M of the
object is giving out rays in every direction. Only those
that fall on the glass can pass through it namely the
bundle of rays cMd. This bundle of rays passes through
the glass and comes to a focus at N. N is the image of
the point M of the object. Every point of the object sends
out rays, and bundles of rays from every such point pass
through the glass and each such bundle comes to a focus
somewhere on the line ab and forms an image of the cor-
responding point of the object. All these separate images,
taken together, make one t image, a picture, of the object.
ab is the image, the picture, of AB.
Now suppose that with a second hand-glass you should
look at the image ab just as you looked at the object AB
with the first hand-glass. If the second glass is held in a
proper position you can magnify the image ab just as the
object AB was originally magnified. A combination of
the two or more lenses to make a magnified image is a tele-
scope. GALILEO'S invention was the use of two lenses in
combination.
All refracting telescopes (telescopes in which rays of light
from the object are bent refracted by the telescope so as
to form an image) consist essentially of two lenses. The
first lens (that one nearest the star) is made as large as pos-
sible so as to collect as much light as possible. All the
bundles of rays that fall upon it are bent refracted by
this lens and brought to a focus; and together they make
an image a picture of the object. This first lens is
called the object-lens (or the object-glass). Its sole use is
to collect as many rays from the object as possible and to
form them into an image a picture at the focus. If
you should hold a piece of ground-glass at the focus of a
telescope you would see a small picture on the glass a pic-
ASTRONOMICAL INSTRUMENTS. 121
tare of the Sun, of the Moon, of a star, according as the
telescope was pointed to the Sun, the Moon, or a star. If
you should put a photographic plate at the focus you could
make a photographic negative of the Sun, the Moon, a
star.
The second lens (it is called the eyepiece) is used to
magnify the image formed by the object-lens. Every tele-
scope is provided with several eyepieces. Some of these
magnify more than others. If a powerful eyepiece is used
the telescope may magnify 1000 times. If one of the less
powerful is employed it may magbify 100 times. You can
change the magnifying power of a telescope by changing
the eyepiece, therefore; and there is not much point to the
common question: " How much does this telescope mag-
nify?" The answer is "it depends upon what eyepiece
you are using." The tube of a telescope is chiefly for the
purpose of keeping the object-glass and the eyepiece at the
right distance apart.
It is found that single lenses of glass give imperfect im-
ages of objects. The images from single lenses are some-
what distorted and they are bordered with fringes of color.
A few experiments with a common reading-glass will prove
this. Much of the imperfection
can be avoided by making the
object-glasses of telescopes out
of two lenses of different kinds
of glass close together, as in
Fig. 67. The light from the
star first falls on a lens of crown- FIG. 67. THE ACHROMATIC
glass and after passing through OBJECT-GLASS.
it falls on a lens of flint-glass. The two lenses act like a
common convex lens in bringing the rays to a focus to form
an achromatic or colorless image. The image from such
an object-glass is much more perfect than that formed by
a single lens. Eyepieces, also, are made of two or more
122
ASTRONOMY.
The telescopes now in use are practically as per-
fect as they can be made from the glass we now have.
Light-gathering Power of a Telescope. It is not merely
by magnifying that the telescope assists vision, bat also by
increasing the quantity of light received from any object
from a star, for example. When the unaided eye looks at
any object, the retina can only receive so many rays as
fall upon the pupil of the eye. The eye is itself a little
telescopic lens whose image is received on the sensitive ret-
ina. By the use of the telescope it is evident that as many
rays can be brought to the retina as fall on the entire ob-
ject-glass. The pupil of the human eye 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 ob-
jective 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 col-
lected with the naked eye, because
(.2)' : (2)' = .04 : 4.0
= 1 : 100.
With a 5-inch object glass the ratio is
10
15 "
20 "
625 to 1
2,500 to 1
5,625 to 1
10,000 to 1
16,900 to 1
32,400 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 ob-
server to see much fainter stars than he could detect with
the naked eye, and also to see faint objects much better
ASTRONOMICAL INSTRUMENTS. 123
than by unaided vision alone. Thus, with a 36-inch tele-
scope we may see stars so minute that it would require the
collective light of many thousands to be visible to the un-
aided eye.
Eeflecting Telescopes. One of the essential parts of a refracting
telescope is tlie object-glass, 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 speculum
metal or silvered glass ground to the shape of a paraboloid. Fig.
G3 shows the action of such a mirror on a bundle of parallel rays,
PIG. 68. THEORY OP THE REFLECTING TELESCOPE.
which, after impinging on it, are brought by reflection to one focus
F. The image formed at this focus can be viewed with an eyepiece,
as in the case of the refracting telescope.
The eyepieces used with such a mirror are of the kind already de-
scribed. In the figure the eyepiece would have to be placed to 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 .F (downwards on the page) to another focus outside of the
main beam of rays. At this second focus the eyepiece is placed and
the observer looks into it in a direction perpendicular to A G (up-
wards on the page). See Fig. 69.
Name some of the instruments used in astronomy. Sun-dial.
Describe the motion of the shadow of an obelisk from sunrise to noon,
from noon to sunset. At what time in the day is the shadow of the
obelisk the shortest ? Prove it by a drawing. At what instant of
124: ASTRONOMY.
the day does its shadow point due north? Say how you could make
a sun-dial with a pole and a common watch. Water-clocks. Tell
what they were. Pendulums. How can you make a pendulum that
swings in a second of time? Divided circles. Say how you could make
one. Describe how to use it in measuring the angle between two stars
(the vertex of the angle is at the eye). Telescopes. When did GALILEO
construct his first telescope? Draw a diagram to show how a com-
mon reading-glass forms an image of an object at a focus. Define a
FIG. 69.
This figure shows the way in which the rays of light move in a reflecting
telescope. They come from a star as a beam of light and cover the whole
of the curved mirror at the bottom of the tube (A). This mirror reflects
them towards a focus (like F in the preceding figure). Before the rays
reach the focus, they fall on a small flat mirror which turns them at right
angles to their former direction and they come to a new focus (G) outside
of the telescope-tube. Here the eyepiece is placed.
telescope. Exactly what was Galileo's invention? What is a re-
fracting telescope ? What is an object-glass ? an eye-piece ? What is
the sole purpose of the object-glass? Why then is it an advantage
to make it as large as may be ? What is the sole purpose of the eye-
piece? What is the answer to the question "How much does this
telescope magnify?" Draw a diagram of a reflecting -telescope.
20. The Transit Instrument. The Transit Instrument
is used to observe the transits of stars over the celestial
meridian. The times of these transits are noted by the
sidereal clock, which is an indispensable adjunct of the
transit instrument. It stands near it so that the dial of
the clock can be seen and so that the beats of the pendu-
lum can be heard every second. A skilled observer can
estimate the time to the nearest tenth of a second. The
first transit-instrument was invented in the XVII century.
The transit instrument consists essentially of a telescope TT fast-
ened to an axis FFat right angles to it. The ends of this axis ter-
ASTRONOMICAL INSTRUMENTS. 125
FIG. 70. A TRANSIT-INSTRUMENT.
126 ASTRONOMY.
miuate in accurately cylindrical pivots which rest in metallic bearings
FF which are shaped like the letter Y, and hence called the Ys.
The object-glass of the telescope is at the upper end of the tube in
the drawing. The eyepiece is at E. The telescope can be moved
so as to point to any point in the celestial meridian to the zenith,
the south point of the horizon, the nadir, the north point, the celes-
tial pole.
The Ys are fastened to two pillars of stone, brick, or iron. Two
counterpoises IF Ware 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 Ys, and thus to diminish the friction upon them and to render
the rotation about FF more easy and regular. The line FF is
placed accurately level ; and also perpendicular to the meridian, or in
the east and west line. The plate gives the form of transit used in
permanent observatories, and shows the observing chair C, the re-
versing carriage It, and the level L. The arms of the latter have
Ys, which can be placed over the pivots FF.
The reticle is a network of fine spider-lines placed in the focus of
the objective.
In Fig. 71 the circle represents the field of view of a transit as seen
through the eyepiece. 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 horizontal wires, guide-wires,
a and 6, mark the centre of the field. A
star will move across the field of view
parallel to the lines ab and will cross the
lines I to VII in succession. The field of
view is illuminated at night by a lamp
FIG. 71. SPIDER-LINES which causes the field to appear bright.
IN THE Focus OF A T j )e w j res are ^ark against a bright ground.
The line of sight is a line joining the centre
of the object-glass and the central one, IV, of the seven vertical
wires.
The axis FFis horizontal; it lies east and west. When
TT is rotated about FFthe line of sight marks out the
celestial meridian of the place on the sphere.
How the Transit-instrument is Used in Observation. It is pointed
at the place where a star is about to CTOSS the meridian in its course
ASTRONOMICAL INSTRUMENTS. 127
from rising to setting. As soon as the star enters the field the
telescope is slightly moved so that the star will cross between the
lines a and &. As the star crosses each spider-line, I to VII, the
exact time of its transit over each line is noted. The average of
these seven times gives the time the star crossed the middle line IV.
(Seven observations are better than one, and this is why seven lines
are used.) Let us call this time T. It will be a number giving
hours, minutes, seconds and fractions of seconds, as 10 h 25 m
37 s . 22 for example. T is then the time by the sidereal clock when the
star was on the meridian. When a star is on the celestial meridian
of a place the sidereal time is equal to the right-ascension of the star.
(See page 88.) Suppose the right-ascension of the star that we
have observed to be known and to be R. A. = 10 h 25 m 36 s . 18.
This number is the sidereal time at the instant of the transit of the
star. But the clock time was 10 h 25 m 37'. 22. Hence the clock is
too fast by 1 s . 04.
By observing the time (T) when a star of known right-
ascension (R.A.) crosses the meridian we can determine
the correction of the clock. The clock should mark a si-
dereal time equal to R.A. It does mark a time T. Hence
its correction is R.A. T, because,
T-}- (R.A. T) R.A. = the sidereal time.
In this way we can set and regulate the sidereal clock, so
that its dial marks the exact sidereal time at any and every
instant. (In practice we do not move the hands but allow
for its errors.) Table V, at the end of the book, gives a
list of the R.A. of a number of stars.
Now suppose the sidereal clock to be correct and the
times of transit T\ T*, T*, etc., of stars of unknown right-
ascension to be recorded.
Then T 1 = the R.A. of the first star,
T * = second star,
T' - " " " " third star, and so on.
The right-ascension of any and every unknown star can
be Determined as soon as we have the clock correction. It
128
ASTRONOMY.
FIG. 72. A SMALL TRANSIT-INSTRUMENT.
The length of the telescope of this instrument is about two feet.
ASTRONOMICAL INSTRUMENTS. 129
is in this way that the transit instrument is employed to
determine the right ascensions of unknown stars.
FIG. 73. A MERIDIAN-CIRCLE.
The Meridian-circle. The meridian-circle (or transit-
circle) is a combination of the transit-instrument with a
130 ASTRONOMY.
circle (or two circles) fastened to its axis. With the
transit-instrument we can determine the right-ascensions
of stars; with the circle we can measure their declinations.
The picture shows a meridian-circle. Its telescope is
pointed downwards and the eyepiece is at its upper end.
The instrument differs from the transit in having two
finely divided circles. Each of these circles is read by four
long horizontal microscopes. The axis of the instrument
is made level by a hanging-level which is shown in the cut.
The level is, of course, removed when observations of stars
are made. Meridian-circles were first made in the XIX
century.
Such an instrument can be used as a transit-instrument
precisely as has been described. Its circle can be used to
determine the declinations of stars.
The telescope is moved (so as to trace out the meridian)
by turning the horizontal axis ( FF, NN, in Fig. 70). As
the axis turns the circles turn with it. The angle through
which they turn can be determined by noticing how many
degrees, minutes, and seconds, , ', ", have turned past
the microscopes. In the same room with the meridian-
circle and a few feet south of it there is a small horizontal
telescope. It has a level which rests on top of it, and it
can be made exactly horizontal. If we point the telescope
of the meridian-circle at the small horizontal telescope (see
the diagram) the meridian-circle telescope will be horizon-
Observer's ( Telescope_of_the meridian- Horizontal telescope
eye. \ circle pointing south. pointing north.
FIG. 74. To DETERMINE THE READING OF A MERIDIAN- CIRCLE
WHEN IT IS POINTED HORIZONTALLY.
tal when it sees directly down the tube of the horizontal
telescope. The circle must now be read. Suppose its
reading in , ', " to be H. This reading H is called the
horizontal point. In practice it is more usual to deter-
ASTRONOMICAL INSTRUMENTS. 131
mine the nadir point instead of the horizontal point H, but
it is a little simpler for the student to consider the hori-
zontal point as the starting-point.
FIG. 75. THEORY OF THE MERIDIAN CIRCLE.
In the figure HR is the observer's horizon, Z his zenith, PZR his meri-
dian, P the pole, E a point of the equator, S and S' the two points where a
circumpolar star crosses his meridian.
When the telescope is pointed south, at R, and is horizontal, the
circle -reading is H. Let us suppose H is equal to 180 0' 0". If the
telescope is pointed to Z the reading will be 90 0' 0", because the
zenith is 90 from the horizon. If the telescope is pointed to the
point PI (the north point of the horizon) the reading will be 0' 0".
If it is pointed to .ZVthe reading will be 270 0' 0". We need to know
the reading for the polar point P, and for the equator point E.
The star Polaris is not exactly at the North Pole, though it is near
it, and so we have no direct way of pointing at the pole. If we
know the latitude of the observer measured by the arc HP, and it is
we must point the telescope at
a star S when it is crossing the meridian and determine its zenith dis-
tance Z8\ and twelve hours later we must again point the telescope
at the same star, when it is crossing the meridian again (at S'}, and
determine the zenith distance ZS'. Then (as has already been proved
on page 106),
The latitude of the observer = $ - 90 - \ z8 + Z8 '\
132
ASTRONOMY.
Thus, whether the latitude of the observer is known or unknown,
we can determine the reading of the circle when the telescope is
pointed to any one of the points JR, E, Z, P, H.
The latitude of the Lick Observatory is 37 20' 24" = (p.
meridian-circle would then have the following readings:
Its
(H\n the figure) =
0' 0"
37 20' 24"
90 0' 0"
127 20' 24"
180 0' 0"
270 0' 0"
For the north -point
" solar- point (P " ) =
" zenith-point (Z " ) =
" equator-point (E " ) =
" south -point (R " ) =
nadir- point (N " ) =
If the telescope was pointed to a star 8 as it crossed the meridian,
and if the circle reading for 8 was 57 40' 36", the north-polar distance
of 8 would be 20 20' 12", and its declination would be 69 39' 48".
Its zenith distance north would be 32 19' 24".
Model of a Meridian circle. The student will do well to make a
simple model of a meridian-circle out of wood. Let him take a piece
of wood (planed on all its sides) about a foot long and exactly square,
and whittle the ends of it till they are nearly cylindrical. This will
serve as the axis. Perpendicular to the axis at its middle point he
should nail on a flat piece of wood, about two feet long, to stand for
the telescope. One end of this last piece should be marked " object-
glass " and the other end " eyepiece." One pasteboard circle 8 inches
in diameter should be prepared and a paper circle divided to 30'
(see page 117) should be neatly fastened to this. A square hole
should be cut in the circle, exactly at its centre, and the circle fitted
to the axis and fastened securely to it. Two wooden boxes at the
right distance apart will serve for piers. On the top of the piers Ys,
sawed out of wood, must be fastened to receive the pivots of the
FIG. 76. Ys OP A MERIDIAN-CIRCLE.
ASTRONOMICAL INSTRUMENTS. 133
The line joining the Ys should be east and west. A pointer
must be fastened to the pier, so that it will just touch the divisions of
the circle as they are moved past it. It will be convenient to make
this pointer of rather stiff copper wire bent to the proper shape and
filed to a point at the index end. With a model of this sort the
whole process of observing with the meridian-circle will be very
clear.
The telescope of a transit-instrument or of a meridian-
circle can only move in one plane, namely in the plane of
the celestial meridian. As the axis is turned the telescope
traces out the celestial meridian in the sky. Stars can
only be seen with these instruments at the moments when
they are crossing the meridian of the observer. For a
couple of minutes at that time a star is seen moving across
the field of view of the telescope. For the rest of the 24
hours (until the next transit) the star cannot be seen.
This arrangement is convenient if the object is to deter-
mine the star's position its right-ascension and its decli-
nation. It is very inconvenient if we desire to examine the
star (or planet) carefully to determine whether it is a
double star, whether it is surrounded by a nebula, whether
its brightness is changing, and so on. Comets, for ex-
ample, are very seldom seen far away from the Sun and
therefore are seldom on the meridian during the dark
hours. Hence they are not often observable by transit-in-
struments.
Equatorial Mountings for Telescopes. For such careful
examinations of the physical appearances of stars and
comets we need to have the telescope mounted on a stand
so contrived that we can keep the star in the field of view
of the telescope for hours at a time. We wish to be able
to point at a star when it is rising in the east and to follow
it as long as it is above the horizon, if desirable. A mount-
ing for a telescope that will permit it to be pointed to any
star above the horizon is called an equatorial mounting.
Before we describe the forms of such mountings that are
134 ASTRONOMY.
actually in use let us see if we can make the principles on
which they must be devised clear.
Suppose we had a very large globe like the one shown in
Fig. 44 bis. Suppose the observer and the eye piece of the
telescope were in the centre of such a globe and that the
object-glass was set in a hole cut through the surface of the
globe at some point (any point) of the equator. It is clear
that the observer could see any star in the equator so long
as it was above the horizon, because he would simply have
to turn the globe (and the telescope with it) until it
pointed to the star and then to move the globe slowly to
the west so as to follow the star as it moved from rising
towards setting. Such a mounting as this would do for a
star in the equator and for no other star; but it would do
for all stars in the equator.
If the object-glass were placed at some point (any
point) in the parallel of 15 north declination, then all stars
in that parallel could be viewed so long as they were above
the horizon by rotating the globe, as before, about its axis
that points to the north pole. The same thing would be
true for stars on the other parallels of 30, 45, 60. It is
plain that the mounting we want must have a polar axis
like that of the globe, so that when the telescope is once
pointed at a star that star can be kept in view from its
rising to its setting by simply rotating the polar axis. It is
also plain that the desired mounting must be so contrived
that the telescope can be set to any and every declination.
Such a mounting would be used :
1st. By setting the telescope to the declination of the
star we wished to examine:
3d. By following that star as long as we pleased by ro-
tating the mounting about its polar axis.
If OP in Fig. 77 were the polar axis of the telescope
and if the telescope were set on the stars A, B, (7, />, in suc-
cession, these stars could be followed from rising to setting.
FIG. 780. THE 36-iNCH REFRACTOR OF THE LICK OBSERVATORY OF THE
UNIVERSITY OF CALIFORNIA,
ASTRONOMICAL INSTRUMENTS. 137
The lines drawn in the different cones A, B, C, D, represent
different positions of the telescope. The circles A, B, C, D,
are different parallels of declination. Suppose then that (in
the diagram Figure 78) TT is a telescope mounted on an
axis DL so that TT can be revolved about the axis DL so
as to point to any declination; and further suppose that
DL and TT together can be rotated about the axis SN
which is pointed to the north pole of the heavens.
The large pictures (Figs. 78#, 80, 81) show a telescope
mounted as in the diagram (Fig. 78). The telescope is
parallel to the polar axis.
If we moved the upper end of the telescope TT towards
the east to point at another star in another declination
such a telescope would look as in Fig. 81. If we moved the
upper end of the telescope TT towards the south to point
at another star such a telescope would look as in Figure
78$, where the tube is pointing towards a star south of the
zenith, but north of the equator and not very far from the
meridian. In the figure (78) to be known also, what is the reading for the polar point Pf
150 ASTRONOMY.
for the equator-point E? Describe how a model of a meridian-circle
can be made. For what purpose are transit instruments and merid-
ian-circles used? Describe the equatorial mounting for telescopes,
and say what its advantages are. Draw a diagram of such a mount-
ing. Explain the construction of a micrometer. How is it used to
determine the angular distance of two stars their position-angle?
How is the value of one revolution of the micrometer determined in
arc? Explain how a photograph of a group of stars is made. What
are some of the advantages of photographic methods of observation Y
With the sextant the altitude of the Sun (or of a star) can be meas-
ured. How is the latitude of a ship at sea determined ? the longitude
of the ship ?
The Nautical Almanac. The governments of the United States,
Great Britain, France, Germany, and other countries issue annually a
Nautical Almanac for the use of navigators and others. Copies of
the Nautical Almanac can be purchased through book-dealers. The
Almanac contains :
Tables of the R.A. and Decl. of the Sun, Moon, and Planets for
every day in the year.
Tables of the R. A. and Decl. of all the brighter stars.
Tables of all eclipses of the Sun, Moon, and of the satellites of
Jupiter, as well as many other data of importance to the astronomer
and the navigator.
To give the student a better idea of the Nautical Almanac a sir all
portion of one its pages for the year 1882 is here printed. (See page
151.)
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, on
Feb. 12, the sun's R. A. was 21 h 44 m KK80. Washington is 5 h 8"'
(5 h .13) west of Greenwich. At Washington mean noon, on the 12th,
the Greenwich mean time was 5 h .l3. 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
Washington mean noon, on Feb. 12, is therefore 21 h 45 ra 1M5. A
similar process will give the sun's declination for Washington mean
noon. In the same manner, the R. 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 90). Thus, for Feb. 1, the
Greenwich mean time of Greenwich mean noon is 0" 0'" 0". The
ASTRONOMICAL INSTRUMENTS.
151
true sun crossed the Greenwich meridian (apparent noon) 13 m 51 s . 34
earlier than this, that is at 23 b 46 m 08 s . 66 on the preceding day ;
i.e. Jan. 31. Having the apparent solar-time by observation (see
page 148) the mean solar time can be found from this table.
Again, when it was O h O m s of Greenwich mean time on Feb. 10,
it was 21 h 21 m 50 s . 70 of Greenwich local sidereal time (see the last
FEBRUARY, 1882 AT GREENWICH MEAN NOON.
Day
a
* ;
THE SUN'S
Equation
of time
b
X)
Sidereal
time
of
to be
h
or right-
tlie
week.
I 1
Apparent
right-
ascension.
Diff.
for 1
hour.
Apparent
declination.
Diff.
for 1
hour.
substracted
from
mean
time.
8
d
S
ascension
of
mean sun.
H. M. S.
s.
/ //
//
M. S.
s.
H. M. S.
Wed.
1
21 13.04
101.75
S 17 2 22.4
+42.82
13 51.34
0.318
20 46 21.70
Thur.
2
21 4 16.84
10.141
16 45 5.4
43.57
13 58.58
0.284
20 50 18.26
Fri.
3
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 11.37
Sun.
5
21 16 23.33
10.040
15 51 30.8
45.69
14 15.41
0.183
21 2 7.92
Mon.
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
0.084
21 13 57.59
Thur.
y
21 32 20.79
9.909
14 36 17.7
48.28
14 26.65
0.052
21 17 54.14
Fn.
10
21 36 18.21
9.877
14 16 51.6
48.88
14 27.51
0.020
21 21 50.70
Sat.
n
21 40 14.88
9.846
13 57 11.2
49.47
14 27.63
0.011
21 25 47.25
Sun.
12
21 44 10.80
9.815
13 37 16.9
50.03
14 26.99
0.042
21 29 43.81
column of the table). Having the sidereal time by observation (see
page 127), the corresponding mean solar time can be found from this
table.
How to Establish a True North and South Line. In order to set the
hands of a sidereal timepiece correctly we must make them indicate
the hours, minutes, and seconds of any star's right-ascension at the
instant that star is crossing the observer's meridian. In order to
make the timepiece keep sidereal time correctly we must regulate
it so that the hands go through 24 O ra s in the interval between two
successive transits of the same star across the meridian. To make
these observations, we need to know the direction of the meridian,
and to mark it permanently.
For students who cannot own a transit instrument it is convenient
to mark the meridian by two plumb-lines, A and B, one due north of
the other, thus:
152
ASTRONOMY.
B
P
A
FIG. 94.
The plumb-lines can be made out of good fishing-line ; the plumb-
bobs out of bits of lead. To prevent them from swinging in the wind
it is a good plan to keep the bobs immersed in pails of water. The
lines can be suspended from nails driven into walls, trees, etc. The
meridian-line should be marked in a place where a good view of
the whole meridian from north to south can be commanded.
The problem is to place the plumb-lines in a true north and south
line. There are several ways of doing this. The following process
FIG. 95. URSA MA JOE,
Zeta () Ursro majoris is the middle star of the handle of the Dipper.
is as simple as any. Mark on the ground a line in the direction of the
needle of a common compass. This will be approximately north and
south. At the north end of this line choose a place for the northern
plumb-line A and hang it there. Ten or fifteen feet south of A sus-
pend the second plumb-bob B from a framework of wood that can
be moved east or west, if necessary. A is always to hang in the
place first chosen. B is to be moved east or west until the right
place is found and then it is to remain there always. The line join-
ASTRONOMICAL INSTRUMENTS. 153
ing A and B (after B is placed correctly) is the meridian line of the
observer.
The plumb-line B is placed correctly when both plumb-lines seem
to pass through the two stars Polaris and Zeta (C) Ursce majoris at the
same time.
The right-ascensions of these two stars differ by 12 hours. When
Polaris is crossing the meridian from east to west (upper culmina-
tion) C Ursa majoris is crossing the meridian from west to east (lower
culmination). A line joining them at this instant is a
celestial meridian. If we move the plumb-line B until
both plumb-lines A and B pass through both stars then the
line joining A and B must be in the plane of the celestial
meridian.
The stars will be approaching their culminations
about 11 P.M. Oct. 20, about 8 P.M. Dec. 5,
" 10 " Nov. 5, " 7 " Dec. 20,
9 " Nov. 20, " 6 " Jan. 5,
about 5 P.M. Jan. 20,
and these are the hours to prepare to observe them.
The observation consists in moving the support of the
plumb-line B (the southern plumb-line) slowly and gently
east or west until both stars seem to be on the two plumb-
lines at the same time, as in Fig. 96. When they are so
let both plumb-lines rest, and see if the stars stay on the Q
two lines for a few minutes. If they do, both lines are
in the right position. If they do not, move the southern plumb-
line B slightly. After the plumb-line B has been put in the right
position its place must be marked; and tbe next morning its nail can
be permanently fixed. It will be well to test the meridian-line, so
determined, by another night's observations. Finally, a meridian-
line can be established by this process; and whenever the observer
wishes he can observe the transit of any celestial body over the two
plumb-lines and note the hour, minute, and second by his sidereal
time piece.* In order to see the plumb-lines in a dark night he
should chalk them well, or paint them white. If this is not enough
they can be illuminated by the light of a lantern placed behind his
back (so as not to interfere with his seeing the stars).
* A cheap watch, regulated to run on sidereal time, is a great con-
venience in making astronomical observations.
CHAPTER VIII.
APPARENT MOTION OF THE SUN TO AN OBSERVER ON
THE EARTH THE SEASONS.
21. Apparent Motion of the Sun to an Observer on
the Earth. Long before the Christian era the ancients
knew that there were two classes of bodies to be seen
in the sky. The stars the first class rose and set, to
be sure; but they were always in the same relative posi-
tion. They kept their configurations. They were fixed.
One star did not move away from others. The stars of
Ursa Major shown in Fig. 1 kept their relative positions
their grouping century after century. There was another
class of celestial bodies which the ancients called planets or
wandering stars. Some of them (Mercury r , Venus, Mars,
Jupiter, Saturn) looked exactly like stars to the naked
eye, but they moved among the fixed stars, sometimes
being near to one fixed star, then leaving it and moving
near another star. You can easily observe such motions
as these for yourself. Mars or Jupiter moves among the
fixed stars with a motion that is quite obvious if you regu-
larly observe its place (and make a sketch of the stars near
by). The Moon moves quite rapidly among the stars.
The Sun also moves among the stars, but as the stars
are not visible in the daytime, it is necessary to observe
the Sun at sunrise and at sunset in order to prove to
yourself that it is moving. The ancients understood this
fact very well and they had mapped the path of the Sun
among the stars quite accurately. You can do the same
thing by observing the Sun at sunrise and sunset each
154
APPARENT MOTION OF THE SUN. 155
day and by marking down on a celestial globe, every day,
the position of the Sun. If you continued this process for
a year you would find that the Sun had apparently made a
complete circuit of the heavens.
If the Sun were near to a bright star on Jan. 1 (so that
the Sun and the star rose and set at the same time) you
would see that the Sun moved eastwards so as to set later
than the star on Jan. 2. It would set still later than the
star on Jan. 3, and so on. In July it would set about
13 hours later than the star. In half a year the Sun has
moved away from the star by half the circuit of the
heavens. In the next January the Sun would be near the
same star again so as to set at the same time with it. The
Sun then has, in the year, made a complete circuit of the
heavens. The ancients proved this and you can prove it
for yourself if you will give a year to the demonstration.
The year is measured by the time required for the Sun to
make this circuit.
The explanation of the apparent motion of the Sun is to
be found in the real motion of the Earth. The Earth
moves round the Sun in a nearly circular orbit (path) and
completes one revolution in about 365 days, one year.
In Fig. 97 let 8 represent the Sun, ABCD the orbit of
the Earth around it, and EFGH the sphere of the fixed
stars. This sphere is 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. A 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 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 celestial sphere at 1'; when
the earth reaches 2 the Sun will appear at 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
156 ASTRONOMY.
stars. The stars do not seem to move because they are at
such enormous distances that a change of the Earth's place
from 1 to 6, or from A to (7, makes almost no change in
the direction of lines joining the Earth and any star. In
space the lines HA, HC, HD, HB are almost (though not
quite) parallel.
FIG. 97. THE ANNUAL REVOLUTION OF THE EARTH ABOUT THE
SUN, IN THE ORBIT ABCD.
The diameter of this orbit is about 186,000,000 miles.
The apparent places of the Sun (!', 2', 3', 4', 5', 6', etc.)
can be defined in the sky by their right-ascensions and
declinations, or by their distances from the stars there
situated. The right-ascensions and declinations of these
stars are known (or if they are not known they can be
determined by observation).
APPARENT MOTION OF THE SUN. 157
It is plain that an observer on the San would see the
Earth projected at points on the celestial sphere exactly
opposite to the corresponding points of the Sun's apparent
path viewed from the Earth. Moreover, if the Earth
moves more rapidly in some portions of its orbit than in
others (as it does) the Sun will appear to move more rapidly
FIG 98. THE REVOLUTION OF THE EARTH IN ITS ORBIT ABOUT
THE SUN.
among the stars in consequence. The two motions must
accurately correspond one with the other. The apparent
motion of the Sun in the heavens is a precise measure of
the real motion of the Earth in its orbit.
The radius-vector of the Earth (the line joining Earth
and Sun) describes a plane surface as the Earth moves.
158 ASTRONOMY.
In the figure this is the plane of the paper. In space this
plane is called the plane of the ecliptic. This plane will
cut the celestial sphere in a great circle; and the Sun will
appear to move in this circle. The circle is called the
ecliptic. The plane of the ecliptic divides the celestial
sphere into two equal parts. A sidereal year is the interval
of time required for the Sun to make the circuit of the sky
from one star hack to the same star again ; or, it is the
interval of time required for the Earth to go once around
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 to every observer on the Earth.
This star being near the Sun rises, culminates, and sets with
him; it is on the meridian of any place at the local noon
of that place (and is therefore not visible except in a tele-
scope since we cannot see stars in the daytime with the
naked eye). The star on the right-hand side of the figure,
near the line CS1 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, that
star is on the lower meridian; when the sun is setting, that
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) from west to east. The star
near 2' will rise, culminate, and set with the Sun to every
observer on the Earth. Like things are true of the Sun
in each of its successive apparent positions 3', 4', 5', 6', etc.
The student should here notice how onr notions of the
direction East and West have arisen. In the first place
men noticed that the Sun rose in one part of the sky
(which they namecl East) and set iu another (West),
APPARENT MOTION OF THE SUN. 159
Secondly, it was found that these risings and settings were
caused by the daily rotation of the Earth on its axis and
that if the stars appeared to move from east to west the
Earth must really turn from west to east. The Sun
appears to move, in consequence of the Earth's annual
motion, from west to east among the stars (from 1'
towards 6' in the figure).
The Earth moves around its circle ABCD in the same
direction that the Sun appears to move around its circle
FGHE. Draw an arrow outside of FGHE parallel to
1', 2', 3', 4', 5', 6', with the point near 6' and the feather
near I'. Draw another arrow outside of ABCD with the
point near D and the feather near G. These arrows are
parallel. Hence the Earth moves in its orbit from west to
east. Or, suppose ABCD and FGHE to be two watch-
dials and 8 A and 8E to be the hands. When 8 A points to
the top of its dial (ABCD) its next movement is towards the
left (in the figure). When SE points to the top of its dial
(FGHE) its next movement is towards the left, likewise.
As the Sun is observed to move from west to east among
the stars, the Earth must also move from west to east in
its orbit.
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 S, 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 apparent 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 (see page 68). The days
would always be twelve hours long, for the sa,m reason
160 ASTRONOMY.
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 is sometimes north of the
equator and sometimes south of it, and therefore it has a
motion in declination.
The Sun was observed with a meridian-circle and a
sidereal clock at the moment of transit over the meridian
of Washington on March 19, 1879. Its position was found
to be
Eight-ascension, 23 h 55 m 23 s ; Declination, 30' south.
The observation was repeated on the 20th and following
days, and the results were :
March 20, E. A. 23 h 59 m 2 s ; Dec. 6' South.
" 21, " O h 2 m 40 s ; " 17' North.
" 22, " O h 6 m 19 s ; " 41' "
If we lay these positions down on a chart, we shall find
them to be as in Fig. 99, the centre of the Sun being south
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
apparent path of the Sun on the celestial sphere, or of the
ecliptic.
It is clear that the Sun crossed the equator on the after-
noon of March 20, 1879, and therefore that the equator
and ecliptic intersect at the point where the Sun was at
that time. This point is called the vernal equinox, the
first word indicating the season, while the second expresses
the equality of the nights and days which occurs when the
Sun is on the equator.
If similar observations are made at any place on the
Earth in any year it will be found that the Sun moves
along the ecliptic from the southern hemisphere into the
northern hemisphere about March 20 of each and every
year; and the point where the ecliptic crosses the equator-
APPARENT MOTION OF TEE SUN.
161
the vernal equinox can be determined by observation.
The declination of this point is zero (because it is on the
equator) and its right-ascension is also zero (because right-
ascensions are counted from the vernal equinox). From
FIG. 99. THE SUN CROSSING THE EQUATOR.
March to September the Sun is in the northern hemi-
sphere. Figs. 49, 50, 51, 52 have the ecliptic marked
upon them, and the student should point out the places of
the Sun for the beginning of each month of the year (so
far as is possible) on each figure. (See the next paragraph.)
Here for example are the positions of the Sun for the first day of
every month of the year 1898 at Greenwich mean noon:
1898 (Jan. 1
South \ Feb. 1
(Mar. 1
(Apr. 1
May 1
June 1
July 1
Aug. 1
( Sept. 1
; Oct. i
South -{Nov. 1
Dec. 1
R. A =
Dccl. =
North
18 h 49 m
21 h l m
22 b 50 m
O b 43 m
2 b 35 m
4 b 38 m
6 b 42 m
8 b 47 m
10 h 43 m
12 b 31 ra
14 h 27 m
16 b 31 m
On June 21, 1898, the Sun had its greatest nortJiern declination
= + 23 27'; on December 22, 1898, the Sun had its greatest southern
declination = - 33 27',
South 23
" 17
7
North 5
" 15
22
" 23-
" 18
go
South 3
15
" 22
162
ASTRONOMY.
If the right-ascensions and
declinations of the Sun dur-
ing the months from March
to September are laid down
on a map we shall have a
diagram like Fig. 100. The
straight line represents the
celestial equator. The vernal
equinox is at the right-hand
side of the picture. The
right-ascension of the vernal
equinox is zero, and the hours
of right-ascension are marked
I, II, ... X, XL These
numbers increase as you go
eastwards; hence the point
XI is east of the point II.
The Sun crosses the equator
(going northwards) at the
vernal equinox in the month
of March. It continues to
move north until June 21,
when it reaches its greatest
northern declination (23 27').
For several days at this time
the Sun moves very little in
declination and seems (so far
as its motion in declination is
concerned) to stand still. For
this reason the ancients called
the Sun's place about June
21 the summer solstice (Latin
sol = the Sun, sistere = to
cause to stand still). Its right-
ascension is VI hours.
APPARENT MOTION OF THE SUN. 163
From June 21 to September 22 the Sun remains north
of the equator, but its declination grows less and less
during these months. Finally on September 23 the Sun
crosses the equator once more going southwards at a point
called the autumnal equinox. Its declination is then zero
(because it is on the equator) and its right-ascension is XII
hours (because it is 180 distant from the vernal equinox,
FIG. 101. THE CELESTIAL SPHERE WITH THE EQUATOR (AB)
AND THE ECLIPTIC (CD).
P is the north pole of the celestial equator ; Q is the north pole of the
Sun's apparent path, the ecliptic.
the zero of right-ascensions). After September 22 and
until the succeeding March the Sun is in the southern half
of the celestial sphere. Its south declination continually
increases until December 22, when it is 23 South, in right-
ascension XVIII hours. This point is the winter solstice.
From the winter solstice to the vernal equinox the Sun is
moving northwards (in declination) and always eastwards
(in right-ascension) along the ecliptic. Finally in the
succeeding March the Sun again crosses the equator at the
vernal equinox (R.A. = O h , Decl. = 0). The point D of
164 ASTRONOMY.
the last figure is the summer solstice ; the point C is the
winter solstice.
The ecliptic, as well as the equator, is marked on all
globes; and the annual motion of the Sun can be illus-
trated by tracing out the Sun's path day hy day. It
requires about 365 days for the Sun to move around the
360 of the ecliptic. Hence the Sun moves eastward
FIG. 102. THE CELEBTIAL SPHERE.
EF is the celestial equator, IJ the ecliptic.
among the stars about 1 per day. The Sun's angular
diameter is about half a degree. Therefore the Sun moves
each day about two of its own diameters.
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 dis-
tance from the vernal equinox, measured on the ecliptic eastwards
from the equinox. The degrees of celestial longitude for half the.
year a.re marked on Fig. 1QO,
LENGTH OF TEE DAY AT DIFFERENT SEASONS. 165
The sidereal year was defined (page 158) as the interval
of time between two successive returns of the Sun to the
same star. Its length is 365 days, 6 hours, 9 minutes,
9.3 seconds.
The astronomical year (the year as commonly used) is
the interval between two successive returns of the Sun to
the same equinox. Its length is 365 days, 5 hours, 48
minutes, 46 seconds. It is shorter than the sidereal year
FIG. 103. THE CELESTIAL SPHERE AS IT APPEARS TO AN
OBSERVER IN 84 NORTH LATITUDE (PON = 34).
The ecliptic is not drawn on this figure.
because the equinoctial points are not fixed (as the stars
are) but move slowly. This will be explained more fully
later on.
Length of the Day at Different Seasons of the Year.
The length of time that any star is above the horizon of
an observer depends first on the observer's latitude, and
166 ASTRONOMY.
second on the star's declination. We have just seen that
the Sun's declination is about 23 south on January 1, 5
north on April 1, 23 north on July 1, 3 south on
October 1.
To every observer the Sun will be above the horizon for
different periods at different times of the year. The
summer days will be the longest and the winter days the
shortest.
Figure 103 represents the celestial sphere to an observer
in 34 north latitude. On January 1 the Sun (Decl. =
south 23) will cross his meridian 23 south of the point (7
(nearly half way from C to $), and will describe a diurnal
orbit parallel to CWD (the equator). It will remain above
the horizon a short time. The night will be longer than
the daylight hours. On March 20 the Sun will be at V
(the vernal equinox). It will cross the meridian at C and
will remain above the horizon (NS) twelve hours. The
days and nights will be equal. On July 1 the Sun is in
declination 23 north and will cross the meridian 11 south
of Z (CZ^ 34; 34 - 23 = 11). The daylight hours
will be long.
By constructing sucli a diagram for his own latitude and by mark-
ing the place of the sun for different days of the year the student
can say, beforehand, just what the apparent diurnal path of the sun
will be for any day in any year. A celestial globe set for his latitude
will show the same things. He should notice that the sun rises north
of his east point in the summer ; in the east point at the equinoxes ;
south of the east point in the winter. The sun's diurnal path at the
equinoxes of Marchand September isthe celestial equator, at the winter
solstice it is the tropic of Capricorn ; at the summer solstice it is the
tropic of Cancer. These tropics are circles of the celestial sphere
drawn parallel to the equator, one (Cancer] 23 north of it, the other
(Capricorn) 23^ south of it. They are called tropics because the Sun
there turns from going north (or south) in declination and begins to
go south (or north). They are marked on all globes. The regions
of the earth between the latitudes 23^ north and south are called the
tropics.
LENGTH OF THE DA Y AT DIFFERENT SEASONS.
167
If the observer is on the equator of the Earth, all the
aays and nights of the whole year will be equal, no matter
what the Sun's declination may be. (See Fig. 105.)
SOUTH POLE
FIG. 104. THE CIRCLES OF THE EARTH.
FIG. 105. THE CELESTIAL SPHERE AS IT APPEARS TO AN
OBSERVER ON THE EARTH'S EQUATOR.
All the stars (and the Sun) are always above the horizon 12 hours and
below it 12 hours. The days and nights are all equal.
168
ASTRONOMY.
The following little table will be found useful and interesting.
THE APPROXIMATE TIME OF SUNRISE FOR OBSERVERS BETWEEN
30 AND 48 OF NORTH LATITUDE.
N. B. The column of the table headed with the observer's latitude is
the one to be consulted.
N. B The approximate time of sunset is as many hours after noon as
the time of sunrise is before it. For instance on May 1 in latitude 44 the
sun rises at 4 h 51 m A.M. i.e. 7 h 9 m before noon. The approximate time of
sunset on that day is therefore 7 h 9 m P.M.
Latitude.
30
32
34
36
38
40
42
44
46
48
Date.
h. m.
h. m.
h. m.
h. m.
h. m.
h. m.
h. m.
h. m.
h. m.
h. m.
Jan. 1.
11
21
6 56
6 57
6 56
7
7 1
7
7 5
7 5
7 3
7 10.
7 10
7 7
7 16
7 16
7 12
7 22
7 21
7 18
729
7 27
7 23
7 36
7 33
7 28
743
7 40
7 34
7 51
7 47
7 41
Feb. 1
11
21
6 50
6 41
6 34
6 54
6 47
6 36
6 57
6 50
6 39
7 1
6 52
6 41
7 5
6 55
6 44
7 9
6 58
6 46
7 13
7 1
6 49
7 18
7 5
6 51
7 23
7 9
6 53
7 28
7 14
6 57
Mar. 1
11
21
6 27
6 14
6 2
6 28
6 15
6 2
6 29
6 16
6 1
6 31
6 16
6 1
6 33
6 17
6 1
6 34
6 17
6 1
6 36
6 18
6 1
6 38
6 19
6
6 40
6 20
6
6 42
6 21
6
Apr. 1...
11
21
5 49
5 37
5 27
5 48
5 35
5 24
5 47
5 34
5 22
5 46
5 as
5 20
5 45
5 31
5 17
5 44
5 29
5 14
543
5 26
5 11
5 42
5 24
5 8
5 41
5 22
5 4
5 39
5 19
5
May 1
11
21
5 17
5 9
5 3
5 14
5 5
4 58
5 11
5 1
4 58
5 7
4 57
4 49
5 3
4 52
4 44
5
4 48
4 39
56
43
33
4 51
4 38
4 27
4 46
4 33
4 20
4 41
4 27
4 13
June 1..
11
21
4 58
4 58
4 59
4 53
4 52
4 54
4 48
4 47
4 48
4 43
4 41
4 42
4 38
4 35
4 36
4 32
4 30
4 30
25
23
23
4 18
4 15
4 15
4 11
4 8
4 8
4 3
3 59
3 58
July 1
11
21
5 2
5 6
5 12
4 56
5 2
5 7
4 51
4 57
5 2
4 45
4 51
4 58
4 39
4 45
4 53
4 34
4 40
4 48
4 27
4 34
4 42
4 19
4 27
4 36
4 12
4 19
4 29
4 4
4 11
4 22
Aug - iJ.:.:..
21
5 18
5 24
5 30
5 14
5 21
5 28
5 10
5 17
5 25
5 6
5 14
5 23
5 2
5 10
5 20
4 57
5 7
5 17
4 52
5 2
5 13
4 47
4 57
5 10
4 42
4 53
5 6
4 35
4 47
5 2
Sept. 1...
11
21
5 36
5 42
5 47
5 34
5 41
5 47
5 32
5 40
5 47
5 31
5 39
5 47
5 29
5 38
5 46
5 27
5 37
5 46
5 25
5 35
5 45
5 23
5 34
5 45
5 21
5 33
5 45
5 18
5 31
5 44
Oct. 1...
11
21
5 54
6
6 6
5 54
6 1
6 9
5 55
6 2
6 11
5 55
6 3
6 13
5 56
6 5
6 16
5 57
6 7
6 18
5 58
6 8
6 21
5 59
6 10
6 23
5 59
6 12
6 25
6
6 14
6 28
Nov. 1 .
11
21
6 14
6 22
6 30
6 17
6 25
6 34
6 21
6 29
6 38
6 24
6 33
6 42
6 26
6 37
6 47
6 29
6 41
6 52
6 33
6 45
6 57
6 37
6 50
7 3
6 41
6 55
7 10
645
7 1
7 17
Dec. 1..
11
21
6 38
6 46
6 53
6 43
6 51
6 58
6 47
6 56
7 3
6 52
7 1
7 8
6 57
7 7
7 13
7 2
7 12
7 19
7 8
7 18
7 26
7 15
7 25
7 33
7 22
7 33
7 40
7 29
7 41
7 48
THE ZODIAC. 169
If the observer is at the Earth's north pole the Sun
would be continuously above his horizon so long as the Sun
was in the northern half of the celestial sphere, that is,
from March to September; and continuously below his
horizon from September to March. An observer at the
south pole of the Earth has daylight continuously from
September to March and continuous darkness from March
to September.
FIG. 106. THE CELESTIAL SPHERE AS IT WOULD APPEAR TO AN
OBSERVER AT THE NORTH POLE OP THE EARTH.
The Sun would be above the horizon all the time from March 20 to Sep-
tember 22. The day would be six months long. The sun would be below
the horizon all the time from September 22 to March 20. The night would
also be six months long.
The Zodiac and the Signs of the Zodiac. The zodiac is
a belt in the heavens, extending some 8 on each side of
the ecliptic, and therefore about 16 wide (see figure 50).
The planets known to the ancients are always seen within
this belt. At a very early day the zodiac was mapped out
into twelve regions known as the signs of the zodiac, the
names of which have been handed down to the present
time. Each of these regions was supposed to be the seat
of a constellation or group of stars. Commencing at the
170 ASTRONOMY.
vernal equinox, the first thirty degrees of the ecliptic
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 the sign Taurus, and so on. The names of the signs
in order are :
Spri ( 1. f Aries. The sun enters the sign Aries, March 20.
sins ) 2 - Tauras - " " " Taurus, April 20.
' ( 3. n Gemini. " " " Gemini, May 20.
e , ^( 4 - Cancer. " " " Cancer, June 21.
ZT 5 -* Leo - " " " Leo.Mj^.
( 6. iTE. Virgo. Virgo, August 22.
Autumn ( 7 " - Libra " " " " Libra > September 22.
< 8. TTI, Scorpius. Scorpius, October 23.
( 9. # Sagittarius. " " " Sagittarius, Nov. 23.
yr. r 10. V3 Capricornus. " " " Capricornus, Dec. 21.
< 11. ^Aquarius. " " " Aquarius, Jan. 20.
SlgnS ' ( 12. K Pisces. " " " Pisces, February 19.
Each of the signs of the zodiac coincides roughly with a con-
stellation in the heavens ; and thus there are twelve constellations
called by the names of these signs, but the signs and the constella-
tions no longer accurately correspond as they formerly did. Although
the Sun now crosses the equator and enters the sign Aries on the 20th
of March, he does not reach the constellation Aries until nearly a
month later. This arises from the precession of the equinoxes, to be
explained hereafter.
Why are the stars fixed? Are the p]&nets fixed? Which way
does the sun move among the stars eastwards or westwards? How
long does it take the sun to make a complete circuit of the heavens ?
What is the reason that the sun appears to move among the stars ?
What is the earth's radius-vector? What is the plane of the ecliptic ?
What is a sidereal year? Describe the way in which our notions of
the directions east and west have arisen. The stars in their diurnal
orbits rise in the - The earth turns on its axis from - to -
The sun moves from - to - among the stars. The earth moves
in its real orbit in the same direction that the sun moves in its ap-
parent path, from - to - therefore. What is the geocentric or the
heliocentric place of a body? What is the vernal equinox? the
autumnal equinox ? the winter solstice ? the summer solstice ? Why
are these points called solstices? How long is the sun in the
OBLIQUITY OF THE ECLIPTIC.
171
northern half of the celestial sphere ? About how far does the sun
move in the sky each day ? What is an astronomical year ? Why
are our winter days shorter than our days in summer ? How long
is a summer day to an observer at the earth's north pole ? How long
is a day to an observer at the earth's equator ? What is the Zodiac ?
What are the signs of the Zodiac ?
22. Obliquity of the Ecliptic. The obliquity of the
ecliptic is the angle between the plane of the ecliptic and
the plane of the celestial equator. It is the angle between
the planes DOC and AOB in the figure. It is measured
FIG. 107. OBLIQUITY OP THE ECLIPTIC.
A B is the celestial equator, CD is the ecliptic.
by the arc DB or A G. DB is the Sun's greatest northern
declination; A C is the Sun's greatest southern declination.
As soon as we have measured either of these (with a
meridian-circle, for example) the obliquity is known. It is
about 23^. It was determined by the ancient astronomers
quite accurately by observing the shadow of an obelisk at
the times of the summer and winter solstices. At the
summer solstice the Sun has its greatest north declination,
and therefore its meridian altitude on that day is a maxi-
172
ASTRONOMY.
mum. Its meridian altitude on the day of the winter
solstice is a minimum.
If AB is an obelisk and the line Ed is a north and south
line, and if the Sun is on the line Ad on December 22 and
on Aj on June 21, then the shadow of the obelisk will be
Bj in June (the shortest shadow of the year) and Bd in
December (the longest meridian shadow of the year) and
Bm at the equinoxes. The angle dAj can be measured.
It is equal to twice the obliquity and mAB measures the
Zenith
m j
FIG. 108. THE OBLIQUITY OF THE ECLIPTIC
determined by the shadow of an obelisk at a place whose latitude is 45* N.
latitude of the place, as the student can readily prove for
himself.
The Cause of the Seasons on the Earth. In each and
every year we, who live in the temperate zones of the
Earth, witness the coming of spring, of summer, of
autumn, of winter. They come and go in a cycle of a
year, and the cause of the change of seasons must therefore
depend on the Earth's annual revolution in its orbit. The
THE SEASONS. 173
different seasons are marked by changes in the quantity of
heat received from the Sun. In the summer the altitude
of the Sun is high and the days are long. In the winter
the altitude of the Sun is not so high and the days are
shorter. The difference between the heat of summer and
winter depends chiefly on the differences named. The
Earth revolves about the Sun in an orbit which is very
nearly a circle, so that the change of seasons does not
depend on the varying distance of the Earth from the Sun.
As a matter of fact the Earth is somewhat nearer to the
Sun in January than it is in July.
FIG. 109. THE ECLIPTIC, CD, AND THE CELESTIAL EQUATOR,
AB, WITH THEIR POLES, Q AND P.
The Sun's apparent motion is in the ecliptic CD. The
vernal equinox is at E, the summer solstice at />, the
autumnal equinox at F, the winter solstice at C. The arc
BD = AC= 23|, the obliquity of the ecliptic.
The Sun's North-polar distance at E is 90;
" " " i( , the
circumstances are like those at the vernal equinox.
THE SEASON'S.
m
The foregoing explanation of Fig. 110 illustrates the
dependence of the seasons upon the length of time that the
Sun is above the horizon. The altitude of the Sun above
the horizon also plays an important part in producing the
change of the seasons. (See Fig. 115).
In the figure a beam of
sunshine having the cross-
section ABCD strikes the
soil cbDA at an angle h. It
is clear that the area cbDA
is greater than the area
ABCD. The amount of
heat in the sunbeam is
always the same. This con- FlG 115 ._ THB EFFECT O F THE
stant amount of heat is dis- SUN'S ELEVATION ON THE
tributed over a larger surface M ? T 8 F IL HEAT IMPARTED
according as the altitude of
the Sun is less. Hence in a winter's day, when the Sun
even at noon is low, each square mile of soil receives less
heat than it receives in summer, when the Sun is high.
FIG. 116. THE MERIDIAN ALTITUDE OF THE SUN AT is
EQUAL TO (90 _ + 5) ; HS = HQ + Q8.
At a place on the Earth whose latitude is 45 (= 0) the
meridian-altitude of the Sun
178 ASTRONOMY.
is 45 on March 20 (90 45 -f 0);
" 68i i( June 21 (90 - 45 + 23^);
" 45 " September 22 (90 45 -f 0);
" 2H " December 22 (90 45 23).
Therefore the Sun's rays are inclined to the soil at very
different angles at different dates, and the amount of heat
received per square mile varies. Not only is less heat per
square mile received in December than in June, but it is
received for a shorter period. In latitude 45 the Sun is
above the horizon for about 15 hours on June 21 (see the
table on page 168), while on December 22 it is above the
horizon for a little more than 8-J hours. There are two
reasons, then, for the change of seasons: first, the duration
of sunshine is longer at some dates than at others, second
the amount of the Sun's heat received per square mile per
hour is greater at some dates than at others.
The student should take a pin and put it on the various parallels
of latitude in the four diagrams ABCD, Fig. 110. The rotation of
the Earth carries an observer round his own parallel of latitude. The
pictures show whether the observer is more or less than 1 2 hours in
the light of the Sun whether his days are longer or shorter than his
nights. They also show how the altitude of the Sun varies at dif-
ferent seasons of the year. Notice that an observer on the Earth's
equator always has days and nights of equal length, no matter what
the season of the year. Prove that the Sun is always in the zenith
to some observer in the Earth's torrid zone.
What is the obliquity of the ecliptic? How many degrees is it?
Show how it can be determined by observing the lengths of the
shadow of an obelisk. What are the two causes of the change of
seasons on the Earth ?
CHAPTER IX.
THE APPARENT AND REAL MOTIONS OF THE PLANETS
-KEPLER'S LAWS.
23. The Apparent Motions of the Planets to an Observer
on the Earth Their Real Motions in Their Orbits. The
apparent motions of the planets were studied by the ancients
by mapping down their positions among the fixed stars from
night to night. The same process can be followed to-day
by any one who will give the time to it. The place of the
planet must be fixed by observation each night, with refer-
ence to stars near it, and then this place must be trans-
ferred to a star-map, like those printed at the end of
this book, for instance. A curved line joining the different
apparent positions of the planet on different nights will
represent its apparent path.
Astronomers, who are provided with accurate instru-
ments such as meridian-circles, fix the positions of the
planets by determining their right-ascensions and declina-
tions every night. By platting these positions on a map
they obtain a representation of the apparent orbit with
great accuracy.
Something of the same sort can be done by the student with much
simpler instruments. He needs only a common watch and a straight
ruler some three feet long, together with a star-map. Suppose that he
wishes to determine the place of the planet Mars ( $ ). The first step
is to identify the planet in the sky, by its brightness, its place, or by
its motion. He then selects two bright stars not very far away from
it (let us call them A and B for convenience).
Holding up the ruler so that its edge passes through the two
stars, he notices that it passes very nearly through the planet, which
179
FIG. 117. COPERNICUS.
Born 1473, died 1543.
180
APPARENT MOTIONS OF THE PLANETS. 181
is, however, let us say, a little to the west of the line. On the star-
map he must find the two stars A and B. Suppose that they are
a and ft Auriga, (between the numbers 105 and 120 at the top of
Plate II). A dot must now be put on the map in the proper position
East
to represent the place of the planet ; and the dot must be numbered
(1). In his note-book opposite 1 the observer must write the year,
the month, the day, and the hour of observation thus :
1. 1899, February 27, 9 h P.M.
The place of the planet is much more accurately fixed if the
observer makes allineations with four stars, thus :
C might be d AurigcB on Plate II and D a star given but unnamed
there.
On succeeding nights other positions of the planet can be obtained
in the same way, and its apparent path can be had by joining the
different positions. The times of each observation are to be noted.
The positions of other planets as Mercury, Venus, Jupiter, and
Saturn can also be studied from night to night, and their apparent
paths fixed in like manner. Observations of this kind, if continued
long enough, will give the apparent paths of the different planets in
the sky. The courses of the Sun and Moon can be studied in the
same manner, except that observations of the Sun must be made near
the times of sunset and sunrise, because it is only at these times that
stars are visible near it.
If snch observations are made the student can discover
for himself what the ancients knew very well, namely, that
182 ASTRONOMY.
there are heavenly bodies with apparent motions of three
very different kinds. The Sun and Moon have apparent
motions of one kind. If we mark down the positions of
the San day by day upon a star-chart, they will all fall into
a regular circle which marks out the ecliptic, and its motion
is always towards the east. 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
towards the east, and always along or very near a certain
great circle.
Venus and Mercury have motions of a different kind.
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 even-
ing, we shall by and by see it 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 it will be lost 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.
The general or average motion of these planets is towards
the east, a complete revolution around the celestial sphere
being performed in two years in the case of Mars, 12 years
in the case of Jupiter, and 30 years in that of Saturn.
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 west-
ward 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.
APPARENT MOTIONS OF THE PLANETS 183
Observations of the planets will show that each one of them
has an apparent motion like those just described. The
problem is to discover the real cause of these observed
motions.
The general motion of the San, Moon, and planets
among the stars being towards the east, observed motions
FIG. 120.
If S is the Sun, E the Earth, CLM the orbit of an inferior planet, then
the planet is in inferior conjunction at 7, at superior conjunction at C, at
its greatest elongation from the Sun at L and M.
in this direction are called direct; motions towards 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.
An inferior planet is said to be in conjunction with the
Sun when both planet and Sun are in the same direction
as seen from the Earth. It is in inferior conjunction when
it is between the Sun and Earth; in superior conjunction
when the Sun is between the Earth and the planet. A
superior planet is said to be in opposition to the Sun when
184 ASTRONOMY.
the planet is directly opposite in direction to the San as
seen from the Earth.
Arrangements and Motions of the Planets of the Solar
System. The Sun is the centre of the solar system and all
FIG. 121. THE ORBITS OF MERCURY, VENUS, THE EARTH, MARS,
AND JUPITER.
The distance from the Sun to the Earth is 93,000,000 miles ; from the Sun
to Jupiter is 481,000,000 miles ; the other distances are in proportion.
the planets revolve about the San. Some of the planets
have satellites or moons that revolve about the planet while
the planet itself revolves about the Sun. Our own Moon
is such a satellite. The orbits of the planets are all nearly,
but not exactly, in the same plane, namely, in the plane of
the Earth's orbit the ecliptic.
ORBITS OF TEE PLANETS.
185
S
J
Stj
NAME.
1
||
Sidereal Period of Revolution.
co
-S ^3
.22 ^
Q
Group of ( Mercury
Planets each Venus . .
9
0.39
0.72
88 days = 3 months J_ .
225 " = 7
about the { EV,/;,
size of the } ^ rm ' '
Earth. L Mars . . .
e
6
1.00
1.52
3654 " = 12
687 " = 22
The Small Planets...
About
2.65
3 to 8 years.
( Jupiter. .
2|
5.20
11 & years.
Groups of Saturn. .
*>
9.54
29i "
ISIS? 8 g~-
(^ Neptune
6
J
19.18
30.05
84
164 A "
* The distance of the Earth = 1.00 = 93,000,000 miles.
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 Mars, Jupiter, and Saturn are more distant
from the San than the Earth is. Uranus and Neptune
are planets generally invisible except in the telescope, and
their orbits are outside of that of Saturn. On the scale
of Fig. 121 the orbit of Neptune, the outermost planet,
would be more than thirty inches in diameter.
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 ancient
astronomers gave these names and they have been retained
in use, although they now have little significance.
The farther a planet is situated from the Sun the slower
is its motion in its orbit. Therefore, as we go outwards
from the Sun, the periods of revolution are longer, for the
186 ASTRONOMY.
double reason that the planet has a larger orbit to describe
and moves more slowly in its orbit. The Earth moves 18
miles per second in its orbit, while Saturn moves but
6 miles per second.
An observer on the Sun at S would see the Earth along
the lines $1, S%, $3, etc. If these lines are prolonged
(to the right hand in the figure) the Earth would seem, to
an observer on the Sun, to move eastwardly among the
FIG. 122. THE MOTION OF THE EARTH IN ITS ORBIT IT is
DIRECT MOTION.
stars (see page 158). The real motion of the Earth seen
from the Sun is direct. We have proved on page 159 that
the apparent motion of the Sun is always direct also. The
plane of the Earth's orbit the ecliptic is the plane in
MOTIONS OF THE PLANETS. 187
which all the other planets revolve very nearly. It is to
the slower motion of the outer planets that the occasional
apparent retrograde motion of the planets is due, as may
be seen by studying Fig. 123. The apparent position of
a planet, as seen from the Earth, is determined by the
line joining the Earth and planet. We see the planet
along this line. Supposing this line to be continued so as
FIG. 123.
The apparent motion of a superior planet, as seen from the Earth, is
sometimes direct and sometimes retrograde. The motion is always retro-
grade when the planet is nearest the Earth, always direct when the
planet is farthest from the Earth.
to intersect the celestial sphere, the apparent motion of the
planet will be defined by the motion of the point in which
the line meets the celestial sphere. If this motion is
towards the east the motion of the planet is direct; if this
motion is towards the west, the motion of the planet is
retrograde.
Let us consider the case of one of the superior planets. Its orbit
is outside of the Earth's orbit. Its motion in its orbit is slower than
188 ASTRONOMY.
the Earth's motion in its orbit. Let S be the Sun, ABCDEF the
orbit of the Earth and EIKLMN the orbit of a superior planet
Mars, for example. The real motion of Mars is direct. It moves
round its orbit in the direction of the arrow, just as the Earth moves
round its orbit in the direction marked. In both cases the real mo-
tion is from west to east.
When the Earth is at A, Mars is at H
" " " " B, " " I
" " " C, " K
" " " " D, " " L
" E, " " M
,< Ff N
As the Earth moves faster than Mars the arcs AB, BC, CD, DE,
EF correspond to greater angles at 8 than do the arcs HI, IK, KL,
LM, MN.
When the Earth is at A and Mars at H, an observer on the Earth
will see Mars along the line AH. This line meets the celestial
sphere at 0. Mars will then appear to be projected among the stars
near 0. When the Earth is at B and Mars at /, the planet will be
viewed along the line BP and it will be seen on the celestial sphere
among the stars near P. While the Earth is moving in its orbit
from A to B Mars will appear to move (eastwards) among the stars
from to P. Its apparent motion is in the same direction as the
Earth's real motion. When the Earth is at C and Mars at K the
planet will be seen along the line (/^(prolonged). Its apparent place
among the stars will be slightly to the west of P it will appear to
have moved backwards its apparent motion is, at this time, retro-
grade.
When the Earth is at C Mars is in opposition to the Sun. The
Sun and Mars are seen from the Earth in opposite directions. The
apparent motion of ail superior planets at the time of opposition is
retrograde.
While the Earth is moving from G to D in its orbit, Mars is mov-
ing from Kto L in its orbit, and the apparent position of Mars on
the celestial sphere is moving to the west in a retrograde direction.
As the Earth moves from D to E Mars moves from L to M and the
planet is seen along the lines DL and EM prolonged. These lines
are parallel. They meet the celestial sphere in the same group of
stars. The planet, therefore, seems to stay in the same position
among the stars. It appears to be stationary just after opposition,
while the Earth is moving from D to E.
As the Earth moves from D to F Mars moves in its orbit from L
APPARENT MOTIONS OF THE PLANETS. 189
to N. Its apparent place on the celestial sphere among the stars
changes from Q to R. Its apparent motion is again direct towards
the East. It is in this way that a superior planet one whose orbit
is outside of the Earth's orbit moves around the celestial sphere.
Its general motion is eastwardly through long arcs. Near opposition
its apparent motion is retrograde and, for a period, it is stationary.
It does not then change its place with reference to stars near it.
The student can study the apparent motion of a superior planet
near conjunction, or of an inferior planet by constructing suitable
diagrams like the foregoing.
The superior planets (Mars, Jupiter, Saturn, etc.) make
the whole circuit of the sky in long forward arcs with short
loops of retrogression. The inferior planets (Mercury and
Venus) do not make the circuit of the sky. They oscillate
on either side of the Sun, never going very far away from
it. When they are west of the Sun they rise before him
and are morning stars. When they are east of the Sun
they set after the Sun and are evening stars. If Venus is
an evening star she will approach the Sun nearer and
nearer and set nearer and nearer to the time of sunset.
By and by she approaches so closely as to be lost in his
rays (at inferior conjunction KCS in Fig. 123, where K
is now the Earth and C Venus). In a few days she has
passed the Sun going westwards and rises before him as a
morning star. The apparent motion of all planets is
retrograde when they are nearest to the Earth and direct
when they are farthest from us.
The apparent motions of all the planets visible to the
naked eye were perfectly familiar to the ancient astronomers,
as has been said. The positions of the planets had been
observed by them for centuries. But the reasons for these
complex movements were not known. It was everywhere
believed that the Earth was the centre of the Universe and
that the Sun, the Moon, the stars, and all the planets were
made for the sole benefit of mankind. All the explana-
tions of the ancient philosophers started with the assump-
190
ASTRONOMY.
tion that the Earth was the centre of the Universe and
that the Sun and all the planets revolved around it. No
one thought of questioning this proposition. It was every-
where believed.
PTOLEMY of Alexandria in Egypt worked out a theory
of the Universe on this scheme about A.D. 140. It was a
very ingenious system and it explained observed appear-
ances fairly well so long as the observations were not very
accurate.
FIG. 124. THE SYSTEM OF THE WORLD ACCORDING TO PTOLEMY.
Each planet was supposed to move round the circumfer-
ence of a small circle called its epicycle (see the cut), while
the centre of the epicycle moved around a larger circle
called the deferent. By taking the epicycles and the
deferents of suitable sizes a very fair representation of the
apparent motions of the Sun and planets was made.
The swinging motions of Mercury and Venus on each
side of the Sun were explained by their motions around
MOTIONS OF THE PLANETS. 191
their epicycles, which would make them appear alternately
east and west of the Sun if their epicycles moved round
their deferents at the same rate that the Sun moved (see
the cut). The retrogradations of the superior planets
Mars, Jupiter, and Saturn were explicable in a similar
fashion.
It is not necessary to go into details in this matter
because PTOLEMY'S explanation of the Universe is not the
correct one. Still the student should know something of
a theory which was believed by every one from the first
centuries of our Christian era until COPERNICUS proposed
the true explanation. It was not until COPERNICUS had
made long-continued observations on his own account and
had given his whole life to solving the problem that it was
known that the Sun and not the Earth was the centre of the
planetary motions. He proposed this explanation in 1543,
but it was not generally accepted until the discoveries of
GALILEO (1610), about three centuries ago.
The theory of PTOLEMY accounted pretty well for the
facts known in his time. It represented the apparent
motion of the planets as he observed them. But the
observations of the Arabian astronomers in Spain (A.D. 762
to 1492) and of TYCHO BRAHE (pronounced Tee-ko Bra-hee)
in Denmark about 1580, and especially the revelations of
GALILEO'S telescope, made PTOLEMY'S explanation impossi-
ble. It was not long before it was found that even the
system proposed by COPERNICUS was not entirely satisfac-
tory. It was certain that the Sun and not the Earth was
the centre of the planetary motions, as he had said. But
accurate observations soon made it equally certain that the
planets did not revolve in circular orbits. They revolved
about the Sun in orbits nearly but not quite circular, in
curves like ovals. They certainly did not revolve in
circles.
From the time of COPERNICUS (1543) till that of
192 ASTRONOMY.
KEPLER (about 1630) the whole question of the true system
of the Universe was in debate. The circular orbits intro-
duced 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 observa-
tion 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.
Describe how the place of a planet may be fixed, among the
fixed stars, by simple observations. If such observations are made
for long periods the apparent paths of the Sun and planets become
known. In what apparent paths do the Sun and Moon move?
Mercury and Venus? The superior planets? Define the inferior
conjunction of Venus the superior conjunction of Mercury the
opposition of Jupiter. Define the inferior planets the superior
planets. Define direct motion retrograde. What was the theory of
the Universe proposed by PTOLEMY in A.D. 140? How long did men
hold the belief that the Earth was the centre about which the planets
revolved ? Who proposed the heliocentric theory of the solar system ?
At what date ? What was the shape of the orbits of all the planets
in this theory ?
24. Kepler's Laws of Planetary Motion. KEPLER (born
1571, died 1630) was a genius of the first order. He had
a thorough acquaintance with the old systems of astronomy
and a thorough belief 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 at 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 BRAHE. The
opportunity for determining the true laws of the motions
MOTIONS OF THE PLANETS KEPLER S LAWS. 193
of the planets existed then as it never had before; and
fortunately he was able, through labors of which it is diffi-
cult 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) is
FIG. 125. JOHN KEPLER,
Born 1571, died 1630.
determined by continuous observations of the planet's
course among the stars.
The periodic times (the sidereal periods) of the planets
were known to KEPLER from the observations of the
ancient astronomers.
194 ASTRONOMY.
Mercury revolved about the Sun in about 88 days== 0. 24 yrs.
Venus " " " " " 225 " = 0.62 "
Earth " " " " " 365 " = 1.00 "
Mars " " " " " 687 " = 1.88 "
Jupiter " " " " l ' 4333 " = 11.86
Saturn il " " " " 10,759 " = 29.46 "
The Relative Distances of Planets from the Sun.
KEPLER had no way of determining the absolute distance
of each planet from the Sun (its distance in miles), but if
the distance of the Earth from the Sun was taken as the
unit (1.000) he could determine the distances of the other
planets in terms of this unit in the following way:
FIG. 126. METHOD OP DETERMINING How MUCH GREATER THE
DISTANCE OF MARS FROM THE SUN is THAN THE DISTANCE OF
THE EARTH FROM THE SUN.
In the figure let be the Sun, EE' the orbit of the earth, and MM
the orbit of Mars. When the Earth is at E and Mars at M the planet
is in opposition, i.e., it is seen from the Earth in a direction exactly
opposite to the Sun. It is on the meridian of the observer exactly at
midnight. After a hundred days, for example, Mars will have
MOTIONS OF THE PLANETS KEPLER 8 LAW 8. 195
moved to M' and the Earth will have moved to E'. The observer
will then see the Sun in the direction E' to 8 ; he will see Mars
in the direction E' to M' . At this time the angle M'E'S can be
measured with a divided circle, and it therefore is a known angle.
The angle ESE' is known, because we can calculate through what
angle the Earth will move in 100 days, since we know that it
moves through 360 in 365 days. The angle MSM' is likewise
known, since we can calculate through what angle Mars will move
in 100 days, because we know that Mars moves through 360 in 687
days. The angle M'SE' is therefore known because ESE' M8M'
= M'8E'. Hence in the triangle M'SE' we know the two angles
marked in the diagram. E'8M' is measured, M'SE' is calculated.
The angle SM'E' = 180 \E'SM' + M'E'8] because in any plane
triangle the sum of the angles is 180. Hence in this triangle we
can determine all three angles. We can therefore construct a
triangle of the right shape. If we assume the Earth's distance SE' to
be 1.000 we can determine the distance of Mars in terms of that
unit. If KEPLER had known the distance SE' in miles (as it is
known nowadays) then he could have determined the absolute dis-
tance, SM', of Mars. As it was, he could say that if the Earth's dis-
tance, SE', was called 1.000 then the distance of Mars, SM', must
be 1.52.
At different points of the Earth's orbit the corresponding
distances of Mars were determined. The same thing was
done for the other planets at different points of their
orbits. KEPLER found that if the mean distance of the
Earth from the Sun was called 1.000 then the mean dis-
tances for all the planets were :
For Mercury, a l = 0.3871; for Mars, a t 1.5237;
". Venus^ 3 = 0.7233; " Jupiter, a, = 5.2028;
" Earth, a, = 1.000; " Saturn, a, = 9.5388.
The radius-vector of a planet is the line that joins it to
the Sun.
KEPLER made thousands and thousands of such calcula-
tions and determined the radius- vector of Mars from the
Sun at all points in its orbit, assuming that the Earth's
average (mean) distance was 1.000. He could therefore
make a map of the orbit of Mars as in the following figure.
196 ASTRONOMY.
In the figure 8 is the place of the Sun. At some date
Mars was somewhere along the line SP (Mars was in a
certain known celestial longitude). If the distance of the
Earth from the Sun was taken as the unit then the dis-
FIG 127. THE OHBIT OP A PLAKET, P, ABOUT THE SUN, 8.
tance of Mars was known in terms of that unit. Mars was
at the point P. At a later time Mars was somewhere along
the radius-vector $P,, which was in the right longitude.
Calculation showed that Mars was at the point P,. At
other times Mars lay somewhere along the radii- vectores
SP SP,, SP 4 , SP b . Calculation showed that the planet
was at the points P 2 , P 3 , P 4 , P 6 . The curved line joining
all these points was the visible representation of the orbit
of Mars. The curve P, . . . P 6 was the true shape of
the orbit. Nothing was known of the size of the orbit
except that it was so and so many times larger than the
Earth's; but at any rate its true shape was known. It
was not a circle; it was something like. an oval.*
KEPLER'S next problem was to determine what kind of
* The real orbit of Mars is very nearly a circle and the oval of this
figure has been exaggerated purposely. The curve that Mars
describes is not exactly circular, but it is much less oval than
Fig. 127.
MOTIONS OF THE PLANETS-KEPLER'S LA WS. 197
a curve the orbit of Mars really was. It was not a circle
at any rate. He tried all kinds of curves and finally dis-
covered that Mars, like every other planet, moved around
the Sun in an ellipse and that the Sun was not at the
centre of the ellipse, but at one of the foci.
FIG 128. AN 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.
The student should draw a number of ellipses for practice. Drive
two tacks into a board at S and S'. Tie a string at S' and the other
end of the string at 8. Let the length of the string be SP -f P8'-
Put a pencil at the point P and move the pencil round the curve,
always keeping the string stretched tight. Wherever the pencil P
may be the length SP plus the length S'Pis a constant quantity.
For every point of the curve SP + S'P a constant. Take a string
of a different length to start with and tie it to 8 and S' and you will
get an ellipse of a different shape. Put the tacks S and 8' nearer
together and the ellipse will be of another shape, but it will still be
an ellipse.
ADCP is an ellipse ; 8 and 3' are the foci. By the definition of
an ellipse SP -f- P8' = AC, and this is true for every point. Sis
the focus occupied by the Sun, "the filled focus." AS is the least
distance of the planet from the Sun, its perihelion distance; and A
198
ASTRONOMY.
is the perihelion, that point nearest the Sun. C is the aphelion, the
point farthest from the Sun. SA, SD, SO, SB, SP are radii vectores
at different parts of the orbit. A C is the major axis of the orbit = 2a.
The major axis of the orbit is twice the mean distance of the
planet from the Sun, a. BD is the minor axis, 2b. The ratio of OS
to OA is called the eccentricity of the ellipse. By the definition of the
ellipse, again, BS + BS'= AC = 2a\ and BS= BS' = a. BS* = BO*
-\-~dS*, or 08= y a 2 - 6*. The eccentricity of the ellipse is
OS _ ^a 2 -^
OA ~ a
After years of laborious calculation KEPLER discovered
three laws governing the motion of the planets. (The
student should memorize these laws.)
The first law of KEPLER is
/. Each planet moves around the Sim in an ellipse,
having the Sun at one of its foci.
Suppose the planet to be at the points P, P,, P a , P t ,
P 4 , etc., at the times T, 7% T^ T 3 , T t , etc., in Fig. 129.
FIG. 129. KEPLER'S SECOND LAW.
Suppose the intervals of time T^ T, T, T T t T t
to be equal. KEPLER computed the areas of the surfaces
P.&P., P*SP* and found that these areas were
MOTIONS OF THE PLANETS KEPLER 8 LAWS. 199
equal also, and that this was true for each and every planet
in every part of its orbit. The second Jaw of KEPLER 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 and their periodic times.
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 l9 T^ T^ etc., are the periodic times of the
different planets whose mean distances are a^ a^ # 3 , etc.,
then
etc. etc.
If T 3 and a 3 are the periodic time and the mean distance
of the Earth and if T 3 (= 1 year) be taken as the unit of
time and a 3 (= 1.000) be taken as the unit of distance,
then for any other planet whose periodic time is T and
mean distance a
T* (its periodic time) : 1 = a 3 (the cube of its mean dist.) : 1.
But the periodic time of each planet was already known
from observation (see page 193); hence its mean distance
can be determined because
a 3 = T 3 or a= (T)*.
If, in the last equation, we substitute the values of the
periodic time of each planet in succession, expressed in
200 ASTRONOMY.
years and decimals of a year, we shall obtain the valne of
a, its mean distance from the Sun, expressed in terms of
the Earth's mean distance = 1.000.
For Mercury, T l = 0.24 years and a l 0.39
" Venus, T^= 0.62 " " a, = 0.72
" Earth, I\ = 1.00 " " a t = 1.00
" Mars, T t = 1.88 " " a, = 1.52
" Jupiter, T 6 = 11.86 " " 6 = 5.20
" Saturn, T t = 29.46 " l< a, = 9.54
KEPLER'S laws are true for the satellites as well as for
the planets. Mars has two satellites, PJiobos and Deimos,
that revolve in ellipses in periods T' and T" at mean dis-
tances a' and a". In their ellipses the line joining the
satellite to Mars sweeps over equal areas in equal times ;
and (TJ : (T"Y = (')' : (")'
KEPLER'S three laws give the dimensions of the orbits of
every planet in terms of the Earth's distance = 1.00.
They do not explain why it is that the planets follow these
orbits (this was not known until the time of NEWTON), but
they enable us to calculate just where any planet will be in
its orbit at any time.
For instance, suppose that Mars was at the place P at the time T
and we wished to know where it will be at the time T'. The whole
area of the ellipse is swept over by the radius-vector of Mars in 1.88
years. We can calculate how much of an area will be swept over in
the time T' T. Then we can calculate what the angle at S of the
sector PSP' must be to give this sector the calculated area. A line
drawn from S to P' making the calculated angle with SP will inter-
sect the orbit at the point P '. The planet will be at the point P' (in
a known celestial longitude) at the time T'.
Elements of a Planet's Orbit. When we know a and b (tbe major and
minor semi-axes) 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 T by KEPLER'S law III.
If we also know the planet's celestial longitude (L) at a given epoch,
MOTIONS OF THE PLANETS KEPLER'S LAWS. 201
say December 31st, 1850, we have all the elements necessary for find-
ing the place of the planet in its orbit at any time, as has just been
explained.
FIG. 130. To CALCULATE THE PLACE OF A PLANET IN ITS
ORBIT AT ANY FUTURE TIME.
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.
Knowing 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.
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 inclina-
tion given, the orbit of the planet may lie anywhere in the plane
whose angle with the ecliptic is . 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 Q .
Now everything is known except the relation of the planet's orbit
to the sun. This is fixed by the longitude of the perihelion, or P.
Thus the elements of a planet's orbit are :
*, the inclination to the ecliptic, which fixes the plane of the
planet's orbit;
Q , the longitude of the node, which fixes the position of the line of
intersection of the orbit and the ecliptic;
202 ASTRONOMY.
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 (see page 198);
T and M, the periodic time and the longitude at the 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.
Moreover it was proved by two great French astronomers (LA-
GRANGE and LAPLACE) about a hundred years ago that all the
planets would always continue to revolve in or near the plane of the
ecliptic; that the eccentricity of each orbit might vary within narrow
limits, but could never depart widely from its present value, and
finally that the mean-distances of the planets would always remain
the same as now. The Earth, for example, will always remain at the
same average distance from the Sun as now, though by a change in
the eccentricity its least and greatest distances from the Sun may be
slightly greater or less than at present. Hence there can never be
any great changes in the seasons of the Earth due to a change in its
distance from the Sun.
If the mean-distances of the planets remain essentially unchanged
their periodic times will also remain unchanged, by the 3d law of
KEPLER, so long as we consider the planets as rigid solids.
What is a planet's periodic-time? How can the relative dis-
tances of the planets from the Sun be determined ? What are the
three laws of planetary motion discovered by KEPLER ? Define an
ellipse. Do KEPLER'S laws explain why the planets move in elliptic
orbits? why their radii- vectores describe equal areas in equal times?
why for any two planets T* : TJ = a s : aS? What are the elements
of a planet's orbit ?
CHAPTEE X.
UNIVERSAL GRAVITATION.
25. The Discoveries of Sir ISAAC NEWTON. Before the
time of Sir ISAAC NEWTON very little was known of the
laws that govern the motion of bodies on the Earth. A
stone dropped from the hand falls to the ground. Why ?
NEWTON'S answer was that the Earth attracted the stone
downwards somewhat as a magnet attracts iron to itself.
The Earth itself was made up of stones and soil. Why did
not the stone attract the Earth upwards? NEWTON'S
answer was that the stone did, in fact, attract the Earth.
But as the Earth had a mass of millions of tons and the
stone a mass of only a few pounds the motion of the Earth
upwards towards the stone was very small compared to the
motion of the stone downwards to the Earth. It was too
small to be appreciable but the Earth moved nevertheless.
The attraction was in proportion to the attracting mass, he
said.
Each particle of a huge mass, like that of the Earth,
would attract the stone, and the whole of the Earth's
attraction would be the sum of all the particular attrac-
tions. The stone would also attract each one of the
Earth's particles, but as they were all joined together it
could move no one of them without moving them all. If
the Earth attracted a stone near its surface why should it
not attract the Moon in the sky ? The Moon would be
attracted less because it was distant, but it would certainly
be attracted, he said. There were reasons for believing
203
204
ASTRONOMY.
that attractions grew less in proportion to the square of the
distance, not in proportion to the simple distance.
His reasoning was something like this: We see that there
is a force acting all over the Earth by which all bodies are
drawn towards its centre. This force is called gravity. It
extends to the tops not only of the highest buildings, but
of the highest mountains. How much higher does it
FIG. 131.
A stone in a sling is whirled round in the direction of the arrows in the
circle CBA. At A the string breaks and the stone flies away in the
tangent AD. It would move away in that direction forever if the Earth
did not attract it downwards
extend ? Why should it not extend to the Moon ? If it
does, the Moon would tend to drop towards 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 towards the Earth; else she
would fly entirely away in a straight line just as a stone
thrown from a sling would fly away in a straight line if the
FIG. 132. SIR ISAAC NEWTON.
Born 1642 ; died 1727.
205
206 ASTRONOMY.
Earth did not attract it. Why should not the force which
makes the stone fall be the same force which keeps the
Moon in her orbit ?
To answer this question, it was necessary to calculate
the intensity of the force which would keep the Moon her-
self in her orbit, and 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. If this force diminished as the inverse square of
the distance, then at the Moon it would be only ^-^ as
great as at the Earth's surface.
Experiments at the Earth's surface had proved that a
body fell 16 feet in a second of time. The Moon in her
orbit ought then to fall towards the Earth (that is, ought to
bend away from a straight line) by ^ 7 part of 16 feet in
each and every second, or the Moon should bend away from
a straight line (a tangent to her orbit) by about T V part of
an inch every second. Now the size of the Moon's orbit
was known and its curvature was known. It was found
that the orbit of the Moon did, in fact, deflect from the
tangent to the orbit by -fa part of an inch per second.
NEWTON proved this point by calculation, and from that
time forward he felt sure that the force that kept the Moon
in its orbit about the Earth was a force of the same kind
as the gravity that made a stone fall to the Earth, and that
it was this very same force that kept all the planets in their
orbits about the Sun.
To prove that his idea was right it was necessary to prove
that if the Sun attracted the planets just as the Earth
attracted the Moon the laws of KEPLER would be a neces-
sary consequence. NEWTON made such a proof. lie
proved strictly and mathematically that any two bodies
which attracted each other in proportion to their masses
and inversely as the square of their distances apart would
obey laws like those of KEPLER. If one of the bodies was
UNIVERSAL GRAVITATION. 207
very large (like the San) and the other much smaller (like
one of the planets) then it necessarily followed from the
single law of gravitation that:
I. The planet would revolve about the Sun in an ellipse
(or in one of a set of curves of the same sort). II. The
radius- vector of the planet would describe equal areas in
equal times. And he further proved that if there were
two planets in the system the following law would be very
nearly true: III. The squares of their periodic times would
be proportional to the cubes of their mean distances from
the Sun. These are the three laws which KEPLER deduced
from observation. All the planets in the solar system obey
these laws. All the planets obey the law of gravitation
therefore.
KEPLER'S laws were proved to be true by observation. NEWTON
showed that if any planet moved about the sun so that its radius-
vector described equal areas in equal times then the planet obeyed a
force that was directed always to the sun as a centre of force. If the
path of any planet was an ellipse (or if it were a parabola or hyper-
bola) then the central force must vary inversely as the square of the
distance, and could vary in no other way. If all the planets were
bound together (as they are) by KEPLER'S third law, then all the plan-
ets are acted on by one and the same kind of force. The amount of
force acting on any planet depends on its distance from the Sun and
on the mass of the Sun. Observations fixed the length of each plan-
et's year and its distance from the Sun.
From these data the mass of the Sun could be calculated in terms
of the Earth's mass. Not only were these things true for all the
planets ; they governed the motions of satellites about their primary
planet. The Moon revolves about its primary, the Earth, in obe-
dience to its attraction ; but it is likewise attracted by the Sun and
hence its orbit is perturbed. NEWTON calculated perturbations of
the Moon's motion that had been known as facts of observation since
the time of HIPPARCHUS, and others that had been observed by TYCHO
BRAHE and FLAMSTEED, and he accounted for all these observed facts
by his theory. He also calculated some of the perturbations of the
path of one planet by the attraction of other planets.
Up to NEWTON'S day the motions of comets had been simply mys-
terious. He showed that they moved according to KEPLER'S laws,
208 ASTRONOMY.
usually in parabolas, not in ellipses. He calculated the shape that a
rotating fluid mass should assume and from this deduced the figure
of the Earth. He showed that it was a spheroid, not a sphere, and
proved that the precession of the equinoxes, observed as a fact by
HIPPARCHUS, and unexplained since his time, was a mere result of
the spheroidal shape of the Earth. The Tides another mystery
were explained by NEWTON as a result of the Moon's attraction of
the waters of the Ocean.
His discoveries in pure mathematics are only second in importance
to his discoveries in celestial mechanics. The binomial theorem was
discovered by him (it is engraved on his tomb in Westminster
Abbey). The Differential Calculus is his invention. He made most
important discoveries in optics also.
The epigram of the English poet POPE expresses the feeling of
awed amazement with which the men of his own time regarded this
mighty genius :
Nature and Nature's laws lay hid in Night :
God said let Newton be and all was Light.
Let us see what NEWTON thought of himself. Towards the end
of his life he said, " I know not what the world will think of my
labors, but to myself it seems that I have been but as a child playing
on the seashore ; now finding some pebble rather more polished and
now some shell rather more agreeably variegated than another, while
the immense ocean of Truth extended itself, unexplored, beyond me."
In science his name is venerated and honored by all those who can
appreciate his marvellous genius. His greatest effect on Mankind
has been to set before them a new path for their thoughts to follow.
Since his day men have a new view-of-the-world, and his discoveries
have influenced the thoughts, beliefs, and ideals of men and nations
as powerfully and as effectively as those of PLATO, ARISTOTLE, CO-
PERNICUS, and GALILEO. We should not now think as we all do if
our thoughts did not run in channels first opened by him.
All the motions of all the bodies in the solar system were
deduced by NEWTON from one single law the law of
Universal Gravitation. The discoveries of PTOLEMY, of
COPERNICUS, of KEPLER, and of all other astronomers were
nothing but special cases of one universal law. PTOLEMY
and other great astronomers before his time had mapped
out the apparent courses of the planets in the sky with
UNIVERSAL GRAVITATION. 209
diligence and with accuracy. COPERNICUS had shown
that these apparent paths were described because the
real centre of the motion was the Sun. KEPLER had
proved that the paths of the planets about the Sun were not
circles as COPERNICUS supposed, but ellipses; and he gave
the laws according to which the planets moved in their real
orbits.
NEWTON started with the simple fact of gravity (Latin
gravitas = heaviness). He said a body is heavy because
the Earth attracts it. The Earth (like every mass) at-
tracts all other bodies in the Universe, the nearer bodies
more, the distant bodies less. The attraction is directly
proportional to the mass; it is inversely proportional to the
square of the distance. If this law is true everywhere (as
experiment proves it to be true on the Earth) then all
KEPLER'S laws are a necessary consequence of it. One
single law accounts for every motion in the solar system.
Probably this law accounts for all the motions of the stars
also.
The student should memorize the law of universal gravi-
tation in the form that NEWTON gave to it as follows:
Every particle of matter in the universe attracts every
other particle with a force directly as the masses of the two
particles and inversely as the square of the distance between
them.
To thoroughly understand the discoveries of NEWTON it is neces-
sary to study Mechanics or the science that treats of the action of
forces on bodies. This science requires a mathematical treatment
too difficult and too long to be given here. After the Mechanics of
terrestrial bodies is understood it must be applied to the special case
of the heavenly bodies Celestial Mechanics. Only the barest out-
line of NEWTON'S achievements can be given in this place. The fol-
lowing paragraphs may help the student to understand the nature
of the questions involved.
If we represent by m and m f the masses of two attracting bodies,
we may conceive the body m to be composed of m particles, and the
other body to be composed of m' particles. Let us conceive that
210 ASTRONOMY.
each particle of one body attracts each particle of the other with a
force that varies as . Then every particle of m will be attracted
by each of the m' particles of the other, and therefore the attractive
force on each of the m particles will vary as 2 . Each of the m
particles being equally subject to this attraction, the total attractive
force between the two bodies will vary as j-.
Each of the two masses attracts the other by a force varying
If a straight stiff rod whose length was r could be slipped in
between the two masses m and m', the pressure on either end of
-m'
FIG. 133.
the rod would be the same. It would be a pressure proportional
mm'
te^r-.
When a given force acts upon a body, it will produce less motion
the larger the body is, the accelerating 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 m', 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 . If m is very large (as in the case of the San) and
if m' is relatively small (as in the case of a planet), the motion of the
planet will be determined by the Sun's accelerating force while the
Sun will be but little affected by the accelerating force of the planet.
It makes no difference at all of what substances m and m' are
made up. A mass of gas (as a comet) attracts in proportion to its
quantity of matter, just as amass of lead attracts in proportion to
its quantity of matter.
It is in this respect, especially, that the force of gravitation differs
from a force like magnetism. A magnet will attract iron but not
wood. But both wood and iron are heavy.
The attraction of a spherical body on a particle outside of itself
is the same as if the whole mass of the spherical body were con-
UNIVERSAL GRAVITATION. 211
centrated at its centre. We may treat the problems of Celestial
Mechanics as if the Sun and all the planets were mere points, the
whole mass of each body being concentrated at their centres. The
attraction of the Earth for bodies on its surface is the same as if the
earth were a mere point, its whole mass being concentrated at
its centre.
A word may be said on the variation of forces inversely as the
square of the distance. Suppose we take the force of gravitation.
At a distance of one radius of the Earth from the Earth's centre (at
the Earth's surface) let us call its intensity one ; at a distance of two
radii (some 4000 miles above the Earth's surface therefore) it will
be ^ ; at a distance of 3 radii it will be ; and so on.
Distances =1,2,3,4,5, 6 .... 100 ... 1000
Forces = 1 , i , i , A *V . A nd ;' nsoW
An excellent practical example of a quantity that varies inversely
as the square of the distance may be had by watching the headlight
of a tram-car as it approaches you. When it is five blocks off the
intensity of the light is ^th, four blocks off y'gth, three blocks ,
two blocks | of the intensity at a distance of a block. Gravitation
varies according to a similar law.
Gravitating force seems to go out from every particle of matter in
the Universe in all directions somewhat as rays of light stream out
in all directions from a lamp. It streams out in straight lines. What-
ever is in its way is attracted. If a planet is there it attracts the
planet. If nothing is there no attraction is exerted on empty space.
The rays of gravitation (so to speak) pass directly through a body and
a second body beyond it is attracted just as if the first body were not
there. There is no gravitational shadow, as it were.
A B C
If A were a lamp and B and C two screens, the screen B would be
lighted and the screen C would be in shadow. But if A is a heavy
body it will attract a body at B and another body C beyond it just as
if B were not there.
Moreover, the storehouse of gravitational attraction in a heavy body
is never exhausted. The sun attracts a planet at a certain distance
just as much in July as in the preceding January, just as much in
1907 as in 1620.
It requires time for the light of the Sun to travel across the space
that separates it from the Earth. A beam of light leaves the Sun
and does not arrive at the Earth for 8 m 19% it does not arrive at
Jupiter for 43 m 15 s . It takes these times to pass over the intervening
212 ASTRONOMY.
spaces. But the gravitating effect of the Sun traverses these spaces
instantaneously, so far as we now know. When gravitation is con-
sidered in this way, as a force inherent in a -body, as sourness is in-
herent in a fruit, a recital of its properties sounds like a fairy-tale.
The explanation of gravitation is not yet known. This force, like
the force of magnetism and other forces, is a mystery. When its ex-
planation comes to be known it will probably be found that a heavy
body must not be considered to be in empty space, but in a space
filled with some substance like the ether which transmits light. The
body influences the ether and sets up strains and stresses within it.
These stresses are transmitted in all directions with immense (prob-
ably not infinitely great) velocities. When these stresses meet a
second body they act upon it to produce the phenomena of gravita-
tion.
A word may also be said as to the intensity of the force of gravi-
tation. The popular notion is that gravitation is a very powerful
force. This is because we live on an earth which is very large in
comparison to our own size, and to the sizes of objects that we use in
our daily life. In reality gravitation may be called a feeble force
compared to such a force as the expansion of water when it freezes
and bursts the stout pipes in which it is contained. Two masses M
and M' , each weighing 415,000 tons, a mile apart, attract each other
with a force of one pound. Imagine two huge cubes of iron, each
weighing 415,000 tons. If at a mile's distance they only exert a force
of one pound we must decide that the force of gravitation is feeble
rather than powerful. If M and M' were two miles apart their mu-
tual attraction would be only four ounces. If M was doubled in size,
their attraction at one mile's distance would be two pounds ; if both
M and M' were doubled their attraction would be four pounds, and
so on. These effects one would call small rather than large.
The discoveries of NEWTON in relation to the force of gravitation
that binds the planets together and that determines every circum-
stance of every motion of everything on the Earth lead to conclu-
sions like those just set down. What the true nature of this force
is we do not know any more than we know the true nature of the
forces of chemical affinity and the like. No doubt a complete under-
standing of it will some day be reached, and what now seems mar-
vellous will then be simple. There is no doubt that the motions of
every particle on the Earth and of every planet in the solar system
are obedient to this law. The simple proof is that the motions of
planets, comets, and of many stars have been calculated beforehand
on this theory and that observation has subsequently verified the
predictions. The pages of the Nautical Almanac (see page 150) are
UNIVERSAL GRAVITATION.
213
nothing but a series of such predictions that are afterwards verified
over and over again in the minutest particular. The place that a
planet will occupy in the sky a century hence can be predicted
nearly as accurately as the planet can then be observed. Not only
this, but the paths of thousands of projectiles to be fired from can-
non have been calculated beforehand, and these predictions have been
subsequently verified by experiment. Every swing of a pendulum
and every fall of a heavy body u obedient to this law, and in thou-
sands and thousands of similar cases the law has been accurately
verified by experiment.
Mutual Actions of the Planets Perturbations. KEPLER'S laws
would be accurately followed in any system of only two heavy
bodies, as the Sun and any one planet, Mars for example. If a third
body exists, the Earth for instance, it will attract the Sun and also
Mars. The Sun and Mars will likewise attract the Earth. The
motion of Mars about the Sun will not be exactly the same in a sys-
tem of three bodies as in a system of two.
The mass of the Sun is so very much
greater than the mass of the Earth that
Mars will travel in an orbit almost the
same as its undisturbed orbit almost, but
not quite. The Earth will produce slight
disturbances perturbations they are called
in the orbit of Mars, and these perturba-
tions can be exactly calculated from NEW-
TON'S law. The orbit of the Earth will
also be perturbed by Mars.
Each of the planets will act on every
one of the other planets to alter its motion.
These disturbances in the solar system are
small, because the Sun's mass is so very
large compared to the mass of the dis-
turbing body. Even Jupiter, the largest
of the planets, has a mass less than y^Vu of
the Sun's mass.
._ A PENDULUM
AT REST HANGS VER-
The Vertical Line. The direction
np and down, the vertical direction, is
defined for any observer by the line
in which a pendulum at rest hangs. The pendulum is at-
tracted hy the whole Earth and if the Earth were a sphere
it would always point to the Earth's centre. As the Earth
ASTRONOMY.
is a spheroid (its meridians being ellipses and not circles)
a pendulum at rest at any point of the Earth's surface does
not point exactly to the centre, although its direction is
FIG. 135. A PENDULUM AT REST ON A SPHERICAL EARTH
POINTS NEARLY TO THE CENTRE OF THE EARTH.
never far from that of the Earth's radius. (The radius of
the Earth and the pendulum never make an angle of more
than 12' of arc a fifth of a degree with each other.)
The zenith of an observer may now be defined as that
point over his head where a pendulum at rest at his station
would meet the celestial sphere if the pendulum were in-
definitely long. A pendulum at rest always lies in the line
of joining an observer's zenith and nadir.
REMARKS ON THE THEORY OF GRAVITATION.
The real nature of the discovery of NEWTON is frequently
misunderstood. Gravitation is sometimes spoken of as if
it were a theory of NEWTON'S, now very generally received,
UNIVERSAL GRAVITATION.
but still liable to be ultimately rejected as a great many
other theories have been.
NEWTON did not discover any new force, but only showed
that the motions of the heavenly bodies could be accounted
for by a force which we all know to exist. Gravitation 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, wherever situated. To put the matter in a terse
form, what NEWTON discovered was not gravitation, but
the universality of gravitation.
What was the principal work of PTOLEMY and his predeces-
sors ? What was the discovery of COPERNICUS? What was KEP-
LER'S discovery? What was the greatest discovery of NEWTON?
Give NEWTON'S law of universal gravitation in his own words. Did
NEWTON discover gravitation ? What, in fine, was his discovery ?
Define the zenith of an observer his nadir.
CHAPTER XL
THE MOTIONS AND PHASES OF THE MOON.
26. The Moon makes the circuit of the heavens once in
each (lunar) month. She revolves in a nearly circular
orbit around the Earth (not the Sun) at a mean distance
of 240,000 miles. At certain times the new Moon, a
slender crescent, is seen in the west near the setting Sun.
On each succeeding evening we see her further to the east,
so that in two weeks she is exactly opposite the Sun, rising
in the east as he sets in the west. Continuing her course
two weeks more, she has approached the Sun 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 towards the east among the stars during
the whole month at the rate of 1 daily (see page 165), 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. The revolution of the Moon among the stars is
performed in about 27 days, so that if the Moon is very
near some star on March 1, for example, we shall find her
in the same position relative to the star on March 28.
The Moon's revolution relative to the stars is performed
in 27 days; relative to the Sun in 29 days. Her periodic
time in her orbit about the Earth is 27 days therefore.
Phases of the Moon. The Moon is an opaque body and
is formed of materials something like the rocks and soils of
216
MOTIONS AND PHASES OF THE MOON. 217
the Earth. Like the planets, she does not shine by her own
light, but by the light of the Sun, which is reflected from
her surface much as sunlight would be reflected from a
rough mirror. As the Moon, like the Earth, is a sphere,
only half of her globe can be illuminated at a time namely,
that half turned towards the San.
M
FIG. 136. THE MOON (M) IN HER ORBIT ROUND THE EARTH (E).
Half of each body is illuminated by the Sun. The Sun is not shown in
the drawing. If it were to be inserted it would have to be on the right-
hand side of the picture about thirty-five feet distant from E.
We can see only half of the Moon namely, that half that
is turned toward us. An eye at S (on the left-hand side
of the page) could see half of the Moon if it were illumi-
nated. But as the dark side is turned toward S an eye
placed there would see nothing. No light would come to
it. An eye at V would see the Moon as a bright circle.
The half turned toward V is fully illuminated.
218
ASTRONOMY.
In this figure 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
FIG. 137. THE PHASES OF THE MOON EXPLAINED.
Sun being some thirty feet away (on the scale of the draw-
ing) in the line BA. For the present purpose we suppose
both Earth and Sun to be at rest and the Moon to move
round her orbit in the direction of the arrows. Eight
positions of the Moon are shown around the orbit at A, E,
whence Ee = 0.01
of a foot, approximately.
The mass of the Sun at 93,000,000 miles causes the Earth to move
towards his centre 0.01 foot. If the Sun were 4000 miles from
the Earth his attraction would be greater in the proportion of
[93,000,000]' to [4000] 2 or as 8,650,000,000,000,000 to 16,000,000 or
as 540,500,000 to 1. If the Sun were at a distance of only 4000 miles
from the Earth (or from any heavy body) the body would fall in a
second 540,500,000 times T ^ of a foot or 5,405,000 feet. The Earth
THE EARTH. 241
makes a heavy body at its surface (4000 miles from its centre) fall
IGyV feet in a second. Hence
Mass of Sun : Mass of Earth = 5,405,000 feet : 16.1 feet,
or as 335,000 to 1. If the exact values of all the quantities are
employed instead of the approximate ones used above the value of
the Earth's Mass (Sun's Mass = 1.0) is aygVnF-
Constitution of the Earth. The body of the Earth is
made up of layers of rocks of different density arranged in
shells like the coats of an onion. The outer layers are the
least dense; the inner layers (those subject to the greatest
pressures) are the most dense. The Earth is composed of
various substances, some simple (elements) like iron, some
compound like clay. There are about 70 or 80 elementary
^substances (gold, iron, carbon, oxygen, hydrogen, etc.), and
v it is noteworthy that nearly all of these elements are known
to exist in the Sun, and that many of them are known to
exist in the stars. It is probable that the Sun, the Earth,
and all the planets are made out of the same elements and
that the amazing differences between them are chiefly due
to differences in their temperature.
The temperature of the solid crust of the Earth increases as we go
downwards at the rate of about 1 Fahr. for every 55 or 60 feet, or
about 90 per mile. At the depth of 10 miles the temperature is
about 900; at the depth of 30 miles about 2700, and so on. Iron
melts at the surface of the Earth (where it is free from great pressure)
at about 3000. If the substances in the Earth's interior were free
from pressure the interior would be a fluid mass, and there would be
great tides in this interior ocean. Astronomical observations show
that there are no such tides, whence it follows that the interior of
the Earth is, on the whole, solid. There are many reservoirs of
melted rocks (lavas) no doubt in the neighborhood of volcanoes, but
on the whole the Earth is solid and about as stiff as a globe of steel.
The spheroidal shape of the Earth seems to show that it once was in
a fluid condition, for a rotating mass of fluid will take the form of a
spheroid. It will be flattened at the poles. Its meridians will be
ellipses. This is the shape, not only of the Earth, but of all the
planets,
242 ASTRONOMY.
All the heat of the Earth comes to it from the Sun. The Sun
sends its heat out in all directions along every possible line that can
be drawn from the San outwards. The Sun would warm the whole
interior surface of a sphere 93,000,000 miles in diameter just as
much as it now warms the Earth which occupies one small point
of such a sphere. So far as mankind is concerned all the heat that
does not fall on the Earth is lost. The Earth receives only the
minutest fraction of it (not more than ju^tfcVinnnF)'
Atmosphere of the Earth. The Earth is surrounded by an ocean of
water in which the attractions of the Sun and Moon produce tides.
It is likewise surrounded by an ocean of air, and in this atmosphere
slight tides are also observed. The effect of the atmosphere on the
climates of the Earth is most important, and it is treated in works
on Meteorology.
Astronomy is chiefly concerned with the effects of the Earth's
atmosphere in producing a refraction (a bending) of the rays of light
that reach us from the stars so that we do not see them quite in
their true directions. The atmosphere of the Earth surrounds it to a
height of a hundred miles or more. Its heavier layers are nearest
the Earth's surface. Even at a height of 3 or 4 miles there is
scarcely enough air for breathing.
Refraction of Light by the Atmosphere. In figure 153
is the centre of the Earth and A the station of an
observer on its surface. 8 is a star. If there were no
atmosphere the observer would see the star along the line
AS. But the atmosphere acts like a lens and bends
(refracts) the light from the star along the curved line
6, d y c, #, a, and the light from the star comes to the
observer along the line AS'. He sees the star projected on
the celestial sphere at $', therefore, and not in its true
place S. The star is (apparently) thrown nearer to his
zenith by refraction. It will rise sooner and set later,
therefore, on this account.
At the zenith the refraction is 0, at 45 zenith distance tLe refrac-
tion is 1', and at 90 it is 34' 30". The ravs of light traverse greater
thicknesses of air at large zenith distances and are more refracted
therefore. Stars at the zenith distances of 45 and 90 appear ele-
vated above their true places by 1' and 34' respectively. If the sun
has just risen that is, if its lower edge is just in apparent contact
THE EARTH. 243
with the horizon it is in fact entirely below the true horizon, for
the refraction (35') has elevated its centre by moie 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.
FIG. 153. REFRACTION OF THE LIGHT OF A STAR BY THE
EARTH'S ATMOSPHERE.
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
particles of matter suspended in the atmosphere. This
produces 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.
244: ASTRONOMY.
The Sun's direct rays do not reach an observer on the
Earth after the instant of sunset, since the solid body of
the Earth intercepts them. But the Sun's direct rays
illuminate the clouds of the upper air, and are reflected
downwards so as to produce a general illumination of the
atmosphere, which is called twilight.
In the figure let A BCD be the Earth and A an observer
on its surface, to whom the Sun 8 is just setting. Aa is
FIG. 154. THE PHENOMENA OF TWILIGHT.
the horizon of A-, Bb of B\ Cc of (7; Dd of D. Let the
circle PQR represent the upper layer of the atmosphere.
Between ABCD and PQR the air is filled with suspended
particles that reflect light. The lowest ray of the Sun,
SAM, just grazes the Earth at A] the higher rays 8N and
SO strike the atmosphere above A and leave it at the points
Q and R.
Each of the lines SAPM, SQN\$ bent from a straight
course by refraction, but SRO is not bent since it just
THE EARTH. 245
touches the upper limits of the atmosphere. The space
MABCDE is the Earth's shadow. An observer at A
receives the (last) direct rays from the Sun, and also has
his sky illuminated by the reflection from all the particles
lying in the space PQRT which is all above his horizon Aa.
An observer at B receives no direct rays from the Sun.
It is after his sunset. Nor does he receive any light from
that portion of the atmosphere below APM\ but the por-
tion PRx, which lies above his horizon Bl) is lighted by the
Sun's rays, and reflects some light to B. The twilight is
strongest at R, and fades away gradually towards P. The
altitude of the twilight at B is bd.
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 at C is cd.
To an observer at D it is night. All of the illuminated
atmosphere is below his horizon Dd.
The twilight arch is more marked in summer than in winter ; in
high latitudes than in low ones. There is no true night in Scotland
at 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
about 20 below the horizon. The student should observe the
phenomena of twilight for himself. It is best seen in the country,
shortly after sunset, as far away from city lights as may be.
Astronomical Measures of Time to the Inhabitants of the
Earth. The simplest unit of time is the sidereal day, that
is the interval of time required for the Earth to turn once
on its axis. It is measured by the interval between two
successive transits of the same star over the observer's
meridian ; and it is divided into 24 sidereal hours.
The most obvious unit of time is the (apparent) solar
day, that is the interval of time between two successive
transits of the true Sun over the observer's meridian. AB
apparent solar days are not equal in length, a more con-
246 ASTRONOMY.
venient unit has been devised, that is the mean solar day,
which is the interval of time between LAVO successive
transits of the mean San (see page 90) over the observer's
meridian. The relation between the sidereal and mean
solar day has been previously given (page 95) and is as
below :
366.24222 sidereal days = 365.24222 mean solar days,
I sidereal day = 0.997 mean solar day,
24 sidereal hours = 23 h 56 m 4". 091 mean solar time,
1 mean solar day = 1.03 sidereal days,
24 mean solar hours = 24 h 3 m 56'.555 sidereal time.
The quantity to be added to (or subtracted from) ap-
parent solar time to obtain mean solar time is calculated
beforehand and printed in the Nautical Almanac under
the heading " Equation of Time." (See page 151.)
The months now or heretofore jn use among the peoples
of the globe may for the most part be divided into two
classes :
(1) The lunar month pure and simple, or the mean
interval between successive new Moons.
(2) An approximation to the twelfth part of a year,
without respect to the motion of the Moon.
The mean internal 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 days alternately.
The interval between two successive returns of the Sun
to the same star is called the sidereal year. Its length is
found by observation to be
365 (mean solar) days 6 hours 9 minutes 9 seconds = 365 d . 25636.
The interval between two successive returns of the Sun to
the same equinox is called the equinoctial year. Its length
is found by observation to be
365 (mean solar) days 5 hours 48 minutes 46 seconds = 365 d . 24220.
THE EARTH. 247
The sidereal year measures the time of the revolution of
the Earth in her orbit. The equinoctial year governs the
recurrence of the seasons, because the seasons depend on
the Sun's declination (see page 175) and the declination
changes from south to north at the vernal equinox at the
passage of the Sun across the celestial equator.
The solar year of 365 days has been a unit of time-
reckoning from very early times. Four such years are
equal to 1461 days. The cycle of four years, three of them
of 365 days and the fourth of 366, which we use, was
adopted in China in the remotest historic times.
The Julian Calendar. The chil calendar now in use
throughout Christendom had its origin among the Romans,
and its foundation was laid by JULIUS C^SAB. Before his
time, Rome can hardly be said to have had a chronological
system. The length of the year was not prescribed by any
invariable rule, and it was changed from time to time to
suit the caprice or to compass the ends of the rulers.
Instances of this tampering disposition are familiar to the histori-
cal 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. CAESAR fixed the year at 365 days, with
the addition of one day to every fourth year. The old Roman months
were afterwards adjusted to the Julian year in such a way as to give
rise to the somewhat irregular arrangement of months which we now
have. The names of our days are partly from Roman, partly from
Scandinavian mythology. The student should consult a dictionary
for the derivations of their names.
Old and New Styles. The mean length of the Julian year is about
11 minutes greater than that of the 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 can cause no inconvenience.
But, in order to have the year as correct as possible, two changes
were introduced into the calendar by Pope GREGORY XIII. with this
object. It was decreed that
248 ASTRONOMY.
(1) The day following October 4, 1582, was to be 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, was to be 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, the Julian calendar is still continued without
change. The Russian reckoning 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.* The 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.
Precession of the Equinoxes. It has just been said that
observation proves the sidereal year to have a length of
365.25636 mean solar days, and the equinoctial year to
have a length of 365.24220 days. The Sun in his annual
circuit of the heavens moves from a star to the same star
again in the sidereal year, from an equinox to the same
equinox again in the equinoctial year.
As the stars are fixed, the Sun's revolution around the
ecliptic from star back to the same star again must be a
revolution through exactly 360 0' 0" of right-ascension.
As the equinoctial year is shorter than the sidereal year,
the Sun's revolution from equinox t equinox must be a
revolution through an angle slightly less than 360.
( 8W.8MM ) ; ( MP.MBN) .
( sidereal year ) ( equinoctial year )
The equinox must therefore be moving in space so that
* Russia will adopt the New Style in A.D. 1901
THE EARTH. 249
v when it is met a second time the Sun has made one revoln-
v tion less 50". The Sun's annual circuit is performed
among the stars from west to east. The equinox therefore
moves (to meet the Sun) westward in right-ascension at the
rate of about 50" per year.
FIG. 155. THE CELESTIAL EQUATOR (AD) AND THE ECLIPTIC
(CD) ; E, is THE VERNAL EQUINOX.
The equinox (E in the figure) is nothing but the point
where the ecliptic (CD) intersects the celestial equator
(AB). If their point of intersection changes it must be
because one or both of these circles is moving. If the plane
of the celestial equator is moving the declinations of all the
stars will change from year to year. Observation shows
that the declinations do change slightly from year to year.*
If the plane of the ecliptic is fixed the celestial latitudes of
all the stars (their angular distances from the ecliptic) will
not change from year to year. Observation shows that
*The right-ascensions also change slightly because the equinox,
which is the origin of R A., is moving. The effect of annual pre-
cession on the places of stars is given in the fourth and sixth columns
of Table V at the end of this book.
250 ASTRONOMY.
while the declinations of all the stars do change annually
by small amounts their celestial latitudes do not change.
Hence the plane of the ecliptic is fixed; and hence the
westward motion of the equinox is entirely due to a motion
of the plane of the celestial equator.
If the plane of a circle of the celestial sphere is fixed the
place of the pole of that circle on the celestial sphere is
stationary. The ecliptic (CD) is fixed (see the figure), and
hence the place of its pole (Q) among the stars is station-
ary. If the pole of the ecliptic is 10 from a star in 1800
it will be 10 from that star in 1900. On the other hand,
if the plane of the celestial equator (AB) is moving, as it
is, the place of its pole (P) among the stars must be
moving. The north pole of the heavens is now near to
Polaris, but it will in time move away from it. At the
time when the pyramids were built, about B.C. 2700,
Polaris was not the " north-star," but the star Alpha
Draconis (see star-map No. VI).
The pole of the ecliptic (Q) is fixed; the pole of the
celestial equator (P) is moving. The angle between the
plane of the ecliptic and the plane of the celestial equator
(POQ = 23%) does not change. Therefore the pole P
must revolve about the fixed pole Q in a circle. The in-
clination of the two planes CD and AB will not be changed
by such a revolution, but their line of intersection (EF)
will move slowly round the celestial sphere. Their line of
intersection is the line joining the two equinoxes. The
annual motion of the equinox is, as we have seen, 50" of
arc, so that in about 25,920 years the equinox (E) will
move completely around the circle of the ecliptic and will
return to its starting-point. In the same period the pole
of the celestial equator (P) will move in a circle completely
around the pole of the ecliptic (Q).
25,920 X 50" 1,296,000" = 360.
THE EARTH.
251
The student can trace the path of the north pole of the heavens
among the stars on Star-map No. IV, following. Turning this map
upside-down let him find the constellations Draco, Ursa minor,
Cepheus, Cygnus, and Lyra.
About 3000 years ago the pole was near a in Draco,
At the present time the pole is near a in Ursa minor,
About 2000 years hence the pole will be very near to a: in Ursa minor,
" 4000 " " " " " " near y in Ceplieus,
" 7500 " " " " " " " a in
" 11500 " " " " " " " d in Cygnus,
" 14000 " " " " " " " am Lyra.
If he has a celestial globe at hand he will find the path of the
north pole of the heavens about the north pole of the ecliptic marked
down among the stars.
FIG. 156. THE SEASONS ON THE EARTH.
The effects of the motion of the pole of the heavens on our sea-
sons may be studied in the figure. The figure represents the Earth in
four positions during its annual revolution. Its axis inclines to the
right in each of these positions. In Chapter VIII it was said that
the Earth's axis always remained parallel to itself. The phenomena
of precession show that this is not absolutely true, but that, in real-
ity, the direction of the axis is changing with extreme slowness.
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 towards
252 ASTRONOMY.
the reader, the amount of the inclination remaining 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 in-
clined towards the reader and therefore from the Sun, 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 towards the left,
and the seasons will be reversed. Another interval of the same
length, and the north pole will be inclined from the reader, the
seasons being shifted through another quadrant. Finally, at the
end of about 25,900 years, the axis will have resumed its original
direction.
FIG. 157. THE EARTH'S Axis AND EQUATOR.
The north pole of the heavens is the point where the
celestial sphere is met by the axis of the Earth prolonged.
The celestial equator is the plane of the terrestrial equator
produced. The axis of the Earth does not move relatively
to the Earth's crust. The Earth's equator always passes
through the same countries Ecuador, Brazil, Africa,
THE EARTH. 253
Sumatra. The latitudes of places on the Earth do not
change. Precession is not due to a motion of the Earth's
axis simply, but to a motion of the whole Earth that carries
the axis with it.
FIG. 158. DIAGRAM TO ILLUSTRATE THE CAUSE OP PRECESSION.
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 precession.
It is, however, ellipsoidal with a protuberance at the equator. The
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. 156
(Seasons).
The Sun's North Polar Distance is 90 at the equinoxes, and 66|*
and 113^ at the solstices. At the equinoxes the Sun is in the direc-
tion Cm ; that is, NCm is 90. At the winter solstice the Sun is in
the direction Cc ; NCc = 113. It is clear that in the latter case the
effect of the Sun on the ring of matter will be to pull the Earth
downwards so that the direction Cm tends to become the direction Cc.
An opposite effect will be produced by the Sun when its polar dis-
tance 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 pre-
sented to the attracting body. The result of all the complex motions
254 ASTRONOMY.
we have described is a conical motion of the Earth's axis NC about
the line CE.
The Earth's shape is of course not that given in the figure, but an
ellipsoid of revolution. The ring of matter is not confined 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 just described. The motion of precession is not uniform, but
is subject to several small inequalities which are called nutation.
The fact of precession was discovered by HIPPARCHUS
more than 2000 years ago. He observed : (1) That the Sun
made a revolution from equinox to equinox in a shorter
time than that required for its revolution from star to star.
(2) As the stars were fixed the equinox must be moving.
(3) The equinox is the intersection of the ecliptic and the
celestial equator, and hence one or both of these planes
must be moving. (4) The ecliptic was not moving because
the celestial latitudes of stars did not change. (5) The
celestial equator was in motion because the declinations of
all the stars (and their right-ascensions also) did change.
This was a mighty discovery, and it required a genius of
the first order to make it.
COPERNICUS, in 1543, declared that precession was due
to a conical motion of the Earth's axis of rotation about
the line joining the Earth's centre with the pole of the
ecliptic.
NEWTON, in 1687, worked out the complete explanation.
This could not possibly have been done until the theory of
gravitation was thoroughly understood nor until the science
of mathematics had been developed (by NEWTON'S own
researches) to a high point. Three of the greatest names
of science are associated in this discovery.
The Progressive Motion of Light, GALILEO made ex-
periments to determine whether light required time to pass
from one place to "another. His methods were not suffi-
ciently refined to decide the question, but the subject was
not lost sight of. In the year 1675, OLAUS ROMER, a
THE EARTH. 255
Danish astronomer (to whom we owe the invention of the
transit instrument, among other things), was engaged in
making tables of the times of the eclipses of the satellites
of Jupiter.
FIG. 159. THE ECLIPSES OF JUPITER'S SATELLITES AND THE
PROGRESSIVE MOTION OF LIGHT.
S, is the Sun : T, is the Earth in its orbit; J, is Jupiter in opposition with
the Sun ; J'" is Jupiter in conjunction with the Sun.
The figure shows the Earth at T. When Jupiter is at J
it is nearest to the Earth ; when Jupiter is at J '" (and the
Earth at T} the two bodies are as far apart as possible.
TJ" r is larger than TJ by the diameter of the Earth's
orbit; by about 186,000,000 miles therefore. Jupiter
casts a long shadow (see the cut) and one of its satellites
(its orbit is the small circle about / and about J" f ) is
eclipsed at every revolution. ROMER calculated the times
at which an observer on the Earth would see such eclipses.
He found that his tables could be reconciled with observa-
tion only by supposing that the light from the satellite
required time to pass from Jupiter to the Earth, When
Jupiter is at /its light has to pass over the luieJT to
reach the Earth. When Jupiter is at J'" its light has to
pass over the longer line J '" T. Accurate observations show
that eclipses of the satellites are seen 16 minutes 38 seconds
earlier when the planet is at ./ than when it is at /'".
Light requires 16 m 38 8 to pass over the diameter of the
Earth's orbit, therefore, or 8 m 19" to pass over the radius of
the orbit.
256 ASTRONOMY.
In 499 8 light travels 92,900,000 miles, or at the rate of
186,200 miles in one second of time.* The sunlight is
499 seconds old when it reaches the Earth. As the velocity
of light is uniform it follows that (approximately):
Sunlight is 3 m old when it reaches Mercury,
"
" 6 m " " "
** Venus,
ft
(t gm
-i -
N
5
a
!
s 2
'Sc-'
ll!
NAME.
Mil-
!p
ll
o.g
"3 H.
11
g
1
JIM
Astronom-
lions
'&'i
Si
ia
S^
fa |
ical Units.
of
go
8*
oH
cJ
5*
Miles.
3
g
3"
S
P
Mercury..
0.387099
36.0
0.21
75
7 0'
47
323
0" 3 ra
Venus... .
0.723332
67.2
0.01
129
3 24
75
244
6'j
Earth...
1.000000
92.9
0.02
100
100
8
Mars. . . .
1.523691
141
0.09
333
1 51
48
83
13
Jupiter . .
5.202800
483
0.05
12
1 19
99
160
43
Saturn . .
9.538861
886
0.06
90
2 29
112
15
1 19
Uranus . .
19.18329
1782
0.05
171
46
73
29
2 38
Neptune..
30.05508
2791
0.01
46
1 47
130
335
4 8
THE SOLAR SYSTfiM.
277
.JL O $>
i5-3 S
I> C? QO
T-l O H gM
co O i i O
S ^
1-2
Cl M
Sc
8-2
S8
0.2
m DBS
I11S
J, *:~ s fr,.,. 8 -,
111
t^-eoo OOOOO
-
OOOOOOJQOO
T-I it 1 ti (-Tf^i^O
SJ|2
a fe P
i t-i O-iC-?C | I-H-H W Tj< 10 j^ Ol W^CXJCO
!g^Is Sil
few
ffi s ^
: es o oi'S , : : : '-2 2 : '!.
: lli luifrlfi!
'f-St> " N co * . ?o t- ao e ^-c o co *
TEE SOLAS SYSTEM.
279
TABLE IV.
THE COMETS OP THE SOLAR SYSTEM (PERIODIC COMETS).
No.
NAME.
Time of Peri-
helion Passage.
r
Perihelion
Distance
(approx.)
11?
Ill
-sjQxS
Inclination
of Orbit
(approx.)
1
Encke
1895 Feb 4
3 30
34
4 10
13
2
Tempel
1894 April 23
5 22
1 35
4 67
13
3
Brorsen
1890 Feb 24
5 46
59
5.61
29
4
Ternpel Swift
1891 Nov 14
5 53
1 09
5.17
5
5
^^innecke
1892 June 30
5 82
89
5 58
15
6
7
Da Vico-Swift
Tern pel
1894 Oct. 12
1885 Sept 25
5.86
6 51
1.39
2 07
5.11
4 90
3
11
8
Biela
1852 Sept
6 6-
86
6.2-
13
9
Finlay
1893 July 12
6 62
0.99
6.06
3
10
D' Arrest
1890 Sept. 17
6.69
1.32
5.78
16
11
Wolf ..
1891 Sept 3
6 82
1 59
5 60
25
13
Brooks ....
1896 Nov 4
7 10
1 96
5 43
6
18
Fave. .
1881 Jan 22
7 57
1 74
5.97
12
14
Tuttle
1885 Sept 11
13 76
1.02
10.46
55
15
16
Pons-Brooks .
Olbers
1884 Jan. 25
1887 Oct 8
71.48
72 63
0.76
1 20
33.6?
83 6
74 Q
45*
17
Halley
1835 Nov 15
76 37
59
35 41
162
CHAPTER XVI.
THE SUN.
31. The Sun is a huge globe 866,400 miles in diameter.
Its mass is 333,470 times that of the Earth, its volume is
1,310,000 times the Earth's volume, its density one fourth
of the Earth's density. The force of gravity on its surface
is nearly 28 times the force of gravity on the Earth. On
the Earth a heavy body falls 16 feet during the first second
of its descent; at the San it would fall 444 feet. Some
idea of its enormous size can be had by remembering that
the Earth and Moon are but 238,000 miles apart while the
Sun's radius is 433,200 miles. If the San were hollow
and the Earth was at its centre the Moon would revolve far
within the outer shell of the Sun's surface. The motions
of all the planets are controlled by its attraction.
The Sun is a star. It is a sphere of incandescent gases
and metallic vapors. It shines by its own light and gives
out enormous quantities of heat unceasingly. Only the
smallest fraction of the Sun's heat reaches the Earth. Yet
that small fraction (about ^oinroVFo UT P ar t) supports all the
life on the Earth, both of animals and plants. It main-
tains the circulation of winds, of ocean currents, the flow
of glaciers and of rivers; it is the cause of the rains, the
clouds, the dews that support vegetation; it controls the
seasons and the climates of all the regions of our globe and
of all the planets in the solar system. In the strictest sense
all the life, energy, and activity on the Earth are main-
tained by the Sun and principally and chiefly by the Sun's
280
THE SUN. 281
heat. If the Sun's heat were cut off all life on the Earth
would quickly cease.
While it is true that the Sun is as different as possible
from the Earth in its present state, it is to be especially
noted that the difference is chiefly due to a difference of
temperature. The spectroscope detects the presence of
(the vapors of) metals and earths in the Sun and it is likely
that there is no " element " on the Earth that is not found
on the Sun. Calcium, carbon, copper, hydrogen, iron,
magnesium, nickel, silver, sodium, zinc, among others,
have been detected, some of them in great abundance.
There is every reason to believe that if the Earth were to
be suddenly raised to the temperature of the Sun it would
become at once, and in virtue of temperature alone, a Sun
that is a star.
Photosphere, The visible shining surface of the Sun 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, dark patches of varied and irregular outline are fre-
quently found upon it. These are called the solar 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 26 days. The Sun, therefore,
has axis, poles, and equator, like the Earth, the axis being
the line around which it rotates. It turns on its axis from
west to east in 25 days, 7 hours, 48 minutes.
Faculae. 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 clouds of the vapors
of metals and are called faculce.
Chromosphere. Just above the solar photosphere there
is a layer of glowing vapors and gases from 5000 to 10,000
282 ASTRONOMY.
miles in depth. At the bottom of it lie the vapors of many
metals, magnesium, sodium, iron, etc., volatilized by the
intense heat, while the upper portions are composed prin-
cipally of hydrogen gas. The vaporous atmosphere is called
the chromosphere. It is entirely 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 (120,000
miles). These masses can never be directly viewed 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
fantastic shapes rising from the edge of the Sun. The
spectroscope shows that they are chiefly composed of in-
candescent calcium, helium, and hydrogen.
Corona. During total eclipses the Sun is seen to be
enveloped by a mass of soft
white light, much fainter than
the chromosphere, and extend-
ing out on all sides far beyond
the highest prominences. It
is brightest around the edge
of the Sun, and fades off
toward its outer boundary by
FIG. 163. A METHOD OF OB- . . U1 -, ,. mi.
SERVING THE SUN WITH A ^sensible gradations. This
TELESCOPE. halo of lis^ht is called the
corona, and is a very striking object during a total eclipse.
(Fig. 163.)
Methods of Observing the Sun. The light and heat of the Sun con-
centrated at the focus of a telescope are very intense. An experi-
ment with a burning-glass will illustrate this obvious fact. Special
THE SUN. 283
eye-pieces are made so that the Sun can be looked at directly with
the telescope, but the method of projecting the Sun's image on a
sheet of cardboard (as in the figure) is very convenient, especially
because several observers can examine the image at the same time.
A sheet of white cardboard is fastened to the telescope (accurately
perpendicular to its axis) by a light wooden or metal frame. The
image of the Sun is projected on the cardboard and must be made
as sharp and neatly denned as possible by moving the eye piece to
and fro till the right focus is found. It is desirable to fasten another
sheet of cardboard over the tube of the telescope to shut off a part
of the daylight, as in the figure.
FIG. 164. COPY OF A PHOTOGRAPH OP THE SUN SHOWING THE
CENTRE OF THE DISK TO BE BRIGHTER THAN THE EDGES.
One of the best ways to study the Sun is to photograph it with a
camera of long focus the longer the better. The exposures must
be very short indeed a few thousandths of a second in most cases.
The surroundings of the Sun its red flames, its corona can be seen
with the naked eye at a total solar eclipse, and they can then be
photographed. The spectroscope is used for the study of the Sun's
surroundings and of its surface, as explained in the Appendix on
Spectrum Analysis. If the student is not already familiar with the
subject through his study of physics, he should interrupt his read-
ing of this chapter and master the principles explained in the Ap-
pendix, as they are necessary to an understanding of what follows.
284
The Photosphere, The disk of the San is circular in
shape, no matter what side of the Sun's globe is turned
towards the Earth, whence it follows that the Sun is a
sphere. The disk of the San is not equally bright over all
the circle of the surface. The centre of the disk is most
brilliant and the edges are shaded off so as to appear much
less brilliant, as in Fig. 164. The deficiency of brightness
at the edges is due to the fact that the rays that reach us
from the centre of the disk traverse a smaller depth of the
Sun's atmosphere than those from the edges and are less
absorbed by the Sun's atmosphere therefore.
FIG
165. THE ABSORPTION OF THE SUN'S RATS is GREATER AT
THE EDGES OP THE DISK THAN AT THE CENTRE.
In figure 165 let 8E be the Sun's radius and 8M the radius of his
atmosphere. A person stationed beyond M (to the left hand of the
figure) looking at the Sun along the lines ME and M'E' would see
the centre of the disk by rays that had traversed the distance ME
only; while the edge of the disk would be seen by rays that had
traversed the much greater distance M' E'.
THE SUN.
285
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 subjected to its
absorptive action.
The Solar Spots, When the Sim's disk is examined with
the telescope several Sun-spots can usually be seen. The
smallest are mere black dots in the shining surface 500
miles or so in diameter. The largest solar spots are
thousands of miles in diameter (100,000 miles or more).
FIG. 166. A LARGE SUN-SPOT SEEN IN THE TELESCOPE.
Solar spots generally have a black central nucleus or
umbra, surrounded by a border or penum bra, intermediate
in shade between the central blackness and the bright
photosphere.
The first printed account of solar spots was given by
FABRITIUS in 1611, and GALILEO in the same year (May,
1611) also described them, GALILEO'S observations showed
286 ASTRONOMY.
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 slowly
across the disk for 12 or 13 days, when it reached the west
limb, behind which it disappeared. After about the same
period, it reappeared at the eastern limb.
The spots are not permanent in their nature, bat dis-
appear after a few days, weeks, or months somewhat as
cyclonic storms in the Earth's atmosphere persist for hours
or days and then are dissipated. But so long as the spots
last they move regularly from east to west on the Sun's ap-
parent disk, making one complete rotation in about 25 days.
This period of 25 days is therefore approximately the rota-
tion 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 regions 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 faculce, mottlings of light
brighter than the general surface of the Sun. Many of the faculce,
are clouds of incandescent calcium.
Solar Axis and Equator. The spots revolve with the surface of the
Sun about his axis, and the directions of their motions must be ap-
proximately parallel to his equator. Fig. 167 shows the appearances 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 Marchand 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 plane of the ecliptic is about 7 9', and the axis of rotation is, of
course, perpendicular to it.
Form of the Solar Spots. The Sun-spots are probably depressions
in the photosphere. When a spot is first seen at the edge of the
disk it appears as a notch, and is elliptical in shape. As the Sun's
rotation carries it further on to the disk it becomes more and more
THE SUN.
287
circular. At the centre it is often circular, and as it passes off the
disk the shape again becomes elliptical. The appearances are shown
in fig. 168, and are due to perspective.
FIG 167. APPARENT PATHS OF THE SOLAR SPOTS TO AN OBSERVED
ON THE EAKTH AT DIFFERENT SEASONS OF THE YEAR.
The Number of Solar Spots varies Periodically. The
number of solar spots that are visible varies from year to
year. Although at first sight this might seem to be what
we call a purely accidental circumstance, like the occur-
rence of cloudy and clear years on the Earth, observations
of sun-spots establish the fact that this number varies
periodically.
288
ASTRONOMY.
That the solar spots vary periodically will appear from the follow-
ing summary :
From 1828 to 1831 the Sun was without spots on only 1 day.
In 1833
From 1836 to 1840
In 1843
From 1847 to 1851
In 1856
From 1858 to 1861
In 186!
FIG. 168. APPEARANCE OF THE SAME SOLAR SPOT NEAR THE
CENTRE OF THE SUN AND NEAR THE EDGE.
Every eleven years there is a minimum number of spots, and about
five years after each minimum there is a maximum. There was a
maximum of spots in 1893 ; the minimum occurred in 1899. If, in-
stead of merely counting the number of spots, measurements are
made on solar photographs of the extent of spotted area, the period
comes out with greater distinctness.
The cause of this periodicity is as yet unknown. It probably lies
within the Sun itself, and is similar to the cause of the periodic ac-
tion of a geyser.
The sudden outbreak of a spot on the Sun is often accompanied by
violent disturbances in the magnetic needle ; and there is a complete
THE SUN. 289
concordance between certain changes in the magnetic declination
and the changes in the Sun's spotted area.
The agreement is so close that it is now possible to say what the
changes in the magnetic needle have been so soon as we know what
the variations in the Sun's spotted area are.
There is a direct action between the Sun and the Earth that we
call their mutual gravitation ; and the foregoing facts show that
they influence each other in yet another way. These actions take
place across the space of 93,000,000 miles which separates the Sun
and Earth. No doubt a similar effect is felt on every planet of the
solar system.
The Sun's Chromosphere and Corona. Phenomena of Total Eclipses.
When a total solar eclipse is ob-
served with the naked eye its
beginning 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,
because the Moon moves from
west to east in its orbit. An
hour or more elapses 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 gradually hidden
until it becomes a thin crescent.
The actual amount of the Sun's
light may be diminished to two T
thirds or three fourths of its FlG ' 169 -~ THE SOLAR CORONA
,. . . AT THE TOTAL SOLAR ECLIPSE
ordinary amount without its op J ANUARY , i 889> FROM PHO .
being strikingly perceptible to TOGRAPHS.
the eye. What is first noticed is
the change which takes place in the color of the surrounding land-
scape, which begins to wear a ruddy aspect. This grows more and
more pronounced, and gives to the adjacent country that weird effect
which lends so much to the impressiveness of a total eclipse.
The reason for the change of color is simple. The Sun's atmos-
phere absorbs a large proportion of the bluer rays, and 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
290 ASTRONOMY.
than ordinary sunlight, as they are those which come from points
near the Sun's limb, where they have to pass through the greatest
thickness of the Sun's atmosphere.
The color of the light becomes more and more lurid up to the mo-
ment of total eclipse. If the spectator is upon the top of a high
mountain, he can then begin to see the Moon's shadow rushing to-
ward 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 sud-
denly 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 edge it is intensely bright,
and to the naked eye uniform in structure ; 5' or 10' from the limb
this inner corona has a boundary more or less denned, and from this
extend streamers and wings of fainter and more nebulous light.
They are of various shapes, sizes, and brilliancy. No two solar
eclipses yet observed have been alike in this respect.
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. They 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, and during this time, as
the eye becomes more and more accustomed to the faint light, the
outer corona becomes visible 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. Photo-
graphs of the corona show even a greater extension. 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 atmos-
phere 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
* The Total Solar Eclipse of May 28, 1900, will be visible in the United States.
Its track will pass from New Orleans to Norfolk in Virginia. The duration of
the total phase will be about 1m. 19s. in Louisiana and 1m. 49s. in North Car-
olina. The totality occurs about 7.30 A.M. (local time) at New Orleans, and
about 9 A.M. at Norfolk. The width of the shadow track is about 55 miles.
THE SUN. 291
naked eye. The corona, as seen through a telescope, is, however,
of a very complicated structure. It is best studied on photographs,
several of which can be taken during the total phase, to be subse-
quently examined at leisure.
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 is also a solar ap-
pendage.
Gaseous Nature of the Prominences. The eclipse of 1868 was total
in India, and was observed by many skilled astronomers. A discov-
ery of M. JANSSEN'S will make this eclipse forever memorable. He
was provided with a spectroscope, and by it observed the promi-
nences. One prominence in particular was of vast size, and when
the spectroscope was turned upon it, its spectrum was discontinuous,
showing the bright lines of hydrogen gas.
The brightness of the spectrum was so marked that JANSSEN de-
termined to keep his spectroscope fixed upon it even after the reap-
pearance of sunlight, to see how long it could be followed. It was
found that its spectrum could be seen perfectly well after the return
of complete sunlight ; and that the prominences could be observed at
any time by taking suitable precautions.
One great difficulty was conquered in an instant. The red flames
which formerly were only to be seen for a few moments during total
eclipses, and whose observation demanded long and expensive
journeys to distant parts of the world, could now be regularly
ob-erved with all the facilities offered by a fixed observatory.
This great step in advance was independently made by Sir NOR-
MAN LOCKYER, and his discovery was derived from pure theory, un-
aided by observations of the eclipse itself. The prominences are
now 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 From this the prominences are
projected sometimes to heights of 100,000 miles or more.
Spectrum of the Corona. The spectrum of the corona was first ob-
served by two American astronomers Professors YOUNG and HARK-
NESS at the total solar eclipse of 1869. Since that time it has been
regularly observed at every total eclipse and often photographed.
Expeditions are sent to observe all total eclipses, no matter in what
parts of the Earth they occur, as up to the present time there is no
other way of investigating the corona and its spectrum.
292 ASTRONOMY.
The spectrum of the corona consists of several bright lines super-
posed on a faint continuous band. The continuous spectrum is
probably due to sunlight reflected from the particles (like fog or dust
particles) present in the corona. The bright lines prove that the
corona is chiefly made up of self-luminous gases and vapors.
FIG. 170. FORMS OF THE SOLAR PROMINENCES AS SEEN WITH
THE SPECTROSCOPE.
The corona is a mass of inconceivably rarefied matter
enveloping the San and extending far out into space. It
is excessively rarefied, as is proved by the fact that comets
moving round the Sun close to it (and thus passing through
the corona) are not appreciably retarded -in their motions.
The gas of which it is chiefly made up has, so far, not been
discovered on the Earth.
The Sun's Light and Heat. The light of the Sun
received at the Earth can be compared with our gas-jets or
electric lights. Our ordinary gas-burners or electric lights
have from ten to twenty " candle-power." The quantity
of sunlight is 1,575,000,000,000,000,000,000,000,000 times
as great as the light of a standard candle. The Sun sends
THE SUN. 293
us 618,000 times as much light as the full Moon, and
about 7,000,000,000 times as much light as the brightest
star Sirius.
Amount of Heat Emitted by the Sun. Owing to the
absorption of the solar atmosphere, we receive only a por-
tion 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, since the blue
end of the spectrum is absorbed proportionally more than
the red end.
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, as it may have been,
less heat would have reached the Earth. Glacial epochs
may, perhaps, be explained in this way. If the Sun has
had different emissive powers at different times, as it may
have had, this again would have produced variations in the
temperature of the Earth in past times.
Amount of Heat Eadiated. 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 the amount of heat
actually received by the Earth.
Experiments upon this question lead to the conclusion that if our
own atmosphere were removed, the solar rays would have energy
enough to melt a layer of ice 170 feet thick over the whole Earth
each 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 at the
Sun would require that a layer of coal nearly 20 feet thick spread
all over the Sun's surface should be consumed every hour. If the
Sun were of solid coal and produced its own heat by combustion alone
it would burn out in 5000 yeais.
294 ASTRONOMY.
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
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.
We have expressed the energy of the Sun's heat in terms of the ice
it would melt daily on the Earth. 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 if it were used to drive a steam-
engine for instance, we shall find that the Sun sends to the Earth an
amount of heat which is equivalent to one horse-power continuously
acting day and night for every 25 square feet of the Earth's surface.
Most of this heat is expended in maintaining the Earth's tempera-
ture ; but a small portion, about y^, is stored away by animals and
vegetables.
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 that govern the absorption within
the solar envelope are almost unknown. Some law of absorption has
to be assumed in any such investigation, and the estimates have dif-
fered widely according to the adopted law.
Professor YOUNG states this temperature at about 18,000 Fahr.
According to all sound philosophy, the temperature of the Sun must
far exceed any terrestrial temperature. There can be no doubt that if
the temperature of the Earth's surface were suddenly raised to that
of the Sun, no single chemical element would remain in its present
condition. The most refractory materials would be at once volatilized.
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. No heat is created by the lens.
If a lens three feet in diameter be used, the most refractory mate-
rials, as fire-clay, platinum, the diamond, are at once melted or volatil-
ized. 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, al-
THE SUN. 295
lowing 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 240,000 miles to the Sun must be vaporized if com-
posed of materials similar to those in the Earth.
How is the Sun's Heat Maintained ? It is certain that
the Sun's heat is not kept np by combustion. If the Sun
were entirely composed of pure coal its combustion would
not serve to maintain the Sun's supply of heat for more
than 5000 years. We know that the Earth has been in-
habited by people of high civilization (in Egypt for example)
for a much longer time than this. Moreover the Sun
cannot be a huge mass once very hot and now cooling
because there has certainly been no great diminution of
terrestrial temperatures in the past 3000 years, as is shown
by what is known of the history of the vine, the fig, etc.
A body freely cooling in space would lose its heat
rapidly.
There are two explanations that deserve mention. The first is
that the Sun's heat is maintained by the constant falling of meteors
on its surface. It is well known 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 atmosphere of the Earth. In fart, if we had a certain
mass available with which to produce heat by burning, it can be
shown that, by burning it at the surface of the Sun, we should pro-
duce less heat than if we simply allowed it to fall into the Sun. 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 can fall upon
the Sun's surface is about 280 miles in a second of time, and the
velocity may be as great as 350 miles.
No doubt immense numbers of meteorites do fall into the Sun
daily and hourly, and to each one of them a certain considerable por-
tion 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 in the highest
degree improbable that a mass so large as this is added to the Sun in
this way per century, because the Earth itself and every other planet
296 ASTRONOMY.
would receive far more than its present share of meteorites, and
would become quite hot from this cause alone.
The meteoric theory deserves a mention, but it is probably not a
sufficient explanation.
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 San itself in the explanation. It is by suppos-
ing the heat, light, etc., to be generated by a constant and gradual
contraction of the dimensions of the solar sphere. As the globe cools
by radiation into space, it must shrink. As it shrinks, heat is pro-
duced and given out.
When a particle of the Sun moves towards the Sun's centre the
same amount of heat is produced if its motion is caused by a slow
shrinking as would be developed by its sudden fall through the same
distance.
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 di-
mensions 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 neces-
sary to suppose that its diameter is diminishing at the rate of about
250 feet per year, or 4 miles per century, in order that the supply of
heat radiated shall be constant. Such a change as 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 invention
of the telescope.
It may seem a paradoxical conclusion that the cooling of a body
may cause it to give out heat. This indeed is not true when we
suppose the body to be solid or liquid. It is, however, proved that
this law holds for gaseous masses but only so long as they are gas-
eous.
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. It can be shown that after about
5,000,000 years, if the Sun radiates heat as at present, and still re-
mains gaseous, his present volume will be reduced to one half. If
the volume is reduced to one half the density will be then two times
greater (since the mass will remain the same). (D = M ^ F, see
page 237.) It seems probable that somewhere about this time the
solidification will have begun, and it is roughly estimated, from this
THE SUN. 297
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 fol-
lowed 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 the process of contraction to
have regularly gone on at the same rate (a very uncertain supposi-
tion), 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 polar
system consisted of but one body, and that a gaseous or nebulous
one.
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 primitive 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 upon 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.
It has been shown that if the Sun has always been
radiating heat at its present rate, and if it had originally
filled all space, it has required some 18,000,000 years to
contract to its present volume. In other words, assuming
the present rate of radiation, and taking the most favor-
able 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 will affect the final number of years to be
assigned. While this number may be greatly in error, yet
the method of obtaining it seems 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
298 ASTRONOMY.
no especial moment even were the data at hand to obtain
them: the essential point is that, so far as we can see, the
San, 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 XVII.
THE PLANETS MERCURY, VENUS, MARS.
32. Mercury Venus Mars. Mercury is the nearest
planet to the Sun. Its mean distance is 36,000,000 miles,
about yVV of tne Earth's distance. Its orbit is quite
eccentric, so that its maximum distance from the Sun is
43,500,000 miles, and its minimum only 28,500,000. At
its mean distance (0.39) it would receive about 6 T 7 times
as much light and heat from the Sun as the Earth, because
(l.OO) 2 : (0.39) 2 = 6.6 : 1.0.
Its sidereal year is 88 days. Its time of rotation on its axis
is not certainly known, but the observations of SCHIA-
PAEELLI and others make it likely that it revolves once on
its axis in the same time that it makes one revolution about
the Sun, just as our own Moon revolves once on its axis
during one of its revolutions about the Earth. The
apparent angular diameter of Mercury can be measured
with the micrometer (see page 144). Knowing the angle
that the diameter of the planet subtends and knowing the
planet's distance (in miles) the diameter of the planet in
miles can be calculated. The diameter of Mercury is about
3000 miles. Its surface is % of the Earth's surface and its
volume about -fa. The mass of the planet is determined by
calculating how much matter it must contain to affect the
motions of comets as it is observed to do. In this way it
results that its mass is about ^ of the Earth's mass. Its
density is about T \ of the Earth's density.
299
300 ASTRONOMY.
Venus' 1 mean distance is 67,200,000 miles. Its sidereal
year is 225 days. It is not yet certain that its period of
rotation may not be about 24 hours one day, bat the
observations of SCHIAPARELLI and others make it likely
that its rotation on its axis is performed in 225 days also.
If this be so Mercury and Venus will always turn the same
face to the Sun, just as our Moon always turns the same
face to the Earth. The diameter of Venus is 7700 miles,
only a little less than the diameter of the Earth (7918) and
it has therefore about the same volume. The mass of
Venus is determined by calculating how much matter the
planet must contain in order to affect the motion of the
Earth as it is observed to do. Its mass is about T 8 ^ of the
Earth's mass and its density about T 9 ^ that of the Earth.
Very little is certainly known about the geography of
Mercury and of Venus. Mercury is never seen far distant
from the Sun and observations of the planet in the daytime
are unsatisfactory because the heated atmosphere of the
Earth is usually in constant motion and produces an effect
on telescopic images like the twinkling of stars to the naked
eye. Venus shows only faint markings on her surface.
It is likely that Mercury has little or no atmosphere ; and
it is certain that Venus has an atmosphere of some kind
which is, in all probability, extensive. If the surface of
Venus which we see with the telescope is nothing but the
outer rim of its envelope of clouds we know nothing of the
real surface of the planet. Nothing whatever is known as
to whether either of these planets is inhabited; and very
little as to whether either of them is habitable.
Apparent Diameters of Mercury and Venus. In Fig. 171 S is the
Sun, E the Earth in its orbit and LIMC the orbit of an inferior
planet. If the Earth is at E and the planet at /, the planet is at
inferior conjunction (nearest the Earth) ; if at C, at superior conjunc-
tion ; if at L or M t at elongation. The Sun will be seen from E along
the line EC. It is plain that the planet can never appear at a greater
angle from the Sun than SEM or 8EL. It is clear from the figure
THE PLANETS MERCURY AND VENU8.
301
that the apparent angular diameter of the inferior planet will vary
greatly. It will be greatest when the planet is nearest the Earth
(inferior conjunction) and least when the planet is most distant.
FIG. 171 THE MOTION OP AN INFERIOR PLANET WITH REFER-
ENCE TO THE EARTH.
In representing the apparent angular magnitude of these planets,
in Figs. 172 and 178 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, those portions of the
disk are alone 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 by us constantly
diminishes as the planet approaches
the Earth, and that the planet's di-
ameter subtends a larger angle. F IG - 172. - APPARENT Di-
AMETER OF MERCURY J A ,
Phase, of Mercury and Venus.
When the planet is at its greatest C, AT LEAST DISTANCE.
distance, or in superior conjunction ((7, Fig. 171), its
whole illuminated hemisphere can be seen from the Earth.
As it moves around and approaches the Earth, the illumi-
nated hemisphere is gradually turned from us. At the
point of greatest elongation, M or Z, one half the hemi-
302
ASTRONOMY.
sphere is visible, and the planet has the form of the Moon
at first or second quarter. As it approaches inferior con-
junction, the apparent visible disk assumes the form of
a crescent, which becomes thinner and thinner as the
planet approaches the Sun. (See Fig. 174.)
FIG. 173. APPARENT DIAMETEU OF VENUS; A, AT GREATEST ;
B, AT MEAN ; G, AT LEAST DISTANCE.
The phases of an inferior planet were first observed by
GALILEO in 1610. They are not visible to the naked eye
and hence their discovery dates from the invention of the
cc
H
FIG. 174. PHASES PRESENTED BY AN INFERIOR PLANET AT DIF-
FERENT POINTS OF ITS ORBIT; K. NEAR INFERIOR A,
NEAR SUPERIOR CONJUNCTION.
telescope. If the student will turn to the plan of the
Ptolemaic system (Fig. 124) he will see that PTOLEMY
supposed both Mercury and Venus to revolve about the
THE PLANETS MERCURY, VENUS, MARS. 303
Earth and to be nearer to the Earth than the Sun. There
was no time, according to PTOLEMY'S system, when the
whole disk of Mercury or Venus could be seen illuminated.
But GALILEO'S telescope showed the disk as a full circle at
every superior conjunction. The inference that the
Ptolemaic system was not true was irresistible. The failure
of PTOLEMY'S theory cleared the way for the adoption of
the heliocentric theory of COPERNICUS.
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 as a dark circle the phenomenon is called a transit. If these
planets moved around the Sun exactly in the plane of the ecliptic, it
is evident that there would be a transit at every inferior conjunction,
but their orbits are inclined to the ecliptic by angles of 7 and 3 re-
spectively.
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. (See page 264.)
Transits of Mercury will occur in 1907, 1914 etc., and of Venus in
2004 and 2012.
Mars is the fourth planet in order going outwards from
the Sun. Its mean distance is 141,500,000 miles, about 1
times the Earth's distance. Its orbit is quite eccentric so
that its distance from the Sun at diiferent times may be as
large as 153,000,000 or as small as 128,000,000 miles. Its
distances from the Earth at opposition will vary in the same
way. When its distance from the Sun is the largest the
distance from the Earth will be about 60,000,000 miles
(= 153,000,000 93,000,000). When its distance from
304: ASTRONOMY.
the Sun is the smallest the distance from the Earth will be
about 35,000,000 miles (= 128,000,000 93,000,000).
When Mars is in conjunction with the Sun its average
distance is about 234,000,000 miles (= 141,000,000 +
93,000,000). Its greatest distance at conjunction is about
246,000,000 miles.
The apparent angular diameter of the planet varies directly as the
distance and is sometimes as small as 3". 6, sometimes seven times
larger (246 -r- 35 = 7). The amount of light received by Mars from
the Sun varies as -^ (where R = Mars' radius vector), so that the
amount of light received by the Earth from Mars varies as
(where r is the distance of Mars from the Earth). The amount of
light icceived by us from the planet varies enormously at different
times, therefore.
The periodic time of Mars is 687 days. Its diameter is
4200 miles a little more than half that of the Earth. Its
surface is about J and its volume is ^ of the Earth's. Its
mass is determined (by calculating the effect of the planet
on the orbits of its satellites) to be about J of the Earth's
mass. Its density is accurately -ffc of the Earth's density,
and the force of gravity at its surface is about T 4 of the
Earth's. A body weighing 100 pounds on the Earth would
weigh a little less than 40 pounds on Mars.
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.
Mars has little or no Atmosphere. The Moon reflects ^ of the
light falling upon it about as much as sandstone rocks. Mercury
reflects I 1 $j. These bodies have little or no atmosphere. Venus re-
THE PLANET MAES. 305
fleets (from the outer surface of its envelope of clouds) ^ of tlie in-
cident light. Jupiter ( T 6 ^), Saturn (&), Uranus ( T n %), Neptune
( T ^), are all bodies surrounded by extensive atmospheres and all of
them have high reflecting powers. The corresponding number for
Mars (y 2 ^) is so small as to indicate that this planet has little atmos-
phere, if any.
The planet's surface has been under careful scrutiny for
many years and observers are all but unanimous in their
report that no clouds are visible over the surface.
The centres of the disks of bodies with extensive atmos-
pheres (the Sun, Jupiter, Saturn, etc.) are always brighter
than the edges (see page 283). The centre of the Moon,
which has no atmosphere, is not so bright as the edge.
Mars is like the Moon in this respect and not like Jupiter.
Finally the only satisfactory spectroscopic observations of
the planet (made independently at the Lick Observatory
by CAMPBELL and at the Allegheny Observatory by
KEELER) show no evidence whatever of an atmosphere to
Mars and no sign of water-vapor about the planet. If
there is any atmosphere at all it can hardly be more dense
than the Earth's atmosphere at the high summits of the
Himalaya mountains not enough to support human life
therefore. As there is no evidence of the presence of
water- vapor and of clouds, etc., it follows that there is
little or no water on the planet's surface. The spectrum
of Mars and the spectrum of the Moon are identical in
every respect. This could not be true if Mars had any
considerable atmosphere.
It is proper to say that a number of astronomers hold different
views and that popular writers on astronomy, with few exceptions,
proclaim the existence of water, air, vegetation and intelligent human
beings on the planet. It is an announcement that finds thousands of
interested listeners who are only too glad to welcome so momentous
a conclusion. The popular writings referred to have little weight in
themselves, but they have undoubtedly spread a general belief among
intelligent people that Mars is a planet much like the Earth (which
it certainly is not), fit for human habitation, and very likely inhabited
306 ASTRONOMY.
by beings like ourselves. The questions involved are inexpressibly
important in themselves and they relate to matters in which every
human being is interested. The duty of Science is to investigate them
by every possible means (and this has been and will be done), but
Science can only be discredited by premature and incorrect announce-
ments made without a proper sense of responsibility.
FIG. 175. TELESCOPIC VIEW OF THE SURFACE OF MARS SHOW-
ING A SMALL "POLAR CAP."
The important and long -continued observations of SCHIAPARELLI
on Mars led him to announce that the planet was provided with an
elaborate system of water-courses ("oceans, seas, lakes, canals, etc."),
and the authority of this distinguished observer is the chief support
of those who maintain that this planet is fit for human habitation,
etc. Complete explanations of all the phenomena presented by the
THE PLANET MARS.
307
planet cannot be given in the light of our present knowledge.
This is not to be wondered at in spite of the industry and ability
of the observers who have spent years in studying the planet. The
case is much the same for the planets Mercury, Venus, Jupiter, Saturn,
Uranus, Neptune. We know very little of the real conditions that
prevail on their surfaces. We know comparatively little of the in-
terior of the Earth on which we live and next to nothing about the
interior of other planets. There is every reason to believe that
FIG. 176. DRAWING OF MARS MADE AT THE LICK OBSERVATORY
MAY 21, 1890.
complete explanations will be forthcoming in time. It is, at any rate,
certain that the conclusions of SCHIAPARELLI, named above, cannot
be accepted without serious modification, as will be shown in this
Chapter.
Appearance of the Disk of Mars in the Telescope. The
appearance of Mars in large telescopes is shown in Figs.
175 and 176. The main body of the planet is reddish
(shown white in the cuts). The portions shown dark in
308 ASTRONOMY.
the pictures are bluish, greenish, or grayish in the tele-
scope. The " cap " in Fig. 175 is a brilliant white. Most
of the markings on Mars are permanent. They are seen
in the same places year after year. Observations on these
permanent markings prove that the planet revolves on its
axis once in 24 h 37 m 22 s . 7. Its equator is inclined to the
ecliptic about 26.
When Sir WILLIAM HERSCHEL was examining Mars in
the XVIII century he called the red areas of Mars " land "
and the greenish and bluish areas " water." It was a
general opinion in his day that all the planets were created
to be useful to man. Astronomers of the XVIII century
set out with this belief very much as the philosophers of
PTOLEMY'S time set out with the fundamental theorem that
the Earth was the centre of the motions of the planets.
For example, HERSCHEL maintained that the Sun was cool
and habitable underneath its envelope of fire. He says
(1795) " The Sun appears to be nothing else than a very
eminent, large and lucid planet . . . most probably also
inhabited by beings whose organs are adapted to the
peculiar circumstances of that vast globe." It is certain
that the Sun is not inhabited by any beings with organs.
This conclusion is now as obvious as that no beings
inhabit the carbons of an electric street-lamp. HERSCHEL'S
guess that the red areas on Mars were "land " and the
blue areas " water " had no more foundation than his guess
that the Sun might be inhabited.
The next careful studies of Mars were made by MAEDLER
about 1840. He also called the red areas of the disk
" land " and the dark areas " water." In this he followed
HERSCHEL. There was no reason why he should not have
called the red areas " water " and the dark areas " land."
He had no evidence on the point. The same is true of
later observers down to the first observations of SCHIA-
PARELH about 1877,
THE PLANET MARS. 309
SCHIAPAKELLI gave reasons for these names, though his
reasons are not convincing. He pointed out that the
narrow dark streaks ("canals") generally ended in large-
dark areas (" oceans ") or in smaller dark areas (" lakes ").
The narrow dark streaks (very seldom less than 60 miles
wide) are quite straight. They cannot be " rivers" then.
If they are water at all the name " canal " is not inappro-
priate though 60 or 100 miles is a very wide canal. If they
are water, then the large dark areas must be " seas." The
narrow dark streaks are not water, however, because it was
discovered by Dr. SCHAEBERLE at the Lick Observatory
that the so-called "seas" sometimes had so-called
"canals" crossing them. A "sea" traversed by a
" canal " is an absurdity. If it could be imagined it
would prove the " inhabitants " and the " engineers " of
Mars to be the exact reverse of " intelligent." It is main-
tained by some recent observers of Mars that some of the
dark areas are water and some are not so. The bluish-
green color of the dark spots is said to " suggest vege-
tation." But who can know what colors the vegetation
on Mars may have ?
The foregoing very brief abstract proves that the dark
areas on Mars are not " water." The red areas are not
known to be "land." The spectroscopic and other evi-
dence proves that Mars has little or no atmosphere little
or no water-vapor no clouds. It is not yet known what
the real nature of the red areas and of the dark areas is.
It is one of the many unsolved problems of Astronomy to
discover the answer to this fundamental question. There is
no doubt the red areas and the large dark areas have a real
existence, since some of the markings on Mars have been
seen for more than two centuries.
It is not certain that all the "canals " that have been mapped really
exist. Some of them are probably mere optical illusions. If they
were real streaks on the planet's surface (like wide fissures, broad
310 ASTRONOMY.
watercourses, etc.) they would always appear broadest when they
were at the centre of the disk and would always be narrower when
they were at the edges. The laws of perspective demand this. It is
found by observation that the reverse is frequently true.
SCHIAPARELLI was the first to observe that many of the " canals"
oftentimes appear to be doubled. That is, a canal running in a certain
direction which generally appeared single, thus,
at certain times was no longer single but attended by a companion,
thus:
Marvels of ingenious speculation have been printed to explain why
"intelligent inhabitants" having one "canal" not sufficient for
"commerce," did not widen it, but preferred to dig another parallel
to it, and why this second "canal " sometimes vanished altogether in
" a few hours." Recent experiments have proved that these com-
panion canals are optical illusions produced by fatigue of the eye and
by bad focusing. Some, at least, of the single narrow dark streaks
("canals") have a real existence. It is probable that many of those
laid down and named on the maps of SCHIAPARELLI, LOWELL and
others are mere illusions. It is likely that all the double canals
were so.
Temperature of Mars. The distance of Mars from the
Sun is 1 times the Earth's distance. The heat received
by the Earth from the Sun is to the heat received by Mars
as (1.5)' J = 2.25 to 1. Mars receives less than one half as
much San heat as the Earth. If the Earth had no more
atmosphere than the Moon the Earth's temperature would
be like that of the Moon. If the Earth had no denser
atmosphere than that on the summits of the Himalayas the
temperature of the Earth would always be below zero.
Human life could not exist here. The case is the same
with Mars. The temperature of the whole surface of the
planet must be extremely low even in its equatorial regions.
The temperature at the poles of Mars must be several
hundred degrees (Fahrenheit) below zero when the pole is
THE PLANET MAES. 31 1
turned away from the Sun and below zero even when the
pole is turned towards the Sun.
Before going further it is worth while to consider the
circumstances under which Mars is seen by an observer on
the Earth. The mean distance of the Moon from the
Earth is 240,000 miles. If it is viewed through a field-
glass magnifying 4 times, it is virtually brought within
60,000 miles of the observer (240,000 -*- 4 = 60,000).
The nearest approach of Mars to the Earth is 35,000,000
miles. The planet can very seldom be viewed to advantage
with a magnifying power so high as 500. If such a power
is employed when Mars is nearest, the planet is virtually
brought within 70,000 miles (35,000,000 -4- 500 = 70,000).
It follows therefore that we never see Mars so advan-
tageously even with the largest telescopes as we may see the
Moon in a common field-glass. If the student will ex-
amine the Moon with a field-glass magnifying 4 times he
will have a realizing sense of the lest conditions under
which it is possible to see Mars, and he will be surprised
that so much is known of the planet. The industry and
fidelity of observers can only be appreciated after such
an experiment.
The Polar Caps of Mars, We have now to present
another result of observation which must be interpreted in
the light of the foregoing facts namely, that Mars has
little or no water- vapor and that its temperature is appal-
lingly low. The main facts of observation are as follows.
CASSINI, the royal astronomer of France, discovered in
16(56 that Mars sometimes had dazzling white circular
patches near his poles (see Fig. 175). In 1783 Sir
WILLIAM HERSCHEL observed these patches to wax and
wane and he called them " snow " caps, thus begging the
question as to their real nature. HERSCHEL'S observa-
tions and those of all later observers show that these caps
wax and wane with the Martian seasons. In the Martian
ASTRONOMY.
polar summer they are smallest, or they even vanish. In
the Martian polar winter they are largest. As HERSCHEL
started out with the conviction that all planets were
analogous to the Earth and were meant to be inhabited,
his conclusion was that the polar winter condensed water-
vapor into snow and that the polar summer melted this
snow and so on. A more scientific conclusion would
have been that some vapor was condensed and subsequently
dissipated by the solar heat. It is practically certain that
the phenomena of the waxing and waning of the caps
depend on solar heat.
If the caps are " snow " condensed from water- vapor the
layer of snow must be exceedingly thin, because when these
caps are " melted " no clouds appear. When snow melts
on the Earth clouds are formed and our atmosphere is
charged with the vapor of water. No clouds are seen on
Mars and no water- vapor is to be found above its surface
by any spectroscopic test.
The polar-caps may be formed by the vapor of some
other substance than water. It is worth while to inquire
whether they may not be carbon-dioxyd in a solid state.
This substance is a heavy gas (carbonic-acid gas) at ordi-
nary temperatures. It would lie at the bottom of valleys
and fill canons or ravines. At a temperature of about one
hundred Fahrenheit below zero it is a colorless liquid. At
temperatures such as must obtain at the pole of Mars
turned away from the Sun it becomes a snow-like solid.
Caps of carbon-dioxyd would wax and wane at the poles of
Mars under variations of solar heat such as obtain at these
poles, very much as caps af snow and ice wax and wane in
our Arctic regions which, under all circumstances, are at a
far higher temperature than the poles of Mars.
There is so far no observational proof that the polar-
caps of Mars are formed of carbon-dioxyd. There is
THE PLANET MARS. 313
convincing proof that they are not formed of water. The
question as to the nature of the polar-caps is still an open
one. There is little doubt that it will, one day, be settled.
The scientific attitude of mind is to wait for proofs of
matters still unsolved; to accept such proofs as exist; and
to eschew unfounded speculations. All that is now known
goes to show that Mars has little or no atmosphere, little
or no water- vapor, no " oceans," no " lakes, "no " canals,"
no clouds. Its general surface is rather flat, although
a few mountain chains exist. It is not a planet like
the Earth. It is much more like the Moon. It cannot
possibly be " inhabited by beings like ourselves."
Satellites of Mars. Until the year 1877 Marsw&s supposed to have
no satellites. 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 wo - Jd 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 instru-
ments in detecting faint points of light like stars or satellites.
The outer satellite, called Deimos, revolves around the planet in
30 h 18 , and the inner one, called Phobos, in 7 h 39 m . The latter is
only 5800 miles from the centre of Mars, and less than 4000 miles
from its surface. It would therefore be almost possible to see an
object the size of a large animal on the satellite if one of our tele-
scopes could be used at the surface of Mars.
The short distance and rapid revolution make the inner satellite of
Mars one of the most interesting bodies with which we are acquainted.
It performs a revolution in its orbit from west to east in less than
half the time that Mars revolves on its axis. In consequence, to the
inhabitant* of Mars it would seem to rise in the west and set in the east.
314
ASTRONOMY.
Let the student prove this statement for himself by drawing a
figure somewhat like Fig. 31. Suppose N to be Mars, a the spec-
tator, ZH the celestial equator, Z to be Phobos on the meridian. In
FIG. 31 Us.
l h the spectator will have moved to ; and Phobos to ; in 2 h ,
etc. etc.
The light of Phobos is about -fa of the light of our Moon ; of
Deimos about
CHAPTER XVIII.
THE MOON THE MINOR PLANETS.
33, The Moon. The Moon the satellite of the Earth
revolves about its primary in a periodic-time of 27 d <32116
at a mean distance of 238,840 miles. Its daily motion
360
among the stars is -^r^^rr^ ~ about 13 11'. The apparent
angular diameter of the Moon is about half a degree, so
that the Moon moves daily among the stars about 26 of its
own diameters. The interval from new moon to new moon
is about 29 days and the Moon comes to the meridian of
an observer about 51 minutes later each day (on the
average). The orbit of the Moon is inclined to the plane
of the ecliptic by a little more than 5.
The velocity of the Moon in her orbit is about 3350 feet
per second. Her diameter is 2163 miles, her surface T ^g-
of the Earth's, her volume ^, and her mass -fa of the
Earth's. The density of the Moon is about 3.4 times the
density of water. The heaviest lavas of the Earth's crust
are about 3.3 in density, so that the conclusion that the
Earth and Moon once formed one body is not contradicted
by these facts. Gravity on the Moon's surface is J as great
as at the Earth's. Hence an explosion of subterranean
steam would form a much more extensive crater on the
Moon than on the Earth, and mountains would stand at a
much steeper average angle on the Moon. As there is no
air and no water on the Moon's surface there is no frost
constantly working to overthrow cliffs and sharp peaks as
315
316
ASTRONOMY.
FIG. 177. LUNAR LANDSCAPE (Mare Grisium) FROM PHOTOGRAPHS
TAKEN AT THE LICK OBSERVATORY.
THE MOON. 317
in the case of the Earth. The albedo of the Moon is
about that of weathered sandstone rocks.* The angle of
slope of the lunar volcanoes is about the same as the angle
of terrestrial lavas. These and many other facts support
the conclusion that the Earth and Moon are made of like
materials.
The Moon has extremely little if any atmosphere
because the occultation of a star by the lunar disk takes
place instantaneously. If the Moon had an atmosphere,
the star's rays would be refracted by it and there would be
a change of the star's color and a gradual disappearance.
The spectrum of the Moon is nothing but a fainter solar
spectrum. This proves that moonlight is reflected sunlight;
and that the Moon has no absorbing atmosphere of its own.
No doubt the Moon, in remote past times had an atmos-
phere. Its constituents have probably been absorbed by
the rocks of the lunar crust as they cooled. The water on
the Moon has probably been absorbed in the same way.
The quantity of light received by the Earth from the
full Moon is Tf-rsViro' f the light received from the Sun.
The temperature of the Moon's surface is probably always
below freezing-point, even in the full sunshine of a long
lunar "day." If the Earth's atmosphere were to be
removed the temperature of our summers would be ex-
tremely low much lower than it now is at the summits of
our highest mountains. The lunar " night " is 14 terres-
trial days long. The temperature of a part of the Moon
after being deprived of the Sun's light (and heat) for 14
days must be extremely low several hundred degrees
Fahr. below zero.f
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
* The albedo of any substance is its power of reflecting rays of
light that fall upon it. If it reflects all such rays its albedo is 100.
f These are the conditions that prevail on airless bodies like the
Moon and Mars,
318 ASTRONOMY.
same as that required for one revolution in her orbit, viz., 27 days.
If a line be drawn from the Earth to the Moon at any time whatever
this line will always touch the same hemisphere of the Moon : and the
Moon does not rotate at all with reference to this line. If a line be
drawn through the Sun parallel to the Moon's axis, the Moon some-
times turns one face and sometimes another to this line. An observer
on the Earth sees but one hemisphere of the moon. An observer
on the Sun would successively see all regions of the Moon (see Fig.
133).
When it became clearly understood after the invention of
the telescope that the ancient notion of an impassable gulf
between the character of " bodies celestial and bodies terres-
trial " was unfounded, the question whether the Moon was
like the Earth became one of great importance. The point
of most especial interest was whether the Moon could, like
the Earth, be peopled by intelligent inhabitants. Accord-
ingly, 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
very well known. Photographic maps of the Moon show
the details of its surface in an admirable way.
With every improvement in the means of research, it has
become more and more evident that circumstances at the
surface of the Moon are totally unlike those on the Earth.
There are no oceans, seas, rivers, air, clouds, or vapors.
We can hardly suppose that animal or vegetable life exists
under such circumstances. 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, as seen from the Earth,
subtend an angle of about 1" of arc. In order that an object may be
plainly visible to the naked eye, it must subtend an angle of nearly
60." 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.
The following table shows the diameters of the smallest objects
I. FIRST QUADRANT.
1. Pallas
2. Gambart
3. Stadius
4. Copernicus
5. Reinhold
6. Kepler
7. Hevelius
8. Eratosthenes
9. Marius
10. Archimedes
11. Timocharis
12. Euler
13. Aristarchus
14. Herodotus
15. Laplace
16. Hei-aclides
17. Bianchini
18. Sharp
l.. Mairan
20. Plato
21. Condamine
22. Harpalus
LIST OF LUNAR CRATERS, E
N. B. The Quadrants are marked I, II, III, IV on the borders of the Map.
N. B. From new moon (O da y s )
to full moon (15") the west limb of
the moon is fully lighted. The
position of the terminator for
each intermediate day Is marked
by the upper set of numbers
along the moon's equator : 2, 3,
4 . . 15 From full moon to the
following new moon the east
SOUT
II. SECOND QUADRANT.
51. Moretus
52. Cysatus
53. Blancanus
54. Scheirier
55. Clavius
56. Maginus
57. Longomontanus
58. Schiller
59. Phocylides
60. Wargentin
61. Saussure
62. Pictet
63. Tycho
61. Heinsius
65. Hainzel
66. Schickard
67. Hell
68. Gauricus
69. Wurzelbauer
70. Pitatus
71. Hesiodus
72. Clchus
73. Capuanus
74. Ramsden
75. Vitello
76. Regiomontanus
77. Purbach
78. Thebit
79. Mercator
80. Campanus
81. Bullialdus
82. Doppelmayer
83. Fourier
84. Vieta
85. Mersenius
86. Arzachel
87. Alphonsus
88. Alpetragius
89. Davy
90. Guericke
91. Lubiniezky
92. Gassendi
93. Billy
94. Hansteen
95. Sirsalis
96. Ptolemseus
97. Herschel
98. Moesting
99. Lalande
100. Damoiseau
* The names are those
of scientific men, usually
of astronomers.
NOR
FIG. 178. THE MOON AS
SHOWN IN FIG. 178.*
see the numbers plainly, a common hand-glass should be used.
III. THIRD QUADRANT.
101. Manzinus
limb is fully lighted, and the
position of the terminator for m% jiutus
each intermediate day is marked 103> Boussingault
by the lower set of numbers ; jo4 Boguslawsky
17, 18 ... 28, 30. These numbers iQ5. Curtius
give the moon's age, in days, jog Zach
when the terminator passes 107. Jacob!
through their positions on the jog Lilius
map. 109. Baco
v 110. Pitiscus
111. Hommel
IV-Y\ 112. Fabricius
n 113. Metius
N %A \ 114. Rheita
\ 115. Nicolai
\ 116. Barocius
' C" >; -\ 117. Maurolycus
\ 118. Clairaut
, \ 119. Cuvier
120. Stoeffler
121. Funerius
a ' A ' 122. Riccius
\ 123. Zagut
\ 124. Lindenau
\ 125. Aliacenus
^ \ 126. Werner
127. Apianus
"V * , 128. Sacrobosco
129. Santbach
^ \ 130. Fracastor
! fc>- ; '-; 131. Petavius
; 132. Vendelinus
\ 133. Langrenus
M. 134. Goclenius
\ 135. Guttenberg
w . \ 136. Theophilus
1S7. Cyrillus
138. Catherina
139. Albategnius
140. Parrot
141. Hipparchus
142. Reaumur
143. Delambre
IV. FOURTH QUADRANT.
151. Taruntius
152. Sabine
153. Ritter
154. Arago
155. Ariadeeufc
156. Godin
157. Agrippa
158. Hyginus
159. Triesnecker
160. Condorcet
161. Azout
162. Picard
163. Vitruvius
164. Plinius
165. Acherusia
166. Menelaus
167. Manilius
168. Einmart
169. Cleomedes
170. Macrobius
171. Roemer
172. Le Monnier
173. Linnaeus
74. Bessel
75. Gauss
76. Messala
77. Geminus
78. Posidonius
179. Calippus
180. Aristillus
181. Autolycus
182. Cassini
183. Atlas
184. Hercules
185. Franklin
186. Burg
187. Eudoxus
188. Aristotle
189. Endymion
THE MOON. 319
that can be seen with different magnifying powers, at the Moon's
distance.
Power 60 ; diameter of object 1 mile.
Power 150 ; diameter 2000 feet.
Power 500 ; diameter 600 feet.
Power 1000 ; diameter 300 feet.
If telescopic power could be increased indefinitely, there would be
no limit to the minuteness of an object that could be seen on the
Moon's surface. But the imperfections of all telescopes are such that
only in exceptional cases can anything be gained by increasing the mag-
nifying power beyond 1000. The influence of warm and cold currents
in our atmosphere will forever prevent the advantageous use of very
high magnifying powers.
Character of the Moon's Surface. The most striking point of dif-
ference between the Earth and Moon is seen in the total absence
from the latter of anything that looks like the water-worn surfaces
of terrestrial plains, prairies, and hills. Valleys and mountain-
chains exist on the Moon, but they are abrupt and rugged, not in the
least like our formations of the same name. 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 surface has different shades of color in
different regions. Some portions are of a bright silvery tint, while
others have a dark gray appearance. These differences of tint seem
to arise chiefly from differences of material.
Upon this surface as a foundation are built numerous formations
of various sizes, usually of a very simple character. Their general
form can be made out by the aid of Fig. 179, and their dimensions by
remembering that one. inch on the figure is about 30 miles. The
largest and most prominent features are known as craters. They
have a typical form consisting of a round or oval rugged wall rising
from the plain in the manner of a circular fortification. These
walls are frequently 10,000 feet or more in height, very rough and
broken. In their interior we see the plane surface of the Moon
already described. It is, however, generally strewn with fragments
or broken up by chasms.
In the centre of the craters we frequently find a conical formation
rising up to a considerable height. The craters resemble the vol-
canic formations upon the Earth, the principal difference being that
some of them are very much larger than anything known here.
The diameter of the larger ones ranges from 50 to 100 miles, while
the smallest are a half-mile or less, in diameter mere crater-pits.
320 ASTRONOMY.
Heights of the Lunar Mountains. When the Moon is only a few
days old, the Sun's rays strike very obliquely upon the lunar moun-
tains, and they cast long shadows. From the known position of
the Sun, Moon, and Earth, and from the measured length of the
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.
Is there any Change on the Surface of the Moon ? When the sur-
face of the Moon was first found to be covered by craters like the
volcanoes of the Earth, it was very naturally thought that the lunar
volcanoes might be still in activity, and exhibit themselves to our
telescopes by their flames. Not the slightest evidence of any erup-
tion at the Moon's surface has been found.
Several instances of supposed changes of shape of features on the
Moon's surface have been described in recent times, however.
Photographs of the Moon. To make a complete map of the Moon
requires a lifetime. The map of the Moon (six feet in diameter)
made by Dr. SCHMIDT, Director of the Observatory of Athens, occu-
pied the greater part of his time during the years 1845-1865.
A photograph of the full moon can now be taken in a fraction of a
second that shows most features far better than SCHMIDT'S map;
and a series of such photographs exhibits substantially every lunar
feature better than any map can do. The first photographs of the
Moon were made in America. The best lunar photographs are
those of the observatories of Mt Hamilton (Lick Observatory) and
of Paris.
Key-chart of the Moon. The accompanying chart of the Moon will
be found of use to the student who has a small telescope or even an
opera-glass at his command. After acquiring a general acquaintance
with the lunar topography by observations continued throughout a
lunation, he should begin to study the craters in detail, making
drawings of them as accurately as he can. Such drawings may not
be of value to science, but they will be invaluable to the student
himself; for they will train him to see what is to be seen, and to
register it accurately. The changes in the appearance of lunar
craters during a lunation are very marked, and to seek the explana-
tion of each particular change is a valuable discipline.
GALILEO supposed some of the plains of the Moon to be seas, and
named them Mare Tranquilitatis (the tranquil sea), etc. The prin-
cipal mountain-chains on the Moon are named Apennines, Alps, Cau-
THE MOON,
321
FIG. 179. A DRAWING OF THE LUNAR SURFACE.
322
ASTRONOMY.
casus, etc. The craters are usually named after noted astronomers,
Kepler, Copernicus, Tycho.
34. The Minor Planets. We have next to consider the
group of minor planets, also called asteroids (because they
resemble stars in appearance) or planetoids (because they
are planets). None of them was known nntil the begin-
ning of the nineteenth century.
First of all, a curious relation between the distances of the planets,
known as BODE'S law, must be mentioned. 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 law was announced) by BODE in 1772.
This is shown in the following table :
PLANETS.
Actual
Distance.
BODE'S Law.
3 9
A ft
7.2
7
Earth
10
10
Mars ..
15 2
16
27 7
28
52
52
95 4
100
191 8
196
300 4
388
Although the so-called law was purely arbitrary, the agreement
between the distances predicted by the law and the actual distances
was sufficiently close to draw attention to tlie fact that a jrap existed
in the succession of the planets between Mars and Jupiter.
It was therefore supposed by the astronomers of the
seventeenth and eighteenth centuries that a new major
planet might be found in the region between Mars and
THE MINOR PLANETS. 323
Jupiter. A search for this object was instituted, but before
it had made much progress a minor planet in the place of
the one so long expected was found by PIAZZI, of Palermo.
The discovery was made on the first day of the present
century, 1801, January 1. It was named Ceres.
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 orbit. Seeing four small planets where one large one
ought to be, OLBERS suggested that these bodies might be
fragments of a large planet that had been broken to pieces
by the action of some unknown force.
A generation of astronomers now passed away without
the discovery of more than these four. It was not until
1845 that a fifth planet of the group was found. In 1847
three more were discovered, and many discoveries have
since been made. The number is now nearly 500, and
the discovery of additional ones is 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. Seventy-seven of them have been discovered by
American astronomers.
The minor planets are distinguished from the major ones
by many characteristics. Among these we may mention
their small size; their positions, all but one being situated
between the orbits of Mars and Jupiter; the great eccen-
tricities and inclinations of their orbits. The inclination
of the orbit of Pallas to the ecliptic is 35, for example.
Number of Small Planets. It would be interesting to know how
many of these planets there are in the group, but it is as ret impos-
sible even to guess at the number. As already stated, about 500 are
now known, and new ones are found every year.
A minor planet presents no sensible disk, and therefore looks
exactly like a small star. It can be detected only by its motion among
the surrounding stars, which is so slow that some hours must elapse
before it can be noticed. Nowadays they are found by photograph-
324: ASTRONOMY.
ing a region of the sky with two or three hours' exposure and noticing
whether any of the objects on the plate show a motion in that time.
A fixed star will show no motion. An asteroid will make a trail on
the plate.
Magnitudes. It is impossible to make any precise measurement of
the diameters of the minor planets. The diameters in miles that are
sometimes quoted are subject to very large errors. The amount
of light which the planet reflects is a better guide than measures
made with ordinary micrometers. Supposing the proportion ol light
reflected to be the same as in the case of the larger planets, the diam-
eters of the three or four largest range between 300 and 600 kilo-
metres, while the smallest are from 20 to 50 kilometres in diameter.
The average diameter is perhaps less than 150 kilometres (say 90
miles) ; 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.
Mass and Density of the Asteroids. Nothing is known of the mass
of any single asteroid. If their density is the same as that of the
Earth the mass of the larger asteroids will be about ^o f tlie
Earth's mass. The force of gravity on the surface of such a body
would be about -fa of the force of gravity on the Earth. A bullet
shot from a rifle would fly quite away from the planet and would cir-
culate about the Sun. It is not probable that any of them has
an extensive atmosphere.
CHAPTER XIX.
THE PLANETS JUPITER, SATURN, URANUS, AND
NEPTUNE.
35. Jupiter. Jupiter is much the largest planet in the
system. His mean distance is 483,300,000 miles. His
mean diameter is 86,500 miles, the polar diameter being
83,000, the equatorial 88,200 miles. His linear diameter
is about y 1 ^, his surface is y^-, and his volume y^o tna ^ of
the Sun. His mass is T oVs- His density is nearly the
same as the Sun's density, that is 1 T 3 ^ times the density
of water. The densities of Venus, the Earth, the Moon,
and of Mars are all more than three times the density of
water. A cubic foot of the materials of each of these
bodies weighs at least 200 Ibs. A cubic foot of the stuff
out of which Jupiter is made weighs, on the average, no
more than 83 Ibs. Jupiter is, in this respect, like the Sun
and not like the inner planets.
He is attended by five satellites, four of which were dis-
covered by GALILEO on January 7, 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. They are large bodies, from 2100 to 3500 miles
in diameter, comparable in size to the Moon or to Mercury.
The fifth satellite was discovered by BARNAHD with the
great telescope of the Lick Observatory in 1892. It is a
very small object, about 100 miles in diameter, revolving
very close to the surface of Jupiter. Observations show
that the larger satellites revolve about Jupiter ', always turn-
325
326 ASTRONOMY.
ing the same face to the planet just as our own Moon tarns
always the same face to the Earth.
The rotation-time of the planet is not the same in all latitudes ;
nor, in the same latitude, at all depths below the outer surface of its
clouds. The average time of rotation is about 9 h 55 m , which is notice-
ably shorter than the rotation-times of Mars and the Earth. The
PIG. 180. DRAWING OF JUPITER MADE AT THE LICK OBSERVA-
TORY, AUGUST 28, 1890.
figure of the planet is markedly spheroidal ; its disk is easily seen to
be elliptical in shape. The pJiases of Jupiter are slight scarcely
noticeable. The reflecting- power (albedo} of the planet is -ffa, not
very much less than that of newly fallen snow ( T W). I n this respect
Jupiter and all the outer planets differ very materially from Mars
and all the inner planets (except Venus). The periodic-time of Jupiter
Tfffi PLANET JUPITER. 327
is 11.86 years, about the period in which the solar spots vary from
maximum to maximum again. Figure 180 shows in the upper third
of the disk an oval spot that has remained on the planet for the past
30 years (The Great Red Spot). Its surface is red and it probably lies
at a deeper level than many of the whitish clouds in the same lati-
tudes. It is remarkable that the red spot has endured for so long a
time on the surface of the planet where all other features are so
changeable. The red spot is not fixed in position, but is slowly drift-
ing to the east. It is as if Australia were slowly moving eastwardly
on the earth. The rotation time of the red spot was 9 h 55 m 34.5 in
1869 ; 34 s . 1 in 1879 : 39 s .O in 1884 ; 40-.4 in 1889 ; 4KO in 1894 ; 41'.9
in 1898. It is as if an island of slag were drifting on the surface of
a lake of liquid lava.
The temperature of Jupiter is, in all probability, very
high. The planet may even be incandescent. The rapid
changes observed in the surface of Jupiter prove that the
visible surface is gaseous an atmospheric envelope. These
changes are due to heat. As the solar heat at Jupiter is
only -jif of the solar heat at the Earth, it is likely that the
changes are due to the internal heat of the planet itself.
The solar heat at Saturn is only -fa of the solar heat at the
Earth, and as it is also surrounded by a gaseous envelope,
there is good reason for supposing Saturn, also, to be a hot
body.
The surface of Jupiter has been carefully studied with
the telescope, particularly within the past thirty years.
Although further from us than Mars, many of the details
on his disk are much more plainly marked. The most
characteristic features are shown in the drawings appended.
These features are,/r,tf, the dark bands of his equatorial
regions, and, secondly, the cloud-like forms spread over
nearly the whole surface. Near the edges of the disk all
these details become indistinct, and finally vanish, thus in-
dicating a highly absorptive atmosphere lik^ that of the Sun.
The light from the centre of the disk is twice as bright as
that from the poles. The bands can be seen with instru-
328 ASTRONOMY.
ments no more powerful than those used by GALILEO, yet
he makes no mention of them.
The general color of the bands is reddish. Their posi-
tion varies slightly in latitude, but in the main they remain
as permanent features of the region to which they belong.
FIG. 181 VIEW OP JUPITER AND HIS SATELLITES IN A SMALL
TELESCOPE.
HERSCHEL, in the year 1793, attributed the aspects of
the bands to zones of the planet's atmosphere more tranquil
and less filled with clouds than the remaining portions, so
as to permit the true surface of the planet to be seen
through these zones, while the clouds prevailing in the
other regions give a brighter tint to the latter. It is not
likely that we see the true surface of the planet, in the
belts, but rather the outer surfaces of the inner layers of
the planet's atmosphere.
The clouds themselves can easily be seen at times, and
they have every variety of shape. In general they are
similar in form to a series of white cumulus clouds such as
are frequently seen piled up near the horizon, and the
spaces between them have the deep salmon color of the
spaces between cumulus clouds before a summer storm.
This color is due to the absorption of the dense atmosphere
of the planet, probably. The bands themselves and the red
THE PLANET JUPITER. 329
spot seem frequently to be veiled over with something like
the thin cirrus clouds of our atmosphere.
Such clouds can be tolerably accurately observed, and
may be used to determine the rotation-time of the planet.
The observations show that the clouds often have a proper
motion of their own.
FIG. 182. VIEW OP JUPITER IN A LARGE TELESCOPE, WITH A
SATELLITE AND ITS SHADOW SEEN ON THE DISK.
Motions of the Satellites. The 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. 182) precisely as the shadow of our Moon is thrown upon
the Earth in a solar eclipse. If the satellite passes through Jupiter's
own shadow in its revolution, an eclipse of the satellite takes place.
If it passes between the Earth and Jupiter, it is projected upon Ju-
piter's disk, and we have a transit of the satellite (see Fig, 182); itJu-
330
ASTRONOMY.
piter is between the Earth and the satellite, an occultation of the
latter occurs. All these phenomena can be seen with a common
telescope, and the times are predicted in the Nautical Almanac.
These shadows are seen black upon Jupiter's surface by contrast,
because Jupiter is very much brighter than the satellites.
Fia 183 THE ECLIPSES OF JUPTTETC'S SATELLITES.
S is the Sun, T the Earth, J, J'. J", J'" are different positions of Jupiter.
Telescopic Appearance of the Satellites. Under ordinary circum-
stances, the satellites of Jupiter are seen to have disks ; under very
favorable conditions, markings have been seen on these disks.
The satellites completely disappear from telescopic view when they
enter the shadow of the planet. This shows that neither planet nor
satellite is self-luminous to any marked degree. If the satellite were
THE PLANET SATURN. 331
self-luminous, it would be seen by its own light ; and if the planet
were luminous, the satellite might be seen by the reflected light of
the planet.
The Progressive Motion of Light. The discovery that light requires
time to travel was first made by the observations of the satellites of
Jupiter, as has been said. (See page 255.) Jupiter casts a shadow
just as our Earth does, and its inner satellite passes through this
shadow and is eclipsed at every revolution.
The eclipses can be observed from the Earth, the satellite vanishing
from view as it enters the shadow, and reappearing when it leaves it.
The astronomers of the seventeenth century made tables by which
the times of the eclipses could be predicted. It was found by ROMER
that these times depended on the distance of Jupiter from the Earth.
When the Earth was nearest Jupiter, the eclipses were seen earlier
than the predicted time. Jupiter and the Earth were near each other.
When the Earth was farthest from Jupiter the eclipses were seen
later than the predicted time. Jupiter and the Earth were far apart.
The light from the satellite required time to cross the intervening
spaces. The velocity with which light travels is 186,330 miles per
second. At that rate it traverses the distance from the Sun to the
Earth in 499 seconds. The sunlight is 8 m 19 8 old when it reaches us.
Longitudes by Observation of the Satellites of Jupiter. Tbe differ-
ence of longitude of two places on the Earth is the difference of their
simultaneous local times. If we know beforehand (by calculation) the
Greenwich time of an eclipse of one of the satellites and if we observe
the eclipse by a clock keeping our own local time, the difference of
the two times (observed and calculated) is our longitude from Green-
wich. GALILEO suggested that a method like this might be useful
in determining terrestrial longitudes and the method has often been
tested. The difficulty of observing the eclipses with accuracy, and
the fact that the aperture of the telescope employed has an important
effect on the appearances seen, have so far kept this method from a
wide utility, which it at first seemed to promise.
36. Saturn and its System, 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
886,000,000 miles. The equatorial diameter of the ball of
the planet is about 75,000 miles and the polar diameter
about 68,000 miles. It revolves on its axis in 10 h 14 m 24%
or less than half a day, which accounts, as in the case of
332
ASTRONOMY.
FIG. 184. DRAWING OF SATURN MADE AT THE LICK OBSERVA-
TORY, JANUARY 7, 1888,
THE PLANET SATURN. 333
Jupiter, for the ellipticity of the disk. The mass of the
planet is only 95 times the mass of the Earth, though its
volume is 760 times greater. The force of gravity at its
surface is only a little greater than that of the Earth. It
is remarkable for its small density, which is less than that
of any other heavenly body, and even less than that of
water. No doubt the planet is in great part, if not en-
tirely, gaseous. The edges of the planet are fainter than
the centre, as in the case of Jupiter, and for the same
reason.
FIG. 185. VIEW OF THE SATURNIAN SYSTEM IN A SMALL TELE-
SCOPE.
Saturn is the centre of a system of its own, in appearance
quite unlike anything else in the heavens. Its most note-
worthy feature is a pair of rings which surround it at a
considerable distance from the planet itself. Outside of
these rings revolve no less than nine satellites. The
334 ASTRONONT.
planet, 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. 185. Fig.
184 was drawn with the great telescope of the Lick
Observatory.
The Kings of Saturn. The rings are the most remark-
able and characteristic feature of the Saturnian system.
Fig. 186 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 a direction at right
angles to the plane of the ring (which it never can be from
the Earth). The shadow of the ball of the planet on the
rings should be noticed in both views. The periodic-time
of the planet is a little less than 29| years.
The first telescopic observers of Saturn 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 attached
to the central one. " On each side of old Saturn were servitors who
aided him on his way." This discovery was announced to his friend
KEPLER in this logogriph :
"smaismrmilmepoetalevmibunenugttaviras," 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 had vanished and the central
body alone remained. GALILEO inquired "whether Saturn had
devoured his children, according to the legend."
It was not until 1655 (after seven years of observation) that the
celebrated HUYGHENS discovered the true explanation of the remark-
able and recurring series of phenomena present by the tri corporate
planet.
THE PLANET SATURN.
335
FIG. 186. THE PLANET SATURN.
1 as it sometimes appears to an observer on the Earth ; 2 as it would
appear to an observer over the polar region of the planet.
336 ASTRONOMY.
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, tenui, piano, nusquam coherente, ad eclipticam
inclinato" (it is girdled by a thin plane ring, nowhere touching,
inclined to the ecliptic).
This description is complete and accurate, as to the appearance in a
small telescope.
In 1675 it was found by CASSINI that what HUYOHENS had seen as
a single ring was really two. A division extended all the way around
near the outer edge. The division is shown in the figures. This
division is permanent. Others are sometimes seen at different places
and this fact of observation suggests that the rings cannot be per-
manent solids, nor liquids.
In 1850 the Messrs. BOND, of Harvard College Observatory, found
that there was a third ring, of a dusky and nebulous aspect, attached
to the inner edge of the inner ring. It is known as Bond's dusky ring.
It is a difficult object to see in a small telescope. It is not separated
from the bright ring, but attached to it. The latter shades off toward
its inner edge, and merges gradually into the dusky ring, Fig. 184.
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, perpendicu-
lar to the plane of the ring, as the axis of the latter, this axis will
always point in the same direction in space among the stars. In
this respect the motion is similar to that of the Earth around the Sun.
The ring of Saturn 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. 110.
The corresponding changes for Saturn are shown in Fig. 187. Dar-
ing each revolution of Saturn (29 years) the plane of the ring
passes through the Sun twice. This occurred in the years 1878 and
1891, at two opposite points of the orbit, as shown in the figure,
and will occur in 1907. 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 (shown in the picture) is little more than
one-tenth as far from the Sun as Saturn is, an observer 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 posi-
THE PLANET SATURN.
337
tion of Saturn in its orbit. The following are the times of some of the
phases :
1878 and 1907. The edge of the ring is turned toward the Sun. It
is seen only as a thin line of light.
1885. The planet having moved forward 90, the south side of
the rings is seen at an inclination of 27.
1891. The planet having moved 90 further, the edge of the ring
is again turned toward the Sun.
FIG. 187. DIFFERENT ASPECTS OF THE RING OF SATURN AS SEEN
FROM THE EARTH IN DIFFERENT YEARS.
1899. The north side of the ring is inclined loward the sun, and
is seen at its greatest inclination.
The rings are extremely thin in proportion to their extent. Conse-
quently, when their edges are turned toward the Earth, they appear
as a mere line of light, which can be seen only with powerful
telesc pes.
Constitution of the Rings of Saturn. The nature of
these objects has been a subject both of wonder and of in-
vestigation by mathematicians and astronomers ever since
338 ASTRONOMY.
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 mathematically by LA PLACE that a homo-
geneous and solid ring surrounding the planet could not
remain in a state of equilibrium, but must be precipitated
upon the central ball by the smallest disturbing force.
It is now established both by mathematical processes and
by spectroscopic observation that the rings do not form a
continuous mass, but are really a countless multitude of
small separate particles or satellites, each of which revolves
in its own orbit. 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 sun-
beam.
The thickness of the rings is not above 100 miles. The outer diam-
eter of the outer ring (ring A) is 173,000 miles. It is 11,500 miles
wide. The CASSINI division separating A from B is 2400 miles wide.
The outer diameter of ring B is 145,000 miles, and it is 17,500 miles
wide. The outer diameter of ring C (the dusky ring) is 100,000. and
its inner diameter is 90,000 miles. Dr. KEELER has proved, spectro-
scopically, that different parts of the rings revolve about the planet
at different rates, so that the rings must necessarily be composed
of discrete particles. The rotation time of the ball of Saturn is 10 h
14 m ; the periodic-time of the innermost particle of the dusky ring is
5 h 50 m . Inside of this particle the space is empty.
Satellites of Saturn. Outside of the rings of Saturn revolve its nine
satellites, the order and discovery of which are shown in the table on
page 339.
The distances are given in radii of the planet. The satellites Mimas
and Hyperion and satellite No. 9 are visible only in the most power-
ful telescopes. The brightest of all is Titan, which can be seen in a
telescope of ordinary size. The mass of Titan is ^Vff of Saturn's mass,
and it is some 3000 miles in diameter. Japetus is nearly as bright as
Titan when west of the planet, and is so faint as to be visible only in
large telescopes when on the other side. Like our moon, it always
THE PLANET URANUS.
339
presents the same face to the planet, and 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 satellite is visible. On the other side of the
planet, the dark side is turned toward us, and it is nearly invisible.
Satellites 3, 4, 5, 6, and 8 can be seen with telescopes of moderate
power.
No.
NAME.
Distance
from
Planet.
Discoverer.
Date of
Discovery.
Periodic-time.
1
Mimas
3.3
Herschel
1789
About O d 23 h
2
Enceladus
4.3
Herschel
1789
l d 9 h
3
Tethys
5.3
Cassini
1684
I d 21 h
4
Dione
6.8
Cassini
1684
2" 18
5
Rhea
9.5
Cassini
1672
4 d 13 h
6
Titan
20 7
Huyghens
1655
15 d 23 h
7
Hyperion
26.8
Bond
1848
21 d 7 h
8
Japetus
64.4
Cassini
1671
79 d 8 b
9
?
225.4
Pickering
1899
510 days.
37. The Planet Uranus, Uranus was discovered on
March 13, 1781, by Sir WILLIAM HERSCHEL (then an
amateur observer) with a ten-foot reflector made by him-
self. He was examining a portion of the sky when one of
the stars in the field of view attracted his notice by its
peculiar appearance. On farther scrutiny, it proved to be
a planet. We can scarcely comprehend 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 31,000 miles, and its
figure is spheroidal.
In physical appearance it is a small greenish disk without
markings. The centre of the disk is slightly brighter than
340 ASTRONOMY.
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 discovered two satellites to
Uranus. Two additional ones were discovered by LASSELL
in 1847.
Days.
I. Ariel (LASSELL) Period = 2.520383
II. Umbriel " " = 4.144181
III. Titania (HERSCHEL) " = 8.705897
IV. Oberon " " = 13.463269
Ariel varies in brightness on different sides of the planet,
and the same phenomenon has also been suspected for
Titania. This indicates that these satellites always
present the same face to the planet.
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 pre-
viously known.
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 satel-
lites, and is therefore an oblate spheroid like the Earth.
If the planes of the satellites' orbits 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 satellites would deviate by different
amounts, and it would be extremely improbable that all the
orbits would be found in the same plane at any particular
epoch. Since we now see them in the same plane, we con-
THE PLANET NEPTUNE. 341
elude that some force keeps them there, and the oblateness
of the planet is the efficient cause of such a force.
The Planet Neptune. After the planet Uranus had been
observed for some thirty years, tables of its motion were
prepared by BOUVARD a French astronomer. He had not
only all the observations since the date of its discovery in
1781, but also observations extending back as far as 1695,
when the planet was observed and supposed to be a fixed
star. It was expected that the ancient observations would
materially aid in obtaining exact accordance between the
theory and observation. But it was found that, after
allowing for all perturbations produced by the known
planets, the ancient and modern observations, though un-
doubtedly referring to the same object, were yet not to be
reconciled with each other, but differed systematically.
BOUVARD was forced to found his theory upon the modern
observations alone. By so doing, he obtained a good agree-
ment between theory and the observations of the few years
immediately succeeding 1820.
BOUVARD made the suggestion that a possible cause for
the discrepancies noted might be the existence of an
unknown planet, exterior to Uranus.
In the year 1830 it was found that BOUVARD'S tables,
which represented the motion of the planet well during the
years 1820-25, were 20" in error. In 1840 the error was
90", and in 1845 it was over 120."
These progressive 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 in Russia, searched
342 ASTRONOMY.
for a new planet with the large telescope of the Imperial
Observatory. BESSEL, at Koenigsberg, set a student of his
own, FLEMING, to make a new comparison of observation
with theory, in order to furnish data for a new determina-
tion. ARAGO, then Director of the Observatory at Paris,
suggested this subject in 1845 as an interesting field of
mathematical research to LE VERRIER. Mr. J. 0. 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 As-
tronomer Koyal of England elements of a new planet so
situated as to produce the perturbations of the motion of
Uranus which had actually been observed. Such a predic-
tion from an entirely unknown 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 ADAMS' elements of the new planet to
have been so near the truth that if it had been really looked
for by the powerful 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. LE VERRIER,
however, continued his investigations, and in the most
thorough manner. He first computed anew the perturba-
tions 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 Saturn and
Uranus, because Saturn would have been more affected
than was the case.
THE PLANET NEPTUNE. 343
If the new planet existed at all it was outside 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, and this striking fact renewed the interest
in ADAMS' work. It was determined to search in the
heavens for the planet foretold by theory.
Professor CHALLIS, the Director of the Observatory of
Cambridge, England, began a search for such an object, and
as no star-maps were at hand for this region of the sky, he
commenced by mapping the surrounding stars. In so
doing the new planet was actually observed, both on August
4 and 12, 1846, but the observations remained unreduced,
and the planetary nature of the object was not recognized
till afterwards.
In September of the same year LE VERRIER 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 new planet was found September 23, 1846.
The strict rights of discovery lay with LE VERRIER, but ADAMS
deserves 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 VERRIER were reached after a most thorough investigation of the
whole ground, and were announced with an entire confidence which,
perhaps, was lacking in the other case.
This brilliant discovery created even more enthusiasm
than the discovery of Uranus, as it was by an exercise of
far higher intellectual qualities that it was achieved. It
was nothing short of marvellous that a mathematician could
say to an observer that if he would point his telescope to a
344: ASTRONOMY.
certain small area, he would find within it a major planet
hitherto unknown. Yet so it was. By somewhat similar
processes previously unknown companions to the bright
stars Sirius and Procyon have been predicted, and these
companions have subsequently been discovered with the
telescope.
FIG. 188. PERTURBATIONS OP Uranus BY A PLANET EXTERIOR
TO IT Neptune.
The general nature of the disturbing force which revealed the new
planet may be seen by Fig. 188, which 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 show the directions of the attractive force of Neptune.
Our knowledge regarding Neptune is mostly confined to
a few numbers representing the elements of its motion.
Its mean distance is more than 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 about 34,000
miles. Gravity at its surface is about nine tenths of the
CONSTITUTION OF THE PLANETS. 345
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. It is not unlikely that the planet
may have a second very faint satellite.
38. The Physical Constitution of the Planets. The solar system is
composed of three groups of planets differing widely in their char-
acteristics. The first group consists of Mercury, Venus, the Earth,
Mars ; the second group is the asteroids ; the third consists of Ju-
piter, Saturn, Uranus, and Neptune. The diameters of the first group
vary from 3000 to 8000 miles, their periodic- times are less than two
years, their masses are never greater than 5^^^ of the Sun's mass,
their densities are from 3 to 5 times the density of water. The Moon,
the satellite of the Earth, belongs in this group. Its density is 3.4
times the density of water. Two planets of this group Venus and
the Earth are certainly surrounded by atmospheres. The others
probably have little or no atmosphere. The planets of this group
were named by ALEXANDER VON HUMBOLDT terrestrial planet*. They
are in some respects like the Earth. At any rate, all of them are
much more like the Earth than like the giant planets beyond Mars.
The asteroids are quite unique among the planets. Jupiter, Saturn,
Uranus, Neptune present many striking resemblances. They are of
giant size. Their diameters vary from 30,000 to 90,000 miles.
Their masses are relatively large (^^^^ to y^^ of the Sun's mass),
their densities are all small (none greater than 1 times the density
of water). At least two of them have a very short period of rotation,
and all of them have a high reflecting power. Their surfaces are
covered with clouds and there is good reason to believe that one of
them Jupiter is still a very hot body. Very likely all of them
consist of masses of molten matter surrounded by envelopes of vapor.
This view is further strengthened by their very small specific grav-
ity, which can be accounted for by supposing that the liquid interior
is nothing more than a comparatively small central core, and that the
greater part of the bulk of each planet is composed of vapor of small
density. Some of the satellites of this group are about as large as
Mars or Mercury.
Finally the central body of the whole system the Sun is im-
mensely larger than all the planets tak> n together; it is very hot ; it
346 ASTRONOMY.
is almost or entirely gaseous ; its density is less than 1 T 4 7 the density
of water and this in spite of the immense pressure on its interior
parts. Mercury, Mars, the Moon, are airless, cold, dense, small.
We know little of Venus except that she is covered with clouds.
Venus may be more like the Earth than any other planet. The aster-
oids are mere fragments, probably all airless and cold. The giant
planets are (probably) all hot, with a solid or liquid nucleus and a
deep atmosphere. And at the end of the series comes the Sun, hot,
gaseous, immensely larger than the planets.
The differences between these different bodies are chiefly due to
temperature. If any one of them were to be suddenly raised to the
Sun's temperature it would probably be a miniature Sun. Each of
these bodies is cooling by the radiation of its heat into space. None
of the heat radiated returns to the body, so far as is known. The
Sun in cooling will probably become a body somewhat like Jupiter.
Jupiter in cooling will probably become a body somewhat like the
Earth. The Earth in cooling will probably become a body somewhat
like the Moon. The Moon has already reached its permanent state.
Its heat has gone; it has no atmosphere; and its temperature on the
side turned away from the Sun is the temperature of space hundreds
of degrees below zero Fahrenheit.
The temperature of any planet in the system thus depends, in an
important degree, on its age. It depends also on a thousand other
circumstances on the kind of matter of which it is made up, on its
size, etc. When we come to consider the Nebular Hypothesis of
KANT and LAPLACE, which is an attempt to explain the evolution of
the solar system, these facts (and others not here explicitly set down)
will be found to be highly significant.
CHAPTEE XX.
METEORS.
39. Phenomena of Meteors and Shooting-stars. Any
one who watches the heavens at night for a few hours will
see shooting-stars or meteors. They suddenly appear as
bright points of light, move along an arc in' the sky and
then disappear. Large meteors aerolites are often as
bright as Venus or even very much brighter; they are
usually followed by brilliant trains ; they frequently explode
in the air, like rockets, and leave clouds of meteoric dust
behind them. Sometimes their bursting or their passage
through the atmosphere is accompanied by an audible noise.
Occasionally fragments of the aerolite fall to the Earth.
Large collections of such fragments are preserved in our
museums, and some of the specimens weigh hundreds of
pounds. Usually, however, they are much smaller.
Most of the specimens of aerolites aie stones; some of
them, are nearly pure iron alloyed with nickel, etc.
When we consider that the aerolites come from regions
beyond the Earth and that they never had any direct con-
nection with it before their fall on its surface, it is a highly
significant fact that they contain no chemical elements not
found on the Earth. It indicates that all the bodies of the
solar system are similar in constitution. Moreover, of the
seventy or more elements known to us more than twenty
have been found in meteoric masses. The minerals formed
by the combination of the elements are often somewhat dif-
ferent in the aerolites from the corresponding minerals
found in the Earth's crust, which seems to show that they
347
ASTRONOMY.
FIG. 189. THE GREAT CALIFORNIA METEOR OF 1894.
METEORS. 349
were combined under quite different conditions of heat,
pressure, etc. An aerolite is a little planet out of the
celestial spaces, evident to our sight, it may be to our
touch.
Path of a Meteor. The positions of a meteor can be observed
by referring it to neighboring stars we can draw its path on a
star-map, and note the time of its appearance or bursting. If such
observations are made by observers at different stations on the
Earth, the orbit of the meteor can be calculated. It is found that
most aerolites, or large meteors, were moving in elliptic orbits about
the Sun before they fell into the sphere of the Earth's attraction.
The Earth, of course, alters such an orbit, and draws the body down-
wards into the atmosphere with a high velocity. In most cases it is
consumed burned up completely in our atmosphere. Occasionally
pieces of it fall to the ground, as has been said.
Cause of the Light and Heat of Meteors. Why do meteors burn
with so great an evolution 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. The more rapid
the motion the warmer the body. By simply blowing air against
any combustible body with high velocity it can be set on fire, and, if
the body is incombustible, it can be made red-hot and finally melted.
Experiments show that a velocity of about 50 metres (about 164
feet) per second corresponds to a rise of temperature of one degree
Centigrade. From this the temperature due to any velocity can be
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. A velocity of 500 metres (about
1640 feet) per second corresponds to a rise of 100 C. above the actual
temperature 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 (4921 feet, about twice the velocity of a
cannon-ball) per second would produce a red heat.
The Earth moves around the Sun with a velocity of about 30,000
metres (18 miles) per second; consequently if it met a body at rest
the concussion between the latter and the atmosphere would corre-
spond to a temperature of more than 300,000. This would instantly
change any known substance from a solid to a gaseous form.
It must be remembered that these enormous temperatures are
potential .[joot actual, temperatures. The body is not actually raised
350 ASTRONOMY.
to a temperature of 300,000, but the air acts upon it as if it were
suddenly plunged into a furnace heated to this temperature. It is
rapidly destroyed just as if it were in such a furnace.
The 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 prob-
able 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 a like
velocity. In the latter case it would probably disappear 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 ms 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.
The amount of heat which is equivalent to the energy of motion
of a pebble having a velocity of 20 miles a second is sufficient to
raise about 1300 times the pebble's weight of water from the freezing
to the boiling point. This is many times as much heat as could
result from burning pure carbon.
Meteoric Phenomena. Meteoric phenomena depend upon the sub.
stance out of which the meteors are made and the velocity with
which they move in the atmosphere. With very rare exceptions,
they are so small and fusible as to be entirely dissipated in the
upper regions of the air. 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 expended in melting and destroying its outer layers, the inner
nucleus remaining unchanged. When a meteor first strikes the
denser portion of the atmosphere, the resistance becomes so great
that the body is generally broken to pieces. A single large aerolite
may produce a shower of small meteoric stones.
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.
Meteors and shooting-stars commonly commence to be visible at a
METEORS. 351
height of about 70 statute miles. The separate results vary widely,
but this is a rough average. They are generally dissipated at about
half this height, and therefore above the highest atmosphere which
reflects the rays of the Sun. The Earth's atmosphere must, then,
extend at least as high as 70 miles.
While there are few aerolites or large meteors, there are
millions of the smaller sort shooting-stars. A single
observer will see, on the average, from four to eight every
hour. If the whole sky is watched at any one place on the
Earth from 30 to 60 are visible every hour. They fill
space like particles of dust, only these particles of the
dust of space are, on the average, about 200 miles apart.
The Earth sweeps along in its orbit at the rate of 18J miles
per second and in its daily journey of some 1,600,000 miles
it meets, or is overtaken by millions of these bodies. From
10 to 15 millions of meteors fall into the Earth's atmos-
phere every day. The mass of the single meteors is ex-
tremely small several thousands of them being required
to make up a pound's weight. If each meteor has a mass
of one grain the Earth is growing heavier daily by about a
ton. Theoretically the Earth is daily receiving heat by the
fall of meteorites, also; but calculation shows that the Sun
sends us ten times as much heat in a second as is received
from meteors in a year; so that there is no noteworthy
effect from this cause.
Meteoric Showers. Shooting-stars may be seen by a
careful observer on almost any clear night. In general,
not more than half-a-dozen will be seen in an hour, and
these are usually so minute as hardly to attract notice.
But they sometimes fall in great numbers as a meteoric
shower. On rare occasions the shower has been so striking
as to fill the beholders with terror. Ancient and mediaeval
records contain many accounts of such phenomena.
One shower of this class occurs at an interval of about a
third of a century. It was observed by HUMBOLDT, on the
352 ASTRONOMY.
Andes, on the night of November 12, 1799, for instance,
and often before that time. A great shower was seen in
this country in 1833. On the night of November 13, 1866,
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 dying away, as it were. This great shower
will appear in 1899, once more.
The occurrence of a shower of meteors evidently shows
that the Earth encounters a swarm of such bodies moving
together in space. The recurrence at the same time of the
year (when the Earth is in the same point of its orbit)
shows that the Earth meets the swarm at the same point in
space in successive years. All the meteors of the swarm
must be moving in the same direction in space or else they
would soon be widely scattered.
Radiant Point. Suppose that, during a meteoric shower, we mark
the path of each meteor on a star-map, as in figure 190. If we con-
tinue the observed 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 the same point owing to the unavoidable
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 stars apparently move toward the west, the radiant point moves
with them.
The existence of a radiant point proves that the meteors that strike
the Earth during a shower are all moving in the same direction.
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 in space seen by an observer
is projected as a great circle of the celestial sphere, with the
observer at its centre. If we draw a line from the observer parallel
to the paths of the meteors, the direction of that line intersects the
celestial sphere in a point through which all the meteor-paths will
seem to pass.
METEORS.
353
Orbits of Showers of Meteors. The position of the radiant point in-
dicates the direction in which the meteors move relatively to the
FIG. 190. THE RADIANT POINT OP A METEORIC SHOWER.
Earth. If we also knew the velocity with which they are really mov-
ing in space, we could make allowance for the motion of the Earth,
354 ASTRONOMY.
and thus determine the direction of their actual motion in space, and
determine the orbit of the swarm around the Sun.
The radiant point of the shower of August 10 (Perseids) is R.A.
3 h 4 m Decl. -f- 57 ; of the shower of November 13 (Leonids) R.A. 10 h
O m , Decl. + 23 ; of the shower of November 26 (Andromedes} R.A.
l h 41 m , Decl. -)- 43. The student should observe these showers.
Relations of Meteors and Comets. The velocity of the
meteors in space does not admit of being determined from
observation of the meteors themselves. It is necessary to
determine their velocity in the orbit from the periodic-time
of the swarm about the Sun. The orbit of the swarm
giving the 33-year shower was calculated shortly after the
great shower of 1866 with the results that follow:
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 orbit of the meteor-swarm presents an extraordinary
likeness to the orbit of a periodic comet discovered by
TEMPEL. The elements of the comet's orbit are:
Period of revolution 33.18 years.
Eccentricity of orbit 0.9054
Least distance from the sun 0.9765
Inclination of orbit 162 42'
Longitude of the node 51 26'
Longitude of the perihelion 42 24'
If the two orbits are compared, the result is evident.
The swarm of meteors which causes the November shoivers
moves in the same orbit with TEMPEL'S comet.
The comet passed its perihelion in January, 1866. The
shower was not visible until the following November.
METEORS. 355
Therefore, the swarm which produced the showers followed
after TEMPEL'S comet, moving in the same orbit with it.
The recurrence of the phenomenon every 33 years was
traced backward in historical records and it was shown that
for centuries this swarm had been revolving about the Sun.
The swarm is stretched out in a long mass and the Earth
crosses the orbit in November of every year. The Earth
finds the swarm in its path every 33 years. The radiant
point of the November shower is in the constellation Leo
and hence these meteors are called Leonids. The August
meteors radiate from Perseus and are called Perseids. The
relation between comets and meteors suggested the question
whether a similar connection might not be found between
other comets and 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 (notably August 10) in which more shooting-stars than
usual are seen, and in which the large majority radiate from one
point of the heavens. They also arise from swarms of ineteoroids
moving together around the Sun.
The honor of the discovery of this remarkable and unexpected
relation between meteors and comets is shared between several
astronomers. Professors OLMSTED and TWINING of Yale College
were the first to show that meteors were extra-terrestrial bodies re-
volving in swarms about the Sun. Professors ERMAN of Germany,
LE VERRIER of France, ADAMS of England, SCHTAPARELLI of Italy
and particularly Professor NEWTON of Yale College developed the
whole subject.
Many meteor-swarms revolve in the same orbits with
comets. In some cases the swarms follow the comet in a
more or less compact mass. In others the meteors are
scattered all around the orbit. If a comet, originally, is
nothing but a close cluster of meteors it will partially break
up into its parts under the influence of planetary attractions
(perturbations) and especially at every one of its perihelion
passages. The longer a comet has been in the solar system
356 ASTRONOMY.
the more the meteors will be spread ont along its orbit.
But it is by no means certain that comets are, in the first
place, only aggregations of meteors, so that it can only be
said that there is, certainly, a very close connection between
meteors and comets, and that it is likely that certain
meteor-swarms are no more than the debris of comets.
Beside the meteors known to be connected with comets
there are millions upon millions of others scattered through
space.
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 southwest 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 can be traced all the way across the heavens.
A brighter mass opposite to the Sun's place is called the Gegenschein.
The Zodiacal Light is probably due to solar light reflected from an
extremely thin cloud either of meteors 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
meteors revolving round the Sun. The student should trace out the
Zodiacal Light in the sky.
CHAPTER XXI.
COMETS.
40. Aspect of Comets. Comets are distinguished from
the planets both by their aspects and their motions. Only
a few comets belong permanently to the solar system (see
Table IV, p. 279). Most of them are mere visitors. They
enter the system, go round the Sun once, and then leave it
forever.
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 head of the great comet of 1858
was 250,000 miles in diameter.
The tail of the comet is a continuation of the coma,
extending out to a great distance, and usually directed
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. The length of the tail varies from 2 or 3
to 90 or more. The tail of the great comet of 1858 was
45,000,000 miles in length and 10,000,000 miles in breadth.
All that area was filled with matter sufficiently condensed
to send light to the Earth and to appear as a continuous
357
358
ASTRONOMY.
FIG. 191. THE GREAT COMET OP 1858.
COMETS. 359
sheet. The mass of comets is extremely small, so small
that no comet has yet been observed to produce perturba-
tions in the motion of any planet. It is to be remembered
that we do not see the tail of a comet in its true shape, but
only its projection on the celestial sphere, and it is further-
more to be noted that the tail is not the debris of the comet
left behind the comet in its motion. The tail of a comet
is behind the nucleus as the comet approaches the Sun, but
it precedes the nucleus as the comet moves away from the
Sun. The vapors that arise from the nucleus, owing chiefly
to the Sun's heat, are repelled by the Sun driven away
from him probably by electric repulsion. The nucleus it-
self is always attracted and performs its revolution about
the Sun in obedience to the attraction of gravitation.
FIG. 192. TELESCOPIC COMET FIG. 193. TELESCOPIC COMET
WITHOUT A NUCLEUS AND WITH A NUCLEUS, BUT WITH-
WITHOUT A TAIL. OUT A TAIL.
When large comets are studied with a telescope, it is
found that they are subject to extraordinary changes. 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 in orbits always so elongated that
the comet is visible in only a very small part of its course
(see Figs. 195, 196, 197) namely, in that part of its orbit
near the Sun (and Earth).
60 ASTRONOMY.
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. (a, Fig. 194.) This
bow will gradually rise and spread out on all sides, finally assuming
the form of a semicircle having the nucleus in its centre, or, to
speak with more precision, 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 joined to it.
Other bows will successively form around the nucleus, all slowly
rising from it like clouds of vapor (Fig. 194).
FIG. 194. FOKMATION OF ENVELOPES.
These distinct vaporous masses are called the envelopes : they
shade off gradually into the coma so as to be with difficulty distin-
guished from it. The appearances are apparently caused by masses
of vapor streaming up from that side of the nucleus nearest the Sun
(and therefore hottest) and gradually spreading around the comet on
each side as if repelled by the Sun. The form of the bow is, of
course, 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 (see Fig. 194) and a fountain, throwing
a vapor horizontally on all sides, to be built upon that part of the
comet which is uppermost. Such a fountain would throw its vapor
in the .form of a sheet, falling on all sides of the cometic nucleus,
but not touching 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 tail also develops rapidly as the comet draws near to the Sun,
and sometimes several tails are developed. The principal tail is
directed away from the Sun, as if under electric repulsion.
COMETS. 361
The 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 matter, 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 which indicates that the comets are
principally made up of gases mostly compounds of carbon and
hydrogen. Sodium and several other substances are often found.
Part of the comet's light is undoubtedly reflected sunlight.
It is, at first sight, difficult to comprehend how a mass of gas of
extreme tenuity can move in a fixed orbit just as if it were a solid
planetary mass. The difficulty vanishes when we remember that the
spaces in which comets move are practically empty as empty as
the vacuum of an air-pump. In such a vacuum a feather falls as
freely and as rapidly as a block of metal.
The Orbits of Comets. Previous to the time of NEWTON only bright
comets had been observed and nothing WHS known of their actual mo-
tions, except that no one of them moved around the Sun in an ellipse
as the planets moved. NEWTON found that a body moving under the
attraction of the Sun might move in anyone of the three "conic
sections," the ellipse, parabola, or hyperbola. Bodies moving in an
ellipse, as the planets, complete their orbits at regular intervals of
time over and over again. A body moving in a parabola or an hyper-
bola never returns to the Sun after once passing it, but moves away
from it forever. Most comets move in parabolic orbits, and therefore
a proach the Sun but once during their whole existence (Fig. 195).
A few comets revolve around the Sun in elliptic orbits, which differ
from those of the planets only in being much more eccentric. (See
p. 279.) But nearly all comets move about the Sun in orbits which
we are unable to distinguish from parabolas, though it is possible
that some of them may be extremely elongated ellipses. It is note-
worthy that the orbits of comets are inclined at all angles to the
ecliptic and that their directions of motion are often retrograde. In
these respects they differ widely from the planets.
In the last chapter it was shown that swarms of minute particles,
small meteors, accompany certain comets in their orbits. This is
probably true of all comets. We can only regard such meteors as
362 ASTRONOMY.
fragments or debris of the comet. On this theory a telescopic comet
which has no nucleus is simply a cloud of these minute bodies. Per-
haps each one of the minute particles has a little envelope of gases
about it. 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 student has difficulty in reconciling this theory of detached
particles with the view already presented, that the envelopes from
which the tail of the comet is formed consists of layers of vapor, he
must remember that vaporous masses, such as clouds, fog, and
FIG. 195 ELLIPTIC AND PARABOLIC ORBITS.
smoke, are in fact composed of minute and separate particles of water,
carbon and so forth.
The gases shut up in the cavities of meteoric stones have been
spectroscopioally examined, and they show the characteristic comet
spectrum. This gives a new proof of the connection between comets
and meteors.
Formation of the Comet's Tail. The tail of the comet is not a per-
manent appendage, but is composed of masses of vapor which ascend
from the nucleus, and afterwards move away from the Sun. The
COMETS. 363
tail which we see on one evening is not absolutely the same we saw
the evening before. A portion of the latter has been dissipated,
while new matter has taken its place, as with the stream of smoke
from a steamship. It is an observed fact that the vapor which rises
from the nucleus of a comet is repelled by the Sun instead of being
attracted toward it, as larger masses of matter are ; as indeed the
nucleus itself is.
No adequate expl nation of this repulsive force has yet been given.
It is probably electrical.
FIG. 196. OKBTT OF HAT.LEY'S COMET.
Periodic Comets. The first discovery of the periodicity of a comet
was made by HALI.KY in connection with the great comet of 1682.
This comet moves in an immense elliptic orbit with a periodic time
of 76 years. HALLEY predicted that it would return in 1758. CLAI-
RATJT, a French astronomer, worked out its orbit by NEWTON'S
methods, and the comet returned, obedient to law, on Christmas
day, 1758. (See Fig. 196.)
Gravitation was thus, for the first time, shown to rule the erratic
motions of comets as well as the orderly revolutions of the planets.
The figure shows the very eccentric orbit of HALLEY'S comet and
the nearly circular 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 also shows the position of the comet in 1874. It will return
to perihelion again in the year 1910.
364
ASTRONOMY.
Orbit of a Parabolic Comet. Figure 197 shows the orbit of a comet
discovered by PERRINE at the Lick Observatory on November 17,
1895. The places of the comet in its parabolic orbit are marked for
November 20 and subsequent dates. The places of the Earth in its
orbit are marked for the same dates. Lines joining the correspond-
\
5.
FIG. 197. THE ORBIT OF COMET 0. 1895, AND THE ORBIT OF
THE EARTH, DRAWN TO SCALE. THE SUN is AT THE CENTRE
OF THE DIAGRAM.
ing dates in the two orbits will show the direction in which the
comet was seen from the Earth. A line shows the direction of the
Vernal Equinox. The plane of the paper is the plane of the Eclip-
tic. All that part of the comet's orbit which is drawn full is north
of the Ecliptic; the dotted portion is south of it. The line of nodes
COMETS.
365
of the comet's orbit is marked on the diagram. The comet was
nearest to the Sun (at perihelion) on December 18, when its dis-
tance was 0.19 (the Earth's distance = 1.00). The positions of the
comet were
Nov. 20
R. A. 208
Decl. -
24
211
- 3
28
214
- 5
Dec. 2
219
- 10
10
286
- 22
18
274
- 31
26
287
- 23
Remarkable Comets. In former years bright comets
were objects of great dread. They were supposed to
DEB
ERN DROHT
BOESE SACHET
TRAV".
GOTT
FIG. 198. MEDAL OF THE GREAT COMET OP 1680-81.
presage the fall of empires, the death of monarchs, the
approach of earthquakes, wars, pestilence, and every other
calamity that could afflict mankind. In showing the entire
groundlessness of such fears, science has rendered one of
its greatest benefits to mankind.
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 few of these, however, have been so
bright as to excite universal notice.
In 1456 the comet, afterwards known as HALLEY'S,
appeared when the Turks were making war on Christen-
dom, and caused such terror that Pope CALIXTUS IIJ
366 ASTRONOMY.
ordered prayers to be offered in the churches for protection
against it. This is the origin of the popular fable that the
Pope once excommunicated a comet.
Comet of 1680. One of the most remarkable of the brilliant comets
is that of 1680. It inspired such terror that a medal was struck to
quiet popular apprehension. A free translation of the inscription is :
"The star threatens evil things; trust only ! God will turn them
to good."* This comet is especially remarkable in the history of
Astronomy because NEWTON calculated its orbit, and showed that it
moved around the Sun obedient 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. It was visible in full daylight close to the Sun.
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 semidiaineter. With a very slight change of
its original motion, it would have actually fallen into the Sun, and
become a part of it.
Great Comet of 1858. It is frequently called DONATI'S comet from
the name of its discoverer. It was visible for about nine months and
was thoroughly studied by many astronomers, particularly by BOND at
Harvard College. At its greatest brilliancy its tail was 40 in length
and 10 in bread that its outer end, about 45,000,000 and 10,000,000
miles in real (no perspective) dimensions. Its period is 1950 years.
(See Fig. 191.)
Great Comet of 1882. It was visible in full daylight at its bright-
est, and it was seen with the telescope until it actually appeared to
touch the Sun's disk. It passed across the face of the Sun (half a
degree) in less than fifteen minutes, with the enormous velocity of
more than 300 miles per second. Its least distance from the surface
of the Sun was less than 300,000 miles, so that it passed through the
denser portions of the Sun's Corona.
The orbit of this comet has been calculated from observations
taken before its perihelion passage, and also from observations taken
after it. If the Corona had had any effect on the comet's motion
these two orbits would have differed ; but they do not differ ; they
*Tho student should notice the care which the author of the inscription has
taken to make it consolatory, to make it rhyme, and to give implicitly the
year of the comet by writing certain Roman numerals larger than the other
letters.
COMETS. 367
agree exactly. This shows of how rare suhstances the Corona is
made up.
The periodic-time of this comet is about 840 years and its orbit
is the same curve in space as the orbits of the comets of 1668, 1843
and 1880 and 1887. But the comets themselves are different bodies.
The comet of 1882 and that of 1880 cannot possibly be the same,
body. They travel in the same path, however, and belong to the
same family of comets.
Observations of comets made at the Lick Observatory and elsewhere
have shown that comets sometimes break up into fragments which
thereafter travel in similar paths one behind the other. Pho-
tographs of comets sometimes actually show the formation of com-
panion comets left behind or rejected by the main comet. From
these photographs it appears that the head of a comet sends out
enormous quantities of matter to form the tail , so that the material
that forms it on one day may not be and probably is not the same
material that formed the tail of a few days previous. The observa-
tions and photographs referred to have opened a new field for investi-
gation, and it is likely that very many important questions as to the
constitution of comets will be settled when the next bright cornet
appears.
Encke's Comet and the Resisting Medium. The period of this
comet is between three and four years. Viewed with a telescope, it
appears simply as a mass of foggy light. Under the most favorable
circumstances, it is just visible to the naked eye. The circumstance
that has lent most interest to this comet is that observations ex-
tended over many years 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 felt only by bodies of extreme tenuity,
like the telescopic comets. The approach of the comet to the Sun is
shown by a gradual diminution of the period of revolution.
If the change in the period of this comet were actually due to the
causes 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
deviations 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
368 ASTRONOMY.
short period which has been observed with sufficient care to decide
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 solid bodies like 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.
CHAPTER XXII.
INTRODUCTION.
41, Although the solar system comprises the bodies
which are most important to us who live on the Earth, yet
they form only an insignificant part of creation. Besides
the Earth, only seven of the bodies of the solar system are
plainly visible to the naked eye, whereas some 2000 or
more stars can be seen on any clear night. Our Sun is
simply one of these stars, and does not, so far as we know,
differ from its fellows in any essential characteristic. 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 in the solar system. In fact, the nearest known star
is about seven thousand times as far from us as the planet
Neptune. If we suppose 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, any nearer
together than this, except in special cases where they are
collected together in clusters.
369
370 ASTRONOMY.
The total number of the stars is estimated by millions,
and they are separated one from another by these wide
intervals. It follows that, in going from the Sun to the
nearest star, we are simply taking a single step in the
universe. The most distant stars are probably a thousand
times more distant than the nearest one, and we do not
know what may lie beyond the distant stars.
The planets, though millions of miles away, are compara-
tively near us, and form a little family by themselves.
The planets are, so far as we can see, worlds not exceed-
ingly different from the Earth on which we live, while
the stars are suns, generally larger and brighter than our
own Sun. Each star may, for aught we know, have
planets revolving around it, but their distance is so im-
mense that even the largest planets will forever remain in-
visible with the most powerful telescopes man can construct.
We shall see in what follows that only a few stars are so
near to us that their light can reach the Earth in 10, 20,
or even 50 years. The vast majority are so distant that
the light which we now see left them a century ago, or
more. If one of these were suddenly destroyed it would
continue to shine for years afterwards. The aspect of
the sky at any moment does not then represent the present
state of the stellar universe, but rather its past history.
The Sun's light is already eight minutes old. when it
reaches us; that of Neptune left the planet about four
hours before; the nearest fixed stars appear as they were
no less than four years ago ; while the Milky Way shines
with a light which may have been centuries on its journey.
The difference between the Earth and the Sun is almost
entirely due to a difference in their temperature. Nearly
every element in the Earth is present in the Sun. If the
Earth were to be suddenly raised to the Sun's temperature
it would become a miniature Sun ; that is, a miniature star.
Some of the elements present in the Sun are found to be
INTRODUCTION. 371
plentiful in other stars, in nebulae, and even in comets and
meteors. All the bodies of the solar system appear to be,
in the main, of like constitution; and their wonderfully
different physical conditions to be due, in the main, to
differences of temperature. The stars, likewise, are made
up of elements often the same as the elements we know on
the Earth. The extraordinary diversity exhibited by the
bodies of the visible universe thus appears to be largely due
to differences in their temperature. The past and the
future of the Sun, the Earth, and the Moon can, therefore,
be investigated by inquiring what temperatures these bodies
have had in past times and what temperatures they are
likely to have in the future.
General Aspect of the Heavens, Constellations. 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 certain
apparent 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 far outnumber the
bright ones; so that if we divide the stars into classes
according to their brilliancy, the fainter classes will contain
the most stars.
There are in the whole celestial sphere about 6000 stars
visible to the naked eye. Of these, however, we can never
see more than a part 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 brightest ones can there be
372 ASTRONOMY.
seen. It is not likely that more than 2000 stars can ever
be taken in at a single view by any ordinary eye. About
2000 other stars are so near the south pole that they never
rise in our latitudes. Hence ont of the 6000 visible, only
4000 ever come within the range of our vision, unless we
make a journey toward the equator.
The Galaxy. The Galaxy, or Milky Way, is a magnifi-
cent 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 be seen at all other
times of the year spanning the heavens like an arch. For
a portion of its length it is 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 (see Fig. 199).
When GALILEO first directed his telescope to the heavens,
about the year 1610, he perceived that the Milky Way was
composed of stars too faint to be individually seen by the
unaided eye. HUYGHENS in 1656 resolved a large portion
of the Galaxy into stars, and concluded that it was com-
posed entirely of them. KEPLER considered it to be a vast
ring of stars surrounding the solar system, and remarked
that the Sun must be situated near the centre of the ring.
This view agrees very well with the one now received,
except that the stars which form the Milky Way, instead
of lying near to the solar system, as KEPLER supposed, are
at distances so vast as to elude all our powers of imagina-
tion.
The most recent researches have shown that the Milky
Way is a vast cluster of stars intermixed with nebulae, and
that these stars and nebulae are, in all probability, physi-
INTRODUCTION.
373
374: ASTRONOMY.
cally connected and not merely perspectively projected in
the same part of the sky. A majority of its stars are of the
same spectral type (like Sirius). Nearly all the gaseous
nebnlae are in this region; and most of the stars with
bright-line spectra are here. We must then consider the
Milky Way as mainly a physical system, and only partly as
a geometrical appearance.
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 therefore divide the stars, with re-
spect to brightness, into two great classes.
Lucid Stars are those which are visible without a telescope.
Telescopic Stars are those which are not so visible.
Magnitudes of the Stars. The stars were classified by PTOLEMY
into six orders of magnitude. The fourteen brightest visible in our
latitudes were designated as of the first magnitude, while those barely
visible to the naked eye were said to be of the sixth magnitude. This
classification is entirely arbitrary, since there are no two stars of ab-
solutely the same brightness. 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.
Between the north pole and 35 south declination there are :
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.
Measures of the light of the stars show that 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 ratio
^ is called the light-ratio.
The Constellations and Names of the Stars. The
ancients divided the stars into constellations, and gave
INTRODUCTION. 375
special names to these groups and to many of the more
conspicuous stars also.
Considerably more than 3000 years before the commencement of the
Christian chronology the star Sirius, 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 (800 B.C.), as well as the group of the
Pleiades, or Seven Stars, and the constellation of Orion. All the
earlier civilized nations, Egyptians, Chinese, Greeks, and Hindoos,
had some arbitrary division of the surface of the heavens into irregu-
lar and often fantastic shapes, which were distinguished by names.
The area within which the Sun and planets move the Zodiac was
probably divided and named before the year 2000 B.C., and the 48
constellations given by PTOLEMY were probably formed at least as
early as this time.
In early times the names of heroes and animals were given to the
constellations. Each figure was supposed to be painted on the sur-
face of the heavens, and the stars were designated by their position
upon some portion of the figure. The ancient and mediaeval astrono-
mers spoke 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 constella-
tions with our modern maps. Otherwise they have ceased to serve
any really useful purpose, and are often omitted from maps designed
for purely astronomical uses.
The Arabians gave special names to a large number of the brighter
stars. Some of these names are in common use at the present time,
as Aldebaran, Fomalhaut, etc.
In 1654 BAYER, of Germany, mapped the constellations and desig-
nated the brighter stars of each constellation by the letters of the
Greek alphabet. When this alphabet was exhausted he introduced
the letters of the Eoman 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 Majoris, or, in English, a of the
Great Dog, is the designation of Sirius, the brightest star in the
heavens. The brightest stars of the Great Bear are called a Ursa
Mujoris, /3 Ursce Majoris, etc. Arcturus is a Bootis. The student
376 ASTRONOMY.
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, only the fifty brightest stars in
each constellation could possibly be designated by this method.
After the telescope had fixed the position of many additional stars,
some other method of denoting them became necessary. FLAMSTEED,
about the year 1700, prepared an extensive catalogue of stars, in
which those of each constellation were designated by numbers in the
order of right-ascension. These numbers 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 nowadays either by their R.A. and Decl., or by
their numbers in some well-known catalogue of stars.
Numbering and Cataloguing the Stars. As telescopic power is in-
creased, we still find fainter and fainter stars. But the number
cannot go on increasing forever in the same ratio as the brighter
magnitudes, because, if it did, the whole night sky would be a blaze
of starlight, instead of a dark sphere dotted with brilliant points.
If telescopes with powers far exceeding our present ones are made,
they will, no doubt, show very many new stars. But it is highly
probable that the number of such successive orders of stars would
not increase in the same ratio as is observed in the 8th, 9th, and 10th
magnitudes, for example.
In special regions of the sky, which have been searchingly ex-
amined by various telescopes of successively increasing apertures,
the number of new stars found is by no means in proportion to the
increased instrumental power. If this is found to be true elsewhere,
the conclusion may be that, after all, the stellar system can be ex-
perimentally shown to be of finite extent, or to contain 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 100,000,000 stars.
In ARQELANDER'S Durchmusterung of the stars of the northern
heavens there are recorded as belonging to the northern hemisphere
314,926 stars from the first to the 9.5 magnitude, so that there are
about 600,000 in the whole heavens.
INTRODUCTION.
377
We can readily compute the amount of light received by the Earth
on a clear but moonless night from these stars. The brightness of
an average star of the first magnitude is 0.5 of that of a Lyrce. 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. 374.)
The total brightness of
10
1st magnitude stars is 5.6]
37
2d
7.4 |
128
3d
102 !
310
4th
9.9 f
1,016
5th
13.0 |
4,328
6th
22 1J
13,593
7th
27 8 )
57,960
8th
47.4 f
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 Lyrce. a Lyrce -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 too faint 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.
The Star Maps printed in this book furnish a means
by which the constellations and principal stars can be
identified by the student.
Maps of the stars down to the 14th or 15th magnitude
are now made by photography, using special telescopes and
long exposures (two or three hours). Such complete maps
as this will throw a flood of light on the distribution arid
arrangement of the constituent stars of the Stellar Uni-
verse.
The Stars are Suns. Spectroscopic observations prove
that nearly all of the stars are suns, very like our own
Sun. They are self-luminous and intensely hot. They
have extensive atmospheres of incandescent gases and
metallic vapors. The light from a whole class of stars is,
378 ASTRONOMY.
so far as can be determined, precisely like sunlight in
quality. We may say in general that stars are suns.
The light received from even the brightest star is a very small
quantity because even the nearest star is very distant. From Sirius,
the brightest star in the sky, we receive of the light
received from the Sun. Let I be the light received from a star
at a distance D from us and L the light we should receive from this
star if it were at the Sun's distance from us (= 1). Then
L : I = 1 : -^j- or L = I . D*.
In the case of Sirius, I = as above, and D = about
542,000 times the Sun's distance. Hence L = *
7 0000000 '
That is, Sirius emits forty-two times as much light (and presumably
about forty-two times as much heat) as the Sun. The Sun is a
small star, compared to Sirius. The pole-star, Polaris, emits about
two hundred times as much light as the Sun, while the light received
from it is insignificant compared to sunlight.
If we compare stars with the Sun in this way we shall
see that some of them emit several thousand times more
light, while some emit perhaps -3-5*5-5- P ar * i as m uch light.
These are great differences, but they are not enormous.
The masses of a few stars are known. It is found that
some of these stars have masses perhaps a hundred times
greater, while others have masses very much smaller, than
the Sun's mass. Here again there are great differences,
but the differences are not enormous. Our Sun is an
average star, we may say.
CHAPTER XXIII.
MOTIONS AND DISTANCES OF THE STARS.
42. Proper Motions. To the unaided vision, the fixed
stars appear to preserve the same relative position in the
heavens through many centuries, so that if the ancient
astronomers could again see them, they could detect only
the slight changes in their arrangement. But the accurate
measurements of modern times show that there are slow
changes in the positions of the brighter stars. Many of
them have small motions on the celestial sphere. Their
right-ascensions and declinations change (slightly) from
year to year, apparently with uniform velocity. The
changes are called proper motions, since they are real
motions peculiar to the star itself.
In general, the proper motions even of the brightest stars
are only a fraction of a second of arc in a year, so that
thousands of years would be required for them to change
their place in any striking degree, and hundreds of thou-
sands to make a complete revolution around the celestial
sphere. The circumference of a sphere contains 1,296,000".
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 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 the
slightest change in the position of this star would break
up this balance, and thus, in general, it follows that stars
must be in motion, since each of them cannot occupy such
a critical position as has to be assumed.
379
380 ASTRONOMY.
If but one fixed star is in motion, all the rest are affected,
and we cannot donbt that every single star, our Sun in-
cluded, is in motion by amounts which vary from small to
great. If the Sun alone has a motion, and all the other
stars are at rest, the consequence 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 sup-
posed, have motions proper to themselves, as they do, then
we shall 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 of the positions of stars of their right-
ascensions and declinations can show only the resultant
of these two motions. It is for reasoning to separate this
resultant into its two components. The first question is to
determine 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 in space along some line, then there will
be a general agreement in the resultant motions of the stars
near the ends of the line along which it moves, while those
at the sides, so to speak, will show comparatively less sys-
tematic 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
MOTIONS AND DISTANCES OF THE STARS. 381
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, that occur in a case where we are
sensible of our own motion, serve to show how we may de-
duce a motion, otherwise unknown, from the appearances
which are presented by the stars in space.
In this way, acting upon suggestions which had been
thrown out previously to his own time, Sir WILLIAM
HERSCHEL demonstrated that the Sun, together with all its
system, was moving 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 or near the constellation Hercules not far
from the bright star Alpha Lyrce (Yega). 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.
Spectroscopic observations will give the direction and the
amount of the solar motion in another and an independent
way (see Chapter XVII).
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 outer-
most known planet. The idea was prevalent that Nature
would not waste space by leaving a great region beyond
Saturn entirely empty.
When COPERNICUS announced the theory that the Sun
382 ASTRONOMY.
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 oscil-
late 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 Mars produced in this way
was described p. 188 et seq. These oscillations were, in
fact, those which the ancients represented by the motion
of the planet around a small epicycle (see Fig. 124). But
FIG. 200. THE THEORY OF PARALLAX.
no such oscillation was detected in a fixed star until the
year 1837; and this fact seemed to the astronomers of
GALILEO'S time to present an almost insuperable difficulty
in the reception of the Copernican system. As the instru-
ments of observation were from time to time improved, this
apparent annual oscillation of the stars was ardently sought
for.
The parallax of a planet (P in the figure) is the angle at
the planet subtended by the Earth's radius (OS' = 4000
miles). The annual parallax of a star (P) is the angle at
MOTIONS AND DISTANCES OF THE STARS. 383
the star subtended by the radius of the Earth's orbit
(CS 1 = 93,000,000 miles). See page 109. The annual
parallax of Saturn is about 6 and of Neptune it is about
2, and these are angles easily detected with the astronomi-
cal instruments of the ancients. It was very evident, with-
ont telescopic observation, that the stars could not have a
parallax of one half a degree. A change of place of one
half a degree could be readily detected by the naked eye.
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 was gained by the improve-
ment of the instruments. Yet the parallax of the fixed
stars eluded measurement. Early in the present century
it became certain that even the brighter stars had not, in
general, an annual parallax so 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
(see page 23). R - 206,264".
Success in actually measuring the parallax of the stars
was at length obtained almost simultaneously by two
astronomers, BESSEL of Konigsberg and STRUVE of Dorpat.
BESSEL selected 61 Cygni for observation, in August, 1837.
The result of two or three years of observation was that
this star had a parallax of 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 probable
parallax is now found to be 0".45, corresponding to a dis-
tance of about 400,000 radii of the Earth's orbit.
The distances of the stars are frequently expressed by the
time required for light to pass from them to our system.
The velocity of light is, it will be remembered, about
384
ASTRONOMY.
300,000 kilometres per second, or such as to pass from the
Sun to the Earth in 8 minutes 18 seconds.
The cut shows the arrangement of some of the nearer
stars in space. They are shown on a plane, and not in
solid space. The dot in the centre of the figure is the
solar system. The circles of the figure stand for spheres,
FIG 201.
whose radii are 5, 10, 15, 20, 25, 30 light-years; that is,
for spheres whose radii are of such lengths that light,
which moves 186,000 miles in a second requires 5, 10, etc.,
years to traverse these radii.
The time required for light to reach the Earth from a
MOTIONS AND DISTANCES OF THE STARS. 385
few of the stars, whose parallax has been measured, is as
follows :
STAR.
Years.
STAR.
Years.
4
Vega (aLyrae)
27
7
AldebaTan (at Tauri)
32
Sirius (a Canis majoris). . . .
Procyon (a: Canis minoris) ..
8
12
Polaris (a Ursae minoris).
Arcturus (aBoOtis) ...
47
160
If the star Polaris were to be suddenly destroyed now
this instant its light would continue to shine for nearly
half a century more.
CHAPTER XXIV.
VARIABLE AND TEMPORARY STARS.
43. Stars Regularly Variable. Since the end of the
sixteenth century, it has been known that all stars do not
shine with a constant light. The period of a variable star
is the interval of time daring which it goes through all its
changes, and returns to its original brilliancy.
The most noted variable stars are Mira Ceti (o Ceti)
(star-map VI, in the southeast) and Algol (/3 Persei) (star-
map I, near the zenith). Mira is usually a ninth-magni-
tude star and is therefore invisible to the naked eye.
Erery eleven months it increases to its greatest brightness
(sometimes as high as the 2d magnitude,, sometimes not
above the 4th), remaining at this maximum for some time,
then gradually decreases until it again becomes invisible to
the naked eye, and so remains for about five or six months.
The average period, from minimum to minimum, is about
333 days, but the period varies greatly. It has been known
as a variable since 1596.
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 4th magnitude in the short
time of 4-J hours, and remains of 4th magnitude for 20
minutes. It then increases 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 2 d 12 h .
These examples of two classes of variable stars give an
idea of the extraordinary nature of the phenomena they
present.
386
VARIABLE AND TEMPORARY STARS. 387
Several hundred stars are known to be variable. A short
list of variables is given in Table VII.
The color of more than three fourths of the variable stars
is red or orange. It is a very remarkable fact that certain
star-clusters contain large numbers of variable stars.
Temporary or "New" Stars. There are a few cases
known of stars that have suddenly appeared, attained more
or less brightness, and slowly decreased in magnitude,
either disappearing totally, or finally remaining as compara-
tively faint objects. A new star that appeared in 134 B.C.
led HIPPARCHUS to form his catalogue of stars.
The most famous new star appeared in 1572, and attained
a brightness greater than that of Jupiter. It was 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 brightness, 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 to the naked eye.
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 brilliancy. As more than a score of such
objects are known to have appeared, many of them before
the making of accurate observations, it is probable that
many others have appeared without recognition. Among
telescopic stars there is but a small chance of detecting a
new or temporary star.
Theories to Account for Variable Stars. Two main
classes of variable stars exist and two theories must be
mentioned here.
I. Stars in general, like the Sun, are subject to erup-
tions of glowing gas from their interior, and to the forma-
tion of dark spots on their surfaces. These eruptions and
388 ASTRONOMY.
formations have in most cases a greater or less tendency to
a regular period, like the period of a gigantic geyser.
In the case of our San, the period is 11 years, but in the
case of many of the stars it is much shorter. Ordinarily,
as in the case of the Sun and of a large majority of the
stars, the variations are too slight to affect the total quan-
tity of light to any noteworthy extent.
In the case of the variable stars this spot-producing
power and the liability to eruptions are very much greater,
and we have changes of light sufficiently marked to be per-
ceived by the eye.
This theory explains why 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 a smaller
proportion of blue ones, the cooler they become. It is
therefore probable that the red stars have the least heat.
This being the case, spots are more easily produced on
their surfaces just as cooling iron is covered with a crust.
If their outside surface is .so cool as to become solid in
certain regions, the glowing gases from the interior will
burst through with more violence than if the surrounding
shell were liquid or gaseous. The cause of the periodic
nature of these eruptions is probably similar to the cause
of the periodic outbursts of geysers.
II. There is, however, another class of variable stars
whose variations are due to an entirely different cause;
Algol is the best representative of the class. The extreme
regularity with which the light of this object fades away
and disappears suggests the possibility that a dark body
may be revolving around it, partially eclipsing it at every
revolution. The law of variation of its light is so different
from that of the light of most other variable stars as to sug-
gest 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
VARIABLE AND TEMPORARY STARS. 389
nearly continuous changes, while the light of Algol remains
constant during nine tenths of its period. Spectroscopic
observations show that Algol (a bright body) is accompanied
by a dark satellite that revolves about it in an orbit which
is presented to us nearly edgewise. The satellite is about
as large in diameter as Algol and is about 3,000,000 miles
distant from it. When the dark satellite is in front of
Algol some of its light is cut off. When it is to one side,
Algol shines with its full brightness, and we do not see the
satellite because it is not self-luminous. Probably both
Algol and its dark companion revolve about a third dark
star. The diameter of Algol is about 1,000,000 miles. The
diameter of the dark satellite is about 800,000 miles.
Each of these stars is about the size of our Sun. The
mass of both combined is about f of the Sun's mass.
Their density is therefore much less than that of water.
They are like heavy spherical clouds.
Dark Stars. The existence of " dark stars " is proved in several
ways. Algol and other stars of its class are accompanied by non-
luminous satellites, as is shown by the phenomena of their variability.
8m us and Procyon are also so accompanied, as is demonstrated by
periodic irregularities of their motion. There is no reason why
there may not be "as many dark stars as bright ones." A bright
star is one that is (comparatively) young. Its heat is still so ardent
as to make it self-luminous. A dark star is one that has lost its heat
in the lapse of centuries probably thousands of centuries. In our
own solar system Jupiter was probably a self-luminous planet not so
very many centuries ago. The Earth and other planets are dark,
but still have some of their native heat. The moon is dark (i. e., not
self-luminous) and it is also cold.
We must figure the stellar universe to ourselves as containing not
only the stars that we see, but also as containing perhaps as many
more that we shall never see, because they have lost the light and
heat that they (probably) once possessed. Most of the dark stars will
forever remain unknown to us, but occasionally we meet with cases
like those of Algol or of Sirius, which make it certain that dark
stars exist. Their is reason to believe that their number is very
large.
CHAPTER XXV.
DOUBLE, MULTIPLE, AND BINARY STARS.
44. Double and Multiple Stars. When 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 appearance.
1. We may suppose that the stars happen to lie nearly
in the same straight line from the Earth, but have no con-
nection with each other. It is evident that in this case
a pair of stars might appear doable, although one was
hundreds or thousands of times farther off than the other.
It is, moreover, impossible, from mere inspection, to deter-
mine which is the farther off. (See Fig. 3, ^, , t).
2. We may suppose that the stars are really near
together, as they appear, and do, in fact, form a connected
pair or group.
A couple of stars in the first case is said to be optically
double.
Stars that are really physically connected are said to be
physically double. Their physical connection can only be
proved by observations which show that the two stars are
revolving about their common centre of gravity. There
are tens of thousands of stars in the sky that appear to be
double and hundreds that have already been proved to be
physically connected.
There are several cases of stars which appear double to the naked
eye. e Lyra is such a star and is an interesting object in a small
telescope, from the fact that each of the two stars which compose it
390
DOUBLE, MULTIPLE, AND BINARY STARS. 391
is itself double. This minute pair of points, capable of being distin-
guished as double only by tlie most perfect eye (without the tele-
scope), is really composed of two pairs
of stars wide apart, with a group of
smaller stars between and around
them. The figure shows the appear-
ance in a telescope of considerable
power.
Revolutions of Double Stars Binary
Systems. It is evident that if stars
physically double are subject to the
force of gravitation, they must be
revolving around each other, as the
Earth and planets revolve around the
Sun, else they would be drawn together FlG - 202. -THE QUADRUPLE
, DTAR IjYR^E.
as a single star.
The method of determining the period of revolution of a pair of
stars, A and B, is illustrated by the figure, whi,h is supposed to rep-
resent the field of view of an inverting telescope pointed toward the
south. The arrow shows the
direction of the apparent diur-
nal motion. The telescope is
pointed so that the brighter star
is in the centre of the field.
The angle of position of the
smaller star (NAB) is measured
by means of a divided ciicle,
and their distance apart (AB) is
measured with the micrometer
(see page 141) at the same time.
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 periodically, it sliows
that one star is revolving around
the other. Such a pair is called
a binary star or Unary system.
The only distinction that 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
FIG.
203. POSITION ANGLE OF A
DOUBLE STAR.
392 ASTRONOMY.
systems, but that many hundreds of years are required to perform
a revolution in some instances, so that their motion has not yet been
detected.
Certain pairs of binary stars whose components are entirely too
close to be separable by the telescope have been discovered by the
spectroscope. If two stars, A and B, are binary, and therefore re-
volving in orbits, they will sometimes be in this position to an ob-
server on the Earth, thus :
AB
T
Earth.
If they are too close to be separated by the telescope, still the spec-
trum of the pair will show the lines of both stars. That is, certain
of the spectrum lines will appear double. At other times one star
will be behind the other, as seen from the Earth, thus :
B
A
1
Earth.
and the spectrum lines will be seen single. If changes like these
occur periodically, as they do, then the orbit of one star about the
other can be calculated. In this way a number of " spectroscopic
binary stars " has been found. The star Zeta Ursce Majoris (Mizar)
(see Fig. 95) is a binary of this class, whose period is about 52 days.
The mass of this system is about 40 times the Sun's mass.
The existence of binary systems shows that the law of gravitation
includes the stars as well as the solar system in its scope, and thus
that it is 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 the stars of such binary
systems as have been investigated do not differ very greatly in mass
from our Sun.
CHAPTER XXVI.
NEBULA AND CLUSTERS.
45. Nebulae. In the star-catalogues of PTOLEMY and
the earlier writers, there was included a class of nebulous
or cloudy stars, which were in reality star-clusters. They
were visible to the naked eye as masses of soft diffused
light like parts of the Milky Way. The telescope shows
that most of these objects are clusters of stars.
As the telescope was improved, great numbers of such
patches of light were found, some of which could be
resolved into stars, while others could not. The latter
were called nebulce and the former star-clusters.
About 1656 HUYGHEXS described the great nebula of
Orion, one of the most remarkable and brilliant of these
objects. It is just visible to the naked eye as a cloudiness
about the middle star of the sword of Orion (a line from
the r of Orion in Fig. 204 to the r of Eridanus passes
through the nebula). The student should look for this
nebula with the eye on a clear winter's night. An opera-
glass will show the nebulosity distinctly; but a telescope is
needed to show it well. Sir WILLIAM HERSCHEL with his
great telescopes first gave proof of the enormous number
of these masses. In 1786 he published a catalogue of one
thousand new nebulae and clusters. This was followed 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 thousand more
393
394
ASTRONOMY.
nebulae. About nine thousand nebulae, mostly very faint,
are now known.
Classification of Nebulae and Clusters. In studying these objects, the
first question we meet is this : Are all these bodies clusters of stars
FIG.
204 THE CONSTELLATION ORION AS SEEN WITH THE
NAKED EYE.
which look diffused only because they are so distant that our tele-
scopes cannot distinguish the separate stars? or are some of them
in reality what they seem to be ; namely, diffused masses of matter?
In his early memoirs, Sir WILLIAM HERSCHEL took the first view.
He considered the Milky Way as nothing but a congeries of stars, and
all nebulae seemed to be but stellar clusters, so distant as to cause the
individual stars to disappear in a general milkiness or nebulosity.
AND CLUSTERS. 395
In 1791, however, he discovered a nebulous star (properly so called)
that is, a star which was undoubtedly similar to the surrounding
stars, and which was encompassed by a halo of nebulous light. His
reasoning on this discovery is instructive.
He says : " Supposing the nucleus and halo 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,
FIG. 205. SPI-RAL NEBULA.
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 produce a star by its
condensation than to depend on the star for its existence."
This was the first exact statement of the idea that, beside stars and
396
ASTRONOMY.
H
NEBULA AND CLUSTERS. 397
star-clusters, we have in the universe a totally distinct series o^ ob-
jects, probably much more simple in their constitution. Observations
on the spectra of these bodies have entirely confirmed the conclusions
of HERSCHEL. The spectroscope shows that the true nebulas are
gaseous.
Nebulae and clusters are divided into classes. A planetary nebula
is circular or elliptic in shape, with a definite outline like a planet.
Spiral nebulae, 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 irom the cuts and descriptions which follow than by formal
FIG. 207. THE MOON PASSING NEAR THE PLEIADES.
definitions. It must be remembered that there is an almost infinite
variety of such shapes. The real shape of the nebula in space ap-
pears to us much changed by perspective.
Vast areas of the sky are covered with faint nebulosity.
Star-clusters. 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, several hundred
stars are seen.
The clusters represented in Figs. 208 and 209 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.
398 ASTRONOMY.
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.
" 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, cceteris
paribus, are the most complete in this figure must have been the
longest exposed to the action of these causes.
FIG. 208. GLOBULAR CLUSTER.
"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 development.
Spectra of Nebulae and Clusters. In 1864, five years after the in-
vention of the spectroscope, the examination of the spectra of the
nebula3 by Sir WILLIAM HUGGINS 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 nebulae
were discontinuous, showing these bodies to be composed of glowing
gas. The nebulae have proper motions just as do the stars. The
great nebula of Orion is moving away from the Sun eleven miles
every second.
NEBULA AND CLUSTERS. 399
The spectrum of most clusters is continuous, indicating that the
individual stars are truly stellar in their nature. In a few cases,
FIG 201). COMPRESSED CLUSTER.
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 from both gaseous
and solid matter.
CHAPTER XXVII.
SPECTRA OF FIXED STARS.*
46. Stellar spectra are found to be, in the main, similar
to the solar spectrum; i.e., composed of a continuous band
of the prismatic colors, across which dark lines or bands
are 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 containing the vapors of metals,
etc. iron, magnesium, hydrogen, etc. The atmosphere
of many stars is quite different in constitution from that of
the Sun, as is shown by the different position and intensity
of the various dark lines that are due to the absorptive
action of the atmospheres of the stars.
Different Types of Stars. In a general way the spectra of all stars
are similar. All of them are bodies of the same general kind as the
San. Yet there are characteristic differences between star and star,
and certain large groups into which stars can be classified certain
types of stellar spectra. It is probable that these different types rep-
resent different phases in the life-history of a star. Of two stars of
the same size and general constitution the whitest is probably the
hottest and the youngest ; the reddest is probably the coolest and
oldest. The hottest stars have the simplest spectra ; the red stars
have complicated spectra and are often variable. The bright stars
of the constellation of Orion have spectra of the simplest type their
atmospheres are mainly made up of helium and hydrogen gases.
Stars like Sirius have little helium in their atmospheres, but much
* See Appendix.
400
SPECTRA OF FIXED STARS. 401
hydrogen and a little calcium. Stars like Procyon have hydrogen
and calcium and magnesium in marked quantities, besides other me-
tallic lines. Stars like Arcturus are characterized by many metallic
lines in their spectra, such as those of iron. Our Sun belongs to
this class. Stars with considerably less extensive hydrogen atmos-
pheres and with considerably more metallic vapors surrounding
them form the next class (like Alpha Orionis, Alpha Herculis and
the variable star Mira Cetis). The red stars, none of which are very
bright, and most of which are variable, form the last type.
It appears that the stars can be arranged in classes corresponding
to diminishing temperatures. The hottest stars have extensive hy-
drogen atmospheres, simple in constitution. They are analogous to
nebulae in many respects and probably are condensed from nebulous
masses. As a star grows older and cooler its spectrum grows more
unlike a nebulous spectrum, more complex, more individual, so to
speak. After passing through a stage like that of our Sun it
reaches the stage of pronounced variability, like the red stars, and
finally becomes a "dark star" like the companion to Algol, for
example.
Stellar Evolution : An irregular and widely extended nebula sub-
ject to gravitating forces tends to become a spherical mass ; spherical
masses of nebulosity subject to central powers tend to become more
condensed and to form nuclei at their centres. It appears to be
likely that such nebulae may condense still further into stars. Stars
very hot and white go through a cycle of changes, and after losing
all their light and heat become "dark stars." This is, in general,
the final stage. If, however, two stellar systems moving through
space should collide, all the bodies of both systems would be quickly
raised to very high temperatures, and in this way a "dark star"
might be re-created and begin a new cycle of existence. If a dark
star like the Earth, for example, were to be suddenly raised to a
very high temperature it would become a gaseous body a miniature
Sun, for example. It is probable that the phenomena of some of
the " new stars " are to be explained in this way.
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
miles per second with which the stars are approaching to
or receding from the Earth along the line joining Earth
402 ASTRONOMY.
and star (the line of sight). The theory of such a de-
termination 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 ex-
periments, 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 the absorptive atmosphere
of the Sun.
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 a, 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 con-
tains in its atmosphere the substance whose existence has been shown
in the Sun hydrogen, for example.
If we contrive an apparatus by which the stellar spectrum is seen
in the lower half, say, of the eyepiece of the spectroscope, while the
spectrum of hydrogen is seen just above it. we find in some cases this
remarkable phenomenon. The three dark stellar lines, a ', b', c', in-
stead 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', c', while preserving its relative dis-
tances the same as those of the comparison group a, b, c, 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 always show a shifting in the same direction, and of
like amount. The figure shows a shifting of the F line in the
spectrum of Sirius, compared with one fixed line of hydrogen. The
bright line of hydrogen is nearer to one side of the dark line in the
stellar spectrum than to the other.
This displacement of the spectral lines is accounted for by a motion
of the star toward or from the Earth. It is shown in Physics that if
the source of the light which gives the spectrum a', b', c' is moving
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 depends
upon the velocity of recession or approach, and this velocity in miles
per second can be calculated from the measured displacement. This
has already been done for many stars.
SPECTRA OF FIXED STARS. 403
The principle upon .which the calculation is made can
be understood by an analogy drawn from the phenomena
of sound. Every one who has ridden in a railway train has
noticed that the bell of a passing engine does not always give
out the same note. As the two trains approach the sound of
the bell is pitched higher, and as they separate after passing
the sound of the bell is lower. It is certain that the driver
of the passing engine always hears his bell give out one and
the same note. The explanation of this phenomenon is as
follows: the bell of the passing engine gives out the note
FIG. 210.^ LINE OF HYDROGEN SUPERPOSED ON THE SPECTRUM
ov Siuius (K#).
C (the middle C of the pianoforte) let us say. That is
it gives oat 512 vibrations, sound-waves, in every second.
Any sonorous body giving out 512 waves per second makes
the note C. If more than 512 sound-waves reach the ear
in a second the note is higher (7jf for example. If fewer
than 512 waves reach the ear in a second the note is lower
Co for example. The engineer hears 512 vibrations
every second. The note of his bell is C'fcj. All the air
around him is filled with sound-waves of this frequency.
404: ASTRONOMY.
The traveller approaching the bell hears the 512 vibrations
given out by the bell every second, and also other vibrations
that his swiftly moving train meets the note of the bell to
him is C% let us say, because his ear collects more than 512
vibrations every second. The traveller receding from the
bell hears fewer than 512 vibrations per second. Not all
of the waves given out by the bell can overtake him as he
moves swiftly away the note of the bell is to him C\> let
us say.
The case is the same for light-waves. The F line of
hydrogen gives out in the laboratory a certain number of
waves per second. If a star is at rest with respect to the
Earth just as many waves reach the observer's eye from the
F line of the star as reach it from the F line of a compari-
son-spectrum of hydrogen. Both sources of light are at
rest with respect to him. If he is moving swiftly towards
the star his eye receives not only the waves sent out by the
star, but also all those that he overtakes. If he is moving
swiftly away from the star his eye receives fewer waves than
the star sends out because not all of them can overtake
him. (It is as if the F% of the star became jPJ in one
case, Ffr in the other.) A shifting of the star-line towards
the violet end of the spectrum indicates an approach of the
Earth to the star; a shifting towards the red end indicates
a recession. The velocity of the motion of approach or
recession is proportional to the amount of the shifting. It
is by a principle of this kind that we can calculate from the
observed shifting of lines in the stellar spectrum the
velocity with which the Earth is approaching a star, or
receding from it.
Motion of the Solar System in Space. If observation
shows that the Earth is approaching a star at the rate of
40 miles per second, we know that the Sun and all the
planets must be moving towards that star, since the Earth
moves in her orbit only 18 miles per second. By making
SPECTRA OF FIXED STARS.
405
allowance for the Earth's motion, the exact velocity of the
Sun towards the star can be calculated. The Sun carries
all his family all the planets with him as he moves
through space. Astronomers are now engaged in solving,
by spectroscopic means, the problem of how fast the solar
system is moving in space, and in what direction it is
moving.
The method employed is somewhat as follows : A large
number of stars is spectroscopically observed and the ve-
locity with which the Sun is approaching each separate
star is accurately determined.
FIG. 211.
Suppose the observations to show that the Sun (O) is ap-
proaching the group of stars A with an average velocity of
12 miles per second ; that it is receding from the group of
stars B (180 away from A opposite to A in the celestial
sphere) at the same velocity ; then it follows that the Sun
with the whole solar system is moving through space to-
wards A with a velocity of 12 miles per second.
406 ASTRONOMY.
Some of the stars of group A may be moving towards the
Sun; some of them may be moving away from the Sun; if
a great many stars are contained in the group their average
motion with respect to the Sun will be zero: there is no
reason to suppose that stars in general have any tendency
to move towards our Sun or away from it. Groups of stars
at C and D and all around the celestial sphere are observed
in the same way, and the final result is made to depend on
air the observed velocities. Researches like this are in
progress at Potsdam, Paris, at the Lick Observatory, and
elsewhere. Final conclusions have not yet been reached.
All that can now be said is that the solar system is moving
towards a point near to the bright star Alpha LyrcB with a
velocity of about 12 miles per second. It will require
some years yet to reach final values. So far as we know
the solar motion is uniform and in a straight line.
CHAPTER XXVIII.
COSMOGONY.
47. A theory of the operations by which the physical
universe received its present form and arrangement is called
Cosmogony. This subject does not treat of the origin of
matter, but only of its transformations.
Three systems of Cosmogony have prevailed at different
times :
(1) That the universe had no beginning, but existed from
eternity in the form in which we now see it. This was the
view of the ancients.
(2) That it was created in its present shape in six days.
This view is based on the literal sense of the words of the
Old Testament. Theological commentators have assumed
that it was created "out of nothing," but the Scripture
does not say so.
(3) That it came into its present form through an ar-
rangement of previously existing materials which were be-
fore " without form and void." This maybe called the
evolution theory. No attempt is made to explain the ori-
gin of the primitive matter. The theory simply deals with
its arrangement and changes.
The scientific discoveries of modern times show conclu-
sively that the universe could not always have existed in
its present form ; that there was a time when the materials
composing it were masses of glowing vapor, and that there
will be a time when the present state of things will cease.
Geology proves beyond a doubt, that the arrangement of
407
408 ASTRONOMY.
the primitive matter to form a habitable Earth has required
millions of years, and Anthropology proves also beyond a
doubt, that the Earth has been inhabited by men for many
thousands. It was not until the latter half of the XVIII
century that such opinions could be held without fear of
persecution, for the lesson " that a scientific fact is as sacred
as a moral principle " has only been fully learned within
the last half century.
An explanation of the processes through which the Earth
and all the planets came into their present forms was first
propounded by the philosophers SWEDENBORG, KANT, and
LAPLACE, and, although since greatly modified in detail,
their fundamental views are, in the main, received. The
nebular hypotheses proposed by these philosophers all start
with the statement that the Earth and Planets, as well as
the Sun, were once a fiery mass.
It is certain that the Earth has not received any great supply of
heat from outside since the early geological ages, because such an
accession of heat at the Earth's surface would have destroyed all life,
and even melted all the rocks. Therefore, whatever heat there is in
the interior of the Earth must have been there from before the com-
mencement of life on the globe, and remained through all geological
ages.
The interior of the Earth is very much hotter than its surface, and
hotter than the celestial spaces around it. It is continually losing
heat, and there is no way in which the losses are made up. We
know by the most familiar observation that if any object is hot inside,
the heat will work its way through to the surface. Therefore, since
the Earth is a great deal hotter at the depth of 50 miles than it is at
the surface, and much hotter at 500 miles than at 50, 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 be-
come as hot as the interior.
Moreover, this loss of heat must have been going on since the be-
ginning, 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 reach a time when the Earth was so hot as to be
COSMOGONY. 409
molten, and finally reach a time when it was so hot as to be a mass of
fiery vapor.
The Sun is 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 know, receiving none back again. A very small portion of
this heat reaches the Earth, and on this portion depends the existence
of life and motion on the Earth's surface. If our supply of solar heat
were to be taken away, all life on the Earth would cease. The
quantity of heat which strikes the Earth is only about 2Tnnnnn>FffT> ^
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.
Since the Sun is constantly losing heat, it must have had more heat
yesterday than it has to-day ; more two days ago than it had yester-
day; and so on. The further we go back in time, the hotter the Sun
must have been. Since we know that heat expands all bodies, it fol-
lows that the Sun must have been larger in past ages than it is now,
and we can calculate the size of the Sun at any past time.
Thus we are led to the conclusion that there must have been a time
when the Sun filled up the whole of the space now occupied by the
planets. It must then have been a very rare mass of glowing vapor.
The planets could not then have existed separately, but must have
formed a part of this mass of vapor. The glowing vapor " a fiery
mist" was the material out of which 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 fife
and motion can no longer exist on our globe.
It is a noteworthy confirmation of this hypothesis that the revolu-
tions of all the planets around the Sun take place in the same direc-
tion and in nearly the same plane. This similarity among the differ-
ent bodies of the solar system must have had an adequate cause. The
Sun and planets were once a great mass of vapor, larger than the
present solar system, that revolved on its axis in the same plane in
which the planets now revolve.
The spectroscope shows the nebulae to be masses of glowing vapor.
We thus actually see matter in the celestial spaces under the very
form in which the nebular hypothesis supposes the matter of our solar
system to have once existed. Some of these nebulae now have the
very form that the nebular hypothesis assigns to the solar nebula in
past ages. (See the frontispiece.) The nebulas are gradually cooling.
The process of cooling must at length reach a point when they will
410 ASTRONOMY.
cease to be vaporous and will condense into objects like stars and
planets. All the stars must, like the Sun, be radiating heat into space.
The telescopic examination of the planets Jupiter and Saturn 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 com-
pare. Such operations can be kept up only through the agency of
heat or some equivalent form of energy. At the distance of Jupiter
and Saturn, the rays of the Sun are entirely insufficient to produce
such changes. Jupiter and Saturn must be hot bodies, and must
therefore be cooling off like the Sun, stars, and Earth.
These and many other allied facts lead to the conclusion that most
bodies of the universe are hot, and are cooling off by radiating their
heat into space.
There is no way known to us in which the heat radiated by the Sun
and stars might be collected and returned to them. It is a funda-
mental principle of the laws of heat that " heat can never pass from
a cooler to a warmer body " that a body can never grow warmer in
a space that is cooler than the body 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 contained in space
will be at a uniform temperature, and then all motion and change of
temperature, and hence the conditions 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
took place in consequence of the cooling and the mutual at-
traction of the parts, and thus arose a number of separate
nebulous masses. One of these masses formed the material
out of which the Sun and planets are supposed to have
been formed. It was probably at first nearly globular, of
nearly equal density throughout, and endowed with a very
slow rotation in the direction in which the planets now
COSMOGONY. 411
move. As it cooled off, it grew smaller and smaller, and
its velocity of rotation increased in rapidity.
The rotating mass we have described had an axis around which it
rotated, and an equator everywhere 90 from this axis. As the velocity
of rotation increased, the centrifugal force also increased. This force
varies as the radius of the circle described by 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 equator would be increased X 4 1 , or eight times. The
gravitation of the mass at the surface, being inversely as the square
of the distance from the centre, or of the radius, would be increased
only four times. Therefore, as the masses continued to contract, the
centrifugal force increased more rapidly 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 contract at the equator, but at the
poles there would be no centrifugal force, and the gravitation of the
mass would grow stronger and stronger in this neighborhood.
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
cooling. At length, 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 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 rotate
around the central part of the mass, which condensed to
form our Sun.
These planetary masses, being very hot, were composed of a central
mass of those substances which condensed at a very high tempera-
ture, surrounded by the vapors of other substances which were more
volatile. We know, for instance, that it takes a much higher tem-
perature to reduce lime and platinum to vapor than it does to reduce
iron, zinc, or magnesium. Therefore, in the original planets, the
limes and earths would condense first, while many other metals would
still remain in a state of vapor.
412 ASTRONOMY.
Each of the planetary masses would rotate more rapidly as it grew
smaller, and would at length form a mass of melted metals and vapors
in the same way as the larger mass out of which the Sun and planets
were formed. These separate 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 in a molten condition, each shining
like the Sun. They would, however, slowly cool by the radiation of
heat from their surfaces. So long as they remained liquid, the sur-
face, as fast as it grew cool, would sink into the interior 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 water at the bottom of the pot is heated, it rises to the sur-
face, 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 gen-
eral mass so viscid, that their motion would be obstructed. The
planet would then begin to solidify. Two views have been enter-
tained respecting the process of solidification.
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 certain 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 outward.
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 com-
COSMOGONY. 413
paratively thin crust. Astronomers and physicists incline to the
former view ; some geologists to the latter one. Whichever view
may be correct, it appears certain that there are lakes of lava im-
mediately beneath the active volcanoes.
It must be understood that the nebular hypothesis is not
a perfectly established scientific theory, but only a philo-
sophical conclusion founded on the widest study of nature,
and supported by many otherwise disconnected facts. The
widest generalization associated with it is that, so far as
can now be known, the universe is not self-sustaining, but
is a kind of organism which, like all other organisms known
to us, 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 that cannot
yet be calculated with certainty, but which cannot in any
event much exceed 20,000,000, and it must end in a system
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 at present
unknown to science.
It must be carefully noted that these conclusions, which
are correct in the main, relate entirely to the transformations
of matter in the past and future time, and say nothing as to
its origin. The original nebula must have contained all the
matter now in the universe, and it must have possessed, po-
tentially, all the energy now operative as light, heat, etc.,
besides the vast stores of energy that have been expended in
past ages. The process by which the physical universe was
transformed from one condition to a later one is the subject
of the nebular hypothesis. The field of physical science is
a limited one, although within that field it deals with pro-
found problems. Astronomy has nothing to say on the
question of the origin of matter nor on the vastly more im-
portant questions as to the origin of life, intelligence,
wisdom, affection.
CHAPTER XXIX.
PRACTICAL HINTS ON OBSERVING.
48. A few Practical Hints on Making Observations.
Lists of a few Interesting Celestial Objects. Stars, Double
Stars, Variable Stars, Nabulae, Clusters. Maps of the Stars.
In the paragraphs that follow a few hints are given for the
benefit of the student who wishes to begin to make simple
observations for himself. Long and detailed instructions
might be set down which would perhaps save many mis-
takes. But it is by mistakes made and corrected that one
learns. A genius is a person who never makes the same
mistake twice. The rest of mankind must educate them-
selves by slow and patient correction of the errors they
commit. Therefore only enough is here set down to start
the student on his way. It will depend on himself and his
opportunities how far he goes.
Observations of the Planets. The accurate places of the planets are
printed in the Nautical Almanac (address Nautical Almanac office,
Navy Department, Washington, D. C.); and many other almanacs
give their approximate positions. The Publications of the Astro-
nomical Society of the Pacific (address 819 Market Street, San Fran-
cisco), and the journal Popular Astronomy (address Northfield,
Minnesota), contain such information, in a form useful to amateurs.
Lists of the eclipses of each year, and of morning and evening stars,
are printed in most diaries, as well as the phases of the Moon, and
the hours of sunrise and moon rise, etc. The daily newspapers fre-
quently print articles naming the planets and stars that are in a favor-
able position for observation.
Mercury is often to be seen, if one knows just where to look. Its
greatest elongation from the Sun is about 29, so that it is seldom vis-
ible in our latitudes more than two hours afte r sunset, or before sun
414
HINTS ON OBSERVING. 415
rise. The student will do well to know its place (from some almanac)
before looking for it, so that no time may be lost in discovering this
planet over agrun. The greatest elongation of Venus from the Sun
is about 45, so that this planet is usually not visible more than about
three hours after sunset, or before sunrise. In a clear sky, however,
Venus may be seen in the daytime, if the position is known. Mars is
easy to distinguish from the other planets by his ruddy color. Jupiter
is the planet next in brightness to Venus, and both Jupiter and Venus
are brighter than the most brilliant fixed star Sirius. The place of
Sirius in the sky can be found on any one of the star-maps, and hence
Sirius can always be distinguished from the planets. Saturn looks
like a rather dull (not sparkling) fixed star. These are the planets
easily visible to the naked eye. If the student finds a bright object
in the sky, he can decide from the star-maps whether it is a fixed
star. If it is not a star, it will not be difficult for him to determine
which of the planets he has found. Uranus is occasionally (just)
visible to the naked eye, but Neptune always is invisible, except in a
telescope. At least one of the asteroids ( Vesta) is sometimes visible
to the naked eye.
The motions of the planets may be studied with the unaided eye,
but nothing can be known of their disks or of their phases without
a telescope. An opera-glass (which usually magnifies about 2 or 3
times) or, better, a field-glass, will be of much use in viewing the
Moon, and if nothing better is available it should be used to view the
planets. But even a small telescope is much more satisfactory.
The student must not expect to see the planetary disks as they are
shown in the drawings of this book. These drawings have usually
been made with large telescopes. Even under very favorable condi-
tions such observations are more or less disappointing to observers
who are not practised.
Observations of Stars, Nebulae, Comets, etc. The brighter stars can
be identified in the sky from the star-maps in this book. Some of
the variable stars and clusters are marked in Fig. 213. Tables V to
VIII (pages 417 to 421) give the places of some of the principal
fixed stars, doub'e-stars, etc. These objects (if they are bright
enough) should first be identified with the naked eye and then studied
with the best telescope available. An opera-glass is better than
nothing ; a good field-glass or a spy-glass is better yet (it represents
GALILEO'S equipment), but a telescope of several inches aperture
with a magnifying power of 50 diameters or more, on a firm stand,
should be used if it is possible to obtain it.
Photography in observation. If the student understands photogra
416 ASTRONOMY.
phy let him try his camera on the heavens. If he directs it to the
north pole and gives an exposure of a couple of hours he will obtain
the trails of the brighter circumpolar stars (see Fig. 29). An expo-
sure of a few minutes on a bright group of stars near the zenith or
in the south (the Pleiades or Orion, for example) will give trails of a
different kind (see Fig. 80). In both these observations the camera
must remain fixed, undisturbed by wind or jars of any kind.
If he can strap his camera to the tube of a telescope (like that
shown in Fig. 79) he can follow a group of stars in their motion
from rising to setting by using the telescope as a finder in the follow-
ing way : I. Select the group to be photographed. It should be
visible in the camera and some bright star of the group should be
visible in the telescope at the same time. The eyepiece of the tele-
scope should be provided with a pair of cross wires, thus -J-, which
the observer can easily insert, if necessary. II. The image of one of
the group of stars must be kept on the cross-wires (by gently and
constantly moving the telescope from east towards west from rising
toward setting) so long as the exposure is going on. In this way
fairly long exposures can be made. If the image of the guiding-star
is put slightly out of focus the guiding is sometimes easier. This
method is also available for photographing a bright comet; only the
student must remember to use the comet itself as a guiding-star (in
the telescope), because the comet has a motion among the stars.
Photographs of the Moon (and Sun) can be made with small cameras,
but unless the camera has a long focus they are disappointingly
small in size. Let the student try to make them, however. For
the Moon, use the quickest plates. For the Sun, use the slowest
plates, the smallest stop and the quickest exposure. In these, as in
all observations, the important matter to the student is to make them
and to find out what is wrong ; and then to make them over again,
correcting mistakes ; and so on until a satisfactory result is obtained.
It is desirable that the school should own apparatus to be used by
the students under the direction of the master. A short list follows :
A celestial globe; a cheap watch regulated to sidereal time; a straight-
edge some three feet long ; a plumb-line ; a field-glass ; a small
telescope ; a star-atlas (UPTON'S, MCCLURE'S edition of KLEIN'S,
PROCTOR'S, are good); books on practical Astronomy (begin with
SERVISS' Astronomy with an Opera-Glass, PROCTOR'S Half Hours with
the Stars, J. WESTWOOD OLIVER'S Astronomy for Amateurs, WEBB'S
Celestial Objects for Common Telescopes, and add to these as needs
arise); books on descriptive Astronomy (begin with the works of Sir
ROBERT BULL, Miss CLERKE'S History of Astronomy in the XIX
Century, FLAMMARION'S Popular Astronomy, etc., and add to these as
LIST OF BRIGHT STARS.
417
opportunity offers); text-books of Astronomy (begin with YOUNG'S
General Astronomy) .
TABLE V.
MEAN RIGHT ASCENSION AND DECLINATION OP A FEW BRIGHT
STARS, VISIBLE AT WASHINGTON, FOR JANUARY 1, 1899.
NAME OF STAR.
Mag.
Right
Ascension.
Annual
Varia-
tion.
Declination.
Annual
Varia-
tion.
a Andromedae
2
h. m. s.
3 9.9
s.
4- 3 08
4 28 31 58
4-20 1
a Cassiopeiae Far.
2U
34 46.3
4- 3.37
4 55 59
4-19.8
/3 Ceti
Q'*
38 31.2
4- 3 00
- 18 32 28
4 19 8
a Ursae Minoris (Pole Star). . .
ft Arietis
2
3
1 22 8.0
1 49 35
4-24.99
4- 3 30
4-88 46 8
-f 20 18 52
418.8
4 17 8
a Arietis ...
2
2 1 28 7
4- 3 36
4 22 59 6
4 17 3
a Ceti
2U
2 56 59 9
4- 3 13
4- 3 41 36
4- 14 4
a Persei
o' 3
3 17 65
4- 4 26
4 49 30 6
4 13 1
TJ Tauri
3
3 41 28 7
4- 3.56
4- 23 47 34
4-ll!4
y 1 Eridani.. .
3
3 53 18 9
4- 2 79
13 47 45
4- 10 5
a Tauri (Aldebaran). ...
1
4 30 74
4 3 43
4- 16 18 23
_i_ 7.7
t Aurigae . .. . .
4 50 24 9
4- 3 90
4- 33 23
_j_ 6
a Aurigae (C'opellit)
1
5 9 13 5
4 4 42
4- 45 53 43
4-44
ft Orionis (Rigel)
ft Tauri
1
2
5 9 41.0
5 19 54 4
4- 2.88
4 3 79
- 8 19 5
4- 28 31 20
+ 4.4
435
S Orionis
214
5 26 50 7
4- 3 06
22 26
429
5 28 16 5
4- 2 65
17 53 41
L 2 8
e Orionis
2
5 31 53
4- 3 04
1 15 59
4-25
a Columbae
2U
5 35 59 5
4- 2.17
- 34 7 40
4- 2.1
a Orionis ....
1
5 49 4' J 2
4- 3 25
4 7 23 18
409
y Geminorum
2
6 31 52 6
4- 3 46
4- 16 29 8
2 8
a Canis Majoris (Sirius) . . . ,
1
6 40 41 9
4 2 68
- 16 34 41
3 5
e Canis Majoris ....
6 54 39 3
4- 36
28 50 4
4 7
a 2 Geminorum (Castor)
a Canis Minoris (Procyori) ....
ft Geminorum (Pollux)
15 Argus
2
1
1
3
7 28 9.4
7 34 1.0
7 39 8.2
8 3 14 5
4- 3.85
4 3.19
-f 3.73
4- 2 56
432 6 36
4- 5 29 3
+ 28 16 12
24 48
- 7.5
- 8.0
- 8.4
10 3
i Ursae Majoris
3
8 52 17 7
4- 4 17
4 48 26 18
13 7
2
9 22 37 4
4 2 95
8 13 15
15 5
9 Ursee Majoris
3
9 26 63
_i_ 4 14
_i_ 52 g 75
T> 7
a Leonis (Regulus)
y 1 Leonis .... ....
1
21^
10 2 59.6
10 14 24 3
-- 3.22
4- 3 29
+ 12 27 39
4 20 21 9
- 17.5
18
a Ursae Majoris
o' &
10 57 29 8
4 3 76
_|_ 62 17 46
19 3
ft Leonis
2
11 43 54 5
4 3 10
-f- 15 8 12
20
y Ursse Majoris
2L<;
11 48 31 2
4- 3 17
-4- *4 TS 2^
20
1-1 t- o so eo co oo oo
5b N Tj< o}nioeo' < t- t- m eo oec
^^g" S oco ^^^ g S Jg 33 g
+++++++++ 4 I I -f++ + 4- + ++ + +414
iili!
1^ " S 3 .
3 s
I 3
If!
liii
/ OQ. ?--^ b
11
S
Mfl
420
ASTRONOMY.
TABLE VII. ;:
A LIST OF A FEW VARIABLE STARS.
STAR.
R. A.
Decl.
Period.
Magnitude.
Remarks.
Max.
Min.
Mira Ceti
h m
2 14
3 2
4 55
6 58
9 42
10 38
13 24
17 10
.17 41
18 46
22 25
23 53
/
- 3 26
+ 40 34
+ 43 41
+ 20 43
+ 11 54
+ 69 18
- 22 46
+ 14 30
-27 48
+ 33 15
+ 57 54
+ 50 50
Days.
331
2%
?
10
313
305
497
90?
7
12.9
5M
429
1.7
2.3
3
3.7
5.2
6
3.5
3.1
4
3.4
3.7
5
uj
3.5J
4.5]
4.5
10
13
9.7
3.9
6
4.5J
...
12
It is best seen about
October.
Observe it in Octo-
ber & November.
Irregular. Of the
Algol type.
Irregular period.
Observe it in June.
Observe it at mid-
summer.
Observe it in Aug.
and September.
Algol (/3 Persei).
e AurigcB
$ Geminorum ....
R Leonis
R Ursce Majoris . .
R Hydrce
X Sagittarii
/3 Lyrce
& Cephei
R Cassiopeia*
LIST OF NEBULAS AND CLUSTERS.
421
^i*l if si l.is*.s3 ..-If^SSIj
ill 113
olibb fV> "I "! o ' = h"S; ^ h ^"So b^S*C ffJ-g ff
5f a 83 5 S-E x- gf = 5 fc ^ lal-g^ 5
Qa^t>3HO0&MI>tthi3l>ptMl>4C>cQHOOi3
+ i
i I +++++++ i +++++
. t- CO T} 05 TO OS OS OS W > in * O 00 -* OS I- 00 -> O O
422
ASTRONOMY.
1 i + l I + i i i ++44- i + i I
c.S a
8* 1
11 2
.
11! fly
p, ~' .i
6* 2 a
^jslS^S
05 G .'tt .
K=
3Jto-a^^
Is51-
2-
52t>,
111 iiillHtlljI^llll
OfeOOfcfeCQDqO>HWHW>-O5Oc
"jf T
e.
iHi
l;ll
= o
^SS
HINTS ON OBSERVING. 423
To see a nebula with advantage it is sometimes advisable to set the
telescope a very little west of it so that the nebula may enter the field
of view by its diurnal motion and pass slowly across it. This can be
repeated as often as desired. Nearly all of these objects are so faint
FIG. 212. MAP OF THE STARS (TO FOURTH MAGNITUDE INCLU-
SIVE) NEAR THE NORTH CELESTIAL POLE.
The names of these stars can be found in figures 214 to 219 following.
that no artificial lights should be near the observer's place. The word
"bright" in the descriptions is a relative term. A bright nebula is
faint compared to a planet.
424 ASTRONOMY.
MAPS OF THE STARS.
The Northern Stars, The constellations near the pole
can be seen on any clear night, while most of the southern
ones can only be seen during certain seasons, or at certain
hours of the night. Fig. 212 shows all the stars down to
the fourth magnitude, inclusive, within 50 of the pole.
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 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. The names of the months
around the margin of the map show the regions near the
zenith during those months. Suppose the observer to
look at nine o'clock (mean solar time) in the evening, to
face the north, and to hold the map with the month up-
ward, he will have the northern heavens as they appear,
except that the stars near the bottom of the map may be
cut off by his horizon.
The Equatorial Stars. The folded map, Figure 213,
shows the equatorial stars lying between 30 north and 30
south declination. The outlines of the constellations are
indicated by dotted lines. The figures of 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 bright-
est stars. The parallels of declination (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 this map 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:
MAPS OF THE STARS. 425
For January 1, 1 hour; For July 1, 13 hours;
February 1, 3 hours;
March 1, 5 "
April 1, 7 "
May 1, 9 "
June 1, 11 "
August 1, 15
September 1, 17
October 1, 19
November 1, 21
December 1, 23
This map and the map preceding it will be found use-
ful in various ways. The six star-maps that follow are
more convenient for ordinary use, however.
Six Star-maps showing the Brighter Stars visihle in the
Northern Hemisphere.* The star-maps in this series were
originally adapted to a north latitude of about 52, so that,
for the latitudes of the United States, they will be slightly
in error, but not so much as to cause inconvenience. Under
each map will be found the date and time at which the sky
will be as represented in the accompanying map ; e. g. , Map
No. 1 shows the sky as it appears on November 22d at mid-
night, December 5th at 11 o'clock, December 21st at 10
o'clock, January 5th at 9 o'clock, and January 20th at 8
o'clock.
The maps are intended for use between the hours of 8
o'clock in the evening and midnight, and the titles are
given with reference to such a use.
It should be borne in mind, however, that the same map represents
the aspect of the constellations on other dates than those given, but
at a different hour of the night. Map No. I, for example, shows the
aspect of the sky on October 23d at 2 A. M., September 23d at 4 A. M.,
and also on February 20th at 6 P. M., as well as on the dates and at
the hours given in the map. For any date between those given, the
map will represent the sky at a time between the hours given ; for
instance, on November 26th, Map No. I will represent the sky at
11:45 o'clock, on November 30th at 11:30 o'clock, and on December 2d
at 11:15 o'clock.
If the maps are held with the centre overhead and the
top pointing to the north, the lower part of the map will be
* From the publications of the Astronomical Society of the Pacific,
1898.
426
ASTRONOMY.
to the south, the right-hand portion will be to the west, and
the left-hand to the east, and the circle bounding the map
will represent the horizon. Each map is intended to show
the whole of the sky visible at these times.
The names of the constellations are inserted in capitals,
while the names of stars and other data are in small letters.
Constellations on the meridian about midnight :
January : Camelopardus, Lynx, Gemini, Monoceros, Orion, Canu
major.
February : Ursa major, Lynx, Cancer, Hydra.
March : Ursa major, Leo, Hydra.
April: Bootes, Libra.
May: Hercules, Ophiuchus, Scorpio.
June: Lyra, Hercules, Sagittarius.
July: Cygnus, Aquila, Sagittarius.
August: Cepheus, Cygnus, Capricornus.
September: Cepheus, Pegasus, Aquarius.
October: Cassiopeia, Andromeda, Pisces.
November: Perseus, Aries, Cetus.
December: Camelopardus, Taurus, Orion
1
+
30
't-
is
15
30
X
W 1C5 150 135 120 1U5 90
x
.-'"' . \
\
j Auriga
"".,"* . "\
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/ -.' 's
+ #
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M .\
* * e . \
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tm nor
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US / /
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We \
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....--" 9*^+y
^ -f^l
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r* -\
1 1 ariu s\
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y
fr Pisce
austrinus
"*?
XXIV XXIII XXII XXI XX XIX XVIII
Fig. 213 .-Map of Stars between 3
# * *
75 CO 45 30 15 345
L *l'e rue u a
t* t.?..
/'-.. Triang'uluni \ ;
'--. n s
...-'
+
^
.'
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... + . a / '+ T
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r} I
*
= V
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ft* j.
+ i
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anus T
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:/
r
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-
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255 240 225 210 195 180 1C5
* * :/ . Jo^-Ai +''''
e : gOHp -V x * '-'
h
* i
30
\ DO
* % + ^ \
p * e
i +
t
''.....'' ''-.;
*8
+ y /
Coma ' ' ,
/
eules
<
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Bootes
^ &
9* / H
r en ice's
*' 6*
4
var
y + *' 8
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ftj
t -. +
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^ *
; ''**. .-
' V +
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^ e
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*
flit '
8*=.
v* ......-'
7ir<7o
y y
i
I
)ph i it
e* /
C A U 8 l\
/8
' IV t*
Ct
+
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^
-
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+ l y /i^
: X
a I
*
."*"* :
Crat e r s ^
' " *
j'i J n
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a* j
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' " +
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% v
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r* : .
y
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= X
.
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o+ .,-".
Centaurus
/Ty
dra
- Lup
US ; :
*?+i
*S
XVII XVI XV XIV XIII XII XI
*th and 30 Soutli Declination,
(Henry Jolt <* OojXjaa York)
MAPS OF THE STARS.
427
MAPI.
North.
-I
South.
FIG. 214.
The sky on November 23, at 12 o'clock P.M.
December 6, at 11 o'clock P.M.
December 21, at 10 o'clock P.M.
January 5, at 9 o'clock P.M.
January 20, at 8 o'clock P.M.
428
ASTRONOMY.
MAPIL
North.
...-*
> xSft-
"""" 4 * * "*$&*
*^\ V"' V '? 5t%
^ ..'^ snWio V JK
U> A
x^a - ^i^v^ / /
w :S|Ko^: >
^H^. fi^j, .^.,. /
;^^SN,S
5IV ' t 3 a . s ,.*'' y' MAOOX
r ^f?^-^
^^ .4V
South.
FIG. 215.
The sky on January 20, at 12 o'clock P.M.
February 4, at 11 o'clock p M.
February 19, at 10 o'clock P.M.
March 6, at 9 o'clock P.M.
March 21, at 8 o'clock P.M.
MAPS OF THE STABS.
429
MAP III.
North,
South.
FIG. 216.
The sky on March 21, at 12 o'clock P.M.
April 5, at 11 o'clock P.M.
A_pril 20, at 10 o'clock P.M.
May 5, at 9 o'clock P.M.
May 21, at 8 o'clock P.M.
430
ASTRONOMY.
MAP IV.
North.
} ,M
*&*
VS >V>*.
<2/
."'
:'*
'"/>!
*>+
\
S^V-'
^^^
,-s
3^f"> va
TS> lf ^'V^
V
^t/
i-A
$
^
K"
/
-%/
V*
J 3 ,.
<^>
South.
FIG. 217.
The sky on May 21, at 12 o'clock P.M.
June 5, at 11 o'clock P.M.
June 21, at 10 o'clock P.M.
July 7, at 9 o'clock P.M.
July 22, at 8 o'clock P.M.
MAPS OF THE STARS.
431
MAP V.
North.
South.
FIG. 218.
The sky on July 22, at 12 o'clock P.M.
August 7, at 11 o'clock p M.
August 23, at 10 o'clock P.M.
September 8, at 9 o'clock P.M.
September 23, at 8 o'clock P.M.
432
ASTRONOMY.
MAP VI.
North.
LV>
.""^
*"'
*>**
X
South.
FIG. 219.
The sky on September 23, at 12 o'clock P.M.
October 8, at 11 o'clock P.M.
October 23, at 10 o'clock P M.
November 7, at 9 o'clock P.M.
November 22, at 8 o'clock P.M.
APPENDIX.
SPECTRUM ANALYSIS.
ALTHOUGH the subject of Spectrum Analysis belongs
properly to physics, a brief account of its relations to
astronomy 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 phys-
ics.
The Prism. When parallel rays of homogeneous light, red for ex-
ample, fall on a face of a prism they are bent out of their course, and
when they emerge from the prism they are again bent, but they still
remain parallel; thus the rays rr, r" ?", are bent into the final di-
rection r' r'. This is true for parallel rays of every color. They re-
main parallel after deviation by the prism. This can be shown by
experiment. If the incident rays r r, in Fig. 220, are red, they will
come to the screen at r' r'. If they are violet rays, they will come to
v f 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 refrangible. The red, with the longest wave-
length, are the least refrangible.
The experiments of Sir ISAAC NEWTON (1704) proved
the,!; 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
433
434 APPENDIX.
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 refrangi-
bility. The rainbow-colored streak on the screen is called
the spectrum; it is a solar, a lunar, or a stellar spectrum
according as the source of the rays is the Sun, Moon, or a
FIG. 220. THE ACTION OP A PRISM ON A BEAM OF WHITE LIGHT.
star. The solar spectrum is very bright; the lunar spec-
trum is much fainter; and the spectrum of a star is far
fainter than either.
If we let parallel rays, r r, of red light come through a circular
hole at Q (Fig. 220), they will form a circular image of the hole at
r' r'. If the hole is square or triangular, a square or 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 wJiite light is passed through a circular hole at Q, circular
images of the hole are formed all along the line r' r f to v' 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 images
will overlap, so that the colors are not pure. If white light falls
SPECTRUM ANALYSIS. 435
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 cer-
tain dark lines, fixed in relative position. These are the
Fraunhofer lines, -so called. He made a map of the solar
spectrum, and on the map he placed the various lines in
their proper places. These lines appear in the same rela-
tive position no matter whether a slit or a very small cir-
FIG. 221. THE SPECTROSCOPE.
cular hole is used, and they belong to the incident light
and are not produced by the apparatus. This simply ren-
ders them visible. They are not seen when the light comes
through wide apertures, on account of the overlapping of
the various images. (See Fig. 222.)
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).
436 APPENDIX.
Fig. 221 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 there-
fore emerge from A in parallel lines. They are deviated
by the prism P, and enter the objective B, forming an
image of the spectrum at 0, which is viewed by the eye
at E.
The Solar Spectrum. Part of this image (of the solar
spectrum) is shown in Fig. 222, except as to color. The
A a B C D Eb F
FIG. 222. A PART OF THE SOLAR SPECTRUM.
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 are lettered A, B, (7,
Z), E) F, G, H. A is below the easily visible red, B is at
its lower edge, C is near the middle of the red, D is a double
line in the orange, J^is in the green, Fis in the blue, G in the
indigo, and H in 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. 221 is pointed toward the Sun
(so that the Sun's rays fall on 8), the spectrum seen is that of the
whole Sun. If we wish to examine the spectrum of a part of the
Sun, as of a spot for example, we must attach the whole instrument
to a telescope, so that 8 is in the principal focal plane of the tel-
escope-objective. An image of the Sun will then be formed by
SPECTRUM ANALYSIS. 43?
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 also
used in order to examine 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 ^J^QJ if J^^..^"~'GontimiOtiB 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 back-
ground the spectrum shows one or more bright lines.
These lines have a definite relative position and are char-
acteristic of the particular gas. The vapor of sodium, for
example, gives two bright lines, whose relative position is
always the same, as laboratory experiments show.
If the source of light is a solid body, intensely heated,
the spectroscope will show a continuous spectrum without
lines, as has been said. If between the solid body and the
slit of the spectroscope 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 ; and these two bright lines
will occupy exactly the same places in the field of view that
the two dark lines formerly occupied.
* Unless under great pressure, when the spectrum is continuous, as
in the case of our Sun, and of stars of similar constitution to the Sun.
438 APPENDIX.
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 by sodium vapor. These
two kinds are the same. What is true of sodium vapor is
true or every gas. Every gas absorbs light of the same kind
(wave length) as that which it emits.
If a spectroscopist had to determine what kind of gas was contained
in a certain jar, he might do it in two ways. He might heat it in-
tensely, 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 measure the positions of the dark lines
of its absorption-spectrum. The positions of the lines will be the
same in both cases. By comparing the measures with previous meas-
ures for known gases, the name of the particular gas in question
would become known to him. New chemical elements have been
discovered by the spectroscope. The spectrum of the mixture that
contained them showed previously unknown spectrum lines. They
were first detected by the presence of these unknown lines and then
separated from the known gases present in the mixture.
Comparison of the Spectra of Incandescent Gases with
the Solar Spectrum, Laboratory experiments on known
gases show the positions of the spectral lines characteristic
of each gas or vapor. The positions of the lines of magne-
sium or of hydrogen, for example, are accurately known.
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 known gas or of the vapor of some known
metal. For example, the vapor of iron has several hundred
lines, whose positions are accurately known by laboratory
experiments. In the solar spectrum there are several
hundred 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.
SPECTR UM ANAL 7 SIS. 439
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 KOCHHOFF and
BUNSEN (1859) to this interpretation of the observation.
We have seen (Part II., Chap. XVI) that the Sun is composed 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 characteristic. If a solid in-
candescent body were placed in a laboratory and surrounded by the
vapors of iron, hydrogen, sodium, etc., we should see the same spec-
trum that we do see when we examine the Sun.
The kind of evidence is easily understood from the foregoing. Only
the spectroscopist can fully appreciate the force of it. The resulting
inference that the Sun's atmosphere contains the vapors of the metals
named is certain. These vapors exist uncombined in the Sun's atmos-
phere. The temperature and the pressure are too high to allow their
chemical combination.
INDEX.
Aberration of light, 257.
Achromatic telescope described,
121.
ADAMS'S work on perturbations
of Uranus, 342.
Algol (variable star), 388.
Altitude of a star defined, 81.
ANAXIMANDER, (B. c. 610), 6.
ANAXAGORAS (B. c. 500), 6.
Angles, 22.
Annular eclipses of the Sun, 230.
Apex of solar motion, 381.
Apparent motion of the Sun, 154.
Apparent motion of a planet, 180.
Apparent time, 90.
ARCHIMEDES, (B. c. 287), 7.
ARISTOTLE, (B. c. 384), 7.
Asteroids, 322.
Astronomical instruments (in
general), 112.
Astronomy (defined), 1.
Atmosphere of the Moon, 317.
Atmospheres of the planets. See
Mercury, Venus, etc.
Azimuth denned, 81.
BARNARD discovers satellite of
Jupiter, 325.
BESSEL'S parallax of 61 Cygni
(1837), 383.
Binary stars, 391.
BOND'S discovery of the dusky
ring of Saturn, 1850, 336.
Books (a list of), 416.
BOUVARD on Uranus, 341.
BRADLEY discovers aberration in
1729 256.
BUNSEN, 439.
Calendar, 247.
CASSINI discovers four satellites
of Saturn (1684-1671), 339.
Catalogues of stars, 376.
Celestial globe, 74.
Celestial photography, 145, 415.
Celestial sphere, 18.
Centre of gravity of the solar
system, 275.
Change of the Day, 101.
Chronology, 247.
Chronometers, 115. .
Clocks, 112.
Clusters of stars, 393.
Comets, 357.
Comets' orbits, 361.
Comets' tails, repulsive force,
363.
Conjunction (of a planet with the
Sun) defined, 183.
Constellations, 371.
Construction of the heavens, 369.
Co-ordinates of a star, 77.
441
442
INDEX.
COPERNICUS, 8, 191.
Cosmogony, 407.
Corona of the Sun, 282, 290.
Dark stars, 389.
Day, how subdivided into hours,
etc., 83.
Days, mean solar and solar, 90.
Declination of a star defined, 30.
Distance of the fixed stars, 381.
Distribution of the stars, 371.
Diurnal motion, 41, 59.
DON ATI'S comet (1858), 358.
Double (and multiple) stars,
390.
Earth, general account of, 232.
Earth's density, 238.
Earth's dimensions, 234.
Earth's mass, 237.
Eclipses of the Moon, 224.
Eclipses of Sun and Moon, 222.
Eclipses of the Sun, explanation,
228.
Eclipses of the Sun, physical
phenomena, 289.
Eclipses, their recurrence, 230.
Ecliptic defined, 161.
Elements of the orbits of the
major planets, 276.
Elongation (of a planet), 183.
ENCKE'S comet, 367.
Epicycles, 190.
Equation of time, 150.
Equator (celestial) defined, 30.
Equatorial telescope, 133.
Equinoxes, 160, 163.
ERATOSTHENES, (B. c. 276), 7.
Eyepieces of telescopes, 121.
FABRITIUS observes solar spots
(1611), 285.
Figure of the Earth, 232.
FRAUENHOFER'S Experiments
with the Prism, 435.
Future of the solar system, 413.
Galaxy or milky way, 372.
GALILEO invents the telescope
(1609), 117.
GALILEO observes solar spots
(1611), 285.
GALILEO'S discovery of satellites
of Jupiter (1610), 325.
GALLE observes Neptune (1846).
343.
Gases, spectra of incandescent,
437; in meteoric stones, 362.
Geodetic surveys, 235.
Globe (celestial), 74.
Gravitation extends to stars, 392.
Gravitation resides in each par-
ticle of matter, 209.
Gravity, terrestrial, 204, 237.
Gregorian calendar, 247.
HALLEY predicts the return of a
comet (1682), 363.
HALL'S discovery of satellites of
Mars, 313.
HERSCHEL (W.) discovers two
satellites of Saturn (1789), 339.
HERSCHEL (W.) discovers two
satellites of Uranus (1787), 340.
HERSCHEL ( W. ) discovers Uranus
(1781), 339.
HERSCHEL'S catalogues of nebu-
la?, 393.
HERSCHEL (W.) states that the
solar system is in motion (1783),
381.
HERSCHEL'S (W.) views on the
nature of nebulae, 395.
Hints on observing, 414.
HIPPARCHUS (B. c. 160), 7.
INDEX.
443
Horizon (celestial sensible) of
an observer defined, 30, 31.
Hour-angle of a star defined, 78.
HUGGINS first observes the spec-
tra of nebulae (1864), 397.
HUYGHENS discovers a satellite
of Saturn (1655), 339.
HUYGHENS' explanation of the
appearances of Saturn's rings
(1655), 334.
Inferior planets defined, 185.
JANSSEN first observes solar
prominences in daylight, 291.
Julian year, 247.
Jupiter, 325.
KANT'S nebular hypothesis, 408.
KEPLER'S laws enunciated, 198.
KIRCHHOFF, 439.
LAPLACE'S nebular hypothesis,
408.
LAPLACE'S investigation of the
constitution of Saturn's rings,
338.
LASSELL discovers Neptune's sat-
ellite (1847), 345.
LASSELL discovers two satellites
of Uranus (1847), 340.
Latitude of a place on the earth
defined, 26, 59.
Latitude of a point on the earth
is measured by the elevation of
the pole, 59.
Latitudes and longitudes (celes-
tial) defined, 164.
Latitudes (terrestrial), how deter-
mined, 105.
LE VERRIER computes the orbit
of meteoric shower, 355.
LE VERRIER'S work on perturba-
tions of Uranus, 342.
Light-gathering power of an ob-
ject-glass, 122.
Light-ratio (of stars) is about ^,
374.
List of bright stars, 417.
List of double stars, 419.
List of variable stars, 420.
List of nebulae and clusters, 421.
Local time, 95.
Longitude of a place, 26, 96.
Longitude of a place on the
earth (how determined), 98.
Longitudes (celestial)defined, 164.
Lucid stars defined, 374.
Lunar phases, nodes, etc. See
Moon's phases, nodes, etc.
Magnifying power of an eye-
piece, 120.
Major planets defined, 270.
Maps of the stars, 423 et seq.
Mars, 303.
Mars's satellites discovered by
HALL (1877), 313.
Mass of the Sun in relation to
masses of planets, 265.
Masses of the stars, 378.
Mean solar time defined, 90.
Mercury, 299.
Meridian (celestial) defined, 34.
Meridian circle, 129.
Meridian line (established), 152.
Meridian (terrestrial) defined, 34.
Meteoric showers, 351.
Meteoric stones, gases in, 362.
Meteors and comets, their rela-
tion, 354.
Meteors, 347.
Micrometer, 141.
Milky Way, 372.
Minor planets defined, 270.
444
INDEX.
Minor planets, general account,
322.
Mira Ceti (variable star), 386.
Model of a meridian circle, 132.
Model of an equatorial, 138.
Months, different kinds, 246.
Moon, general account, 315.
Moon's light ti^nro of Sun's, 317.
Moon's phases, 216.
Moon's parallax, 262.
Moon photographs, 320.
Moon, spectrum of the, 317.
Moon's surface, does it change ?
320.
Motion of solar system in space,
404.
Motion of stars in the line of
sight, 401.
Nadir of an observer defined, 30.
Nautical almanac described, 150.
Nebulae and clusters in general,
393.
Nebular hypothesis stated, 407.
Neptune, discovery of, by LE
VERRIER and ADAMS (1846),
341.
Neptune, 341.
New stars, 387.
NEWTON (H. A.) on meteors, 355.
NEWTON (I.), The Principia
(1687), 8; calculates orbit of
comet of 1680, 361 ; Spectrum
Analysis experiments, 433,
Objectives, or object-glasses, 120.
Obliquity of the ecliptic, 171.
Occultations of stars by the Moon
(or planets), 230.
OLBERS'S hypothesis of the origin
of asteroids, 323.
Old style (in dates), 247.
Opposition (of a planet to the
Sun) defined, 183.
Parallax (in general) defined, 107.
Parallax of the Sun, 262.
Parallax of the stars, general ac-
count, 109.
Pendulum, 115.
Periodic comets, 363.
Penumbra of the Earth's or
Moon's shadow, 131.
Perturbations, 213.
Photography its use in astron-
omy, 145.
Photographic star- charts, 323.
Photosphere of the Sun, 281.
PIAZZI discovers the first asteroid
(1801), 323.
Planets, their relative size ex-
hibited, 277.
Planetary nebulae defined, 397.
Planets, their apparent and real
motions, 179.
Planets, their physical constitu-
tion, 345.
Pole of the celestial sphere de-
fined, 46.
Precession of the equinoxes, 248.
Prism, The, 434.
Problem of three bodies, 213.
Progressive motion of light, 254,
331.
Proper motion of the sun, 379.
Proper motions of stars, 379.
PTOLEMY (B. c. 140), 7, 190.
PTOLEMY'S system of the world,
190.
PYTHAGORAS (B. c. 582), 6.
Radiant point of meteors, 352.
Radius vector, 195.
Reflecting telescopes, 123.
INDEX.
445
Refracting telescopes, 119.
Refraction of light in the atmos-
phere, 242.
Resisting medium in space, 367.
Reticle of a transit instrument,
126.
Retrogradations of the planets
explained, 187.
Right ascension of a star defined,
30, 80.
Right ascensions of stars, how
determined by observation, 127.
ROEMER discovers (1675) that
light moves progressively, 254.
Saturn, 331.
Seasons, The, 174
Sextant, 146.
Sidereal time explained, 83.
Sidereal year, 246.
Signs of the Zodiac, 169.
Solar corona, etc. See Sun.
Solar heat, its amount, 293.
Solar motion in space, 404.
Solar parallax, 262.
Solar prominences gaseous, 291.
Solar system, description, 269.
Solar system, its future, 413.
Solar temperature, 294.
Solar time, 90.
Solstices, 162, 163.
Space, 15.
Spectroscope, The, 435.
Spectrum Analysis, 433.
Spectrum ; Solar corona, 291 ;
Lunar, 317 ; Nebulae and Clus-
ters, 398; Fixed Stars, 400 ; as
indicating motions of stars, 401 ;
Solids and Gases, 437; Solar,
436.
Standard time (U. S.), 99.
Star-clusters, 397.
Stars had special names 3000
B. c., 375; magnitudes, 374;
parallax and distance, 381, 382;
about 2000 seen by the naked
eye, 371; proper motions, 379;
spectra, 400.
Star-maps, 423 et seq.
STRUVE (W!) determines stellar
parallax (1838), 383.
Summer solstice, 162.
Sun's apparent path, 159.
Sun's atmosphere, 281, 289.
Sun's constitution, 280.
Sun-dial, 114.
Sun's (the) existence cannot be
indefinitely long, 413.
Sun's mass over 700 times that
of the planets, 275.
Sun, physical description, 280.
Sun's proper motion, 404.
Sun's rotation-time about 25 days,
286.
Sun, Spectroscopic observations
of the, 436.
Sun-spots and faculae, 285.
Sun-spots are confined to certain
parts of the disk, 286.
Sun-spots, their periodicity,
287.
Superior planets (defined), 185
SWEDENBORG'S nebular hypothe-
sis, 408.
Telescopes, 119.
Telescopes (reflecting), 123.
Telescopes (refracting), 119.
TEMPEL'S comet, its relation to
November meteors, 354.
Temporary stars, 386.
THALES (B. c. 640), 5.
446
INDEX.
Tides, 219.
Time, 83, 94.
Total solar eclipses, description
of, 289.
Trails (of stars), 51, 52.
Transit instrument, 124.
Transits of Mercury and Venus,
303.
Transits of Venus, 264.
Triangulation, 235.
Twilight, 243.
TYCHO BRAHE observes new star
of 1572, 387.
Units of mass and distance,
Universal gravitation discovered
by NEWTON, 214.
Uranus, 339.
Variable and temporary stars,
386.
Variable stars, theories of, 387.
Velocity of light, 255.
Venus, 300.
Vernal equinox, 160.
Weight of a body defined, 237.
Winter solstice, 163.
Years, different kinds, 246.
Zenith defined, 30.
Zodiac, 169.
Zodiacal light, 356.
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