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AMERICAN SCIENCE SERIES, ELEMENTARY COURSE 



ELEMENTARY ASTRONOMY 



tA BEGINNER'S TEXT-BOOK 



EDWARD S. HOLDER M.A., Sc.D., LL.D. 

Sometime Director of the Lick Observatory 



NEW YORK 
HENRY HOLT AND COMPANY 

1899 



/ 



TWO COPIES RECEIVED, 

Office of ths 
Register of Coevrl.k.. 



Copyright, 1899, 

BY 

HENRY HOLT & CO. 



SECOND COPY, 



ROBERT DRUMMOND. PRINTER, NFW 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 } 7 oung 
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 



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 nebulas are not exceptional bodies of unique nature, 



INTRODUCTION. V 

but they are examples of what our own solar system 
was in 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 nebulae 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 hoio 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. vil 

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 Simon 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. 
Keeler, 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 of 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 
Newtok'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 nebulas, 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. Proc- 



INTRODUCTION. ix 

tor, Sir Eobert 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 nebulae 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. tS. 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 1 79 

X. Universal Gravitation 203 

XL 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. 


o 


The Sun. 


3 Mars. 


© 


The Moon. 


U Jupiter. 


» 


Mercury. 


^ Saturn. 


9 


Venus. 


5 Uranus. 


or $ 


The Earth. 


f 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 : 



Letters. 


Names. 


Letters. 


Names. 


A a 


Alpha 


N v 


Nu 


B (3 


Beta 


E ? 


Xi 


r r 


Gamma 


o 


Omicron 


J d 


Delta 


n % % 


Pi 


E e 


Epsilon 


p P 


Rho 


z c 


Zeta 


^ a s 


Sigma 


Hr, 


Eta 


T v 


Tau 


$ e 


Theta 


T v 


Upsilon 


I i 


Iota 


£ (p 


Phi 


K K 


Kappa 


X X 


Chi 


A X 


Lambda 


W tft 


Psi 


M ju 


Mu 


£1 GO 


Omega 



THE METRIC SYSTEM. 

MEASURES OF LENGTH. 

1 kilometre = iOOO metres = 0.62137 mile. 
1 metre = the unit = 39.370 inches. 

1 millimetre = j^ of a metre = 03937 inch. 

MEASURES OF WEIGHT. 

1 kilogramme = 1000 grammes = 2.2046 pounds. 



1 gramme = the unit 



= 15.432 grains. 



The following rough approximations may be memorized 



of a mile, but less than ^Tof 



The kilometre is a little more than 
a mile. The mile is 1 T % kilometres. 

The kilogramme is 2i pounds. The pound is less than half a kilo- 
gramme. 

One metre is 3.3 feet. One metre is 39.4 inches. 



ASTRONOMY. 



CHAPTER I. 

INTRODUCTORY— HISTORICAL. 

1. Astronomy denned. — Astronomy (from the Greek 
acrrr/p, a star, and vojaos, a law) is the science that is con- 
cerned abont the laws that the heavenly bodies obey, and 
with a description of the bodies themselves both as they ap- 
pear to be and as they really are. For instance the Snn ap- 
pears to ns very different from a bright star; bnt astron- 
omy shows that the Sun is itself a star like thousands of 
others that we see in the sky at night. The Sun appears to 
move across the sky from east to west, from rising to set- 
ting, every day. Astronomy explains that this motion is 
only apparent and that, in fact, it is caused by the 
Earth's turning on its axis, daily. 

The Sun appears to move among the stars so as to go 
completely around the sky from one star back to the same 
star again every year. Astronomy proves that, in fact, 
the San does not move, but that its apparent course is 
nothing but the result of the Earth's real motion around 
an orbit — a path — with the Sun near its centre. The 
planets, like the stars, appear to shine by their own light. 

1 



2 ASTRONOMY. 

Astronomy shows that the planets shine by reflected sun- 
light, while the light of the stars is native to them. As- 
tronomy is the science that seeks the trne explanation of 
the appearances presented by the stars. Astronomy is the 
science of the stars; or more particularly, it is the science 
that explains what the stars really are, how they really 
move, and why they appear to move as they do. The 
word star is used so as to include planets, comets, the 
San, the Moon, etc. It is used as the Greeks used it, to 
mean any heavenly body. 

2. How we get our notions of the Universe of Stars. — We 
know things on the Earth through our senses, by touching 
them, tasting, smelling, hearing, or seeing them. A piece 
of iron can be felt and weighed as well as seen. If one 
of our senses makes a mistake, another sense often comes 
in to correct the error. A piece of cork might be painted 
so as to look precisely like a piece of iron of the same size. 
The sight alone could not distinguish between them. But 
if we take the two things in our hands, the sense of touch 
or of weight detects a difference at once. 

Stars in the sky are known to us only through the sense 
of sight. If that sense is deceived, there is no other one 
to correct it. A blind person can know much about things 
on the Earth, but he can know very little indeed about 
the stars that he cannot see. All our first-hand notions of 
the universe of stars come to us through our sense of sight. 

Our eyes tell us how things appear to be, and we do not 
know how they really are until we have reasoned about the 
appearances and sifted out the truth. A bright rainbow 
looks almost like a solid arch in the sky, while it is, in 
fact, not in the sky at all. It is in our own eyes. When 
we travel in a railway train, parts of the landscape seem 
to be moving about other parts ; yet nothing is more cer- 
tain than that the landscape is really unchanged. It re- 
quires reasoning to interpret such appearances. 



INTROD UGTOB Y— HISTORICAL. 3 

— What senses can you use to learn about things on the Earth ? 
Give an example of a thing that you can touch ? of a thing that you 
can taste ? of a thing that you can hear ? From all these separate 
senses you gain notions of things on the Earth. How do you get your 
ideas about a star ? It is by the sense of sight alone, is it not ? If 
you have only one sense to help you, you have to be extremely care- 
ful not to be deceived by it. Give some examples of how the sense 
of sight deceives in appearances on the Earth. 

3. The Heavens were carefully observed by the An- 
cients. — The very first man could not fail to notice the 
rising and setting of the Sun. The coming of Night — 
often a time of terror and danger to him — was a mystery ; 
and the advent of successive days was a perpetual miracle. 
The Sun brought cheerfulness, safety, warmth, comfort. 
His rays made plants grow and provided food. He was 
worshipped as a God by the men of early times. When 
the Suu was darkened by an eclipse and the day itself grew 
black the people were filled with dread. Special men — 
priests — were appointed to observe such occurrences and 
to foretell them. It was by the diligent watching of these 
priests that the different appearances in the sky were first 
carefully noted, and the first lists of the stars made. 

By and by, as men in general had more leisure, the 
science of the stars, like other sciences, was studied for its 
own sake. Men were curious to understand lohy the Sun 
rose and set; why it was sometimes eclipsed, and so forth. 
Moreover, their knowledge of astronomy was put to prac- 
tical uses. In the earliest times navigators did not dare to 
venture out of sight of land, or to make voyages at night. 
They sailed from headland to headland during the day, and 
tied their little vessels to the shore at night. They steered 
their course by landmarks. But wise men had noticed 
that while the stars in general rose and set, there were 
some stars that were always visible — the North Star, for 
example. They could use the North Star for a steering- 
mark by night, then ; and so they did. 



4 ASTRONOMY. 

Nearly three thousand years ago (1012 B.C.) Solomon 
built the Temple at Jerusalem and ornamented it with gold 
brought by ships from South Africa. The Phoenicians 
(who lived on the north shores of Africa) brought tin 
from England about the same time. These long voyages 
must have been made by using the stars as guides by night. 




Fig. 1.— The Stars of the Northern Sky. 

The Pole-star is at the centre of the cut. The Great Bear (the Dipper) is 
at the left-hand side. The arrows show the direction in which the stars 
move round the pole. 

The mariner's compass, which is our guide nowadays, was 
not known in Europe before a.d. 1300, though the Chi- 
nese sailors used it long before that time. 






IN TROD UCTOR Y-HISTORICAL. 5 

— What was tlie earliest observation of astronomy? Who were 
the first astronomers? After the priests, who studied the stars? 
How did astronomy make itself useful to navigation ? What star is 
always visible on clear nights in our part of the world ? Does the 
North Star rise and set ? Mention some long voyages made by the 
ancients. 

4. Some of the great astronomers of ancient times. 

"We do not know the names of the ancient priests and 
wise men of Assyria, Babylon, China, and Egypt who first 
studied the stars. A few of their records that have come 
down to ns date back to 2200 B.C. in Chaldsea and to 2900 
B.C. in China. Our history of astronomy begins long 
after their time, with the Greeks, about six centuries be- 
fore Christ, about 2500 years ago. The Greeks of that time 
were a very intelligent, clever, hardy, adventurous people, 
eager to learn and to practice what they learned. They 
were good sailors and good soldiers. 

Thales (pronounced tha'lez), one of the seven wise men 
of Greece, was born about 640 B.C. He showed his coun- 
trymen how to divide the year into seasons. At midsum- 
mer the Sun at noon was higher in the heavens than at any 
other time of the year (about June 21). At midwinter 
the Sun, at noon, was lowest (about December 22). These 
were the two solstices (pronounced soTsti-ces). About 
March 20 and September 22 the days and nights were of 
equal length (at the two equinoxes). March 20 was the 
vernal, or spring, equinox; September 22 was the autum- 
nal equinox. Each and every year could be divided into 
seasons in this way because the Sun was always highest in 
the heavens (nearest to the point overhead) in June, al- 
ways lowest in December ; because the days and nights 
were always of equal length in March and in September. 
Thales did not know why this was so. But he knew the 
facts. And he first showed the Greeks how to divide their 
year into parts. Before his time the Greek sailors had 



6 ASTRONOMY. 

steered their ships by the stars of the Great Bear (see Fig. 
1). He showed them, it is said, that the stars of the 
Little Bear, which were nearer the pole, would serve the 
purpose better. " . 

Anax'i^andee, a friend of Thales (610 B.C.) invented 
the sun-dial. The shadow of an upright column made by 
the Sun moved during the day, and the motion of the 
shadow marked the passing of the hours. Sun-dials were 
the first clocks. He explained why it is that the Moon 
changes every month from a crescent (new Moon) to a 
full Moon ; and other matters. 

Pythag'oras (born 582 B.C.) travelled in Egypt and 
learned much of the science of the Egyptian priests. Sev- 
eral of the Egyptian pyramids were built at least a thou- 
sand years before Christ, and many of them were built by 
astronomical rules, so as to face the North Star and so 
forth. Pythagoras brought much foreign science home 
to the Greeks. It was he who first taught his countrymen 
that the morning and the evening star ( Venus) was the 
same body. It had formerly been thought that Phos- 
phorus (the name for the morning star) and Hesperus (the 
evening star) were two different planets. It was a great 
discovery to learn that there was only one planet, some- 
times seen in the west at sunset, sometimes in the east 
about sunrise. You know the fact, just as Pythagoras 
did twenty-four centuries ago. He did not thoroughly 
understand why it was so, but the reason will be plain to 
you before you have finished this little book. 

Anaxag'oras (born 500 B.C.) knew all the bright plan- 
ets — Mercury j Venus, Mars, Jnpiter, and Saturn — and 
understood how they moved in the heavens, among the 
stars. He knew that the stars did not move among each 
other. A group of stars like the Great Dipper (see Fig. 
1) keeps the same shape during centuries. Planets (wan- 
dering stars) move among the fixed stars. Anaxagoras 



INTROD UCTORY— HISTORICAL. 7 

explained eclipses too. He said that the dark body of the 
Moon came in between the Sun and the Earth and shut off 
the Sun's light, just as your hand held in front of a candle 
shuts off its light. 

Ar'istotle (born 384 B.C.) was the first Greek to prove 
that the Earth is a globe. He was the friend of Alexan- 
der the Great and the pupil of Plato, who was the pupil 
of Socrates. He studied every kind of science and wrote 
many books. (Books in his day were manuscripts of 
course ; printing was not invented in Europe till about 
a.d. 1450, though the Chinese had practiced the art long 
before.) Alexander the Great founded a splendid city 
— Alexandria, in Egypt — and endowed it with schools, col- 
leges, libraries, museums, observatories. It was full of 
learned men of all sorts : physicians, geographers, gram- 
marians, mathematicians, and among them were many 
famous astronomers. Euclid, the geometer, was born 
there about 300 B.C. ; Archime'des, the famous mathe- 
matician (born 287- B.C.), studied there ; Eratos'thenes 
(born 276 B.C.) was the keeper of the Royal Library, and 
there he made a great map of the world and tried to 
measure the circumference of the earth. 

Hipparchus (born 160 B.C.) was an Alexandrian, too, 
and he is the Father of Astronomy. He collected all the 
observations of the men who had gone before him and 
made great discoveries of his own, of which we shall hear 
more. Most of his writings are lost, but his discoveries 
are described by Ptolemy of Alexandria (who lived in the 
first century after Christ) in his great work the Almagest. 
This book, which sums up all the astronomical knowledge 
of the ancients, was the greatest scientific work of the Old 
World. Its doctrines were believed and taught in all the 
schools and universities of Europe from Ptolemy's time 
up to the time of Galileo (died 1642) — that is, for fifteen 
centuries. 



8 ASTRONOMY. 

Ptolemy's book declared that the Earth was the centre 
of the Universe, and that the Sun and all the planets moved 
round it. Another great book was written by Copernicus 
(died 1543) to prove that the Snn and not the Earth was 
the centre of the system; and that the Earth was only one 
of the planets, all of which moved round the Snn. This 
was and is the truth ; but it was not established until the 
discoveries made by Galileo (1610) with the telescope 
that he constructed. 

Still another great book, the Principia, was written by 
Sir Isaac Newton in 1687, to prove that all the motions 
of all the planets and all the stars are the results of one 
single force — the force of gravitation or attraction exerted 
by every heavy body on every other such body. New- 
ton is the Father of Modern Astronomy, just as Hip- 
parchus was the Father of the Astronomy of the Ancients. 
The books of Ptolemy, of Copernicus, and of Newton 
are landmarks in the history of Astronomy. Their dates 
should be remembered: A.D. 140, a.d. 1543, A.D. 1687. 

— When does the history of astronomy begin? To what nation 
did the first learned astronomers belong? What sort of a people 
were the Greeks ? Who showed the Greeks how to divide the year 
into seasons ? When did Thales live ? Who invented the sun- 
dial ? Who first explained the changes in the Moon's shape ? 
When did Anaximander live ? What Greek brought home the 
learning of the Egyptians ? When did Pythagoras live ? Who 
first taught how the planets moved among the stars ? and that the 
stars were fixed? and explained eclipses? About what time did 
Anaxagoras live ? When did Aristotle live? He was the friend 
of what great King? Who founded Alexandria in Egypt? What 
sorts of learning were encouraged there ? Name some of the famous 
men who studied and taught there. Who is called the Father of 
Astronomy ? What is the name of Ptolemy's great book ? How 
long was the Ahnagest the greatest authority on astronomy ? Where 
was the centre of the Universe acording to Ptolemy ? Where did 
Copernicus (1543) place it ? Whose discoveries proved Coperni- 
cus to be right ? Who constructed the first telescope ? When did 



INTROD UCTOR Y— HISTORICAL. 9 

Galileo live ? Who is the Father of Modern Astronomy ? When 
was the Principia of Sir Isaac Newton written? 

5. How Astronomy might be studied. 

In the paragraphs just preceding, a few of the names of the great 
men of past times have been mentioned and something has been said 
of their discoveries. If there were time enough there could be no 
better way to study Astronomy than to follow its history step by step 
from the most ancient times until now. Six centuries before Christ, 
2500 years ago, the earliest Greek philosophers began to study 
science for its own sake. They were curious about the world around 
them and about all the appearances they saw in the sky. They 
wished to understand the motions of the planets, their distances, the 
shape and size of the Earth, the cause of eclipses, and so on. One 
after another of their great men accurately described or fully ex- 
plained motions or appearances in the sky. 

Each philosopher taught what he had learned to his favorite 
pupils by word of mouth. They in their turn taught others in the 
same way. Finally in the time of Alexander the Great (332 B.C.) 
the city of Alexandria in Egypt was founded, and splendidly en- 
dowed with colleges, schools, museums, observatories, and so forth. 
Learned men were invited thither from every other city. For sev- 
eral centuries it was the centre of learning for the whole world. Its 
libraries contained 700,000 manuscripts. Here a succession of great 
astronomers and mathematicians laid the foundations of the science. 
The work of Hipparchus was gathered together in a systematic 
treatise (the Almagest) by Ptolemy, and this book held its place of 
authority for fifteen centuries. 

Alexandria was conquered by Rome in 30 B.C. When the Roman 
Empire was ruined in the IV century the fortunes of the city de- 
clined, and it was itself captured and sacked by the Saracens in 641 
A.D. Learning, especially scientific learning, was at a very low ebb 
in Europe during the Dark Ages (a.d. 400 to 1400). It was not 
until the time of Columbus (1492) and Copernicus (1543) that ad- 
vances were made, except by the Moors in Spain (709 a.d. to 1492). 
The universities and schools established in these centuries still 
taught the astronomy of Aristotle and of Ptolemy. 

The great book of Copernicus (De Orbium ccelestium revolutioni- 
bus — on the revolutions of the celestial bodies) was printed in 1543. 
It announced and proved the great discovery that the Sun and not 
the Earth was the centre of the celestial motions. The doctrine of 
Ptolemy declared that the Sun and planets moved around the 
Earth. Galileo constructed the first astronomical telescope in 1609, 



10 ASTRONOMY. 

and in 1610 he made such discoveries by its aid that the Copernican 
doctrine was fully established in the minds of all competent judges. 
But there were few such judges in his day. 

Kepler discovered the laws according to which the planets move 
in their orbits in the years 1609-1618. But it was not until the ap- 
pearance of Sir Isaac Newton's Principia in 1687 — a little more 
than two centuries ago — that modern astronomy was born. He an- 
nounced and proved that all the motions and all the appearances in 
the Universe were mere consequences of a single law of gravitation, 
of attraction. Since his time immense advances have been made, but 
most of them are but consequences of his law, and are explained by it. 
Astronomical instruments have been wonderfully improved also, and 
great discoveries have been made. The system of Copernicus, as 
explained by Newton, has been firmly established by all these ad- 
vances. 

If there were leisure to follow out in detail all these discoveries 
and advances, the pupil could be taken through the experience of 
the race and could successively master each great problem just as it 
was mastered by Thales, Hipparchus, Copernicus, and Newton. 
There is no more satisfactory and thorough method of study than 
this. Unfortunately it requires far more time than is available. It 
is impossible, here, to explain the system of the world according to 
Ptolemy and to take the time to prove it to be wrong. All that can 
be done is to explain the system of Copernicus and to prove it to be 
right. It is necessary, therefore, to study Astronomy in our High 
Schools in a different order. Each subject must be so treated as to 
prepare the way for other topics, and everything must be presented 
in the briefest manner. The science of Astronomy is so vast, and so 
many brilliant discoveries have been made by so many able men, that 
the limits of this little book do not permit an historical treatment. 

— How long ago were the beginnings of the Astronomy of the 
Greeks? How did the ancient Greek philosophers teach their pupils? 
When was the city of Alexandria founded ? How many manuscripts 
were contained in its libraries? (The National Library at Washing- 
ton has not even now so many books.) Ask your teacher to tell you 
about the Dark Ages in Europe, or else read about them in an en- 
cyclopaedia. What system of Astronomy was taught in European 
universities in those times ? Where did Ptolemy say the centre of 
the universe was? Copernicus (1543) taught that the centre of the 
world was — where ? Which is right ? It will be abundantly shown 
in this book that Copernicus was right. 



INTROD UCTOR Y— HISTORICAL. 1 1 

6. General notions of Astronomy. 

Even before beginning the study of Astronomy every 
one of us has a certain knowledge of it. All of us have 
studied Geography and know what is there said of the Sun 
and planets; all of us have heard certain facts of Astron- 
omy talked about; and every one of us has observed a few 
things for himself. Let us set down something like an in- 
ventory of this general knowledge here. It is well to find 
out just what we know now before going on to new things. 

The Earth is a huge globe, so large that any small part of it, where 
we live, looks flat and not round. Its diameter is nearly 8000 miles. 
We know that the Earth is a globe because it was circumnavigated 
by Magellan's ships in the years 1519-1522, and by hundreds of 
vessels since that time ; and because nearly every part of it has been 
visited by travellers ; and finally because surveys have been made of 
most civilized countries. The Earth is certainly a globe ; and its size 
is enormous compared to our houses, cities, etc. It is not large com- 
pared to the Sun and to some of the other planets. It is isolated in 
space. It does not touch any other planet or star. Even the Moon 
is very distant from it r and the Sun is much further away. The stars 
are further off still. 

The Earth turns round on its axis once in every day, and its turn- 
ing makes the Sun and the Moon and the stars appear to rise and set. 
Moreover the Earth, like the other planets, moves round the sun in 
an orbit — a path — once in a year, and this revolution of the Earth 
has something to do with the seasons — Spring, Summer, Autumn, 
Winter — which recur regularly every year. 

The Sun looks to us like a large flat disc, but it is, in fact, a huge 
globe, much larger than the Earth. It is the source from which 
comes all our light and all our heat. Our seasons — Spring, Summer, 
Autumn, and Winter — depend upon the amount of heat received from 
the Sun at different times. Just what makes the light and heat we 
do not learn from Geography, and that is one of the important things 
taught in our text-books of Physics. All the planets — the Earth, 
Venus, Jupiter, etc., move round the Sun in orbits — paths — and to- 
gether make up the Solar System — the Family of the Sun. 

The Moon also looks to us like a flat disc, but it is, in fact, a globe, 
smaller than the Earth. It revolves about the Earth, not about the 



12 ASTRONOMY. 

Sun, in an orbit — path, and it is very far away from us. Sometimes 
its shape is that of a crescent ; sometimes it is circular. It regularly 
goes through all its shapes and comes Back to the same shape again 
once in every month, and so on forever. The Moon sometimes comes 
between the Earth and the Sun and shuts off some or all of the Sun's 
light in the daytime and makes an eclipse, just as a book held in 
front of a candle will cut off the candlelight and eclipse it. The 
Moon is usually bright, but it is itself sometimes eclipsed. The face 
of the Moon seen by the naked eye at night (or seen through an 
opera-glass or a telescope) is not everywhere the same. Parts of it 
are much brighter than other parts ; and there are mountains on the 
Moon. 

The Planets look to us like bright stars. Venus is often seen to- 
wards the west at sunset, and is called the Evening Star ; and some- 
times we may have seen it towards the east about sunrise, when it is 
called the Morning Star. It is brighter than most of the stars. 
Jupiter, Mars, and Saturn are planets that look like stars, too. 

The Comets are sometimes very bright, we have heard. They 
move about in space, and people say that if one should hit the Earth 
there would be a great disaster.* 

The Stars lie all around us, and they are visible by hundreds at 
night. Most of them rise and set, but there are some near the North 
Pole that are always visible whenever it is night. They are 
divided into constellations, or groups ; and one of the groups is called 
the Great Bear or the Dipper. Some of the stars are quite bright, 
others much fainter. If a telescope is used, many thousands of stars 
can be seen that are invisible to the naked eye. The stars are ex- 
ceedingly far away from us. 

If some one who had not yet studied Astronomy were 
asked to give his notions about the heavenly bodies he 
would probably say something like what has been printed 
in the preceding paragraphs. The information is generally 
correct so far as it goes, but there are many things lacking 
to make it complete. We ought to know why it is that 
the seasons come back to us year after year in order; why 

* It may as well be said here that in the first place such a collision 
is very unlikely to happen ; and that if it did happen it is probable 
that the Earth would not suffer. 



INTROD UCTOR Y— HISTORICAL. 1 3 

the Sun gives us light and heat ; why the Sun is eclipsed 
by the Moon sometimes, and why it is not eclipsed every 
month; why the Moon itself is sometimes eclipsed, and so 
forth. Perhaps the most important thing that is left out 
of this account is the fact that the Sun shines by its own 
light (just as an electric light does), while the Moon and 
all the planets do not shine by their own light, but by re- 
flected sunlight. They appear bright just as a mirror that 
is shined upon appears bright. If you shut off the light, 
the mirror is no longer bright. If the Sun were to be an- 
nihilated, all the planets and the Moon would instantly be 
dark. They are only bright because the sunlight shines 
upon them and because they reflect the sunlight back to the 
Earth much as a mirror might do. All the stars are suns, 
and each and every star shines by its own light, just as the 
Sun does. 

With these additional facts about the Sun, which shines 
by its own light; about the planets, which shine by reflect- 
ed light; and about the stars, which shine, like the Sun, by 
native light, we can go on to study Astronomy in detail. 
We have a general idea of it to begin with, and we know 
some, at least, of the lacks in our present knowledge. 
This book does not take such general knowledge to be 
proved. On the other hand the facts above set down will 
be explained and proved. But as every one has some 
knowledge of astronomical facts, the book is not written as 
if no one had any information of the kind. 

— How do we know that the Earth is a globe ? Who first circum- 
navigated it? How long ago? How do we know that the Earth is 
isolated in space? Two of the Earth's motions make the day and the 
year — which two? "What heavenly body that you know of goes 
through a series of changes every month ? Does the Sun shine by his 
own light? Does the Moon shine by her own light? Do the planets 
so shine ? If you could stand a long way off from the Earth, would 



14: ASTRONOMY. 

the Earth be dark or would it shine like the other planets? Do the 
stars shine by the light of the Sun ? Suppose the Sun suddenly be- 
came dark so that it gave out no more' light, what changes would 
this make in the appearance of the sky at night ? What bodies 
would no longer be visible ? What others would continue to shine 
unchanged ? 



CHAPTER II. 

SPACE— THE CELESTIAL SPHERE— DEFINITIONS. 

7. Space. — The Sun, the planets, and all the stars are 
moving in Space. It is often called " empty " Space be- 
cause it contains no large masses except the Snn and plan- 
ets, the stars, the comets, and so forth. It is necessary to 
have some idea of its vastness, for it contains all these 
bodies and every other thing that exists. It is infinite — 
without any limits or boundaries. For suppose it had a 
boundary, what would lie beyond that ? Only more and 
further extensions of space. We cannot realize exactly or 
even imagine what Space is; but we can obtain a few cor- 
rect ideas about it. " 

Suppose that on a clear night you look up at the full 
Moon in the heavens. It seems to be, and it is, extremely 
distant. It is 240,000 miles away. It is 240 times as dis- 
tant from us as New York is from Chicago. Now think of 
the Sun, which is 870,000 miles in diameter. The diam- 
eter of the globe of the Sun is about 3^ times the distance 
of the Moon from the Earth. The Sun is one of the stars, 
aud there are hundreds and hundreds of bright stars visi- 
ble to the naked eye. There are millions and millions of 
stars visible in a great telescope. All these stars are scat- 
tered about in space somewhat as pictured on page 16. 

Space contains millions of stars, and each star (as a, b, 
c, etc.) is at least as far from every other star (as/, g, h, i, 
k, I, m, etc.) as the nearest stars (Z>, c, g, 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 Sim? 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- 





* 




* 




* 




* 




* 




- 


a 




b 




c 




d 




e 




>K 




* 




* 




* 




* 




>K 


/ 




9 


* 
I 


Sun 


m 


h 


* 

n 


i 


* 
o 


j 










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-TEE 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 San 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 Sun 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 must 
contain millions of stars. Even this model will be incon- 
ceivably large. The real universe — 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 ^ 3000 1 000 th 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 tliem 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 been 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. ISTow 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 be 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, t, t, t, 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 




The Earth is supposed to be at O, a few of the stars at p, q, r, s, f, t, t, u, 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, U, 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, Ou, 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 you could only see one bright point 
— at T. You do not see the other stars r, s, #, etc., 
where they really are, but at places on the celestial sphere 
at E, S, V. 




Fig. 4.— The Earth (n, q, s) in the Centre op the Celestial 

Sphere. 

On the surface of the celestial sphere meridians and parallels are sup- 
posed to he 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- 
ful. 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 nse 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. 

Axgles: 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 2 E is the amount of diver- 
gence of these lines. The angle 
S' 6 ES* is the amount of divergence 
of the two lines S*E and S 4 E. 
The eye sees at once that the 
angle S*ES* in the figure is 
greater than the angle S l ES*, 
and that the angle S*ES 3 is 
greater than either of them. 




Fig. 5. —Angles : their 
Measurement. 



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 3 ES 4 is about 
22°, S^ES* is about 30°, and S l 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 4 , or on any circumference drawn from £asa 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" 
1' = 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 nE, 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 ==-=■ a s great as its distance from us. If it 
5^.o 

subtends an angle of 1", its distance from us is over 200,000 times as 

great as its diameter. 



The instruments employed in astronomy may be used to 
measure the angles subtended at the eye by the diameters 
of the heavenly bodies. In other ways we 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- 



u 



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, 
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 
Triangle. 




Fig. 



7. — Two Similar Plane 
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 CEDE 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 Great 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°, b = 7°, c = 4°. 

Its angles will be (A is opposite to a, B to b, to c) : 

A = 128° 44' 45". 1 
B = 83° 11' 12' 
C= 18° 15' 31". 1 

Latitude and Longitude of a Place on the 
Earth'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. 

The longitude of a place on the Eartli'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° ivest of Greenwich, and that Syd- 
ney (Australia) is 151° east of Greenwich. For astronom- 




Fig. 9. — Latitude and Longitude of 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 ASTRONOMY. 

moves 360° in 24 hours, 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 Pb 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 Horizon. — 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 conntry 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 
Fig. IO.-Hu.f of the Ce- the horizon (pronounced hor-i'- 
lestial 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 he hounded by the circle * . , 

nhs. n is the north point, s is overhead is called the zenitn- 

the south point of the horizon. Z , .• „ ,, 

is the zenith-point or the point point, or more briefly tne 

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 S 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 -f- the altitude of the star = 90°. 




Fig. 11.— The Earth's Axis and the Plane op its 
Equator EQ. 

NP is the earth's north pole ; SP is the south pole ; eg is the earth 1 
equator ; EQ is the plane of the celestial equator. 



30 ASTBONOMY. 

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, eg 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. N is 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). HE 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 tvest 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 nierid. 
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 a A 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 -f- the star's declination = 90°. 

Right-ascension of a Star. — The right- ascension of a 
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 head. 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. The zenith- 
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, s 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 pinprick 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— TEE CELESTIAL SPHERE— DEFINITIONS. 35 




Fig. 14.— Correspondence of the Terrestrial and Celestial 
Meridians of an Observer. 




Fig. 15. — The Celestial Sphere. 



38 



ASTRONOMT. 



zon. P is the north celestial pole. PZS is the observer's celestial 
meridan. XXI, XXII ... O, 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° (-f- 40°) ; on the parallel C, of 4- 30° ; on the equa- 
tor, of 0° ; on the parallel Bof— 30°. The student should mark the 
following places on the figure : 



R. A. = 22 h and Decl. = + 80° 

= 23" " = - 30° 

= 24" " = 0° 

- o h " = + 40° 



R. A. — h and Decl. = - 40 c 
= 1" " = +60° 

= 2 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 ; 



: ro,/ 




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 




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, 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 



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 op 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 



II 



, ■ 





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 Eig. 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, 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 m p.m. 

Things will look as in Fig. 20. The lath 01 will 
point to the star at 8 h 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 STABS. 43 



East 



West 



The 



Ground 




Fig. 20.— A Pointer Directed at a Star. 



B^ 



East 



West 



The 



Ground 




Tig. 21. — A Pointer Directed at a Star. 



East 



The 



III 



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 m 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 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 


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, 310 ON, AND STABS. 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 C, 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 where 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 caref ally 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 STABS. 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 — noio 
— 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: 

>£ Polaris. 



v* 


< i 
*y 


Fig. 26.- 


—Ursa Major and Polaris. 



48 



ASTRONOMY. 



They are called by these names : a [Alpha) TTrsse ma- 
joris; (3 {Beta) Ursse majoris; y {Gamma) Ursae majoris; 
S {Delta) Ursae majoris; e (Epsilon) Ursae majoris ; rj 
{Eta) Ilrsae majoris; C (Zeta) TTrsse 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 j3 (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 Stars 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 you 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 round 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 hours 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 
celestial pole. 

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. 



revolution 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 Dippek; 

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 pole 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 wliy 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. 

(B.) 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. 

(C.) 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. 




The real motion of the horizon of an observer among the stars makes 
them aimear to rise and set. 



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 WZE is one of the circles of the celestial 
sphere. W is towards the west and ^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 Z '. His 
horizon will have moved to HH'. 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 HWIT and these stars 
will have " set " — they will 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 lime 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 STABS. 57 

moves round a circle every day, will his 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 iVT^/Shis 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. 38 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 G is now 5 U 



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. 



1 








•^fA^X / * ^/^Ov> 


p 


'M$j>w 


tea 


B@HQfiS«KfiS#JB^iQ^E 




r x>^v v ^ 




„ 





Fig. 33.— Part of 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" 

59 



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 radios 
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 the north point of 
his horizon (if he is in the northern hemisphere). The 
latitude of an observer at L is P"LHm 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 HZRN. 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 gTnnfTni tu °f !"• 



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 declination 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 PN and CZ). 

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 us, 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. 37. 
The circles of a celestial sphere for an observer in north latitude PN or 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 WOE 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 NS. 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 ivest point; Ehis east point; 
the line EWis 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 EN. Im is the 
diurnal orbit of a circumsolar star. Some stars would 
never rise to this observer. His horizon would hide them. 
All the stars further south than the circle SB, (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. 38. 

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. 



6' 



the lowest broken line of the figure. The Sun is on the 

hour circle 7" on April 6, on II on April 22, on 111 (near E) on May 
8, on IV on 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 0° ; the 
elevation of the north celestial pole above his horizon will 
be 0° ; the star Polaris will be in his horizon. 

Fig. 40 shows the celestial sphere as it appears to an 



68 ASTRONOMY. 

observer on the Earth's equator. The zenith of the ob- 
server is in the celestial equator. The latitude of the ob- 
server is 0° 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 B 
is 3 b , 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 THE 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 



10 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. 11 

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 borizon 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 
zenith 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 denned 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 zenitb 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 



DIURNAL 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, along the other half of the parallel ZL. In 24 
lio irs the zenith Zof the observer has moved from Z to L and from 
L back to Z again. The celestial meridian lias also swept across the 
heavens from the position N P., Z, Q, S, S.P., through every inter- 
mediate position to N.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, R, S.P., A's will be the first one (in the fig- 
ure) 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, iVthe nadir, and W the west point 
of the observer. P is 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\ Decl. = + 20°) is 4 h west of the merid- 
ian ; the star B (R.A. = 10 h , Decl. = -|- 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. 



75 




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 NS is placed 
north and sooth, 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 circnmpolar 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 culmination 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 of Co-ordinates on the Celestial Sphere. 

Any great circles of the celestial sphere which pass 
through the two celestial poles are called how-circles. 
Each hour-circle is the celestial meridian of some place on 
the Earth. 

77 



78 ASTRONOMY. 

The hoar-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 the position of the Earth, in the centre of the 
celestial sphere NZ8D. 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°. 

EG WD is the celestial equator ; E and W are the east and west 
points. The Earth is turning from Wto E. The celestial meridian, 
which at the instant chosen in the" picture contains PZp, was in the 
position P V about three hours earlier. 

PC, PB, PV, PD are parts of hour-circles. If J. 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, PF"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 denning 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. Tlie 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 counted from the 
meridian towards the west from 0° to 360° (or from h to 
24 L ). The hour-angle of a star at A at the instant chosen 
for making the picture is ZPB. The hour-angle of a star 
at iT is 0°. The hour-angle of a star at Fis ZPV; of a 
star at D is ZPB = 180° = 12 h ; and so on. 

The hour-angle is measured by the arc of the celestial 




Fig 45 bis. 

equator between the celestial meridian of the observer and 
i he 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 V 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 0° 
to 360° (from h to 24 h ). That is, from V through B 9 C, 
E, D, IF, 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, toivards 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 
(E.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 K is VC. Of a star at 
E it is VOB; of a star at D it is VCED ; of a star at W it 
is VCEDWfund 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° - S; d = 90° - N.P.D. 

North declinations are -f- ; 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 1 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 
pl.t ne 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 (£) of S, 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. Nil ox 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 jnst 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 tlie 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.B. = 50°, zenith distance = the arc ZA, altitude = 90° 
— ZA, azimuth, the arc measured on the horizon S WN f rom £ 
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 B. 




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-OBDINATES. 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 — Sidekeal 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 0° 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 EC WD is the apparent diurnal path of a star in 
the equator. It is on the meridian at C.) 

Instead of choosing a star as the determining point whose 
transit marks sidereal hours, it is found more 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 by the hour-angle of the vernal equinox. The 
fundamental theorem of sidereal time is: The 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. Vis 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 op 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 0); 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 V will have moved to TFand its hour-angle 
will be 6 b . The sidereal time of the particular observer whose zenith 



86 



ASTRONOMY. 



is Z will then be 6 h . When Fhas moved to D, the sidereal time will 
be 12 1 '. When V has moved to E, the sidereal time will be 18 h . 
When V has moved to Cthe sidereal time will be 24 h (or 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 B, the right-ascension of the celestial meridian (of the 



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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 C) is 2 h . The right-ascension of any star on the 
meridian at that instant must be 2 hoars. Speaking gen- 
erally, when the vernal equinox is anywhere (as at V 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, 0, 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" 30 m 



Sirius is 


6 h 41 m 


Regulus is 


10 h 3 m 


Spica is 


13" 20 m 


Arcturus is 


14" ll ra 


Vega is 


18" 34 m 



Fomalhaut is 22 h 52 m 



88 ASTRONOMY. 

Suppose further that we had 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 m . (For the R.A. 
of Sirius is 6 h 41™ 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, 0, 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 Fomalhaut is on the 
celestial meridian of an observer at another instant, the sidereal time 
at that instant must be 22 h 52 ra , and so on. The sidereal clock must 
show on its dial 6 1 ' 41 m 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 



SIDERIAL 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 Sirius 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 betiveen 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 intei'val 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 (7 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 j9, in Fig. 
48, it is midnight (12 h ) of Sunday — Monday begins. 
When the mean Sun is at (7, 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 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 
31 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™, 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 hi.s celestial meridian. If the right 
ascension of that star is 3 h 24 m 16. 93 9 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 hoar 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 h 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° farther to the west; in two hours it will be 30° fur- 
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 dav. Wbat 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 siderealtime of that 
place at that instant ? If you knew that the R A. of Sirius was 6 h 
-I 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 7? (Answer : It is 
ZP V— poiut out this angle.) In an hour from now where will Fbe? 
in two hours ? in 24 hours ? Why does V have different positions 
in the sky at different instants ? In speaking of sidereal time we 
refer everything to F= the vernal equinox. JSow, suppose that in- 
stead of considering the motions of V }o\x 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 watca to be keeping local mean solar 
time) ? 



CHAPTER VI. 

TIME— L0NG1TITUDE. 

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 «-© 

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 Snn in right- 
ascension is not uniform, so that intervals of time that are 
really equal are not measured by equal angnlar motions of 
the true Sun. The true Sun moves in the ecliptic — not 
in the celestial equator. Hence a " mean Sun " has been 



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"' 4 s . 091 mean solar time, 

1 mean solar day = 1.003 sidereal days, 

24 mean solar hours = 24 h 3 m 56 s . 555 sidereal time, 

and 

366.24222 sidereal days = 365.24222 mean solar days. 

Local Time. — When the mean Sun is on the 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 oar 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. Now 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 15° 
to each hour. 



LONGITUDE. 



97 



The difference of longitude between any two places depends upon 
the 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 the longitude 
of a place is the same whether expressed as the difference of two 
sidereal or of two solar times. The longitude of Washington west 
from Greenwich is 5 h 8 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 
¥ 7 g 7 o of 24 hours, or of a whole circumference. 




Fm. 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 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 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 our 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 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 ; 

" " " 8 " " " Pacific time. 

Eastern time 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 
eastern half of the two Dakotas, 



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 hoars 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 m 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\ 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 s 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 the 
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 
enough. 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) 
-|- 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 



CHANGE OF THE DAY. 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 ASTRONOMT. 

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 eashvards 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 westivards 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^ar 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 Greenwich? 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 ok 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 S 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 culminations. 



the pole in its apparent diurnal orbit. PS — PS' in the 
star's north-polar-distance, and PH = <p = the latitude 
of the observer. 



106 



ASTRONOMY. 



Therefore 



ZS+ZS' 
2 

= 90° 



ZP = 90° - 0. 

\ ZS+ ZS ' ) 
i 2 -[' 



ZS and ZS ' can be measured by the sextant or by the 
meridian-circle, as will be explained in the next chapter. 
Granted that these arcs can be measured, it is plain that 
the latitude of a place is known as soon as they are known. 
Latitude by the Meridian Altitude of the Sun or of a 
Star. — In the figure Z is the observer's zenith, P the pole, 

HH the horizon, PZH the 
observer's meridian, Q a 
point of the celestial equa- 
tor. The star S is on the 
meridian (and just at its 
greatest altitude at that in- 
stant). Its altitude HS can 
be measured by one of the 
instruments described in the 
ZS is there- 
1 fore known, for ZS = 90° 




Fig. 55. 
The latitude of a place on the earth Hex t chapter. 
v of a ship at sea) can be determined 
by measuring the meridian altitude 
of the sun (or of a star). HS. 

tion of the Sun (or of a star), and 
Nautical Almanac. 

ZS + QS — QZ — the declination of the observer's zenith, 
or 



QS is the declina- 
QS is given in the 



Q + d = = the latitude of the observer. 

If the star (or Sun) S' culminates north of the zenith 

QS' - ZS' = QZ, 



at/S" 



or 



6 - C = 0. 
This is the method uniformly used at sea, where the 



PARALLAX. 



107 



meridian altitude of the Son 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 



HT 


c 




k 


I / 



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 x 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 C.) 

S' 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 S' 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 x . 

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 w r hich 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 G represents the Sun, around which the 
Earth S' moves in the nearly circular orbit 8' S" 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 S' the 

iN'.E ,S.E. 



N.W, 



1 






1 




III 

f 


2 




Pointer 


II 


1 




I 


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 S", the star will be projected on the celestial sphere at 
P". While the Earth is moving from S' to S" the star P will appear 
to move from P' to P" . It will not really move in space at all, but 



Fig 




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 S') he would see the star at Pi ; if the ob- 
server S" were at the Sun (C) he, also, would see the star at P x . 



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', P" due to changes in the position of the observer (S', 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 



PARALLAX. 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 San 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 meals depends on the Sun ! 

\n 




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 Sun 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. and X II 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 39^ 
inches long made a swing in one 
second (from its lowest point to its 
lowest point again in one second). 
It made 86,400 vibrations in a 
meau 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 8, 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- 
bob. The length of the pendulum may 

be varied by turning the spool so as to Fig^61.— A Home-made 
wind or unwind the string. Small 
adjustments are best made by gently 
turning the spool. 

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. 



Pendulum whose 
Length can be 
readily Varied. 



* 60 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 S* 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° 11'. 
of Angles by a Circle The angle between the two stars 

Circle). A PART ° F A S '^ 2 is 12 ° 6 '> the difference of 
the two readings. In the figure 
the angle S 'ES 2 is about 12° ; S *ES 4 is about 22° ; S 2 ES 3 
is about 30°; S'ES* 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 V 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 
C. Through this knob bore a hole with an awl at the exact centre of 



ASTRONOMICAL INSTRUMENTS. Ill 

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 fiat 
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 BC 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 been 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 Sum, 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 

ble- convex " bodies were shown to them. The greatest 

Lens of 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 sbows 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 cAd. 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 b; 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 # 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 

ture 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 magnify 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 qnestion: " 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 witli 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. 

lenses. 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 : (2) 2 = .04 : 4.0 
= 1 : 100. 

With a 5-inch object-glass the ratio is 625 to 1 



10 " 


<< « 


" 2,500 to 1 


15 " 
20 " 


< < 


" 5,625 to 1 
" 10,000 to 1 


26 " 


(i 


" 16,900 to 1 


36 " 


< « 


" 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 the 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. 
63 shows the action of such a mirror on a bundle of parallel rays, 




Fig. 68. — Theory of 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 C (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 f 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 W &t right angles to it. The ends of this axis ter- 



ASTRONOMICAL INSTRUMENTS. 



125 




Fig. 70. — A Transit-instrument. 



126 ASTRONOMY. 

minate in accurately cylindrical pivots which rest in metallic bearings 
VV 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 TFTTare 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 VV more easy and regular. The line VV 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 0, the re- 
versing carriage E, and the level L. The arms of the latter have 
Ys, which can be placed over the pivots VV. 

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 db 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 The wires are dark aga-inst a bright ground. 

Telescope. Tbe lin& ^ sight . g ft Une j om j n g the centre 

of the object-glass and the central one, IV, of the seven vertical 
wires. 

The axis VV is 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 cross 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 b. 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 s . 22. Hence the clock is 
too fast by l 8 . 04. 

By observing the time (T) when a star of Jcnow?i right- 
ascension (E.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 2 , T*, etc., of stars of unknown right- 
ascension to be recorded. 

Then T x = the R.A. of the first star, 
T' = " " " " second star, 
T 3 = " " " " 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-ascensioas 
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 instrnment can be used as a transit-instrnment 
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 ( VV, JVJV, 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 H (the north point of the horizon) the reading will be 0° 0' 0". 
If it is pointed to iVthe 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 
(f>, then the polar reading P will be <p; and the equator reading 
E will be 90° + <p (because the arc PE is 90°). 

If we do not know the latitude <p we must point the telescope at 
a star S when it is crossing the meridian and determine its zenith dis- 
tance ZS; 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 = <p = 90° - | gJH~ ZST 



132 



ASTRONOMY. 



0° 


0' 





37° 


20' 


24' 


90° 


0' 


0' 


127° 


20' 


24' 


180° 


0' 


0' 


270° 


0' 






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 R, E, Z, P, H. 

The latitude of the Lick Observatory is 37° 20' 24" = <p. Its 
meridian-circle would then have the following readings: 

For the north-point (II m the figure) 
" polar-point (P " ) 

" zenith-point (Z " ) 

" equator-point (E ) 

" south-point (R " ) 

" nadir-point (IV il ) 

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 S 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 
axis. 





Fig. 76. — Ys of 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 Ms. 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 Ave 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: 

2d. 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, C, D, in suc- 
cession, these stars could be followed from rising to setting. 




Fig. 78a. — 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, 0, D, 
are different parallels of declination. Suppose then that (in 
the diagram Figure 78) TTis 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. 78a, 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 
78a, 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 (78a) the polar axis (on top of 
the pier) is pointing to the north pole of the heavens. The 
north end of the axis is the highest. The declination axis 
is fastened to the end of the polar axis, and the telescope 
is fastened to one end of the declination axis. By taking 
hold of the eye-end of the telescope it can be pointed to 
any desired declination whatever — it can be made to point 
sooth (horizontally), to the zenith (vertically), or to the 
pole (as in Fig. 80). After it is pointed to the desired 
declination the polar axis can be rotated in its bearings 
(about the line NS in figure 78) so that the telescope 
sees the desired star. The star can be followed from ris- 
ing to setting by slowly rotating the telescope and declina- 
tion axis (together) towards the west. 

If we point such a telescope to a star when it is rising (doing this 
by rotating the telescope first about its declination axis and then 
about the polar axis), we can, by simply rotating the whole apparatus 



138 



ASTRONOMY. 



on the polar axis, cause the telescope to trace out on the celestial 
sphere the apparent diurnal path which this star will follow from 
rising to setting. In most telescopes of the sort a driving-clock is 
arranged to turn the telescope round the polar axis at the same rate 
at which the earth itself turns about its own axis of rotation — at the 
rate at which all stars move from rising to setting. Hence such a 
telescope once pointed at a star will continue to point at it so long as 
the driving-clock is in operation, thus enabling the astronomer to 



SOUTH 




NORTH 



Fig. 79. 



-A Small Equatorial Telescope Mounted on a 
Portable Stand. 



make an examination or observation of it for as long a time as is re- 
quired. If we place a photographic plate in the focus of a suitable 
objective mounted equatorially we can obtain a long-exposure picture 
of the star-groups to which it is directed, and so on. 

The student should make a model of the essential parts of an 
equatorial mounting out of wood. The model should have a polar 
axis NS capable of being turned round the line NS; a declination 



ASTRONOMICAL INSTMUMENT8. 139 



Fig. 80. -An Equatorial Telescope Pointed towards the 

Pole. 



140 



ASTRONOMY. 




x m: 



Fig. 81.— An Equatorial Telescope Pointed at a Star in 
the North-eastern Region of the Sky. 



ASTRONOMICAL INSTRUMENTS. 



141 



axis DL capable of being turned round the head of the polar axis N; 
a long stick TT to stand for a telescope (mark the object-glass end of 
it). The whole should be mounted on a box so that NS lies in a 
north and south line, and so that the line NS makes an angle with 
the horizon equal to the latitude of the observer. A surveyor's 
theodolite becomes an equatorial wlien its horizontal circle is tilted 
up into the plane of the celestial equator. 




a z 



I n . I 




Fig. 82. — The Micrometer. 

An apparatus used in connection with a telescope for measuring small 

angular distances. 



The Micrometer. — A telescope on an equatorial mount- 
ing is very suitable for long-continued observations, such 
as the examination of the surface of a planet during the 
greater part of a night, but in order to fully utilize it, 
some means of measuring must be provided. The equa- 
torial cannot be used to measure large arcs with exactness 
— such an arc as the difference of declination of two stars 
several degrees apart. When it is provided with a 
micrometer it is exactly fitted to measure small distances 
with great precision — such a distance as that between two 
stars separated by a few minutes of arc, for example. 

The principle of the micrometer is illustrated in figure 82. A 
metal box is fitted with two slides b and c and with two accurate 
screws A and B. The screw A has a head divided into 100 parts. 
A hole is cut in each of the slides. A spider-line, n, is stretched 
across the hole in the slide moved by the screw A, and a spider-line 
m is stretched across the hole in the slide moved by the screw B. 



142 



ASTRONOMY. 



The micrometer is fastened to the end of the telescope, at right 
angles to its axis, so that the lines m and n are in the focus of the 
telescope, thus : 



B 



Fig. 83. 



OP is the object-glass of a telescope whose focus is F; AB is the microm- 
eter. 

When the screw A is moved the spider-line n moves, and the line 
m moves with the motion of the screw B. The oval hole in Fig. 82 
represents the field of view of the telescope. The observer sees the 
two spider-lines m and n, a fixed spider-line at right angles to them, 
a comb-scale at the bottom of the field and whatever stars the tele- 
scope is viewing. One complete revolution of the screw A moves the 
line n from one tooth of the comb-scale to the next tooth and whole 
revolutions of A are counted in this way. Fractions of a revolution 
are counted on the divided head of screw A as its divisions move past 
a fixed index or pointer. 

Suppose that it is desired to measure the distance between two 
stars S and Tthat are visible in the field of view. During these 
measures the telescope is driven by the clock so as to follow the stars 
as they move from rising towards setting. 



Fig. 84. 



The micrometer is moved so that its long fixed spider-line passes 
through S and Tthus : 



B- 



*■ 



Fig. 85. 



ASTRONOMICAL INSTRUMENTS. 



143 



The lines m and n will appear as in the figure 85. The screw B is 
then moved until the line m passes through S and the screw A is 
moved till the line n passes through T, thus : 



B- 



"*- 



Fig. 



The "reading" of the screw A is then taken. Suppose it to be 21 
whole revolutions (read on the comb-scale) and f^ of a revolution 
(read on the divided head — the mark 57 being opposite to the index). 
The screw A is then moved (B remaining as before) until the line n 
exactly coincides with the line m, and a second "reading" of A is 
made. Suppose it to be 9 whole revolutions (from the scale) and 
T ^ (from the index). The distance between the two stars S and 
T is evidently ST = 2K57 — 9 r .33 = 12 r .24. If one whole revolu- 
tion of the screw is known and equal to 11". 07 then the distance ST 
= 12.24 X 11.07 = 135". 50. 

When the value of one revolution of the screw is known in sec- 
onds of arc all distances measured in revolutions and parts can be 
reduced to arc. The value of one revolution in arc is determined 
once for all by placing the lines m and n perpendicular to the direc- 
tion of the diurnal motion of a star and at a known distance — say 50 
revolutions — apart, thus: 

m 



- S 



Fig. 87. 



If the telescope is kept in a fixed position the star, by its diurnal 
motion, will move across the field of view in the direction of the 
arrow. The exact times of its transits over n and m are observed. 



144 



ASTRONOMY. 



Suppose that it requires 6 m 9. s of sidereal time to pass from the line 
n to the line m. 

6 m 9 3 = 369" = 553". 5 because l 8 = 15" (see page 84). 



Fifty revolutions of the screw = 533". 5, therefore, and 1 revolu- 
tion = 11".07. 

The relative position of two stars A and B is not completely de- 
fined when we know their distance apart and nothing more. We 
need to know the angle that the line joining them makes with the 
celestial meridian (or with the parallel). To determine this the microm- 
eter is attached to a position-circle, so that the micrometer-box can 
be rotated in a plane perpendicular to the axis of the telescope. To 
measure the position-angle of two stars the telescope is kept in a fixed 

position and the micrometer-box 
is turned until one of the stars 
moves by its diurnal motion 
along the spider-line m. The 
circle is then "read." Suppose 
its "reading" to be 90°. The 
direction of the parallel (E~W) is 
then 90° to 270° ; of the celestial 
meridian (NS) 0° to 180°. The 
telescope is then pointed at A 
and moved by the driving clock 
so that A remains at the middle 
of the field. The micrometer-box 
is turned until the spider-line m 
passes through the two stars A 
and B (see the figure) and the 
circle is again read. Suppose 
Fig. 88. — Measurement of the the reading to be 46°. This is 
Position Angle of Two the measure of the angle NAB 
Stars A and B. _ of tlie ang ] e t h at t^ i ine j j n _ 

ing the two stars makes with the celestial meridian passing through 
A. When we know the position- angle and the distance of two stars 
we know all that can be known about their relative situation. 

Hie diameters of planets can be measured with the micrometer. 

Photography. — If we put a photographic plate in the focus of the 
telescope instead of a micrometer, and if we give the proper ex- 
posure (the telescope being moved by the driving-clock) we shall 
have on the plate a photograph of all the stars in the field. 




ASTRONOMICAL INSTRUMENTS. 145 

If we stop the clock and allow a star to move by its diurnal motion 
across part of the field of view it will leave a "trail" from the 






# 



Fig. 89. 



east to the west side of the plate. After the plate is developed, 
we shall have a map of all the stars and can measure their 

W< E 

position-angles one from another, at leisure, and in the daytime. 
Their distance apart can be measured in inches and fractions of an 
inch. The value of one inch on the plate expressed in seconds 
of arc can be determined once for all by observing transits of a star 
over two pencil lines ruled on a ground-glass plate in the focus one 
inch apart. It is clear that a photographic plate will give us first, 
a map of all the stars in the field ; second, the means of measuring 
their precise relative positions just as measures with the micrometer 
will do. One great advantage of the photographic method over 
visual measures with the micrometer is that the plate gives a per- 
manent record, so that the actual micrometric measurements can be 
made at leisure and repeated as often as necessary. Another marked 
advantage is that many pairs of stars are photographed at one ex- 
posure, whereas only one pair can be observed at one time by the 
eye. 

Celestial Photography. — Photographs of the Sun, Moon, Planets, 
Stars, Comets, and Nebulae can be made with telescopes specially con- 
structed for photography, and these photographs can be subsequently 
studied under microscopes, just as if the object itself were visible. 
The intervals of clear sky can be utilized to obtain the photographs, 
and they can be measured when the sky is cloudy. A great saving 
of time is thus practicable. A second great advantage of the photo- 
graphic plate in Astronomy is that the exposures can be made as 
long as desired. Objects can be registered in this way that are too 
faint to be seen with the eye using the same telescope. The eye soon 



146 



ASTRONOMY. 



becomes fatigued with the extreme attention required for astronomi- 
cal observing. The photographic plate is not subject to fatigue. It 
has certain disadvantages that need not be discussed here, and the 
plate will never supersede the eye. On the other hand, it has 
already been of immense importance in Practical Astronomy and is 
destined to be employed in many new ways. Some of its applications 
are mentioned in Part II. of this book. 

The Sextant. — The sextant is a portable instrument universally 




Fig. 90.— The Sextant. 
The radius of its divided circle is usually from 6 to 10 inches. 



used by navigators at sea. It was invented by Sm Isaac Newton, 
and quite independently by Thomas Godfrey, a sea-captain of 
Philadelphia. The figure shows its general appearance. Its pur- 
pose is to measure the altitude of a star (or of the Sun), It consists 



ASTRONOMICAL INSTRUMENTS. 147 

essentially of a divided circle ; of a movable index arm SM which 
carries a mirror M (called the index-glass) firmly fastened to it ; of 
another mirror m (called the horizon-glass) fastened to the frame of 
the instrument ; and of a small telescope E. It is held by a handle 
H. When altitudes are measured, the plane of the instrument is 
vertical. 

The instrument is used daily at sea to measure the altitude of the 
Sun. The chronometer-time at which the altitude is measured is 
noted. The method of making the observation is to point the 
telescope E at the sea-horizon, which will appear like a horizontal 
line across its field of view, thus : 



The rays from the Sun strike the index-glass A (or Mm Fig. 90), 
and are reflected from it. By moving the index-arm (the glass 
moves with it) the reflected rays from the Sun (AB) may be made to 




Fig 91.— Theory of the Sextant. 

fail on the horizon-glass B (or m in Fig. 90). When the index-arm 
has been moved so that the image of the Sun (©) appears to touch 

the horizon — - the index-arm reads the altitude of the 

Sun on the divided circle. 

The altitude of the Sun is also measured daily at apparent noon, that 
is when the Sun is highest, by every navigator to obtain his latitude. 

In the figure Z is an observer on the Earth CP'Z'Q' , Z is his 
zenith, HH his horizon, P is the celestial pole, PZH his celestial 
meridian, Q a point of the celestial equator. 5 is the Sun on hi§ 



148 



ASTRONOMY. 




Fig. 92. — The Latitude of an 
Observer Determined by 
Measuring the Meridian 
Altitude of the Sun. 



meridian. The altitude of the Sun HS is measured by the sextant. 
90° — HS = ZS, and ZS is thus a known arc. The declination of the 
Sun at that instant is QS. It is a known quantity because it can be 
taken from tables in the Nautical Almanac that have been calculated 

beforehand. QZ = the declina- 
tion of the observer's zenith = his 
latitude = ZS + QS = the sum of 
two known arcs. If the Sun is on 
the meridian north of the observ- 
er's zenith, as it may be in certain 
latitudes, QZ = the observer's lati- 
tude = QS' — ZS'= the Sun's decli- 
nation (a known quantity) minus 
the Sun's zenith distance (which 
is known as soon as US', the alti- 
tude, has been measured with the 
sextant). Thus the ship's latitude 
is determined. 

The altitude of the Sun is meas- 
ured daily in the morning (or afternoon, or both) to determine the 
ship's longitude, or rather to determine the local mean time of the 
ship's position. If we know that the local mean time of the ship is 
Tat the instant that the Greenwich time is O the west longitude of 
the ship will be O — 7 7 (=the difference of the simultaneous local 
times). The Greenwich time is always known, on the ship, from the 
dial of the Greenwich chronometer that she carries. The local time 
of the ship is calculated from the triangle ZPA as soon as the Sun's 
altitude has been measured. 

In figure 93 PZS is the celestial sphere, the place of the Earth, 
Zthe zenith of an observer, NS his horizon, E his east point, A the 
place of the Sun in the afternoon, BA the Sun's declination, PA the 
Sun's north polar distance, OA the Sun's altitude, ZA the Sun's 
zenith distance. The angle ZPA is the local apparent solar time 
because it is the hour-angle of the Sun (see page 90). We wish to 
determine ZPA. In the triangle ZPA, PA is known (it is 90° minus 
the Sun's declination which is given in the Nautical Almanac) ; ZP 
is known (it is 90° minus the latitude PN) ; ZA is known (it is 90° 
minus the Sun's altitude which has been measured by the sextant). 
Hence every part of the triangle is known and the angle ZPA (ex- 
pressed in hours, minutes and seconds, not in degrees, etc.) corrected 
for the difference between mean and apparent solar time gives the 
local time of the ship = T. If G is the Greenwich time (from the 



ASTRONOMICAL INSTRUMENTS. 149 

Greenwich chronometer) at that instant, the ship's west longitude is 
O — T, a known quantity. 

Thus a little instrument that can be held in the hand enables the 
navigator to determine his position on the Earth's surface with con- 
siderable accuracy and in a very few minutes. Sextant observations 
at sea will give the position of a ship to within a mile or so. 

— Make a sketch of the transit instrument and name the impor- 
tant parts— the telescope, the axis, the Ys, the piers. When the in- 




Fiu. 93 — The Local Time of an Observer Determined by 
Measuring the Altitude of the Sun. 

strument is revolved, what circle of the celestial sphere does it trace 
out? If a star of known R.A. = A crosses the meridian at a clock 
time T, what is the correction of the clock ? If the sidereal clock is 
correct, and a star of unknown R.A. crosses the meridian at a time 
B, what is the R.A. of this star? 

Make a sketch of the important parts of the meridian-circle, and 
name the parts. How may the horizontal-point H of the circle be 
determined ? Suppose Hto be known, what is the reading for the 
zenith-point Z? lor the nadir? Suppose the latitude of the observer 
(= 0) to be known also, what is the reading for the polar point Pt 



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 aDgular 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 ? 
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 E.A. and Decl. of the Sun, Moon, and Planets for 
every day in the year. 

Tables of the K. 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 snail 
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 10 8 .80. Washington is 5" S<" 
(5''.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 s . 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 m I s . 15. 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" m 0\ The 



AST1WN0M1CAL INSTRUMENTS. 



151 



true sun crossed the Greenwich meridian (apparent noon) 13 m 51 s . 34 
earlier than this, that is at 23 h 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 0' 1 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 

of 


5 ■ 
o = 

a 
i 

2 
3 




The Sun 


'S 




Equation 
of time 
to be 
substracted 
from 
mean 
time. 


U 
O 

3 


Sidereal 

time 
or right- 


the 
week. 


Apparent 

right- 
ascension. 


Diff. 
fori 
hour. 


Apparent 
declination. 


Diff. 
fori 
hour. 


ascension 

of 
mean sun. 


Wed. 
Thur. 
Fri. 


H. M. 

21 
31 4 

21 8 


s. 
13.04 
16.84 
19.82 


s. 
101.75 
10.141 
10.107 


S 17 
16 
16 


2 

45 
27 


22.4 
5.4 

30.9 


+42.82 
43.57 
44.30 


M. s. 
13 51 34 

13 58.58 

14 5.01 


s. 
0.318 
0.284 
0.250 


H. M. s. 
20 46 21.70 
20 50 18.26 
20 54 14.81 


Sat. 
Sun. 
Mou. 


4 
5 
6 


21 12 
21 16 
21 20 


21.98 
23.33 
23.88 


10.073 

10.040 
10.007 


16 
15 
15 


9 

51 
33 


39.2 

30.8 
6.1 


+44.99 
45.69 
46.36 


14 10.61 
14 15.41 
14 19.40 


0.216 
0.183 
0.150 


20 58 11.37 

21 2 7.92 
21 6 4.48 


Tues. 
Wed. 
Thur. 


8 
9 


21 24 
21 28 
21 32 


23.63 

22.60 
20.79 


9.974 
9.941 
9.909 


15 

14 
14 


14 

55 
36 


25.4 
29.1 
17.7 


+47.03 
47.66 
48.28 


14 22.60 
14 25.01 
14 26.65 


0.117 

0.084 
0.052 


21 10 1.03 
21 13 57.59 
21 17 54.14 


Fn. 
Sat. 
Sun. 


10 
11 
12 


21 36 
21 40 
21 44 


18.21 
14.88 
10.80 


9.877 
9.846 
9.815 


14 
13 
13 


16 
57 
37 


51.6 

11.2 
16.9 


48.88 
49.47 
50.03 


14 27.51 
14 27.63 
14 26.99 


0.020 
0.011 
0.042 


21 21 50.70 
21 25 47.25 
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° m 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. 



4 



South 



North 



> 



B 



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 









IMraK 










3BH 


- 




BBs 


M 


i | ' 














H 










. MR - 1 * : 










I ; 










1 

■ 


«a 


i§< 




1 
1 



Fig. 95.— Ursa Majoe. 
Zeta (£) Ursae 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 (£) 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) £ Ursm 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 -™ ofi 
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 the 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; bat 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, Venus, Mars, 
Jupiter, Saturn) looked exactly like stars to the naked 
eye, but they mo^ed 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 TEE 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 San 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 
12 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 # represent the Sun, ABGD 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 C, 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 A BCD. 

The diameter of this orhit is about 186,000,000 miles. 

The apparent places of the Sun (1', 2', 3', 4', 5', 6', etc.) 
can be denned 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 iu 
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 Snn is rising at any place, that star will be 
setting; when the Snn 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 our 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 named East) and set in 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 V 
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 V. Draw another arrow outside of ABCD with the 
point near D and the feather near C. 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 SA and SE to be the hands. When SA 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 same 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, 0° 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. 0° 6' South. 
" 21, " h 2 m 40 s ; " 0° 17' North. 
" 22, " h 6 m 19 s ; " 0° 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 THE 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 


R. A 


= 


18 h 49 m 


Bed 


= 


South 23° 


South \ Feb. 1 




= 


21 h l m 




= 


" 17° 


(Mar. 1 




= 


22 b 50 m 




= 


7° 


fApr. 1 
| May 1 




= 


b 43 m 




— 


North 5° 




= 


2 h 35 m 




= 


" 15° 


North H u . ne \ 
1 July 1 







4 h 38 m 
6 h 42 m 




= 


" 22° 
" 23* 


1 Aug. 1 




= 


8 b 47m 




= 


" 18° 


I Sept. 1 




= 


10 h 43 m 




= 


go 


( Oct. 1 




— 


12 b 31 m 




= 


South 3° 


South \ Nov. 1 




= 


14 h 27m 




— 


" 15° 


(Dec. 1 




= 


16 h 31 m 




= 


" 22° 


On June 21, 1898, 


, the S 


5un 


had its greatest : 


northern declination 


= -f 23° 27; on December 22, 


1898, the Sun had its greatest southern 


declination =s — 23° 


37', 













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, XI. 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 TEE 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 sonth 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, = 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 by 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 Celestial 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 are marked on Fig. 100, 



LENGTH OF THE 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 34° 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 jast 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 C 
(nearly half way from C to S), 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 (GZ= 34°; 34° - 23° = 11°). The daylight hours 
will be long. 

By constructing such 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 DAY 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. 



Date. 



Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 



1... 
11... 
181.. 

1... 
11. . 
81... 

1... 
11.. 
81... 

1... 
11... 
81... 

1... 
11... 
81... 

1 . 
11... 
21... 

1... 
11... 
81... 

1... 
11... 
81... 

1... 
11... 
81.. 

1... 
11... 
81... 

1 . 
11.. 
81... 

1.. 
11... 
81... 



30° 



h. m 



6 56 
6 57 
6 50 

6 50 
6 44 
6 34 

27 
6 14 
6 2 

5 49 

5 37 
5 27 

5 17 
5 9 
5 3 

4 58 
4 58 

4 59 

5 2 
5 6 

5 12 

5 18 
5 24 
5 30 

5 36 
5 42 
5 47 

5 54 

6 
6 6 

6 14 

6 22 
6 30 

6 38 
6 46 
6 53 



38° 34 



h. m. 



7 
7 1 
7 

6 54 
6 47 
6 36 



28 
15 
2 

48 
35 
24 

14 
5 

58 

53 
52 
54 

56 
2 
7 

14 
21 

28 

34 
41 
47 

5 54 

6 1 
6 9 

6 17 

6 25 
6 34 

6 43 

6 51 
6 58 



h. m. 



36° 



h. m 



7 5 
7 5 
7 3 

6 57 

6 50 



6 29 
6 16 
6 1 

5 47 
5 34 
5 22 

5 11 
5 1 

4 58 

4 48 
4 47 

4 48 



5 32 
5 40 
5 47 

5 55 

6 2 
6 11 

6 21 
6 29 
6 38 

6 47 

6 56 

7 3 



7 10 
7 10 

7 7 

7 1 
6 52 
6 41 

6 31 
6 16 
6 1 

5 46 
5 33 
5 20 

5 7 
4 57 
4 49 

4 43 
4 41 
4 42 



5 55 

6 3 
6 13 



6 42 

6 52 

7 1 
7 8 



38° 40 



h. m 



7 16 
7 16 
7 12 

7 5 
6 55 
6 44 

6 33 

6 17 



5 3 
4 52 
4 44 

4 38 
4 35 
4 36 

4 39 
4 45 

4 53 

5 2 
5 10 
5 20 






6 26 
6 37 
6 47 

6 57 

7 7 
7 13 



h. m. 



7 22 

7 21 
7 18 

7 9 
6 58 
6 46 

6 34 

6 17 
6 1 

5 44 
5 29 
5 14 



4 
4 
4 

4 
4 
4 

4 
5 

5 

5 
5 
5 46 

5 57 

6 7 
6 18 

6 29 
6 41 

6 52 

7 2 

7 12 
7 19 



42 c 



h. m. 



7 27 
7 23 

7 13 

7 1 
6 49 

6 36 
6 18 
6 1 

5 43 
5 26 
5 11 

4 56 
4 43 
4 33 

4 25 
4 23 
4 23 

4 27 
4 34 
4 42 

4 52 

5 2 
5 13 

5 25 
5 35 
5 45 

5 58 

6 8 
6 21 

6 33 
6 45 

6 57 

7 8 
7 18 
7 26 



44 c 



h. m. 



7 36 
7 33 

7 28 

7 18 
7 5 
6 51 



4 IS 
4 27 
4 36 



47 
57 
10 

23 
34 
45 

5 59 

6 10 
6 23 

6 37 

6 50 

7 3 

7 15 

7 25 
7 33 



46° 



h. m 



7 43 

7 40 
7 34 

7 23 
7 9 
6 53 

6 40 
6 20 
6 



5 41 
5 22 
5 4 

4 46 
4 33 
4 20 

4 11 
4 8 
4 8 

4 12 
4 19 
4 29 

4 42 

4 53 

5 6 

5 21 
5 33 
5 45 

5 59 

6 12 
6 25 

6 41 

6 55 

7 10 

7 22 
7 33 
7 40 



48= 



h. m. 



7 51 

7 47 
7 41 

7 28 
7 14 
6 57 

6 42 
6 21 
6 



4 41 
4 27 
4 13 

4 3 
3 59 
3 58 



4 4 
4 11 

4 22 

4 35 

4 47 

5 2 

5 18 
5 31 

5 44 

6 
6 14 
6 28 

6 45 

7 1 
7 17 

7 29 
7 41 



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 : 



Spring 
signs. 

Summer 
signs. 

Autumn \ 
signs. ~) 

Winter 
signs. 



1. ¥ Aries. The sun enters the sign Aries, March 20. 



2. » Taurus. 

3. n Gemini. 

4. SB Cancer. 

5. ^ Leo. 

6. TT£ Virgo. 

7. =s= Libra. 

8. Tr\, Scorpius. 

9. $ Sagittarius. 

10. V3 Capricornus. 

11. ^ Aquarius. 

12. *€ Pisces. 



Taurus, April 20. 
Gemini, May 20. 
Cancer, June 21. 
Leo, July 22. 
Virgo, August 22. 
Libra, September 22. 
Scorpius, October 23. 
Sagittarius, Nov. 23. 
Capricornus, Dec. 21. 
Aquarius, Jan. 20. 
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]smets 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 





An 


» 




A kl 


__\r 


$/' 


Ad 


c V- 


2^=* 


^ 


J 




^ 


V 


/ 




^\^^ 


\^\ 




p > a 



Fig. 107. — Obliquity of the Ecliptic 
AB is the celestial equator, CD is the ecliptic. 

by the arc DB or AC. DB is the Sun's greatest northern 
declination; AC is the Snn'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. 



muni. Its meridian altitude on the day of the winter 
solstice is a minimum. 

If AB is an obelisk and the line Bd 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 B 

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 



TEE 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 San 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 D, 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°; 

" D " 66£°; 
" F « 90°; 
" " " 113^°, 



it 


si 


a 


a 


16 


K 



174 



ASTRONOMY. 



In Fig. 110 the oval line represents the path of the Earth 
in its annual revolution about the Sun in the ecliptic. The 
line NS in each picture of the Earth represents the Earth's 
axis, JVits north end. The Earth's axis is always directed 
to a point very near to the star Polaris at all times of the 
year, that is, wherever the Earth may be in her orbit. 
Hence the four lines N8 are drawn parallel to each other. 




Fig. 110.— The Seasons. 

The Earth is shown in four positions in its orbit. A = the winter sol- 
stice ; B = the vernal equinox ; C = the summer solstice ; D = the au- 
tumnal equinox. The orbit of the Earth is nearly a circle. It is much 
foreshortened in the picture. 



The Earth's axis is perpendicular to the celestial equator, 
but it is inclined to the ecliptic by an angle of 23^°, and 
it has been so drawn. 

If the student will join the centre of the Sun (S) with 
the centre of the Earth in each one of the four positions 
drawn he will see that, as has been said, 

The Sun's N.P.D. at A (winter solstice) is 113i°; 
" " " " B (vernal equinox) is 90°; 

" C (summer solstice) is 66^°; 
« « M • " D (autumnal equinox) is 90°, 



THE SEASONS. 



175 



He can also prove that the Sun's altitude to any observer 
in the northern hemisphere is greater in summer than in 
winter by drawing the horizon of an observer on the same 
parallel of the Earth at A and at C. 

The Sun shines on one half of the Earth only — namely 
on that half which is turned toward him. This hemi- 
sphere is left bright in each of the figures ABCD. The 
other half of the sphere is dark. Consider the picture at 





Fig. 111. — A. The Earth at the Winter Solstice. 

A (winter solstice) and remember that the Earth is turning 
on its axis every 24 hours. Every observer on the Earth, 
in any latitude, is carried round his parallel of latitude by 
the Earth's rotation once in every 24 hours. The parallels 





Fig. 112.— B. The Earth at the Vernal Equinox. 

of latitude are drawn in the picture. A person near N 
will remain in darkness during the whole 24 hours. A 
person anywhere in the northern hemisphere of the Earth 



176 



ASTRONOMY. 



will be less than half the time in the light, more than half 
the time in darkness. The Sun will be less than half the 
time above his horizon. The daylight hours will be shorter 
than the hours of darkness. This is the time of winter in 
the northern hemisphere of the Earth. 

Take, next, the Earth at the vernal equinox B. Half 





Fig. 113.— C. The Earth at the Summer Solstice. 

of the Earth is lighted by the Sun, and the Sun's rays just 
reach the two poles iVand S. The days and nights are 
equal. At the summer solstice C an observer at the 
Earth's north pole has perpetual day; and the Sun is 
above the horizon of every person in the northern hemi- 





Pig. 114.— D. The Earth at the Autumnal Equinox. 



sphere for more than half the 24 hours. The days are 
longer than the nights. At the autumnal equinox, Z), the 
circumstances are like those at the vernal equinox, 



THE SEASONS. 



m 



The foregoing explanation of Fig. 110 illustrates the 
dependence of the seasons upon the length of time that the 
San 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 A BCD 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- 
stant amonnt of heat is dis- 
tributed over a larger surface 
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. 115.— The Effect of the 
Suns Elevation on the 
Amount of Heat Imparted 
to the Soil. 




Fig. 116. — The Meridian Altitude of the Sun at £ is 
Equal to (90° - <f> + 8) ; 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° + 0°); 
" 68i° " June 21 (90° - 45° + 23^°); 
" 45° " September 22 (90° - 45° + 0°); 
" 21i° << December 22 (90° - 45° - 23i°). 

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-J 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 mnst be trans- 
ferred to a star-map, like those printed at the end of 
this book, for instance. A carved 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 (5 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 





Fig. 118. 



Fig. 119. 



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 b p.m. 

The place of the planet is much more accurately fixed if the 
observer makes allineations with four stars, thus : 

G might be 8 Auriga 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 such observations are made the student can discover 
for himself what the ancients knew Tery 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 San 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 Sun, 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 /, 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 Sun 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 abont the Sim. 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 THE PLANETS. 



185 



Name. 


o 

PQ 

S 

CO 


s 

2*. 

"n a 

<D 3 

3.S 

5 


Sidereal Period of Revolution. 


Group of f Mercury 
Planets each i Venus 

about the < JTnrfh 
size of the f &*rl/i . . 
Earth. 1 Mars . . . 


9 

© 
6 


0.39 
0.72 
1.00 
1.52 


88 days = 3 montlis JL . 
225 " = 7i 
365£ " = 12 

687 " = 22| 


The Small Planets. . . 




About 
2.65 


3 to 8 years. 


[ Jupiter.. 
Groups of Saturn. . 

p£,e a ts ge granus. 

i, Neptune 


U 


5.20 

9.54 

19.18 

30.05 


11A years. 
29| « 
84 
IMA " 



* 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 SI, S%, S3, 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 denned 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 che 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, ABOBEF the 
orbit of the Earth and HIKLMN 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 


t ( 


" D, " 


" L 


li 


" E, " 


" M 


" 


" F, " 


" ir 



As the Earth moves faster than Mars the arcs AB, BO, CD, BE, 
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 OZf (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 Mars is in opposition to the Sun. The 
Sun and Mars are seen from the Earth in opposite directions. The 
apparent motion of all superior planets at the time of opposition is 
retrograde. 

While the Earth is moving from to D in its orbit, Mars is mov- 
ing from Kto L'm 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 — ECS 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 ail 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 Ttcho 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) k 




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 Keplek 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 " li " " " 4333 " = 11.86 ' f 

/Sfl^m " <f <f <f " 10,759 " = 29.46 f ' 

The Relative Distances of Planets from the Sun. — 
Keplee had no way of determining the absolute distance 
of each planet from the Sun (its distance iu miles), but if 
the distance of the Earth from the San 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 of Determining How Much Greater the 
Distance of Mars from the Sun is than the Distance of 
the Earth from the Sun. 

Iu the figure let She 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 S LAWS. 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' — MSM' 
= M'SE'. Hence in the triangle M'SE' we know the two angles 
marked in the diagram. E'SM' is measured, M'SE' is calculated. 
The angle SM'E' = 180° - [E'SM 1 + M'E'S] 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 1 = 0.3871; for Mars, a K = 1.5237; 
" Vemis, a q = 0.7233; " Jupiter, a 6 = 5.2028; 
" Earth, a 3 = 1.000; " Saturn, a 6 = 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 Okbit of a Plaket, P, about the Sun, S. 

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 8P iy 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 
8P 9 , SP 3 , 8P A , SP b . Calculation showed that the planet 
was at the points P 3 , P 3 , P 4 , P b . The curved line joining 
all these points was the visible representation of the orbit 
of Mars. The curve P 1 . . . 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 siwi 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 S. Let the length of the string be SP -f- PS'' 
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'P'is a constant quantity. 
For every point of the curve SP -f- S'P = a constant. Take a string 
of a different length to start with and tie it to S and S' and you will 
get an ellipse of a different shape. Put the tacks S and S' nearer 
together and the ellipse will be of another shape, but it will still be 
an ellipse. 

ADCP is an ellipse ; S and 8' are the foci. By the definition of 
an ellipse SP -f- PS' = AG, and this is true for every point. S is 
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, SB, 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. BB is the minor axis, 2b. The ratio of OS 
to A is called the eccentricity of the ellipse. By the definition of the 
ellipse, again, BS+ BS'= AC - 2a; and BS=BS' = a. BS* = BO* 



+ OS*, or OS — \* a* — b' 1 . The eccentricity of the ellipse is 



OS _ Vgi-W 
0A~ 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 — 

I. Each planet moves around the Sun in an ellipse, 
having the Sun at one of its foci. 

Suppose the planet to be at the points P, P 1? P a , P $ , 
P 4> etc., at the times T, T x , T %% T % , T K , etc., in Fig. 129. 




Fig. 129. — Kepler's Second Law. 

Suppose the intervals of time T x - T, T s - T„ T b — T K 
to be equal. Kepler computed the areas of the surfaces 
P/SP,, P t SP 9 , P i SP b and found that these areas were 



MOTIONS OF THE PLANETS— KEPLER S 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 — 

II. 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: 

177. 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 7 ,, T^ T^ etc., are the periodic times of the 
different planets whose mean distances are « 1} « a , a 3 , etc., 
then 

T? : T; = a? :«/; 

7V :77 = <:<; 

etc. etc. 

If T 3 and a % 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 z (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' or a = (T)K 

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 value of 
a, its mean distance from the Sun, expressed in terms of 
the Earth's mean distance = 1.000. 



For Mercury, 
" Venus, 


T t = 0.24 years 
T % = 0.62 " 


and a x — 0.39 

" a 2 = 0.72 


" Earth, 


T s = 1.00 " 


" a % = 1.00 


" Mars, 


T K = 1.88 " 


" a K = 1.52 


" Jupiter, 
i ' Saturn, 


T 6 = 11.86 " 
T 6 = 29.46 " 


" a b = 5.20 
" a % = 9.54 



Kepler's laws are true for the satellites as well as for 
the planets. Mars has two satellites, Photos 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 (T'Y : (T") % = {a')* : (a")\ 

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 8 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 $Pwill 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 (the 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 (Z) at a given epoch, 



MOTIONS OF THE PLANETS— KEPLER'S LAWS. 201 

say December 31st, 1850, we Lave 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 i. 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 : 

i, 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 i : TV = a 3 : a x 3 ? What are the elements 
of a planet's orbit ? 



CHAPTEK 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 ^g^o 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 -^-gVo P ar ^ 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 -^ 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. He 
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 GBAYITATION. 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. Ift\\e 
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 ASTBONOMY. 

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 
Copekntcus, of Keplee, 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' 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 rri 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 

m! 
force on each of the m particles will vary as --. Each of the m 

particles being equally subject to this attraction, the total attractive 

force between the two bodies will vary as — — . 

Each of the two masses attracts the other by a force varying 

mm' 
as — — . 
r l 

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 
to ~Za- 



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 



m 



which determines the amount of motion, will be — ; and conversely 

the accelerating force acting on the body m will be represented by 

m! 

the fraction -j. If m is very large (as in the case of the Sun) 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 a mass 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 , A» A »■■■'■ nmnr » - • • tot>W 

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 ^jth, four blocks off yjth, 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 G 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 G 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 s , 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 is 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— pertui'bations 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 T oVo °^ 
the Sun's mass. 




The Vertical Line.— The direction FlG 134 _ A Pendttlum 
up and down, the vertical direction, is at Rest Hangs Ver- 
defined for any observer by the line TICALLY - 
in which a pendulum at rest hangs. The pendulum is at- 
tracted by the whole Earth and if the Earth were a sphere 
it would always point to the Earth's centre. As the Earth 



214 



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. 21 5 

bat 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 conld 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 tlie principal work of Ptolemy and bis 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 



THE 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 Sun. 




Fig. 136.— The ^!oon (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 8 (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 op 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, 
0, etc., and the right-hand hemisphere of the Moon is 
illuminated in each position. Outside of these eight posi- 
tions are eight pictures showing how the Moon looks as 
seen from the Earth in each position. 

At A it is " new Moon," the Moon being nearly between 
the Earth and the Sun. Its dark hemisphere is then 



THE MOTIONS AND PHASES OF THE MOON. 219 

turned towards the Earth, so that it is entirely invisible. 
The Sun and Moon then rise and set together. They are 
in the same direction in space. 

At E the observer on the Earth sees about a fourth of 
the illuminated hemisphere, which looks like a crescent, as 
shown in the outside figure. In this position a great deal 
of light is reflected from the Earth to the Moon and back 
again from the Moon to the Earth, so that the part of the 
Moon's face not illuminated by the Sun shines with a 
grayish light. At C the Moon is in her first quarter. The 
Moon is on the meridian about 6 p.m. She is about 90° 
(6 hours) east of the Sun. When the Sun is setting the 
Moon is therefore near the meridian. At G three-fourths 
of the hemisphere that is illuminated by the Sun is visible 
to the observer; and at B the whole of it is visible. The 
Moon at B is exactly opposite to the Sun and it is then 
"full Moon." The full Moon rises at sunset. As the 
Moon moves to H, D, F, the phases change in a reverse 
order to those of the first half of the month. 

The Tides. — •The phenomena of the tides are familiar 1o those who 
live near the seashore. Twice a day the waters of the ocean rise 
high on the beach. Twice a day they recede outwards. The first 
" high tide " occurs at any place (speaking generally) about the time 
when the Moon is on the meridian of that place. About six hours 
later comes "low tide"; about twelve hours after the first "high 
tide" comes a second " hi^h tide," and finally, about six hours after 
this a second " low tide." The Moon revolves about the Earth once 
in about 25 h (not 24 h ), for it is moving eastwards among the stars 
nearly 15° daily. 

In figure 138 suppose to be the centre of the Earth and m a 
place on its surface. Suppose, for simplicity, that the whole Earth 
is surrounded by a shallow shell of water. There is a high tide at 
m when the Moon (M) is on the meridian of m. Let us see why this 
is so. The Earth is attracting the Moon, and by its attraction the 
Moon is kept in her orbit. 

The Moon moves towards the Earth a little every second. 

The Moon likewise attracts every particle of the earth, solid and 
fluid alike. The fluid particles nearest M (at m) are perfectly free 



220 



ASTRONOMY. 



to more, and tliey are therefore headed up into a kind of a wave 
whose crest is at m. The particles of water near rri' and m!" are 
drawn towards m. The Moon at M also attracts the solid body of 



HI 




■^V K 





Fig. 138. — The Tides of the Ocean are Produced by the 
Moon's Attraction. 



the Earth with a force that is inversely proportional to the square of 

the distance MO — to , , , „„ — and the Earth moves towards the Moon 
{MOy 

a little every second. The Moon also attracts the fluid particles 
near m', in the further hemisphere of the Earth, with a force pro- 
portional to . If they were a solid separate from the main 

body of the Earth, they would move less than the rest of the Earth, 
because they are less attracted, being more distant. 

The Moon at M attracts the solid Earth as a whole, more than it 
attracts the waters of the distant hemisphere m"m'm"'. The solid 
Earth, which must move as a whole, moves towards M in consequence 
of its attraction more than the waters of the distant hemisphere, 
which are therefore left behind as it were, heaped up into a kind of 
wave whose crest is at m' opposite to the moon M. The shape of 
the tidal ellipsoid is shown by the shaded area in the figure. 

When the moon is at M on the meridian of a place at m, the tidal 
ellipsoid is as drawn. There is high tide at m, low tide at a place 
90° distant (ra"), high tide at m' , low tide again at m'" . Whenever 



THE MOTIONS AND PHASES OF THE MOON. 221 

the moon is on the meridian of any place such an ellipsoid is formed. 
As the Moon moves round the earth each day from rising to setting, 
this ellipsoid moves with it. 

In an hour the moon will have moved to V and the crest of the 
wave to 1. The tide will be high at 1 and falling at ra. As the 
moon moves by the diurnal motion to 2', 3', M'" ', M' , the crest will 
move with it. When the moon is at M'" it is low water at m and 
m'. When the moon is at M' , it is again high water at ra ; and 
so on. 

If we suppose M to be the sun, a similar set of solar tides will be 
produced every 24 hours. The actual tide is produced by the super- 
position of the solar and lunar tides. 

The foregoing explanation relates to an Earth covered by an ocean 
of uniform depth. To fit it to the facts as they are a thousand cir- 
cumstances must be taken into account which depend on the modify- 
ing effects of continents and islands, of deep and shallow seas, of 
currents and winds. Practically the time of high tide at any station 
is predicted in the " Tide-Tables" by adding to the time of the 
Moon's transit over the meridian a quantity that is determined from 
observation and not from theory. 

— Describe the changes of the shape of the Moon's disk from 
new moon to the next new moon. Does the Moon shine by her own 
light? What part of the globe of the Moon is illuminated by the 
Sun ? About what time does the new moon rise ? the full moon ? 



CHAPTER XII. 
ECLIPSES OF THE SUN AND MOON 



27. The Earth's Shadow — the Moon's Shadow — Lunar 
Eclipses — Solar Eclipses — Occultations of Stars by the 
Moon. — A point of light L sends out rays in every direc- 
tion. If an opaque disk VO is interposed in the path of 
some of these rays it will form a shadow on the side 
furthest from the light. All the space between the lines 




Fig. 139. 



-The Shadow of a Disk VO Formed by a Point op 
Light L and Projected on a Screen TS. 



LV, LO, and other lines drawn from the point L to the 
borders of VO will be dark. The regiou VOSTis dark and 
it is called the shadow of VO, If the source of light is 
not a mere point the shadow is not so simple. The candle- 
flame AB shines on the sphere DC and illuminates one- 
half of it. The region to the right of the sphere and 
between the lines BDS' and ACS receives no light at all. 
If a screen is interposed the shadow is shown quite black 
at S'S. None of the region to the right of the sphere 
between the lines AP' and BP is fully illuminated. Some 
of ihe candle-flame is cut off from every part of this region 

222 



ECLIPSES OF THE SUN AND MOON. 



223 



by the sphere. Let the student mark a point half way 
from S to P (call it a). From a draw a line tangent to 
the sphere near C and prolong it till it meets the candle- 




Fig. 140.— The Shadow— Umbra and Penumbra— of a Sphere 
Formed by a Candle. 

flame (at a point that we may call b). Draw also the lme 
a A. The point a is illuminated by part of the flame (the 
part between b and A) and it receives no light from the 
part of the fl me between b and B. It is impossible to 
draw a straight line through a that will meet the flame 
between b and B unless such a line passes through the 
sphere DC The region DS'SC is the umbra of the 
shadow; the region DP'S', CSP, etc., is the penumbra. 
If the shadow is received on a screen the circle SS' is often 
called the umbra and the riug PSP'S' the penumbra. 

The Shadow of the Earth. — In figure 141 S is the Sun, 
E the Earth. The cone BVB' is the umbra; that part of 
the cone BPB'P' which is not umbra is the penumbra. 

Dimensions of the Earth'' s Shadow. — Let us investigate the distance 
EV from the centre of the Earth to the vertex of the shadow. The 
triangles VEB and VSD are similar, having a right angle at B and 
at D. Hence 



VE: EB = VS: SD = ES: (SD - EB). 



224 



ASTRONOMY. 



So if we put 

I = VE, the length of the shadow measured from the centre of 

the Earth, 
r = ES t the radius -vector of the Earth, = 92,900,000 miles, 
11= SB, the radius of the Sun, = 483,000 " , 

ft — EB the radius of the Earth, = 4000 " , 

we have 

ES X EB rft 



l = VE 



SB-EB B- p 




Fig. 141.— Dimensions of the Shadow of the Earth. 

That is, I is expressed in terms of known quantities, and thus is 
known. 

Its length is about 866,000 miles. 




Fig. 142.-^45 is the Ecliptic ; OB is the Moon's Orbit. 

The three dark circles on AB are three positions of the Earth's shadow. 
Sometimes the Moon is totally eclipsed as at G, sometimes partially 
eclipsed as at F, sometimes she just escapes eclipse as at E. 

Eclipses of the Moon. — The mean distance of the Moon 
from the Earth is about 238,000 miles and the Moon often 
passes through the Earth's shadow-cone {EV). While 



ECLIPSES OF TEE SUN AND MOON. 225 

the Moon is within that cone none of the light of the Sun 
can reach her surface and she is said to be eclipsed. 

If the Moon moved exactly in the plane of the ecliptic 
she would pass through the Earth's shadow-cone at every 
full Moon (for it is at full Moon that the Sun and Moon 
are oh opposite sides of the Earth) and would be totally 
eclipsed once every lunar month. The Moon's orbit is, 
however, inclined to the ecliptic at an angle of about 5°, 
and therefore she often escapes eclipse, as is shown by the 
diagram. As a matter of fact it is very seldom that more 
than two lunar eclipses occur in any calendar year. 

Eclipses of the Moon are calculated beforehand and the phases are 
printed in the almanac. Supposing the Moon to be moving around 
the Earth from below upward in figure 141, its advancing edge first 
meets the boundary B'P' of the penumbra. The time of this ocur- 
rence is given in the almanac as that of Moon entering penumbra. 
A small portion of the sunlight is then cut off from the advancing 
edge of the Moon, and this amount constantly increases until the 
edge reaches the boundary B'V of the shadow. Tbe eye can 
scarcely detect any diminution in the brilliancy of the Moon until 
she has almost touched the boundary of the true shadow. The 
observer must not, therefore, expect to detect the coming eclipse 
until very nearly the time given in the almanac as that of Moon 
entering shadow. As the Moon enters the true shadow the advancing 
portion of the lunar disk will be entirely lost to view. It takes the 
Moon about an hour to move over a distance equal to her own diam- 
eter, so that if the eclipse is nearly central the whole Moon will be 
immersed in the shadow about an hour after she first strikes it. 
This is the time of beginning of total eclipse. So long as only a 
moderate portion of the Moon's disk is in the shadow, that portion 
will be entirely invisible, but if the eclipse becomes total the whole 
disk of the Moon will nearly always be visible, shining with a red 
coppery light, 

This is owing to the refraction of the Sun's rays by the lower 
strata of the Earth's atmosphere. We shall see hereafter that if a 
ray of light DB (see Fig. 141) passes from the Sun to the Earth, so 
as just to graze the latter, it is bent by refraction more than a degree 
out of its course. At the distance of the Moon the whole shadow of 
the Earth is filled with this refracted light. Some of it is reflected 
back to the Earth, and as it has passed twice through the Earth's 



226 ASTBONOMY. 

atmosphere the light is red for the same reason that the light of the 
setting Sun is red. 

The Moon may remain enveloped in the shadow of the Earth 
during a period ranging from a few minutes to nearly two hours, 
according to the distance at which she passes from the axis of the 
shadow and the velocity of her angular motion. When she leaves 
the shadow, the phases which we have described occur in reverse 
order. 

It very often happens that the Moon passes through the penumbra 
of the Earth's shadow without touching the shadow at all. The 
diminution of light in such cases is scarcely perceptible unless the 
Moon at least grazes the edge of the shadow. 

Eclipses of the Sun. — The shadow of the Earth falling 
upon the Moon cuts off the Sun's light from it and causes 
a lunar eclipse. The shadow of the Moon falling on a part 
of the Earth cuts off the light of the San from all observers 
in that region of the Earth and causes a solar eclipse. 




Fig. 143. — Dimensions of the Shadow of the Moon. 

In this figure let 8 represent the Sun, as before, and let 
E represent the Moon. The cone B VB' is now the umbra 
of the Moon's shadow. We wish to know the length of 
the Moon's shadow VE. By a method similar to that 
given on page 224, using accurate values of the different 
quantities, it is found that VE at new Moon is about 
232,000 miles. The average distance of the centre of the 
Moon from the centre of the Earth is about 239,000 miles 
(or from the centre of the Moon to the surface of the Earth 



ECLIPSES OF TEE SUN AND MOON. 227 

abont 235,000 miles), and hence generally the Moon's 
shadow will not quite reach to the Earth's surface and 
generally there will be no solar eclipse at new Moon. If 
the Moon's orbit were a circle with a radius of 239,000 
miles we should have no solar eclipses at all. It is, how- 
ever, an ellipse, and at favorable times (that is when the 
Moon's shadow is long enough and when it points at the 
Earth) the Moon's shadow may reach the Earth and even 
beyond it. At such times the Sun's light will be cut off 
from all observers on the Earth within the shadow and a 
solar eclipse will occur. The conditions at such favorable 
times are illustrated by the figure. 



Fig. 144. 

The Sun is eclipsed to all observers on the Earth within the shadow of 
the new moon (A). The full Moon is eclipsed whenever it passes through 
the Earth's shadow (B). 

It is clear that all observers on the Earth within the 
umbra of the Moon's shadow at A cannot see the Sun at 
all. To them the Sun will be totally eclipsed. Observers 
on the Earth within the penumbra of the Moon's shadow 
(see the figure) will see a part of the Sun only. To such 
observers the Sun will be partially eclipsed. 

The diameter of the Moon's umbra at the surface of the 
Earth is seldom more than 160 miles. It is usually much 
less. Observers within this umbra see a total solar eclipse. 
As the Moon moves in its orbit at the rate of over 2000 
miles per hour (which is about twice the velocity of a 
cannon-ball) the shadow moves correspondingly. It sweeps 



228 ASTRONOMY. 

over the surface of the Earth in a curved line or belt. The 
observers within this belt see the total eclipse one after 
another. At any one place the totality cannot last more 
than 8 minutes and it usually lasts much less than this. 

At the total solar eclipse of July, 1878, for example, the shadow of 
the Moon travelled diagonally across North America from Behring's 
Straits through Alaska west of the Rocky Mountains of British Co- 
lumbia and entered the United States not far east of Vancouver. 
From thence the shadow crossed Washington, Idaho, the south- 
western part of Wyoming, the State of Colorado (near Denver), the 
State of Texas, and, curving across the Gulf of Mexico, traversed 
Cuba. The duration of totality was about 3 minutes near Van- 
couver, about 2| minutes near Galveston. The shadow-path of the 
total solar eclipse of May 28, 1900, is described in Chapter XVI. 

In order to see a total eclipse an observer must station 
himself beforehand at some point of the Earth's surface 
over which the shadow is to pass. These points are gen- 
erally calculated some years in advance, in the astronomical 
ephemerides. 

Eclipses of the Sun are useful to astronomy because 
during an eclipse the Sun's light is cut off from the Earth's 
atmosphere and we have a short period of darkness during 
which the surroundings of the Sun can be examined with 
the spectroscope or with the photographic camera. Great 
discoveries have been made at these times, as we shall see. 
Eclipses are useful to history and to chronology because they 
afford a precise means of fixing dates. Total solar eclipses 
are so impressive (see Chapter XVI for a description of the 
phenomena) that they are often recorded in ancient annals. 
Calculation can fix the date at which such an event was 
visible, and thus render a service to chronology. Lunar 
eclipses are often serviceable in the same way. 

There is another way of looking at the problem of solar 
eclipses which is worth attention. An observer on the 
Earth sees the Sun as a bright circle in the sky. The 
apparent angular diameter of the Sun (the angle between 



ECLIPSES OF THE SUN AND MOON. 



229 



two lines drawn from the observer's eye to the upper edge 
and to the lower edge of the San, respectively) is greatest 
when the Earth is nearest to the Sun, least when the Earth 
is farthest away. In the same way the apparent angular 
diameter of the Moon to an observer on the Earth is 
greatest when the Moon is nearest, least when the Moon is 
furthest away. 

These apparent angular diameters have been measured 
and the results of observation are given in the following 
little table: 



Average. 



Apparent diameters of the Moon . 
Apparent diameters of the Sun. . . 



Greatest. 


Least. 


33' 33" 
32' 33" 


29' 24" 

31' 28" 



31' 08' 
32' 00' 



If at any new Moon the centres of the Sun, Moon, and 
Earth are in a straight line, an eclipse will occur. If the 



Fig. 145. 



angular diameter of the Moon is less than that of the Sun 
we shall have an annular eclipse of the Sun. When the 
centre of the Moon just covers the centre of the Sun the 
appearance will be like figure 146. As the Sun at this time 
has a larger angular diameter it will appear, at the moment 
of central eclipse, like a bright ring round the dark 
(unilluminated) body of the Moon. The Moon will move 
across the disk of the Sun from west towards east and the 
ring will only endure for a short time. 

If the centres of the Earth, Sun, and Moon are in a 
straight line at any new Moon, and if at that time the 
apparent angular diameter of the Moon is greater than that 
of the Sun there will be a total eclipse of the Sun. 



230 



ASTRONOMY. 



If at the time of new Moon the Moon does not pass 
centrally across the Sun's disk, but above the centre or 
below it, there may be a total eclipse (or an annular eclipse), 
but usually there will only be a partial eclipse. Only a 
part of the Sun's disk will be covered in such a case. 

There are more eclipses of the Sun than of the Moon. 
A year never passes without at least two of the former, and 
sometimes five or six, while there are rarely more than two 
eclipses of the Moon, and in many years none at all. But 
at any one place on the Earth more eclipses of the Moon 
than of the Sun will be seen. The reason of this is that an 

eclipse of the Moon is 
visible over the entire 
hemisphere of the Earth 
on which the Moon is 
shining, and as it lasts 
several hours, observers 
who are not in this hemis- 
phere at the beginning of 
the eclipse may, by the 
Earth's rotation, be 
brought into it before it 
ends. Thus the eclipse 
Fig. 146.— The Dark Body of w \\\ usually be seen over 
the Moon Projected on the . *_•,*,<, -n j_i 

Disk of the Sun at the Mid- more than half the Earth s 
dle of an Annular Eclipse, surface. But each eclipse 
of the Sun can be seen over only so small a part of the 
Earth's surface, and while there are many more solar 
eclipses than lunar for the whole Earth taken together, 
fewer are visible at any one station. 

Occultation of Stars by the Moon. — Since all the bodies of the solar 
system are nearer than the fixed stars, it is evident that they must 
from time to time pass between us and the stars. The planets are, 
however, so small that such a passage is of very rare occurrence. 
But the Moon is so large and her angular motion so rapid that she 




ECLIPSES OF THE SUN AND MOON. 231 

passes over some star visible to the naked eye every few days. 
Such phenomena are termed occultations of stars by the Moon. 

The Nautical Almanac contains predictions of all occultations, 
These predictions are obtained by calculating the Moon's path on 
the celestial sphere and by noticing what bright stars (or planets) 
her disk will cover to observers at different stations on the Earth. 

— What is a shadow ? its umbra ? penumbra ? Draw a diagram 
showing the shadow of the Earth cast by the Sun. Point out the 
umbra and the penumbra of this shadow. What is the cause of a 
lunar eclipse ? Why do we not have lunar eclipses at every full 
moon — once a month ? What is che color of the totally eclipsed 
moon ? Why does it have this color ? What is the cause of a solar 
eclipse ? Why do we not have solar eclipses at every new moon ? 
(Answer: because in the first place the Moon's shadow is often too 
short to reach the surface of the Earth and also because it often 
does not at new Moon point at the Earth, but above the Earth or 
below it.) 




Fig. 147. — A Schoolroom Experiment to Illustrate a 
Solar Eclipse. 
The room must be darkened. The lamp should have a ground glass or 
an opal globe to represent the circle of the Sun's disk. An orange (B) 
fastened to a pincushion by a knitting-needle may stand for the Earth. 
A golf -ball suspended by a string (C) may stand for the Moon. By placing 
C on the other side of B the circumstances of a lunar eclipse may be illus- 
trated. 

What is a partial eclipse of tbe Moon ? of the Sun ? a total 
eclipse of the Moon? of the Sun? an annular eclipse of the Sun? 
Why can there never be an annular eclipse of the Moon ? What is 
an occultation f Longfellow has a poem, " The Occultation of 
Orion." Could the Moon cover a whole constellation ? 



CHAPTER XIII. 

'the earth. 

28. Astronomy has to do with the Earth as a planet. 
Physical Geography treats of the Earth without considering 
its relation to the other bodies of the solar system. But 
our only means of understanding the conditions on other 
planets is to be found in a comparison of these conditions 
with circumstances on the Earth. For this reason it is 
convenient to recall some of the facts taught by Physical 
Geography and to group them with others derived from 
Astronomy. 

The Earth's average distance from the Sun is about 92,800,000 
miles. Its least distance (in December) is 91,250,000 miles; its 
greatest distance (in June) is 94,500,000 miles. The seasons on the 
Earth depend chiefly on the north-polar distance of the Sun and not 
on the Earth's proximity to it. The Earth revolves on its axis once 
in 24 (sidereal) hours. By its rotation an observer at the equator is 
carried round at the rate of more than 1000 miles per hour. It was 
a favorite argument of the men of the Middle Ages against the 
theory that the earth was in rotation that so great a velocity as this 
could not possibly fail to be remarked. If the rotation were not 
uniform and regular the argument would be convincing. 

The Earth travels around the circumference of its orbit once in 
365 days, at the rate of about 66,000 miles per hour, at the rate of 
about 18| miles per second. 

Figure of the Earth. — Ptolemy taught in the Almagest 
(a.d. 140) that the Earth was a sphere. Five hundred 
years before his time Aristotle had proved the same 
thing, and before Aristotle there were philosophers who 
held the same opinion. Ptolemy maintained that the 

232 



THE EARTH. 



233 



Earth was rounded in an east-to-west direction because the 
Sun, Moon, and stars do not rise and set at the same 
moment to all observers, but at different moments. The 
Earth was rounded in a north and south direction because 
new stars appeared above the southern horizon as men 
travelled southwards, or above the northern horizon as they 
travelled northwards. 

It was well known in his time that a journey of a few 
hundred miles to the north or south would change the 
horizon of an observer so that new stars became visible. 
Such short journeys could not produce such results on a 
globe of very large size. The voyage of Magellan at the 
beginning of the sixteenth century first established in all 
men's minds the fact that the Earth was a spherical body. 




Fig. 148.— An Ellipse. 
AC = 2a is the major axis ; BD = 2b is the minor axis. 

The popular opinion for many centuries was that the Earth 
was a flat disk everywhere surrounded by water. 

The Earth is not a sphere, but a spheroid. If it is cut 
by meridian planes (through the poles) the curves cut out 
of its surface are ellipses, not circles. 



234 



ASTRONOMY. 



If an ellipse is revolved about the axis BD the resulting 
solid is a spheroid. The Earth's meridian is very little 
different from a circle. The minor axis, the line joining 
the two poles, is the axis of rotation. 



NORtH POLE 




SOUTH POLE 

Fig. 149— The Earth— its Axis, its Poles, its Equator. 

Its equatorial semi-diameter = a = 20,926,202 feet, 

- 3963.296 miles, 
= 6,378,190 metres. 

= b = 20,854,895 feet, 
= 3949.790 miles, 
= 6,356,456 metres. 

= 2a = 7926 6; miles, 
= 26 = 7899 6 " 

= about 500,000,000 inches. 

The circumference of the equator = 24.899 miles, 
" «• " a meridian =24,856 " 

= 40,000,000 metres. 

A railway train travelling a mile a minute would require 17 days 
and nights of continuous travel to go once around the Earth. 
The area of the whole Earth is about 197,000,000 square miles. 
" " ' " dry land " " 50,000,000 " " . 



Its polar semi-diameter 



The equatorial diameter 
" polar " 






THE EARTH. 



235 



So that the area of the Earth is more than fifty times that of the 
United States. We shall see that the planets Jupiter, Saturn, 
Uranus, and Neptune are, each one of them, far larger than the 
Earth ; and the Sun is immensely larger. Its diameter is 866,400 
miles. 

Geodetic Surveys. — Since it is practically impossible to 
measure around or through the Earth, the figure and the 
size of our planet has to be found by combining measure- 
ments on its surface with astronomical observations. Even 
a measurement on the Earth's surface made in the usual 
way of surveyors would be impracticable, owing to the in- 
tervention of mountains, rivers, forests, and other natural 
obstacles. The method of triangulation is therefore uni- 
versally adopted for measurements extending over large 
areas. 




Fig. 150.— A Part of the French Triangulation near Paris. 



Triangulation is executed in the following way: Two points, a and 
b, a few miles apart, are selected as the extremities of a base-line. 
They must be so chosen that their distance apart can be accurately 
measured; the intervening ground should therefore be as level and 
free from obstruction as possible. One or more elevated points, EF, 
etc., must be visible from one or both ends of the base-line. The 
directions of these points relative to the meridian are accurately 
observed from each end of the base, as is also tbe direction ab of the 
base-line itself. Suppose F 10 be a point visible from each end of 
the base, then in the triangle abF we have the length ab determined 



236 ASTRONOMY. 

by actual measurement, and the angles at a and 6 determined by 
observations. With, these data the lengths of the sides aJ^and bF 
are determined by a simple computation. 

The observer then transports his instruments to F, and determines 
in succession the direction of the elevated points or hills DEGHJ, 
etc. He next goes in succession to each of these hills, and deter- 
mines the direction of all the others which are visible from it. 
Thus a network of triangles is formed, of which all the angles are 
observed, while the sides are successively calculated from the first 
base. For instance, we have just shown how the side aFis calcu- 
lated; this forms a base for the triangle EFa, the two remaining 
sides of which are computed. The side EF forms the base of the 
triangle GEF, the sides of which are calculated, etc. 

Chains of triangles have thus been measured in Russia and Sweden 
from the Danube to the Arctic Ocean, in England and France from 
the Hebrides to the Sahara, in this country down nearly our entire 
Atlantic coast and along the great lakes, and through shorter dis- 
tances in many other countries. An east and west line has been 
measured by the Coast Survey from the Atlantic to the Pacific 
Ocean. 

Suppose that we take two stations, a and^*, Fig. 150, situated north 
and south of each other, determine the latitude of each, and calcu- 
late the distance between them by means of triangles, as in the 
figure. It is evident that by dividing the distance between them by 
the difference of latitude in degrees we shall have the length of one 
degree of latitude. Then if the Earth were a sphere, we should at 
once have its circumference by multiplying the length of one degree 
by 360. It is thus found that the length of 1 degree is a little more 
than 111 kilometres, or between 69 and 70 English statute miles. Its 
circumference is therefore about 40,000 kilometres, and its diameter 
between 12,000 and 13,000.* (25,000 and 8000 miles.) 

The general surface of the Earth is found, to be rather smooth. 
The highest mountain is about 5^ miles high; the deepest ocean is 
about 5| miles deep. Eleven miles covers the range of height and 
depth. The average elevation of the continents above the sea-level 
is about 2000 feet. The average depth of the ocean is about 
12,000 feet. 

* When the metric system was originally designed by the French, it was in- 
tended that the kilometre should be i^Tsrs of the distance from the pole of the 
Earth to the equator. This would make a degree of the meridian equal, on the 
average, to 11 1£ kilometres.. But the metre actually adopted is nearly T $ n of an 
inch too short. 



THE EARTH. 237 



Mass and Density of the Earth. 

The mass of a body is the quantity of matter it contains. It is 
measured by the product of its volume ( V) by its density (D) 

M - V . D. For another body M'-V'.D'. 
For equal volumes V —V and M : M' = D : D'. 

That is, the densities of equal volumes of two substances are pro- 
portional to the masses of the substances, to the quantity of matter 
in them. For example, copper is of greater density than water 
because a cubic foot of copper contains more matter than a cubic 
foot of water. The density of pure water at about 39° Fahr. is 
taken as the unit-density. The unit-volume may be taken as a 
cubic foot. The unit-mass will then be that of a cubic foot of pure 
water at 39° Fahr. 

The weight of a body is the force with which it is attracted to the 
centre of the Earth. A body of mass m is attracted by the Earth's 

mass M by — — , where r is the distance Mm. (See page 210.) The 

3fm 
weight w of m is then — ^ • The weight w' of any other body m 

Jkfm' 
is w — — 7T . If the bodies are at the same place on the Earth r = r' 
r ' 

and w\ w' — m\ m! ', or the weights of bodies at the same place on the 

Earth are proportional to their masses. It is easy to measure the 

relative weights of two bodies by balancing them in scales against 

certain pieces of metal. Hence by weighing two bodies of weights 

w and w' we can determine the ratio of their masses m and m'. If 

m is a cubic foot of water, m! is the absolute mass of the other 

substance. 

The weight of a body m due to the Earth's attraction is 

— . If the body is at the pole of the Earth r = 7899.6 

miles. If it is at the equator r = 7926.6 miles. Its 
weight will therefore be greater at the pole than at the 
equator. If we wish to weigh out a certain quantity of 
gunpowder in Greenland we may balance it against a piece 
of metal that we call an ounce. If we take the gunpowder 
to Peru it will " weigh" less because it will there be 



238 ASTRONOMY. 

farther from the Earth's centre. Bat it will still balance 
the oance in Peru, because that also is less attracted by the 
Earth in precisely the same proportion. A piece of iron a 
cubic foot in volume " weighs " less in a balloon than at 
the Earth's surface. In practical life no note need be 
taken of the differences of the Earth's attraction at differ- 
ent latitudes. But in Astronomy these differences of at- 
traction due to differences of distance must be taken into 
account. The attraction of the Earth for the Moon is 
different at different times because the Moon is sometimes 
near the Earth, sometimes further away. 

The density of pure water at about 39° Fahr. is taken as the unit- 
density. For equal volumes of any two substances M : M' = D : D' 
or, their densities are proportional to their masses. At the same 
place on the Earth W : W = M : M' or, their weights are also pro- 
portional to their masses, hence 

W:W'= D:D'. 

If one of these substances is pure water (W, D') we have 

W. D' 

D = w , and we can determine D, the density of any substance, 

as copper, by weighing it against an equal volume of water. In 
this way the densities of all substances on the Earth have been 
determined. 

The surface-rocks of the Earth are about 2£ times as dense as 
water, and volcanic lavas deep down in the Earth are about 3 times 
as dense. The deeper the origin of the rocks the denser they are, 
because they are subject to greater pressures. We can determine 
the density of any single specimen of rock that can be brought to 
the surface. We can get no specimens of rock from depths greater 
than a few miles. How then shall we determine the average density 
of the whole Earth ? 

To determine the density of the Earth we must find hoic much matter 
it must contain in order to attract bodies on its surface with forces 
equal to their observed weights, that is, with such intensity that at the 
equator a body shall fall nearly five metres {about 16 feet) in a second. 
To find this we must know the relation between the mass of a body and 
its attractive force. This relation can be found by measuring the 
attraction of a body of known mass. 




THE EARTH. 239 

We may measure the attraction of a body of known mass in the 
following ingenious way. In Fig. 151 H1KL is a cube of lead 1 metre 
on each edge. Two holes are bored 
through the cube at DF and EG- 
A pair of scales ABC bas its scale- 
pans HE connected by fine wires 
to other scale-pans EG, below the 
block. Suppose the pans empty 
and everything at rest. 

I. Put a weight W in H, and 
balance the scales by weights in G. 
At H the total attraction on W is 
the attraction of the Earth plus the Fig. 151 — Experiment to 
attraction of the block, while at Determine the Density op 
G we have the attraction of the THE Earth - 

Earth (downwards) minus the attraction of the block (upwards); 
hence 

The weight in H 4- (attraction of the block) = The weights in G — 
(attraction of the block), whence 

(1) Weights in G = weight in H -f- 2 (attraction of block). 

II. Put the weight W in F, and balance the scales by weights in 
E. At F the total attraction is earth minus block, and at E it is 
earth plus block. 

The weight in F — (attraction of the block) = The weights in E -)- 
(attraction of the block), whence 

(2) Weights in E = weight in F — 2 (attraction of block). 

Subtract equation (2) from (1), remembering that the (weight in 
H) = (weight in F). 

Weights in G — weights in E = 4 (attraction of block), 

after small corrections have been applied for the difference of height 
of H, E, F, G, etc. 

The attraction of this block, which has a known mass in kilo- 
grammes (or pounds), is thus known, and hence the general relation 
between mass in kilogrammes (or pounds) and attractions. 

The attraction of the Earth is known. It is such as to cause 
bodies to have their observed weights. Hence the mass of the Earth 
becomes known. The volume of the Earth is known from geodetic 



240 



ASTRONOMY. 



surveys. The density of the whole Earth is therefore known from 

M 

the equation D = -—. 



The density of the Earth is about 5$ times that of water, 
" copper " " 8^ " " " " , 

" « «< C ] ft y << << 2 " " " " 

The mass of the Earth is 6, 000, 000, 000, 000, 000, 000, 000 tons. 




Fig. 152. 

Determination of the Mass of the Earth in Terms of the Mass of the 
Sun. — The mass of the Earth expressed in tons or pounds is known 
The mass of the Earth in fractions of the Sun's mass (= 1.0) can be 
determined by calculating how far the Earth is deflected by the Sun's 
attraction each second, as she travels in her orbit. Her motion 
along her orbit is 18$ miles per second (because the circumference of 
her orbit is 584,600,000 miles and because it is traversed in a sidereal 
year of 365 d 9 h 9™ 9 s ). (Fig. 152.) Her deflection from a straight 



line each second is 



100 



of an inch, as may be proved from the 



foregoing diagram, in which E is the place of the Earth at the 
beginning of a second, E' its place at the end of the second, EE' the 
orbit of the Earth, 8 the place of the Sun, X another point of the 
Earth's orbit, Ee the Earth's fall towards the Sun in a second. 

In the two right triangles XE'E and EE'e we have EX : EE' 
= EE' : Ee, or (twice 93,000,000) : 18$ = 18| : Ee, 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 fo 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 
16 T X (5 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 33^70- 

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 
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 s^^VuFffo)- 

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 
O is the centre of the Earth and A the station of an 
observer on its surface. S 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 
e, d, 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 S\ 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 the 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 344' 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 ABCD 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 C; 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 /S^and 
SO strike the atmosphere above A and leave it at the points 
Q and R. 

Each of the lines SAPM, SQNis bent from a straight 
course by refraction, but SRO is not bent since it just 



THE EAUTR. 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 San, 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 San. 
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 Bb 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 id. 

To an observer at C the twilight is derived from the 
illumination of the portion PQz which lies above Ins 
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. As 
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 two 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, 
1 sidereal day = 0.997 mean solar day, 
24 sidereal hours = 23 h 56 m 4 9 .091 mean solar time, 
1 mean solar day = 1.03 sidereal days, 
24 mean solar hours = 24 h 3 m 56 s . 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 in 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 interval between consecutive new Moons being 
nearly 29^ days, it was common in the use of the pure lunar 
month to have months of 29 and 30 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. 2^7 

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 360, which we use, was 
adopted in China in the remotest historic times. 

The Julian Calendar.— The civil calendar now in use 
throughout Christendom had its origin among the Romans, 
and its foundation was laid by Julius C^sar. 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 tbe 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 eqainoctial year to 
have a length of 365.24220 days. The San 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°. 

j 365 d . 25636 ) j 365 d . 24220 ) OCAO 0Kft0 Kn , 1A „ 

i ., . J- : j .. . f = 360 : 359 59 10", approx. 

( sidereal year ) ( equinoctial year ) rtr 

The equinox must therefore be moving in space so that 

* Russia will adopt the New Style in A.D. 1901 



THE EARTH. 249 

when it is met a second time the San has made one revolu- 
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 (AB) 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, 
Cepheu?, 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 Cephevs, 

" 7500 " " " " *' " " a in 



11500 
14000 



8 in Cygnus, 
a in 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 equaior. 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 NG about 
the line GE. 

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 mast 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 Homer, 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'" 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 J and about J'") is 
eclipsed at every revolution. Eomee 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 J" its light has to pass over the line J I 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 J'". 
Light requires 16 m 38 s to pass over the diameter of the 
Earth's orbit, therefore, or 8 m 19 8 to pass over the radius of 
the orbit. 



Sunlight 


is 3 m 


(t 


" 6 m 


a 


« gm 


(l 


i< -J^m 


a 


i< 43m 


a 


« ^10™ 


a 


"2 h 38 ra 


it 


• <4h gm 



256 ASTRONOMY. 

In 499 s 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) : 

old when it reaches Mercury, 

" " " " Venus, 

" " " " Earth, 

" " " " Mars, 

" " " Jupiter, 

" " " Saturn, 

" " " " JJranus, 

" " " " Neptune. 

The time required for the light of a planet to reach the Earth is 
called the planet's aberration-time. For instance, the aberration-t me 
of Neptune is about 4 h 8 m . This means that the light by which 
we see Neptune now — this instant — is 4 h 8 m old when it reaches us. 
Neptune may have vanished 4 U 7 m ago for all we know. We can only 
find out by waiting. The stars are very much further away than 
Neptune. We shall see, later on, that the light of even the nearest 
star is more than 4 years on its passage to the Earth. The light from 
Polaris takes more than 40 years to reach us. Polaris may have 
vanished 40 years ago for all we know — now ; we can only find out 
by waiting. Only a very few of the stars are so near as this. Most 
of them are immensely further away. 

The theory of Romer was not fully accepted by his contemporaries. 
The velocity of light was so much greater than any known terres- 
trial velocity that it seemed difficult to accept it. Even the motion 
of the Earth in its orbit was only 18 \ miles per second. The velocity 
of light was 10,000 times as large. In the year 1729 James Bradley, 
afterwards Astronomer Royal of England, observed a phenomenon of 
a different character that entirely confirmed Romer's conclusions. 
Bradley discovered that the stars are not seen in their true places, 
but that each star is displaced by a small angle (never more than 
21"). This displacement occurs because the Earth is moving among 
the stars with a velocity that is comparable with the velocity of light. 

In the figure suppose AB to be the axis of a telescope, S a 
star, and SAB' a ray of light which emanates from the star. The 

* The most accurate determinations give 186,330 miles. 




ABERRATION. 257 

student may imagine AB to be a rod which an observer at B seeks 
to point at the star 8. It is evident that he must point this rod in 
such a way that the ray of light shall run 
accurately along its length. If the observer 
(and the Earth) were at rest at B he will 
point the rod along the line SB. 

Suppose now that the observer (and the 
Earth) are moving from B toward B' with 
such a velocity that he moves from B to 
B' during the time required for a ray of 
light to move from A to B'. Suppose, 
also, that the ray of light from 8 (SA) 
reaches A at the same time that the end of 
his rod does. Then it is clear that while 
the rod is moving from the position AB 
to the position A'B', the ray of light will Fig. 156. 

move from A to B, and will therefore run accurately along the 
length of the rod. 

For instance, if 6 is one third of the way from B to B ', then the 
light, at the instant when the rod takes the position ba, will be one 
third of the way from A to B' , and will therefore be accurately on 
the rod. Consequently, to the observer, the rod will appear to be 
pointed at the star. In reality, however, the pointing will not be in 
the true direction of the star, but will deviate from it by a certain 
angle depending upon the ratio of the velocity with which the 
observer is carried along to the velocity of light. 

If the Earth stood still there would be no aberration. If the 
velocity of light were 10,000 times greater than it is the aberration 
would be vanishingly small. 

Effects of Aberration. — The velocities of light and of the Earth 
being what they are, the apparent displacement of a star's position, 
due to aberration is always less than 21". 

Aberration phenomena can be observed on the Earth 
on any rainy day with no wind. (See fig. 157.) The 
rain-drops descend vertically. If the observer stands still 
he must hold his umbrella straight above his head. Now 
let him walk briskly towards the south. He will find that 
he must incline his umbrella southwards (in the direction 
of his motion) to protect himself. If he walks towards the 
west he most incline his umbrella westwards (in the 



258 ASTRONOMY. 

direction of his motion). If instead of walking he runs, 
the same effects are produced, only he will find that he 
must incline his umbrella still more. All this while each 
rain-drop is falling vertically ; yet every change of his 
direction of motion and of his velocity (relative to the 
velocity of the falling drops of rain) requires him to alter 
the inclination of his protecting umbrella. The experiment 
is so easy that the student should not fail to try it. 

— What is the Earth's distance from the Sun? (Answer, about 
93,000,000 miles.) Do the seasons depend on the Earth's proximity 
to the Sun ? What is the shape of the Earth? How is the figure of 
the Earth determined? Define the mass, the density, the volume 
of a body. Define the weight of a body. Does a body — say a cubic 
inch of copper — weigh the same in Brazil and in Iceland ? If you 
could take it 10,000 miles above the Earth would it weigh less or 
more than in New York ? How is the density of specimens of rocks 
determined? How is the density of the whole Earth, considered as 
one mass, determined ? Is the temperature of the Earth greater 10 
miles below the surface than 5 miles deep ? Does the Earth receive 
all the Sun's heat? What is the refraction of light by the Earth's 
atmosphere ? Does refraction increase or diminish the apparent zenith 
distance of the Sun? Describe the phenomena of twilight? Did 
you ever see it yourself? Define the different kinds of day. What 
is a month? Define the sidereal and the equinoctial year. Which 
is the longer? What does that prove? Will Polaris always be our 
pole-star? What is the cause of precession? What three great 
names are connected with the discoveries regarding precession ? and 
at what dates ? How was it first proved that light required time to 
pass from place to place ? About how long does it take sunlight to 
reach the Earth? to reach Neptune? About how long does it require 
for the light of the nearest star to reach the Earth ? (Answer, 4 
vears.) 



ABERRATION. 



259 




Fig 157.— Effects of Aberration. 



CHAPTER XIV. 
CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. 

29. The Celestial Scale of Measurement. — The units of 
length and mass employed in Astronomy are necessarily 
different from those used in daily life. The distances and 
magnitudes of the heavenly bodies are never reckoned in 
miles or other terrestrial measures for astronomical pur- 
poses; when so expressed it is only for the purpose of 
making the subject clearer to the general reader. The 
mass of a body may be expressed in terms of that of the 
San or of the Earth, but never in kilogrammes or tons, 
unless in popular language. 

There are two reasons for this course. One is that in 
most cases celestial distances have first to be determined in 
terms of some celestial unit — the Earth's distance from the 
Sun, for instance — and it is more convenient to retain this 
unit than to adopt a new one. The other is that the 
values of celestial distances in terms of ordinary terrestrial 
units are more or less uncertain, while the corresponding 
values in astronomical units are known with great accuracy. 

An example of this practice is afforded when we deter- 
mine the dimensions of the solar system. By a series of 
observations of their positions on different dates, investi- 
gated by means of Keplek's laws and the theory of 
gravitation, it is possible to determine the forms of the 
planetary orbits, the positions of their planes, and their 
relative dimensions, with great precision. 

Kepler's third law enables us to determine the mean 
distance of a planet from the Sun when we know its 

260 



CELESTIAL MEASUREMENTS. 261 

period of revolution (see page 200). All the major planets, 
as far out as Saturn, have been observed through so many 
revolutions that their periodic times can be determined with 
great exactness — in fact within a fraction of a millionth 
part of their whole amount. The more recently discovered 
planets, Uranus and Neptune, will, in the course of time, 
have their periods determined with equal precision. Then, 
if we square the periods expressed in years and decimals of 
a year, and extract the cube root of this square, we have 
the mean distance of the planet with the same order of 
precision. 

Again, the eccentricities of the orbits are exactly deter- 
mined by careful observations of the positions of the planets 
during successive revolutions. Thus we can draw a map 
of the planetary orbits so exact that its errors will entirely 
elude the most careful scrutiny, though the map itself 
might be many yards in extent. 

On such a map we can lay down the magnitudes of the 
planets as accurately as our micrometers can measure 
their angular diameters. Thus we know that the mean 
diameter of the Sun, as seen from the earth, subtends 
an angle of 32'. We can therefore, on such a map of the 
solar system, lay down the Sun in its true size, on the scale 
of the map. This can be done in the same way for each 
of the planets, the Earth and Moon excepted. There is no 
immediate and direct way of finding how large the Earth 
or Moon would look from the Sun or from a planet; 
whence the exception. 

But without further research we shall know nothing 
about the scale of our map. That is, we shall have no 
means of knowing how many miles in space correspond to 
an inch on the map. If we can learn either the distance 
or magnitude of any one of the planets laid down on the 
map, in miles or in semi diameters of the Earth, we shall 
be able at once to find the scale. 



262 ASTRONOMY. 

The general custom of astronomers is not to attempt to 
use a scale of miles at all, but to employ the mean distance 
of the Sun from the Earth as the unit in celestial measure- 
ments. Thus, in astronomical language, we say that the 
distance of Mercury from the Sun is 0.387, that of Venus 
0.723, that of Mars 1.523, that of Saturn 9.539, and so 
on in terms of the Earth's distance = 1.000. But this 
gives us no information respecting the distances in terms 
of terrestrial measures. 

The distance of the Earth in miles is not the only 
unknown quantity on our map. We know nothing respect- 
ing the distance of the Moon from the Earth, because 
Kepler's laws apply directly to bodies moving around the 
Sun. We must therefore determine the distance of the 
Moon as well as that of the San. When these two things 
are done a map of the solar system can be made in which 
every measurement can be expressed in miles. 

The Solar and Lunar Parallax. 

The problem of distances in the solar system is thus 
reduced to measuring the distances of the Sun and Moon 
in miles or in terms of the Earth's radius (= 4000 miles). 
The most direct methods of doing this are as follows: 





fmSn 



Fig. 158. — Determination of the Distance of the Moon. 



SOLAR AND LUNAR PARALLAX 263 

Distance of the Moon. — In the figure C is the centre of 
the Earth, and S' and S" are the positions of two 
observers on its surface. P is the Moon in space and PC 
is the distance to be determined (in miles). The observer 
at S" sees the Moon on the celestial sphere at P" , and he 
measures its zenith distance Z"P". At the same instant 
the observer at 8' sees the Moon on the celestial sphere at 
P' and he measures its zenith distance Z'P'. (The student 
must imagine the circle Z" P" to be completed, and Z' a 
point in the circle.) Z"P" and Z'P' are then known arcs 
and Z"S"P" and Z'S'P' are known angles, since they are 
measured by known arcs. The angle PS "Cm known; it 
is 180° - PS"Z". The angle PS'C is known; it is 
180° — PS'Z'. As the two observers are at stations whose 
latitudes are known, the angle S'CS" is known. It is the 
difference of their latitudes (for if H'H i is the plane of the 
Earth's equator, S" CH X is the latitude of S" and S'Cff l 
is the latitude of S' and therefore S'CS" is known). 

In the quadrilateral S'CS"P the three angles whose 
vertices are at C, at S\ and at S" are known, and therefore 
the fourth angle whose vertex is at P is known. In this 
quadrilateral two of the sides are known because they are 
radii of the Earth. Hence the distances S'P and S"P 
are known. From either of the triangles S'CP or S"CP 
the distance of the Moon, CP, can be calculated. 

This is one method of determining the distance of the 
Moon. Knowing the actual dimensions of the Earth in 
miles, observations of the Moon made at stations widely 
separated in latitude, as Paris and the Cape of Good Hope, 
can be combined so as to give the Moon's distance in miles. 
On precisely the same principles the distances of Venus or 
Mars have been determined in miles. 

The Distance of the Sun from Transits of Venus. — When 
Venus is at inferior conjunction she is between the Sun 
and the Earth. If her orbit lay in the ecliptic, she would 



264 



ASTRONOMY. 



be projected on the Sun's disk at every inferior conjunc- 
tion. The inclination of her orbit is, in fact, about 3£°, 
and thus transits of Venus occur only when she is near the 
node of her orbit at the time of inferior conjunction. In 
Fig. 159 let E, V, S be the Earth, Venus, and the Sun. 
DC is a part of Venus' 1 orbit. An observer at B will see 
Venus impinge on the Sun's disk at /, be just internally 
tangent at II, move across the disk to III, and off at IV. 




Fro. 159. — Determination of the Distance of the Sun. 



Similar phenomena will occur for A at 1, 2, 3, 4. When 
A sees Venus at a, B will see her at b. ab : AB :: Va : VA ; 
but VA : Va as 1 : 2-J nearly, ab therefore occupies on 
the Sun's disk a space 2-j- times as large as the Earth's 
diameter. If we measure the angular dimension ab in any 

E 




Fig. 160. 



way, and divide the resulting angle by 2|, we shall have 
the angle subtended at the Sun by the Earth's diameter; 
or if we divide it by 5, the angle subtended at the Sun 
by the Earth's radius. (Fig. 160.) Having this angle 



MASSES OF THE PLANETS. 265 

we can calculate the Earth's distance from the Sun in 
miles from the right triangle 8EG, where S is the Sun, 
the Earth's centre, and E the end of the Earth's radius. 

The angular space ab can be calculated at a transit of 
Venus, when we know the length of the chords II, III, 
and 2, 3. The length of each chord is known by observing 
the interval of time elapsed from phase // to phase III. 

Other Methods of Determining Solar Parallax. — The 
most accurate method of measuring the Sun's distance 
depends upon a knowledge of the velocity of light. The 
time required for light to pass from the Sun to the Earth 
is known with considerable exactness, being very nearly 
498 seconds.* If we can determine experimentally how 
many miles light moves in a second, we shall at once have 
the distance of the Sun in miles by multiplying that 
quantity by 498. The velocity of light is about 186,330 
miles per second. Multiplying this by 498, we obtain 
92,800,000 miles for the distance of the Sun. The time 
required for light to pass from the Sun to the Earth is 
still somewhat uncertain, but this value of the Sun's 
distance is probably the best yet obtained. 

Relative Masses of the Sun and Planets. 

In estimating the masses as well as the distances of celestial bodies 
it is necessary to use what we may call celestial units; that is, to take 
the mass of some celestial body as a unit, instead of any multiple of 
the pound or kilogram. The reason of this is that the ratios be- 
tween the masses of the planetary system, or, what is the same 
thing, the mass of each body in terms of that of some one body as 
the unit, can be determined without knowing the mass of any one 
of them in pounds or tons. To express a mass in kilograms or 
other terrestrial units, it is first necessary to find the mass of the 
Earth in such units, as already explained. This, however, is entirely 
unnecessary for astronomical purposes. In estimating the masses of 

* See page 256. 



266 ASTRONOMY. 

the individual planets, that of the Sun is generally taken as a unit. 
The planetary masses are then all very small fractions. 

The ma<s of the Sun being 1.00, the mass of Mercury is t^-^o^u^; 



Venus 


1S sofVott; 


Earth 


i S 733TT1P 


Mars 


1S ToTOTTff 


Jupiter 


1S iVls! 


Saturn 


i s T502> 


Uranus 


18 2"r<rm>> 



" " " Neptune is T g^ 7 . 

The mass of the Earth being 1, the mass of the Moon is -g T . 

The masses of the planets that have satellites are determined by 
measuring the attraction that is exerted by the planet on the satellite. 

If the distance of the planet from the Sun (M) is R and its peri- 
odic time is T, and if the planet whose mass is m has a satellite re- 
volving in a circular orbit whose radius is r in a time t, it is proved 
in Mechanics that 

by which expression we can determine m, the mass of the planet, in 
fractions of the Sun's mass M, because R, T, r, t are known. In this 
way the masses of all the planets that are attended by satellites are 
calculated, after making suitable allowances for the fact that the 
orbits of the satellites are ellipses and not circles. 

Mercury and Venus have no satellites, and their masses are calcu- 
lated by determining the perturbations that they cause in the motions 
of other planets (and of comets) in their vicinity. 

The angular diameters of the planets are measured with a microm- 
eter attached to a telescope. The result is expressed in seconds of 
arc. Knowing the distance of the planet in miles, the diameter can 
also be expressed in miles. (See page 144.) 

The surface of a planet is proportional to the square, and its vol- 
ume to the cube of its diameter. The mass of a planet is deduced as 
above described. Its density is obtained by dividing its mass by its 
volume. 

In what has gone before the methods of determining the 
mass, the distance, the diameter, the orbit, etc., of each 
planet have been described with more or less fnllness. The 
fundamental principles of the methods are all that can be 



CELESTIAL MEASUREMENTS. 267 

given here. The details of the processes of observation 
are explained in works on Practical Astronomy. The 
mathematical forms involved are treated in works on 
Celestial Mechanics. It will at least be obvious to the 
student that the masses, the distances, and the orbits of 
the planets can be determined in the ways that have been 
explained, though he will not know the details of the 
processes actually employed. 

The results that have been obtained are given in two 
tables printed in Chapter XV. These two tables contain 
data sufficient to enable us to construct the map of the 
solar system that was spoken of on page 261. With the 
numbers there set down a plan of the solar system can be 
made with great exactness. The orbit of each planet can 
be drawn in its true shape and situation. The place of 
each planet at any past or future time can be assigned. 
The diameter of each planet can be marked on the map to 
the proper scale. The mass, the force of gravity at the 
surface, the volume, the density of each planet is known. 
The problems that were attacked by Ptolemy, Coper- 
nicus, Kepler, and Newton are solved. The solar 
system considered as a collection of heavy bodies revolving 
in space under the law of gravitation is explained. 

In order to complete the description of the solar system 
something more is necessary. We desire to know the 
topography, the meteorology, the physical condition of 
each planet just as we know the topography, the climates, 
the physics of our own Earth. We wish to know the 
geology and the chemistry of the stars just as we know 
the geology and the chemistry of the Earth. The science 
that treats of the physical condition of the Sun, Moon, 
planets, stars, and other celestial bodies is called Astro- 
nomical Physics or Astro-physics. The methods of this 
science are the methods of terrestrial physics extended so 
as to deal -with all celestial bodies. A description of the 



268 ASTRONOMY. 

physical condition of the heavenly bodies is called Descrip- 
tive Astronomy. The second part of this book is chiefly 
devoted to such a description, which it is necessary to give 
in a very abbreviated form. The student can supplement 
what is printed here by consulting articles on the Sun, 
Moon, and planets, etc., in any good encyclopedia, or by 
reading some of the excellent books on Popular Astronomy 
written by Sir Kobekt Ball, Flammakion, Proctor, and 
others. 

— What is the most convenient unit of length in the description 
of the solar system ? How is the periodic-time of a planet deter- 
mined ? Knowing the periodic-time, how do you obtain its mean- 
distance ? How is the angular diameter of a planet found ? Explain 
the principle by which the distance of the Moon from the Earth may 
be determined. Explain how the distance of the Sun from the Earth 
is found from Transits of Venus over the Sun's disk. Explain how 
the Sun's distance can be found when we know the velocity of light. 
What is the most convenient unit of mass in the description of the 
solar system ? On what principle are the masses of Mars, Jupiter, 
etc., determined? — the masses of Mercury and Venus f When the 
mass and the volume of a planet is known, how is its density 
obtained ? 



PART II. 
THE SOLAR SYSTEM. 



CHAPTER XV. 

THE SOLAR SYSTEM. 

30. The solar system consists of the sun as a central 
body, around which revolve the major and minor planets, 
with their satellites, a few periodic comets, and a number 
of meteor swarms. These are permanent members of the 
system. Other comets appear from time to time and make 
part of a revolution around the sun, and then depart into 
space again, thus visiting the system without being per- 
manent members of it. 

The bodies of the system may be classified as follows: 

I. The central body — the Sun. 

II. The four inner planets — Mercury, Venus, the Earth, 
Mars. 

III. A group of small planets, called Asteroids, re- 
volving outside of the orbit of Mars. 

IV. A group of four outer planets — Jupiter, Saturn, 
Uranus, and Neptune. 

V. The satellites, or secondary bodies, revolving about 
the planets, their primaries. 

VI. A number of comets and meteor swarms revolving 
in very eccentric orbits about the Sun. 

The eight planets of Groups II and IV are classed 

269 



270 ASTRONOMY. 

together as the major planets, to distinguish them from the 
five hundred or more minor planets of Group III. Mercury 
and Venus are inferior planets ; the other major planets 
are called superior planets. 




Fig 1(51. — Plan of the Solar System. 

Dimensions of the Solar System. — The figure gives a plan 
of part of the solar system as it would appear to a spectator 
immediately above or below the plane of the ecliptic. It is 
drawn approximately to scale, the mean distance of the 
Earth (=1) being half an inch. On this scale the mean 
distance of Saturn would be 4.77 inches, of Uranus 9.59 
inches, of Neptune 15.03 inches. On the same scale the 



TEE SOLAR SYSTEM. 271 

distance of the nearest fixed star would be over one and 
one half miles. The student should remember that the 
immense spaces between the planets and between the stars 
are empty except for a few comets and for swarms of 
meteors. The striking fact is how few are the bodies that 
circulate in these immense regions of space. 

The arrangement of the planets and satellites is, then — 

The Inner Group. Asteroids. The Outer Group. 

Mercury. ^ ,. n ~ . , r Jupiter and 5 satellites. 

tt 500 mmor planets, Lf ■ 

V enus. I , , , , J Saturn and 9 satellites. 

Earth and Moon. f 1 Uranus and 4 satellites. 

Mars and 2 satellites. J I Neptune and 1 satellite. 

The different planets are at very different distances from 
the Sun. To the nearest planets, Mercury and Ve?ius, the 
Sun appears as a very large disk. To the earth the Sun 
appears as a disk about half a degree in diameter. The 
amount of light and heat received from the San by any 

planet varies as -^ where r is the planets' distance. The 

surface of the circles in figure 162 also vary as - 2 and hence 

the surfaces show the relative amounts of light and heat 
received by the planets (Flora and Mnemosyne are two of 
the asteroids). The distance of Neptune from the Sun is 
eighty times that of Mercury and it receives only ^jVo P art 
as much light and heat. 

To avoid repetitions, the elements of the major planets 
and other data are collected into the following tables, to 
which the student should constantly refer in his reading. 
The units in terms of which the various quantities are 
given are those familiar to us, as miles, days, etc., yet some 
of the distances, etc., are so immensely greater than any 
known to our daily experience that we must have recourse 
to illustrations to obtain any idea of them at all. 



272 



ASTRONONY. 



For example, the distance of the sun is said to be about 93 million 
miles. It is of importance that some idea should be had of this dis- 
tance, as it is the unit, in terms of which not only the distances in 
the solar system are expressed, but also distances in the stellar 




Fig. 162. 



-The Apparent Size of the Sun as Viewed from 
the Different Planets. 



universe. Thus when we say that the distance of the nearest star is 
over 200,000 times the mean distance of the sun, it becomes 
necessary to see if some conception can be obtained of one factor in 
this. 

Of the abstract number, 93,000,000, we have no idea. It is far too 



THE SOLAR SYSTEM. 273 

great for us to have counted. We have never taken in at one view 
even a million similar discrete objects. The largest tree has less 
than 500,000 leaves. To count from 1 to 200 requires, with very 
rapid counting, 60 seconds. Suppose this kept up for a day without 
intermission ; at the end we should have counted 288,000, which is 
about 3I3 of 93,000,000. Hence over 10 months' uninterrupted 
counting by night and day would be required simply to enumerate 
the number, and long before the expiration of the task all idea of it 
would have vanished. 

We may take other and perhaps more striking examples. We 
know, for instance, that the time of the fastest express-trains between 
New York and Chicago, which average 40 miles per hour, is about a 
day. Suppose such a train to start for the sun and to continue run- 
ning at this rapid rate. It would take 363 years for the journey. 
Three hundred and sixty-three years ago there was not a European 
settlement in America. 

A cannon-ball moving continuously across the intervening space 
at its highest speed would require about eight years to reach the sun. 
In a little less than a day it would go once round the earth if its 
course was properly curved. To reach the sun it would have to 
travel for eight years at this velocity. The report of the cannon, if 
it could be conveyed to the sun with the velocity of sound in air, 
would arrive there four years after the projectile. Such a distance 
is entirely inconceivable, and yet it is only a small fraction of those 
with which astronomy has to deal, even in our own system. The 
distance of Neptune is 30 times as great. 

If we examine the dimensions of the various orbs, we meet almost 
equally inconceivable numbers. The diameter of the sun is 866,400 
miles ; its radius is but 433,200, and yet this is nearly twice the 
mean distance of the moon from the earth. Try to conceive, in 
looking at the moon in a clear sky, that if the centre of the sun could 
be placed at the centre of the earth, the moon would be far within 
the sun's surface. 

Or again, conceive of the force of gravity at the surface of the 
various bodies of the system. At the sun it is nearly 28 times that 
known to us. A pendulum beating seconds here would, if transported 
to the sun, vibrate with a motion more rapid than that of a watch- 
balance. The muscles of the strongest man would not support him 
erect on the surface of a planet of the mass of the sun : even lying 
down he would be crushed to death under his own weight of more 
than two tons. At the moon's surface the weight of a man would be 
about one-sixth of his weight on the earth (since the Moon's mass is 



274 ASTRONOMY. 

about one-sixth of the Earth's), and his muscular force, on such "a 
planet, would enable hirn to bound along with leaps of 30 feet or 
more. There are, of course, no human beings on the sun or on the 
moon. One of these bodies is too hot, the other too cold, to support 
human life. We may by these illustrations get some rough idea of 
the meaning of the numbers in these tables, and of the incapability 
of our limited powers to comprehend the true dimensions of even the 
solar system. When we come to a description of the stellar uni- 
verse we shall meet with distances and dimensions almost infinitely 
larger. 

It is important that the student should realize, so far as 
he can, the data given in these tables; and there is no 
better way to do this than to make drawings to scale from 
the numbers there set down. For instance, let the student 
draw lines to represent the apparent angular diameters of 
the different planets as seen from the Earth (Table II) on 
a scale of one inch = 30", and then draw the circles corre- 
sponding to these diameters. None of the circles for the 
planets will be more than two and a half inches in diam- 
eter; but if he wishes to draw a circle to represent the 
apparent disk of the Sun on this scale it will have to be 
over five feet in diameter. If a diagram of this sort is 
actually constructed it will impress the student's mind far 
more than a mere reading of the figures of the table. If 
he makes a drawing, to scale, of the system of Jupiter's 
satellites putting in the data of Table III and whatever 
else he can find in Chapter XVIII, a definite idea of the 
arrangement and sizes of these satellites will be acquired 
and it will not soon be forgotten. The distances of the 
periodic comets given in Table IV should be platted to 
scale along with the major axes of the Earth, Mars, 
Jupiter, Saturn, Uranus, and Neptune. 

Similar diagrams of the inclinations of the planetary 
orbits, of their periodic times, volumes, masses, densities, 
etc., will serve to impress the mind with the resemblances 
and with the differences in the different bodies of the 
system. 



THE SOLAR SYSTEM. 275 

The mass of the sun is far greater than that of any single planet in 
the system, or indeed than the combined mass of all of them. If the 
mass of the earth is represented by a single grain of wheat the mass 
of the Sun will be represented by about four bushels of such grains. 
It is a remarkable fact that the mass of any given planet exceeds the 
sum of the masses of all the planets of less mass than itself. 

The total mass of the asteroids, like their number, is unknown, but 
it is probably less than one-thousandth that of our Earth. The Sun's 
mass is over 700 times greater than that of all the other bodies, and the 
fact of its central position in the solar system is thus explained. In 
fact, the centre of gravity of the whole solar system is very little out- 
side the body of the Sun, and will be inside of it when Jupiter and 
Saturn are in opposite directions from it (when their celestial longi- 
tudes differ by 180°). 

There are very few persons who realize in any vivid way 
the distances and dimensions of the planets of the solar 
system. No very keen realization is to be had by merely 
reading the figures of the tables. If it is practicable the 
student should, once in his life, make a plan of the solar 
system in the following way. If a whole class can make 
the experiment in company it will be an advantage. 

From the Tables I and II it should first be proved that if the Sun 
were two feet in diameter instead of 866,400 miles the different 
planets would be fairly well represented in bulk as follows : 

Mercury by a grain of mustard-seed, Venus by a very small green 
pea, The Earth by a common sized green pea, Mars by the head of a 
rather large pin, Jupiter by a ball of the size of an orange, Saturn 
by a golf-ball, Uranus by a common marble, Neptune by a rather 
larger marble. 

The scale of the plan of the solar system is to be two feet — 870,- 
000 miles. To make the plan a level road about 2$ miles long is 
needed. A stake should be driven into the ground to represent the 
place of the Sun, and if the length of the stake above ground is two 
feet the Sun's diameter will be represented by it. 

The distances of the planets must be laid off on the same scale of 
two feet = 870,000 miles. Steps of two feet long will serve to 
measure the distances. The student should first verify the following 
from the numbers given in Table I. On the adopted scale the dis- 
tance from the Sun to Mercury is 82 steps ; from Mercury to Venus 
is 60 steps ; from Venus to the Earth is 73 steps ; from the Earth to 



276 



ASTRONOMY. 



Mars is 108 steps ; from Mars to Jupiter is 785 steps ; from Jupiter 
to Saturn is 934 steps ; Saturn to Uranus is 2,086 steps ; and from 
Uranus to Neptune is 2,322 steps. 

With these distances let the student set oat from the stake that 
represents the Sun and deposit the models of the different planets at 
their proper distances — Mercury at 82 steps from the stake, Venus at 
142 steps, and so on to Neptune, which will be 6,450 steps away — 
nearly 2\ miles. 

A marble 2£ miles away from a globe 2 feet in diameter represents 
the relation in distance and in size between Neptune and the Sun. A 
few other globes, all very small, at large intervals, represent the 
major planets A few grains of sand represent the asteroids. The 
spaces of the solar system between the planets are empty except for 
a few comets and meteor-swarms. 

On the scale of the model the distance of the nearest fixed star 
from the stake that represents the Sun is 8,000 miles. A globe 
about three or four feet in diameter at Peking might stand for this 
star if the model of the solar system were made in New York. A 
morning spent in actually making such a model of the solar system 
will not be wasted. There is no better way of realizing the dimen- 
sions of the bodies of the solar system and the immense extent of 
empty space between them. 

TABLE I. 

(Approximate) Elements of the Orbits of the Eight 
Major Planets. 





Mean Distance 
from Sun. 


o 
>> 


o a 


o 


o . 


Do 








'3 


©. 2 


a * 




31 


3-~ _ 


Name. 




Mil- 






Astronom- 


lions 


11 


'Sc'aS 


_C— . 


'"Ecu 


p 2 ^ 


0) s-, - «3 




ical Units. 


of 


Bo 


§£ 


^H 


o *- J 


<V O 


££££ 




0.387099 


Miles. 


w 


J 


a 


J 


323° 


H 


Mercury.. 


36.0 


0.21 


75° 


7° 0' 


47° 


h 3 m 


Venus.. . . 


0.723332 


67.2 


0.01 


129 


3 24 


75 


244 


6! 


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 SYSTEM. 



277 



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278 



ASTRONOMY. 



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TEE SOLAR SYSTEM. 



279 



TABLE IV. 
The Comets op the Solar System (Periodic Comets). 



No. 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 



Name. 



Encke 

Tempel 

Brorsen 

Teinpel- Swift 
Winnecke . . . 
Da Vico-Swift 

Tempel 

Biela 

Finlay 

D' Arrest 

Wolf 

Brooks 

Faye 

Tuttle 

Pons-Brooks.. 

Olbers 

Halley 



Time of Peri- 


c . 


a _ 
- c X 


o u X 


helion Passage. 


-f 


<D = O 


s a o 

<Z> Cj t; 






~ *- P- 


JC ^ C 




%>< 


fe"& 


P..5S g. 




Pn 


£cS 


<QS 


1895 Feb. 4 


3.30 


0.34 


4.10 


1894 April 23 


5.22 


1.35 


4.67 


1890 Feb. 24 


5.46 


0.59 


5.61 


1891 Nov. 14 


5.53 


1.09 


5.17 


1892 June 30 


5.82 


0.89 


5.58 


1894 Oct. 12 


5.86 


1.39 


5.11 


1885 Sept. 25 


6.51 


2.07 


4.90 


1852 Sept. — 


6.6- 


0.86 


6.2- 


1893 July 12 


6.62 


0.99 


6.06 


1890 Sept. 17 


6.69 


1.32 


5.78 


1891 Sept. 3 


6.82 


1.59 


5.60 


1896 Nov. 4 


7.10 


1.96 


5.43 


1881 Jan. 22 


7.57 


1.74 


5.97 


1885 Sept. 11 


13.76 


1.02 


10.46 


1884 Jan. 25 


71.48 


0.76 


33.67 


1887 Oct. 8 


72.63 


1.20 


33.62 


1835 Nov. 15 


76.37 


0.59 


35.41 



13° 
13° 
29° 

5° 
15° 

3° 
11° 
13° 

3° 
16° 
25° 

6° 
12° 
55° 
74° 
45° 
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 daring the first second 
of its descent; at the San it woald 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 San is a star. It is a sphere of incandescent gases 
and metallic vapors. It shines by its own light and gives 
oat enormoas quantities of heat unceasingly. Only the 
smallest fraction of the Sun's heat reaches the Earth. Yet 
that small fraction (about ¥ -owoV o"o o "o part) 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 faculm. 

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, sodiam, 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 -, ,. i,. 

serving the Sun with a insensible gradations. This 

Telescope. halo of light 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 defined 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 of 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 



ASTRONOMY. 



The Photosphere. — The disk of the Sun 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 Sun 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 



105.— The Absorption of the Sun's Rays is Greater at 
the Edges of the Disk than at the Centre. 



In figure 165 let SE be the Sun's radius and SM 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 bad 
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 Sun'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 penumbra, intermediate 
in shade between the central blackness and the bright 
photosphere. 

The first printed account of solar spots was given by 
Fabrititjs 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, but 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. 



r 


g N - 


c 

MAF 


> 

\CH ■ J U 

4 h 


1 






S S 
SEPT DEC 



Fig. 167. — Apparent Paths op the Solar Spots to an Observer 
on the Earth 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 " " " 139 days. 

From 1836 to 1840 " " " 3 " 

In 1843 " " " 147 » 

From 1847 to 1851 " " « 2 " 

In 1856 " " " 193 " 

From 1858 to 1861 " " '« no day. 

JtoitfbV M * l * 4 195 days. 




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 
thirds or three fourths of its 
ordinary amount without its 
being strikingly perceptible to 
the eye. What is first noticed is 

the change which takes place in the color of the surrounding 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 




Fig. 169.— The Solar Corona 
at the Total Solar Eclipse 
of January, 1889, from Pho- 
tographs. 



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 tbe dark lurid sky, tbe thin crescent 
of tbe 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 defined, 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 lm. 19s. in Louisiana and lm. 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 
observed 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 oat into space. It 
is excessively rarefied, as is proved by the fact that comets 
moving round the San 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 onr gas-jets or 
electric lights. Our ordinary gas-barners 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 Suq'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 Radiated. — There is at present no way of determin- 
ing accurately either the absolute amount of heat emitted from the 
central body or the amount of this heat stopped by the solar atmos- 
phere itself. All that can be done is to measure 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 years. 



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 j^V o» * s 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 fact, 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 Sun 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). (Z> = M '-*- V, 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 solar 
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 
Sun, and incidentally the solar system, has a finite past 
and a limited futnre, 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 3%V of the 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 6 q- times 
as much light and heat from the Sun as the Earth, because 

(1.00) 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- 
pakelli 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 fi ¥ 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 jet certain that its period of 
rotation may not be about 24 hours — one day, but 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 F 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 8 is the 
Sun, E the Earth in its orbit and LIMG the orbit of an inferior 
planet. If the Earth is at E and the planet at 2", the planet is at 
inferior conjunction (nearest the Earth) ; if at C, at superior conjunc- 
tion ; if at L or M, at elongation. The Sun will be seen from E along 
the line EG. It is plain that the planet can never appear at a greater 
angle from the Sun than SEM or SEL. It is clear from the figure 



THE PLANETS MERCURY AND VENUS. 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 of an Inferior Planet with Refer- 
ence to the Eakth. 

In representing the apparent angular magnitude of these planets, 
in Figs. 172 and 173 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. ^ 1G - 172. — Apparent Di- 
ameter of Mercury ; A , 

Phases of Mercury and Venus. f « T R ™ £Si 
When the planet is at its greatest 0, at Least Distance. 
distance, or in superior conjunction (6', Fig. 171), its 
whole illuminated hemisphere can be seen from the Earth. 
As it moves arocmd and approaches the Earth, the illumi- 
nated hemisphere is gradually turned from us. At the 
point of greatest elongation, M or X, 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 Diameter of Venus; A, at Greatest 
B, at Mean ; C, at Least Distance. 



The phases of an inferior planet were first observed by 
Galileo in 1610. They are not visible to the naked eye 
nnd hence their discovery dates from the invention of the 



• » > ) 



B c 



• < c c 



K 



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 



TEE PLANETS MERCURY, VENUS, MARS. 303 

Earth and to be nearer to the Earth than the Snn. 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 \\ 
times the Earth's distance. Its orbit is quite eccentric so 
that its distance from the Sun at different 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 Sua 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 -4- 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 ■ 

Krr* 

(where r is the distance of Mars from the Earth). The amount of 

light leceived 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 \ 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 y 1 ^ of the Earth's density, 
and the force of gravity at its surface is about f^ 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 j\ 7 ^ of the 
light falling upon it — about as much as sandstone rocks. Mercury 
reflects ^fa. These bodies have little or no atmosphere. Venus re- 






THE PLANET MAES. 305 

fleets (from the outer surface of its envelope of clouds) T %% of the in- 
cident light. Jupiter ( T % 2 <,), Saturn ( r ^ 2 o), Uranus ( T %%), Neptune 
( T 4 ¥ 6 o), are all bodies surrounded by extensive atmospheres and all of 
them have high reflecting powers. The corresponding number for 
Mars (yo%) 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 San, 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. 



ffPSi 



I 



■I 



Fig. 175. 



-Telescopic Yiew 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 M> ercury, Venus, Jupiter, Saturn, 
TJranus, 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 Suu 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- 
parelli about 1877, 






TEE PLANET MARS. 309 

Schiaparelli 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)* = 2.25 to 1. Mars receives less than one half as 
much Sim 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 MARS. 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 -f- 500 = 70,000). 
It follows therefore that we never see Mars so advan- 
tageously even with the largest telescopes as we mag 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 best 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 
1666 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 



312 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 of »now 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 Mars was 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 m , and the inner one, called Phobos, in 7 1 ' 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 
inhabitants of Mars it would seem to rise in the west and set in the east. 



314 



ASTR0N0M7. 



Let the student prove this statement for himself by drawing a 
figure somewhat like Fig. 31. Suppose iVto be Mars, a the spec- 
tator, ZH the celestial equator, Z to be Phobos on the meridian. In 




Fig. 31 



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 T ^W 






CHAPTER XVIII. 

THE MOON— THE MINOR PLANETS. 

33. The Moon.— The Moon — the satellite of the Earth — 
revolves abont its primary in a periodic-time of 27 d . 32116 
at a mean distance of 238,840 miles. Its daily motion 

among the stars is Q011fi = 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 J^, and her mass -fo 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 i 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 T Vo ; 
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 conclnsion 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 lnnar 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 eTsV or °^ 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 



LIST OF LUNAR CRATERS, : 
N. B.— The Quadrants are marked I, II, III, IV on the borders of the Ma 



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. Heraclides 

17. Bianchini 

18. Sharp 

19. Mairan 

20. Plato 

21. Condamine 

22. Harpalus 



N. B. — From new moon (0 da >' s ) 
to full moon (15 d ) the icest 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 




II. SECOND QUADRANT. 



■/>/,.■ 



51. Moretus 

52. Cysatus 

53. Blancanus 

54. Schemer 

55. Clavius 

56. Maginus 

57. Longomontanus 
53. Schiller 

59. Phocylides 

60. Wargentin 

61. Saussure 

62. Pictet 

63. Tycho 
6i. Heinsius 

65. Hainzel 

66. Schickai'd 

67. Hell 

63. 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. 



V, 



". \ • M a r 



-<. 



r p uua.ti s 




I 



Fig. 178. 



NC 

-The Moon a; 



f 



!., SHOWN IN FIG. 178.* 

o see the numbers plainly, a common handglass should be used. 

limb is fully lighted, and The 
— ^_. position of the terminator for 

each intermediate day is marked 

_ ^^-~- by the lower set of numbers ; 

■: .'/-- ^ 17, 18 . . , 28, 30. These numbers 

\ - A V :<;' . give the moon's age, in days, 

'52 >•». when the terminator passes 

^■v. through their positions on the 

X v -&v.C\ map. 



, 









;•:■■' 



v/ 



e/f 






III. 

101. 

102. 
103. 
104. 
105. 
106. 
107. 
108. 
109. 
110. 
111. 
112. 
113. 
114. 
115. 
116. 
117. 
118. 
119. 
120. 
121. 
122. 
123. 
124. 
125. 
126. 
127. 
12s. 
129. 
130. 
131. 
132. 
133. 
134. 
135. 
136. 
137. 
138. 
139. 
140. 
141. 
142. 
143. 

IV. 
151. 
152. 
153. 
154. 
155. 
156. 
157. 
158. 
159. 
160. 
161. 
162. 
163. 
164. 
165. 
166. 
167. 
168. 
169. 
170. 
171. 
172. 
173. 
174. 
175. 
176. 
177. 
178. 
179. 
180. 
181. 
182. 
183. 
184. 
185. 
186. 
187. 
188. 
189. 



THIRD QUADRANT. 

Manzinus 

Mutus 

Boussingault 

Boguslawsky 

Curtius 

Zach 

Jacobi 

Lilius 

Baco 

Pitiscus 

Homme] 

Pabricius 

Metius 

Rheita 

Nicolai 

Barocius 

Maurolycus 

Clah-aut 

Cuvier 

Stoeffler 

Funerius 

Riccius 

Zagut 

Lindenau 

Aliacenus 

Werner 

Apian us 

Sacrobosco 

Santbach 

Fracastor 

Petavius 

Vendelinus 

Langrenus 

Goclenius 

Guttenberg 

Theophilus 

Cyrillus 

Catherina 

Albategnius 

Parrot 

Hipparchus 

Reaumur 

Delambre 

FOURTH QUADRANT. 
Taruntius 

Sabine 

Ritter 

Arago 

Ariadeeus 

Godin 

Agrippa 

Hyginus 

Triesnecker 

Condorcet 

Azout 

Picard 

Vitruvius 

Plinius 

Acherusia 

Menelaus 

Man il ius 

Einmart 

Cleomedes 

Macrobius 

Roemer 

Le Monnier 

Linnaeus 

Bessel 

Gauss 

Messala 

Geminus 

Posidonius 

Calippus 

Aristillus 

Autolycus 

Cassini 

Atlas 

Hercules 

Franklin 

Biirg 

Eudoxus 

Aristotle 

Endymion 



:AWN BY LOHRMANN. 



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 fiat, 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 tliey 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 until 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. 



Bode's Law. 



Mercury 

Venus 

Earth 

M ars 

[Ceres] (one of the asteroids) 

Jupiter 

Saturn . 

Uranus 

Neptune , 




4 

7.0 

10.0 

16.0 

28.0 

52.0 

100.0 

196.0 



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 the fact that a srap 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, bat 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, thongh 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 bow 
many of tbese planets tbere are in tbe group, but it is as vet impos- 
sible even to guess at tbe 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 
tbe 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 oi 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 gu^oo °f tue 
Earth's mass. The force of gravity on the surface of such a body 
would be about ^ 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 T ^ , and his volume y^Vo that of 
the Sun. His mass is T oVs- His density is nearly the 
same as the Sun's density, that is 1^- 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 lbs. A cubic foot of the stuff 
out of which Jupiter is made weighs, on the average, no 
more than 83 lbs. 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 Barnard 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 turns 
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 




Fig. 180. — Drawing op 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 phases of Jupiter are slight — scarcely 
noticeable. The reflecting-power {albedo) of the planet is y 6 ^, 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 



TEE 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 tor 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 8 .4 in 1889 ; 41 8 .0 in 1894 ; 41v 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 2* T 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 -J^- 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, first, 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 like 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- 



S28 



ASTRONOMY. 



ments no more powerful than those nsed 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 of Jupiter and his Satellites in a Small 
Telescope. 



Herschel, iu 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 oater 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 oar 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 of 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); if Ju- 



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, aod 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. 




Ftg 183 —The Eclipsep of Jupttep's Satellites. 

S is the Sun, Tthe 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, marking's 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 s old when it reaches us. 

Longitudes by Observation of the Satellites of Jupiter. — The 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 s , 
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 ASTRONONY. 

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 Rings 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-J 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 — 

" Altissimura 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. 



TEE 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 Htjyghens 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. Dur- 
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 SATUEN. 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 toward 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 G (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 T ^^ 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. 



Mimas 


3.3 


Enceladus 


4.3 


Tethys 


5.3 


Dione 


6.8 


Rhea 


9.5 


Titan 


20 7 


Hyperion 


26.8 


Japetus 


64.4 


? 


225.4 



Herschel 


1789 


Herschel 


1789 


Cassini 


1684 


Cassini 


1684 


Cassini 


1672 


Huyghens 


1655 


Bond 


1848 


Cassini 


1671 


Pickering 


1899 



About d 23 h 

u ld g h 

l d 21 h 
« 2 d 18* 

" 4 d 13 h 
" 15 d 23 h 
'« 21 d 7 h 
" 79 d 8 h 
" 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 further 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 Heeschel 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 

clade 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. C. Adams, 
a student in Cambridge University, England, had become 
aware of the problems presented by the anomalies in the 
motion of Uranus, and had attacked this question as early 
as 1843. 

In October, 1845, Adams communicated to the 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 lo'oked 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 companious to the bright 
stars Sir ins and Procyon have been predicted, and these 
companions have subsequently been discovered with the 
telescope. 



185 

I830>---— 3 

1840// A | 
ff A /^830 
- / 9 1840 


- 2 ■<■—-&. 

~~~Xl8IO 
* ^ 1 \l800 

l8l0 \ /1\ \\ 

■ y t 

' 1800 1 ™\ 


x ■ .S- 


x ^ 



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 aoo^nru °f tne 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 planets. 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 (^3^07 to ttjfo °f tne 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 ASTBONOMY. 

is almost or entirely gaseous ; its density is less than 1 T % 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 



348 



ASTRONOMY. 




Ita. 189. -THE GREAT CAI.IFOBWA 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,' not 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 beat evolved is measured not by that which would 
result from the combustion of the body, but by the vis viva (energy 
of motion) which the body loses in the atmosphere. The student of 
physics knows that motion, when lost, is changed into a definite 
amount of heat. 

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 18£ 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 movirjg 
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 of 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 u 
ra , Decl. -f- 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 Snn. 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 showers 
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 eve, 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 meteoroids 
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 w r ere extra-terrestrial bodies re- 
volving in swarms about the Sun. Professors Erman of Germany, 
Le Verrier of France, Adams of England, Schiaparelli 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 out along its orbit. 
Bat 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 XXL 

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 of 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. — Formation op 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 was 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 
spectroscopieally 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. — Orbtt of Halley's Comet. 

Periodic Comets. — The first discovery of the periodicity of a comet 
was made by Halley 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 



ASTBONOMY. 



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- 

0«Vv\ o\ Coma c \&5 5. C"S«xW) 




Fig. 197— The Orbtt of Comet C. 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 ihe 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 



v. 20 


R. A. 208° 


Decl. 


- 0° 


24 


211° 




- 3° 


28 


214° 




- 5° 


:. 2 


219° 




- 10° 


10 


236° 




- 22° 


18 


274° 




- 31° 


26 


287° 




- 23° 



Remarkable Comets. — In former years bright comets 
were objects of great dread. They were supposed to 




Fig. 198. — Medal of the Gkeat 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 III 



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 semidiameter. 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 substances 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 comet 
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 powerf al 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 ove*r 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 out 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 Millcy Way, is a magnifi- 
cent stream or belt of white milky light 10° or 15° iu 
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. Huyghexs 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 
nebalse 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 


974 " 


" 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 
■3*3 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, FomaUiaut, 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 Roman alphabet. In general, the brightest star 
was designated by the first letter of the alphabet, a, the next by the 
following letter, ft, etc. 

On this system, a star is designated by a certain Greek letter, fol- 
lowed by the genitive of the Latin name of the constellation to which 
it belongs. For example a Ganis 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 Ursce 
Majoris, ft Ursa 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 Argelander'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 5.0") 

•4 | 
9. I 



37 


2d 


128 


3d 


310 


4th 


1,016 


5th 


4,328 


6th 


13,593 


7th 


57,960 


8th 



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 and 
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 

In the case of Sirius, I = as above, and D = about 

542,000 times the Sun's distance. Hence L = - l^'^^n = 42. 

7,000,000,000 

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 yoVo P ar ^ 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. 



CHAPTEE 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 conld again see them, they coald 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 San in- 
cluded, is in motion by amonuts 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 TEE 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 (Vega). 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 (CS' = 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' = 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- 
out 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* 

7 

8 

12 


Vega (tfLyrae) 

Aldebaran (a Tauri) 

Polaris (a Ursae minoris). 
Arcturus (<xBootis)... .... 


27 


61 Cygni 

Sirius {a Canis majoris). . . . 
Procyon (a Canis minoris) .. 


32 

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 (fi Per set) (star- 
map I, near the zenith). Mira is usually a ninth-magni- 
tude star and is therefore invisible to the naked eye. 
E\rery 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-J- days, it falls to 4th magnitude in the short 
time of 4^ 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 handred 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 Jnly 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 § 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. 
Sirius 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, t, 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 Lyrm 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 the 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 

. . i ° Star e Lyrje. 

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, whLh 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 shows 
that one star is revolving around 
the other. Such a pair is called 
a binary star or binary 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 



1 

■ 

Kb 


31 


H . . B 


• KfluB 

- H 1 ' * 



Fig. 203.— Position-angle of a 
Double Star. 



892 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 

I 

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 : 



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 Ursa 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 nebulm and the former star-clusters. 

About 1656 Huyghens 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. 



nebulas. About nine thousand nebulas, 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 



r 


• 








Tau,ru.s blades. 


Ah 
GeirvLruv 




* 
Orion, 


• 


11 i '. ■'•■.' 9 


* 


[ 


. 


* 


• vi 


m PI " 


• 


• • 


Evidanus 


■ m Wxm 


• 


* • . 

• 





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. 






NEBULA 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.— Spfral Nebttla. 

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. 




NEBULjE 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 nebulae 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 lrom 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 
nebulas 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 nebulas 
were discontinuous, showing these bodies to be composed of glowing 
gas. The nebulas have proper motions just as do the stars. The 
great nebula of Orion is moving away from the Sun eleven miles 
every second. 



NEBULM 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, 




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 tbem are bodies of the same general kind as the 
Sun. 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 



SPECTBA 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 Mir a 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 nebula? 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', V , 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.— F Line of Hydrogen Superposed on the Spectrum 
ov Sirius ( VR). 



C (the middle C of the pianoforte) let us say. That is 
it gives out 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 — C'jf 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 Cft. 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 (?j( 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 G\> — 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 
inline of the star as reach it from the inline 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 F$ in one 
case, F\) 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. 



A 

* 3* * * * * 



c * * 



* D * 



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 
all the observed velocities. Eesearches 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 Lyrm 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 
%\iis 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 ^w^^wmos^ °^ 
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 nebulae 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 s , 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 tbey 
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, Nabulse, 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 moonrise, 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 tbe 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 agrin. 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, double-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 of a few Bright 

Stars, visible at Washington, for January 1, 1899. 



Name of Star. 



15 



Andromedas 

Cassiopeiee Var 

Ceti 

Ursae Miuoris (Pole Star). . 

Arietis 

Arietis 

Ceti 

Persei 

Tauri 

Eridani 

Tauri (Aldebaran) 

Aurigae 

Aurigae (Capella) 

Orionis (Rigel) 

Tauri 

Orionis 

Leporis 

Orionis 

Columbae 

Orionis 

Geminorum 

Canis Majoris (Sirius) 

Canis Majoris 

Geminorum (Castor) 

Canis Minoris (Procyon) . . . 

Geminorum (Pollux) 

Argus 

Ursae Majoris 

Hydrae 

Ursae Majoris 

Leonis (Regulus) 

Leonis 

Ursae Majoris 

Leonis 

Ursae Majoris 

Corvi 

Corvi 

Canum Venaticorum 

Virginis (Spica) , 

Ursse Majoris , 

Bootis (Arcturus) , 

Librae 

Ursae Minoris 

Librae. .. 

Coronas Borealis 

Serpentis 

Scorpii 

Draconis 

Scorpii (Antares) 

Herculis 

Draconis 



Mag. 



2 

2^ 



2 
3 
3 

1 
2^ 

1 

2 

2^ 

2)4 

2 

2^ 

1 

2 

1 

2 
1 
1 



2 
3 

1 
2^ 



2^ 



2 

2y 2 

2^ 



3 

1 
3K 2 



Right 
Ascension. 



m. s. 

3 9.9 

34 46.3 

38 31.2 

22 8.0 

49 3.5 

1 28.7 

2 56 59.9 

3 17 6.5 
3 41 28.7 
3 53 18.9 



30 7.4 

50 24.9 

9 13.5 

9 41.0 

19 54.4 



26 50.7 
28 16.5 
31 5.3 
5 35 59.5 

5 49 42.2 

6 31 52.6 
6 40 41.9 

6 54 39.3 

7 28 9.4 
7 34 1.0 

7 39 8.2 

8 3 14.5 

8 52 17.7 

9 22 37.4 
9 26 6.3 

10 2 59.6 
10 14 24.3 

10 57 29.8 

11 43 54.5 

11 48 31.2 

12 4 55.7 
12 29 4.8 

12 51 18.2 

13 19 52.2 

13 43 33.7 

14 11 3.2 
14 4F 17.3 

14 50 59.7 

15 11 34.2 
15 30 24.6 
15 39 17.5 

15 59 33.7 

16 22 37.4 

16 23 12.7 

17 10 2.5 
17 28 9.0 



Annual 


Varia- 


tion. 


s. 


+ 3.08 


+ 3.37 


+ 3.00 


+24.99 


+ 3.30 


+ 3:36 


+ 3.13 


+ 4.26 


4- 3.56 


-J- 2.79 


4- 3.43 


4- 3.90 


4- 4.42 


4- 2.88 


4- 3.79 


4- 3.06 


4- 2.65 


4- 3 04 


4-2.17 


4- 3.25 


4- 3.46 


4- 2.68 


4- 2.36 


+ 3.85 


4- 3.19 


4- 3.73 


4- 2.56 


4- 4.17 


4- 2.95 


4- 4.14 


4- 3.22 


4- 3.29 


4- 3.76 


4- 3.10 


4- 3.17 


4- 3.08 


4- 3.14 


4- 2.83 


4- 3.16 


+ 2.38 


4- 2.81 


4- 3.32 


- 0.21 


4- 3.23 


4- 2.53 


4- 2.94 


4- 3.48 


+ 0.81 


+ 3.67 


4- 2.74 


4- 1.36 



Declination. 



+ 28 
4-55 

- 18 
4-88 
+ 20 
4-22 
4- 3 
4-49 
4-23 

- 13 
+ 16 
-f-33 
4-45 

- 8 
4-28 

- 

- 17 

- 1 

- 34 
4- 7 
4-16 
-16 

- 28 
+ 32 
+ 5 
+ 28 

- 24 
+ 48 

- 8 
+ 52 
+ 12 
+ 20 
+ 62 
+ 15 
+ 54 

- 22 
-22 
+ 38 

- 10 
+ 49 
+ 19 

- 15 
+ 74 

- 9 
4-27 
+ 6 

- 19 
+ 61 
-26 
4-14 
+ 52 



31 58 
59 

32 28 

46 8 
18 52 
59 6 

41 36 

30 6 

47 34 
47 45 

18 23 
23 

53 43 

19 5 

31 20 

22 26 
53 41 

15 59 

7 40 

23 18 
29 8 
34 41 
50 4 

6 36 

29 3 

16 12 
48 

26 18 
13 15 

8 15 

27 39 
21 9 

17 46 
8 12 

15 23 

3 30 

50 18 

51 50 
38 3 
49 2 

42 30 



37 20 

34 6 

38 

3 16 

44 36 

31 45 

44 34 

12 28 

30 19 

22 34 



Annual 
Varia- 
tion . 



+ 20.1 
+ 19.8 
+ 19.8 
4-18.8 
4-17.8 
4-17.3 
4-14.4 
+ 13.1 
+ 11.4 
+ 10.5 



7 

+ 6.0 
+ 4.4 
+ 4.4 
+ 3.5 
+ 2.9 
+ 2.8 
+ 2.5 
+ 2.1 
+ 0.9 

- 2.8 

- 3.5 

- 4.7 

- 7.5 

- 8.0 

- 8.4 

- 10.3 

- 13.7 

- 15.5 

- 15.7 

- 17.5 

- 18.0 

- 19.3 

- 20.0 
-20.0 
-20.0 

- 19.9 

- 19.6 

- 18.8 

- 18.0 

- 16.9 

- 15.1 

- 14.7 

- 13.4 

- 12.2 

- 11.6 

- 10.1 

- 8.3 

- 8.2 

- 4.3 

- 2.8 



418 



ASTRONOMY. 



TABLE V '.—Continued. 



Name of Star. 



Ophiuchi 

Lyrae (Vega) 

Lyrae (var.) 

Aquilae (Altair) 

Cygni 

Cephei 

Aquarii 

Aquarii 

PiscisAustralis(FomaZ/iau£) 

Pegasi (Markab) 

Piscium 







Annual 








Annual 


Mag. 


Right 
Ascension. 


Varia- 
tion. 


Declination. 


Varia- 
tion. 




h. m. s. 


s. 


o 


, 


a 


a 


2 


17 30 14.7 


+ 2.78 


+ 12 


38 





- 2.6 


1 


18 33 31.1 


+ 2.01 


+ 38 


41 


22 


+ 2.9 


3*-4* 


18 46 21.0 


+ 2.21 


+ 33 


14 


43 


+ 4.0 


1 


19 45 51.3 


+ 2.89 


+ 8 


36 


5 


+ 8.9 


m 


20 37 59.3 


+ 2.04 


+ 44 


55 


9 


+ 12.8 


2% 


21 16 10.1 


+ 1.41 


+ 62 


y 


27 


+ 15.1 


3 


21 26 14.5 


+ 3.16 


- 6 





56 


+ 15.7 


3 


22 35.7 


+ 3.08 


- 


48 


38 


+ 17.4 


1V« 


22 52 4.1 


+ 3.30 


-30 


9 


27 


+ 19.2 


*y» 


22 59 43.7 


+ 2.98 


+ 14 


39 


42 


+ 19.4 


4 


23 54 7.4 


+ 3.07 


+ 6 


18 


15 


+ 20.0 



N.B. — The Mean Right Ascension and Declination for any other year than 1899 
may be found from this table by multiplying the annual variation by the num- 
ber of years elapsed, and applying the result to the quantities given in this 
table. If the required date be earlier than 1899, the signs of the annual varia- 
tions must be changed. In applying such corrections to the Declinations the 
corrections must be added algebraically. For example, the mean place of 
Aldebaran for July 1, 1901 (= 1901.5) is R. A. 4 h 30 m 16 8 .0 Decl. + 16° 18' 42". 

N.B.— The Nautical Almanac gives the apparent R.A.'s of these and other 
stars at intervals of ten days. 

N.B. — When any one of these stars is on the observer's meridian at any date, 
his local sidereal time is equal to that star's apparent right ascension on that 
date. 



The foregoing table will serve to set the observer's watch to side- 
real time within a few minutes so soon as he knows his meridian 
(see page 151). A watch set approximately to sidereal time is, of 
course, necessary in identifying objects in the sky. 



LIST OF DOUBLE STARS. 



419 



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420 



ASTRONOMY. 



TABLE VII. 
A List of a few Variable Stars. 



Star. 



Mir a Ceti 

Algol (jB Persei) . 

e Aurigce 

£ Geminorum 

R Leonis 

R Ursoz Majoris . . 

R Hydros, 

a Herculis 

X Sagittarii 

/3 Lyrce 

& Cephei ... 

R Cassiopeia 



R. A. 






Magnitude. 








Max. 


Min. 


h m 


o 


/ 


Days. 






2 14 


- 3 


26 


331 


1.7 


9.5-j 


3 2 


+ 40 


34 


2% 


2.3 


3.5J 


4 55 


+ 43 


41 


? 


3 


4.5-j 

4.5 
10 
13 

9.7 

3.9 

6 


6 58 
9 42 
10 38 
13 24 
1? 10 
17 41 


+ 20 
+ 11 
+ 69 
- 22 

+ 14 

-27 


43 

54 
18 
46 
30 
48 


10 
313 
305 
497 

90? 
7 


3.7 
5.2 

6 

3.5 
3.1 
4 


18 46 


+ 33 


15 


12.9 


3.4 


4.5] 


22 25 


+ 57 


54 


5y 3 


3.7 


4.9-j 


23 53 


+ 50 


50 


429 


5 


12 



Remarks. 



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. 



LIST OF NEBULA AND CLUSTERS. 



421 



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■9sa§ 



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■213 ^T^ 



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ASTRONOMY. 



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HINTS ON OBSERVING. 423 

To see a nebula with advantage it is sometimes advisable to set tbe 
telescope a very little west of it so that the nebula may enter tbe field 
of view by its diurnal motion and pass slowly across it. This can be 
repeated as often as desired. Nearly all of tbese 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 STAES. 



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; " August 1,15 " 

" March 1, 5 " " September 1, 17 " 

" April 1, 7 " " October 1, 19 " 

" May 1, 9 " " November 1, 21 " 

" June 1, 11 " " 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 visible 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, Canis 

major. 

February : Ursa major, Lynx, Cancer, Hydra. 

March : Ursa major, Leo, Hydro,. 

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, Getus. 

December: Camelopardus, Taurus, Orion 



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MAPS OF THE STABS. 



427 



MAP I. 

North. 



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Fig. 214. 

The sky on November 22, 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. 



MAPH. 

North. 



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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 STARS. 



429 



MAP III. 

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The sky on March 21, at 12 o'clock p.m. 
April 5, at 11 o'clock p.m. 
April 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. 

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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 STABS. 



431 



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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. 

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Fra. 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" 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' 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 
that white light (as sunlight, moonlight, starlight) was not 
simple, but compound. That is, white light is made up of 
light of different wave-lengths. Difference of wave-length 
shows itself to the eye as difference of color. Seven colors 
were distinguished by Newton; viz., violet, indigo, blue, 
green, yellow, orange, red. (Memorize these in order. It 
is the order of the colors in the rainbow.) If parallel rays 
of white light, as sunlight, r r, fall on a prism, the red rays 

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 wliite light is passed through a circular hole at Q, circular 
images of the hole are formed all along the line r' r' 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 8, 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 





1 1 


I 


111 




III 


111 HI 


111 


in 


'III ill 












1 


11 


| 






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alili 


ill 


1 


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A a B C D El F 

Fig. 222.— A Part op 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, C, 
D, 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, Eis in the green, i^is 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 S is in the principal focal plane of the tel- 
escope-objective. An image of the Sun will then be formed by 




SPECTRUM ANALYSIS. 437 

the telescope-objective on the slit plate S, 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 off light, has a continuous spectrum. 
That is, there are no Fraunhofer lines in it, but prismatic 
colors only. A gaseous body, heated so intensely as to give 
off light, has a discontinuous spectrum.* That is, the 
colors red to violet are no longer seen, but on a dark 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 hind 
(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 KM ANAL TS18. 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 Kirchhoff 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 pholosp7iere, 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 defined, 81. 
Barnard discovers satellite of 

Jupiter, 325. 
Bessei/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. 
Bun sen, 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. 
Donati'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- 
las, 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 nebulse 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. 
Mir a 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 gisViiff °f 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 denned, 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) denned, 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 faculse, 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, 

260. 



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 denned, 30. 
Zodiac, 169. 
Zodiacal light, 356. 






DEC 13 1899 




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