Full text of "The stars; a study of the universe"

THE SCIENCE SERIES

1. The Study of Man. By A. C. H ADDON. Illustrated. 8

2. The Groundwork of Science. By ST. GEORGE Mi-

VART.

3. Rivers of North America. By ISRAEL C. RUSSELL.

Illustrated.

4. Earth Sculpture ; or, The Origin of Land Forms.

By JAMES GEIKIE. Illustrated.

5. Volcanoes; Their Structure and Significance. By

T. G. BONNEY. Illustrated.

6. Bacteria. By GEORGE NEWMAN. Illustrated.

7. A Book of Whales. By F. E. BEDDARD. Illustrated.

8. Comparative Physiology of the Brain, etc. By

JACQUES LOEB. Illustrated.

9. The Stars. Bv SIMON NEWCOMB. Illustrated.

10. The Basis of Social Relations. By DANIEL G. BRINTON.

For list of ivor ks in preparation see end of this volume.

ZTbe Science Series

EDITED BY

professor 3. flDcTKeen Cattcll, /B.B., ipb.S).

AND

3f. .

THE STARS

A STUDY OF THE

SIMON NEWCOMB

RETIRED PROFESSOR ' .

ni slud^l/l bfthT

srf) xftiw baifq;
iJ aril \o

a mundi"

UNIVERSITY 1

G. P. PUTNAM'S S'

JOHN MURK
1902

'he Trifid Nebula in Sagittarius

Photographed with the Crossley Reflector
of the Lick Observatory

THE STARS

A STUDY OF THE UNIVERSE

SIMON NEWCOMB

RETIRED PROFESSOR U. S. NAVY

l ff<zc sunt fastigia mundi '

NEW YORK

G. P. PUTNAM'S SONS

LONDON

JOHN MURRAY
1902

BY
SIMON NEWCOMB

GENERAL

"Cbc Untcfccvbocfccr press, Hew

1( o

PREFACE

WHEN the author accepted the flattering invita-
tion of the editor to prepare a volume for the
present " Science Series," he supposed that it would
be an easy task to sketch in simple language for the
lay as well as the scientific reader the wonderful ad-
vances of our generation in the knowledge of the
fixed stars. But, as the work went on, it became
more evident at every step that such was not the
case. The problem was, now to study whole chapters
of observations and researches on some minute branch
of the subject, and condense their gist into a few sen-
tences ; now to search volumes of periodicals, perhaps
in vain, to find who was first in some field, or what
result some investigator had reached; now to do
justice to the respective works of students of the
same subject ; now to recast or rewrite passages in the
light of some newly published research. The author
must say in all candour that he has failed to sur-
mount the difficulties thus arising in a way satisfactory
to himself, and that in consequence the professional
reader, if any such shall take up the book, will find
defects that may seem to him serious in nearly every

iii

101608

iv PREFACE

chapter. In palliation can be only pleaded the extent
and complexity of the subject, and the impossibility
of entering far into technical details in a work de-
signed mainly for the general use.

In treating such a subject it is impossible always
to avoid the use of language more or less technical,
except at the expense of precision and completeness
of statement. An effort has however been made
to limit the use of such language to the necessities
of the case.

The most gratifying experience associated with the
work has been the cordial assistance and support
rendered by a number of the author's friends and col-
leagues, who have supplied him with the material ne-
cessary to the presentation of their latest researches.
Professor Campbell has supplied nearly all the ma-
terial relating to spectroscopic binary systems, com-
pleted and revised the list of those objects, and freely
placed at the author's disposal photographs taken at
the Lick Observatory, including the frontispiece to
the volume. Professor Kapteyn has supplied a large
mass of material, published and unpublished, relating
to his researches in stellar statistics, of which, how-
ever, only inadequate use could be made. Professor
Pickering has permitted the free use of the treasures
contained in the circulars and other publications of
the Harvard Observatory, and Sir William Huggins
has communicated the results of his latest studies in
the life-history of the stars. Sirs A. A. Common and
Isaac Roberts have each supplied a specimen of
their photographs of nebulae, and Father Sidgreaves,

PREFACE

S. J., of his photographs of spectra taken at the
Stonyhurst College Observatory. Professor Barnard
has allowed the use of his photographs of the Milky
Way.

CONTENTS.

CHAPTER I.

REVIEW OF RECENT PROGRESS.

PAGE

Extension of Research into the Southern Hemisphere The Revelations

of the Spectroscope The Lick and Harvard Observatories . . i

CHAPTER II.

MAGNITUDES OF THE STARS.

The Brightness of a Star Depends on Distance Ancient System of Mag-
nitudes Modern Conception of Magnitude Effect of Color on
Magnitude Photographic Magnitudes Photometric Surveys of the
Heavens Stellar Magnitude of the Sun ...... 15

CHAPTER III.
CONSTELLATIONS AND STAR NAMES.

Study of the Constellations The Uronometria Argentina Naming the

Stars Relation of Names to Constellations ..... 28

CHAPTER IV.
CATALOGUING AND NUMBERING THE STARS.

Right Ascension and Declination Ancient and Mediaeval Catalogues of
Stars Modern Catalogues Durchmusterung of Argelander Schon-
feld, Thome, Gill, and Kapteyn Numbering the Stars ... 38

viii CONTENTS

CHAPTER V.
THE SPECTRA OF THE STARS.

PAGE

Principles of Spectrum Analysis Description of the Visible Spectrum
Special Lines and Wave-Lengths Classification of Stellar Spectra
General Results of Spectrum Analysis ...... 56

CHAPTER VI.
PROPER MOTIONS OF THE STARS.

Apparent and Real Motions Swiftness of the Motions Stars of Large
Proper Motion Moving Systems of Stars Radial Motions of the
Stars The Motion of the Sun Position of the Solar Apex Speed
of the Solar Motion .......... 75

CHAPTER VII.
VARIABLE STARS.

Periodic Stars Light Curve of a Star The Omicron Ceti Type The
Algol Type The Beta Lyrae Type Combination of the Two
Types Variations of Eta Aquilae Classification of Variable Stars
Possible Secular Variations of the Brillancy of Stars Spectra of
Variable Stars . . . . . . . . -94

CHAPTER VIII.

NEW STARS.

Eta Argus List of New Stars Tycho's Star of 1752 Kepler's Star of

1604 T Corona Nova Aurigse Nova Persei . . . .123

V
CHAPTER IX.

THE PARALLAXES OF THE STARS.

Early Attempts to Measure Parallax First Measures of Parallax
Modern Methods The Heliometer and Photographic Telescope
Surveys for Parallax ......... 140

CONTENTS ix

i/"

CHAPTER X.
SYSTEMS OF STARS.

PAGE

Double Stars Position, Angle, and Distance Orbits of Double Stars
Binary Systems of Sirius and Procyon Orbit of Alpha Centauri
System of Capella Triple and Multiple Systems Spectroscopic
Binary Systems Star-Clusters Variable Stars in Clusters . 153

CHAPTER XI.

NEBULAE.

Great Nebula of Orion Other Remarkable Nebulae Discovery of

Nebulae by Photography Physical Constitution of the Nebulae . 178

CHAPTER XII.
CONSTITUTION OF THE STARS.

Masses and Densities of the Stars Diversities among the Stars Masses
and Densities of the Binary Systems Gaseous Constitution of the
Stars . . '. . . . . . ... . 191

CHAPTER XIII.

STELLAR EVOLUTION.

Life History of a Star Changes in the Spectra ..... 217

CHAPTER XIV.
THE STRUCTURE OF THE HEAVENS.

Is the Universe Finite ? Arrangement of the Stars in Space Relation of
the Milky Way to the Universe Possible Hypotheses as to the
Arrangement of the Stars . . . . . . . 226

CHAPTER XV.
APPARENT DISTRIBUTION OF THE STARS IN THE SKY.

Distribution of the Lucid Stars Distribution of the Fainter Stars Dis-
tribution of the Stars having Sensible Proper Motions Distribution
of Fifth Type ...... . . . . .238

x CONTENTS

CHAPTER XVI.
THE CLUSTERING OF THE STARS.

PAGE

The Pleiades Coma Berenices Praesepe Orion .... 258
CHAPTER XVII.

THE STRUCTURE OF THE MILKY WAY.

Description of the Milky Way Lucid Stars belonging to the Milky
Way Fainter Stars belonging to the Milky Way Rifts in the
Milky Way ..... .264

CHAPTER XVIII.

THE PROGRESSION IN THE NUMBER OF STARS AS THE
BRIGHTNESS DIMINISHES.

Ratio of this Increase in Different Regions of the Sky Higher ratio in

the galaxy ........... 277

CHAPTER XIX.

STATISTICAL STUDIES OF PROPER MOTIONS.

Components of the Proper Motion Mean Parallax of the Stars of the
Second Magnitude Motions of the Two Principal Spectral Types
of Stars Kapteyn's Researches Relation of the Proper Motions to
the Solar Motion .......... 286

CHAPTER XX.
THE DISTRIBUTION OF THE STARS IN SPACE.

Number of Stars at Different Distances Probable Thickness of the Stars
in Space Mean Parallaxes of the Stars Possible Distance of the
Milky Way ...... . 305

ILLUSTRATIONS

PAGE

THE TRIPHID NEBULA ....... Frontispiece

LAW OF CHANGE OF THE MAGNITUDE OF A STAR WITH ITS DISTANCE . 15

PLAN OF THE SPECTRUM 65

EXAMPLES OF STELLAR SPECTRA ........ 68

SPECTROGRAM OF POLARIS TAKEN BY CAMPBELL AT THE LICK

, OBSERVATORY 84

THE MILLS SPECTROGRAPH OF THE LICK OBSERVATORY . . .86

LIGHT-CURVE OF A VARIABLE STAR 98

FORM OF LIGHT-CURVE OF AN ALGOL VARIABLE 102

LIGHT-CURVE OF U PEGASI in

LIGHT- AND VELOCITY- CURVES OF rj AQUIL^E . . . . .114
SPECTRUM OF o CETI NEAR MAXIMUM OF 1897 . . . . . 120

SPECTRUM OF NOVA AURIGA . . . 133

DISTANCE AND POSITION-ANGLE OF A DOUBLE STAR . . . . 155

APPARENT ORBIT OF a CENTAURI 162

RADIAL MOTION OF A BINARY SYSTEM 166

THE GREAT STAR-CLUSTER OF HERCULES .171

THE GREAT STAR-CLUSTER OF GO CENTAURI . . . . . .175

THE GREAT NEBULA OF ORION 180

THE GREAT SPIRAL NEBULA M. 51 181

THE GREAT NEBULA OF ANDROMEDA 182

NEBULOUS MASS IN CYGNUS ......... 186

Two BINARY SYSTEMS ON THE SAME MODEL ..... 196

POSSIBLE SECTIONS OF THE GALAXY 235

SCHIAPARELLI'S PLANISPHERES SHOWING THE RICHNESS OF THE SKY

IN LUCID STARS 244, 245

PHOTOGRAPH SHOWING STRUCTURE OF THE MILKY WAY . . . 270

RIFTS IN THE MILKY WAY . . . 272

COMPONENTS OF PROPER MOTION 294

THE STARS

CHAPTER I
REVIEW OF RECENT PROGRESS

These are thy glorious works, Parent of good,
Almighty, thine this universal frame, <

Thus wondrous fair. MILTON. \ *

WE begin our study of the stars by a glance at the
structure of the universe. What are familiarly
known as the heavenly ^bodies belong to two classes
which are very different as regards their relation to
our earth. Those nearest to us form a sort of colony
far removed from all the others, called the solar sys-
tem. The principal bodies of this system are the
sun and eight great planets, with their moons, re-
volving round it. On one of these planets, small
when compared with the great bodies of the universe,
but large to our every-day conceptions, we dwell. The
other planets appear to us as stars. Four of them,
Venus, Mars, Jupiter, and Saturn, are distinguished
from the fixed stars by their superior brightness and

2 REVIEW OF RECENT PROGRESS

characteristic motions. Of the remaining three, Mer-
cury will rarely excite notice, while Uranus is nearly
invisible to the naked eye, and Neptune quite so.

The dimensions of the solar system are vast when
compared with any terrestrial standard. A cannon-
shot going incessantly at its usual speed would be five
hundred years in crossing the orbit of Neptune from
side to side. But vast as these dimensions are, they
sink into insignificance when compared with the dis-
tances of the stars. Outside the solar system are
spaces which, so far as we know, are absolutely void,
save here and there a comet or a meteor, until we look
far outside the region which a cannon-shot would cross
in a million of years. The nearest star is thousands
of times farther away than the most distant planet.
Scattered at these inconceivable distances are the
bodies to which our attention is directed in the present
work. If we are asked what they are, we may reply
that the stars are suns. But we might equally well
say that the sun is one of the stars ; a small star,
indeed, surrounded by countless others, many of
which are much larger and brighter than itself. We
shall treat our theme as far as possible by what we may
call the natural method, beginning with what, being
most obvious to the eye, was first noticed by man, or
will be first noticed by an observer, and tracing know-
ledge up step by step to its present state.

Several features of the universe of stars will be evid-
ent at a glance. One of these is the diversity of the
apparent brightness, or, in technical language, of the
magnitudes of the stars. A few far outshine the great

REVIEW OF RECENT PROGRESS. 3

mass of their companions. A greater numbfer are of
what we may call medium brightness ; there 1 is a yet
larger number of fainter ones, and about one-hajf of all
those seen by a keen eye under favourable conditions
are so near the limit of visibility as to escape ordinary
notice. Moreover, those which we see are but an in-
significant fraction of the number revealed by the
telescope. The more we increase our optical power,
the greater the number that come into view. How
many millions may exist in the heavens it is scarcely
possible even to guess. The photographic maps of
the heavens now being made probably show more than
fifty millions, perhaps one hundred millions, possibly
twice this number.

Another evident feature is the tendency of the
brighter stars to cluster into groups, known as con-
stellations. The latter are extremely irregular, so that
we cannot always decide where one constellation
should end and another begin, or to which constella-
tion a certain star may belong. Hence, the definition
and mapping out of the constellations and the division
of the stars among them are somewhat arbitrary
proceedings.

A third feature is the Milky Way or Galaxy, which
to ordinary vision appears as an irregular succession
of cloud-like forms spanning the heavens. We now
know that these seeming clouds are really congeries
of stars too faint to be individually visible to the na-
ked eye. We shall hereafter see that the stars of the
Galaxy form, so to speak, the base on which the uni-
verse appears to be constructed.

4 REVIEW OF RECENT PROGRESS

Each of these three features will be considered in
its proper place. In the present chapter we shall
make a rapid survey of what has been done in our
time to advance our knowledge of the stars.

A natural result of the northern hemisphere being
the home of civilised peoples was that, until recent
times, the study of the southern heavens had been
comparatively neglected. It is true that the curiosity
of the enquiring astronomers of the past would not be
satisfied without their knowing something of what was
to be seen south of the equator. Various enterprises
and establishments had therefore contributed to our
knowledge of the region in question. As far back as
1677, during a voyage to St. Helena, Halley cata-
logued the brighter stars in the region near the South
Pole. About 1 750 Lacaille, of France, established an
observing station at the Cape of Good Hope, and
made a catalogue of several thousand stars, which has
remained a handy-book for the astronomer up to the
present time. In 1834-38 Sir John Herschel made a
special voyage to the Cape of Good Hope, armed with
the best telescopes which his father had shown him
how to construct, for the purpose of doing for the
southern heavens as much as possible of what his
father had done for the northern. The work of this
expedition forms one of the most important and inter-
esting chapters in the history of astronomic science.
Not only is Herschel's magnificent volume a classic
of astronomy, but the observations which it contains
are still as carefully and profitably studied as any that
have since been made. They may be said to form

REVIEW OF RECENT PROGRESS 5

the basis of our present knowledge of the region which
they included in their scope.

Herschel's work may be described as principally in
the nature of an exploration. He had no instruments
for accurately determining the positions of stars. In
the latter field the first important contributions after
Lacaille were made by Sir Thomas Brisbane, Gov-
ernor of New South Wales, and Rumker, his assist-
ant, at Paramatta. Johnson, of England, about 1830,
introduced modern accuracy into the construction of a
ratherlimitedcatalogue of stars which he observed at St.
Helena. About the same time the British Government
established the observatory at the Cape of Good Hope,
which has maintained its activity to the present time.
About the middle of the century the Government of
New South Wales established, first at Williamstown
and then at Melbourne, an observatory which has
worked in the same field with marked success.

An American enterprise in the same direction was
that of Captain James M. Gilliss, who, in 1849,
organised an astronomical expedition to Chili. The
principal motive of this enterprise was the determina-
tion of the solar parallax by observations upon Venus
and Mars about the time of their nearest approach to
the earth. As these observations would take but a
small part of his time, Gilliss determined to take with
him instruments for determining the positions of the
stars. He established his observatory at a point near
Santiago, where he continued his observations for
nearly three years. He was an excellent practical
observer, but an untoward circumstance detracted

6 REVIEW OF RECENT PROGRESS

from the value of his work. His observatory was
built upon a rocky eminence, a foundation which
seemed to afford the best possible guaranty of the
stability of his instruments. He made no attempt to
reduce his observations till after his return home.
Then it was found that the foundation, through the
expansion and contraction due to the heat of the sun,
was subject to a diurnal change which made it ex-
tremely difficult to derive good results from his care-
ful work. It was not until 1896, more than thirty
years after his death, that the catalogue of the stars
observed by him was at last completed and published.

We do not derogate in any way from the merit of
these efforts in saying that they could not lead to
results comparable with those of the score of richly
equipped northern observatories which the leading na-
tions and universities of Europe had endowed and sup-
ported for more than a hundred years. Only within
the last thirty years has it been possible to bring our
knowledge of the southern heavens up to a satisfac-
tory stage. Now, however, the progress of southern
astronomy, if we may use the term, is such that in
several points our knowledge of the southern heavens
surpasses that of the northern ones. If we measure
institutions by the importance of the work they are
doing, there are several in the southern hemisphere
which must to-day be placed in the first rank.

The history and work of the Cordoba Observatory
are of special interest. In 1870 Dr. B. A. Gould,
who might fairly be considered as the father of
modern American astronomy, conceived the idea of

REVIEW OF RECENT PROGRESS 7

establishing an observatory of the first class in South
America. He found the President and Government
of the Argentine Republic ready to support his
scheme with a liberality well fitted to impress us with
a high sense of their standard of civilisation. In a
year or two the observatory at Cordoba was in active
operation. The discussions to which its work gives
rise belong to a subsequent chapter. But there is
one branch that is worthy of special mention in the
present connection. The Uranometria Argentina,
published in 1879, m a quarto volume, with a large
atlas, must be regarded as one of the most remark-
able contributions yet made to our knowledge of the
southern sky. It is concerned exclusively with the
objects visible to the naked eye, or at most with an
opera-glass. These were studied, described, cata-
logued, and mapped with a minuteness of detail
exceeding anything yet done in that line for the north-
ern sky. The notes to the catalogue alone comprise
fifty pages, but being duplicated in the English and
Spanish languages, really fill more than a hundred.
A particular watch was kept up for variable stars ;
and the evidence, conclusive or doubtful, for varia-
bility, takes up an important part of the notes. These
are followed by a discussion of the distribution of the
stars, primarily of the southern hemisphere, but in-
cidentally including the northern, which must still be
regarded as a standard study of the subject. Dr.
Gould continued in active charge of the Cordoba
Observatory until 1885, when he returned home, and
was succeeded by Thome, the present director.

8 REVIEW OF RECENT PROGRESS

A few years after Gould went to Cordoba, Gill was
made director of the Royal Observatory at the Cape
of Good Hope. The rapid growth of this institution
to one of the first rank is due no less to the scientific
ability of the new director than to the unflagging
energy which he has devoted to the enlargement of
the resources of the institution. The great fact which
he sought to impress upon his supporters was that
the southern celestial hemisphere was as large as the
northern, and therefore equally worthy of study.

In any general review of the progress of stellar as-
tronomy during the past twenty years, we should find
the Harvard Observatory before us at every turn.
What it has done will be seen, though in an imperfect
way, in subsequent chapters. Not satisfied with the
northern hemisphere, it has established a branch at
Arequipa, Peru, in which its methods of observation
and research are extended to the south celestial pole.
Its principal specialty has been the continuous ex-
ploration of the heavens. Celestial photography,
photometry, and spectroscopy sum up its fields of
activity. For more than ten years it might be almost
said that a sleepless watch of the heavens has been
kept up by an all-seeing photographic eye, with an
accuracy of which the world has hardly had a concep-
tion. The completeness with which its work has been
done has recently been shown in a striking way.

Our readers are doubtless acquainted with the
singular character of the minor planet Eros, whose
orbit passes through that of Mars, as one link of a
chain passes through another, and which comes nearer

THE SPECTROSCOPE 9

the earth at certain times than any other celestial
body, the moon excepted. When the character of
the orbit became established, it was of interest to
know whether the planet had ever been observed as
a fixed star at former oppositions. Chandler, having
computed the path of the planet at the most import-
ant of the oppositions, beginning with 1892-94, com-
municated his results to Director Pickering, and
suggested a search of the Harvard photographs to
see if the planet could be found on them. The result
was the discovery of the planet upon more than a
Score of plates taken at various times during the pre-
ceding ten years.

New stars were formerly supposed to be of very
rare occurrence, but since the Harvard system of
photographing the heavens has been introduced, five
or six have been known to burst forth.

Although the first application of the spectroscope
to the study of the heavenly bodies was made within

the memory of the present generation, its

u i i 11 i i The Spec-

results have been only less epoch-making troscope

than those of the telescope. The two in- and Photo-
struments differ in that the one, bringing g piate C
all the light from a star which falls on its
object-glass to one focus, sends it all into the eye,
thus multiplying it hundreds or thousands of times,
and bringing into view a universe of stars formerly in-
visible. The newer instrument operates by analysing
the light collected by the telescope into its separate
colors or kinds, which it arranges, as it were, on a
sheet. The sheet is simply the retina of the eye on

io REVIEW OF RECENT PROGRESS

which the spectrum is formed. Thus the eye is en-
abled to see the quantity of light on every part of the
sheet, and by the immense variety of arrangement
which the method admits of, remarkable conclusions
respecting the constitution and motion of the body
that emits the light can be drawn. The most dis-
tinctive feature of the spectroscopic method arises
from the fact that the composition of the light is in-
dependent of the distance of the body. The spec-
troscopist can therefore draw conclusions as to the
constitution and motion of the most distant star, as
readily as he can about those of the flame within his
laboratory.

Spectroscopy has, in recent times, been re-enforced
by photography. In the early '4o's, Dr. Draper took
a daguerreotype of the moon. As the photographic
art was developed, astronomers naturally occupied
themselves with photographing celestial bodies by the
light which they emitted. For this purpose the tele-
scope could be used as a camera. The first important
step in this direction was taken by Bond at Harvard.
The next great advance was made by Rutherfurd of
New York, who photographed clusters of stars and
used the plates in determining the positions of the
individual bodies of the cluster.

When more sensitive chemicals were introduced
into photography, another step in advance was made
by combining the spectroscopic and the sensitive
plate into a spectrograph. In all the more serious
spectroscopic work of the present day the spectrum is
photographed, and the astronomer, or astrophysicist

THE SPECTROSCOPE AND PHOTOGRAPHY n

as he now calls himself, can study and measure the
plates at his leisure.

The great revelations of our times have come
through the application of this method to the meas-
urement of motions in the line of sight from us to a
star. No achievement of the intellect of man would
have seemed farther without the range of possibility
to the thinker of half a century ago than the dis-
coveries of invisible bodies which are now being made
by such measurements. The revelations of the tele-
scope take us by surprise. But if we consider what
the thinker alluded to might regard as attainable, they
are far surpassed by those of the spectroscope. The
dark bodies, planets we may call them, which are re-
volving round the stars, must be for ever invisible in
any telescope that it would be possible to construct.
They would remain invisible if the power of the in-
strument were increased ten thousand times. And
yet if there are inhabitants on these planets, our as-
tronomers could tell them more of the motions of the
world on which they live than the human race knew
of the motions of the earth before the time of
Copernicus.

The men and institutions which have contributed
to this result are so few in number that it will not be
tedious to mention at least the principal actors. The
possibility of measuring the motions of the stars in
the line of sight by means of the spectroscope was
first pointed out by Mr. now Sir William Huggins.
He actually put the method into operation. As soon
as its feasibility was demonstrated it was taken up at

12 REVIEW OF RECENT PROGRESS

Greenwich. In these earlier attempts, eye methods
alone were used, and the results were not always re-
liable. Then spectrum photography was applied at
the German astrophysical observatory of Potsdam by
Vogel, who introduced into the method a degree of
precision which had never before been reached. His
measures of the motions of the stars in the line of sight
opened up the last era in science. Applying the
method to the variable star Algol, he proved that the
loss of light which it undergoes at intervals of nearly
three days is merely a partial eclipse by a dark planet,
almost as large as itself, revolving round it. Thus was
discovered a new order of bodies in the universe,
telescopic binary systems, pairs of stars, or stars and
planets, revolving round each other by their mutual
gravitation ; although no telescope that it is possible

to make would ever show that more than a single

body was present. Thence the photographic method
soon spread to Meudon and Pulkova. But, as often
happens when new fields of research are opened, we
find them cultivated in quarters where we should least
expect. The successful application of the method re-
quires not only the best spectroscope, but the most
powerful telescope at command. Ten years ago the
most powerful telescope in the world was at the Lick
Observatory. A few years later Mr. D. O. Mills put
at its eye end the best spectrograph that human art
could make at that time, the work of Brashear. It is
Campbell who, with this instrument, has inaugurated
a series of discoveries in this line which are without
a parallel. He finds that about one star in thirteen

THE SPECTROSCOPE AND PHO TOGRAPHY 1 3

has a planet revolving round it, so massive as to
change the motion of the star by an amount visible
in the spectroscope. The more or less eccentric
orbits of these bodies are being determined. The
final conclusion from all his work is that isolated stars
may be the exception rather than the rule ; that pos-
sibly a great majority at least of the stars are composed
of two or more bodies revolving round each other,
though they appear in our telescopes as single.

The study of variable stars from being little more
than a scientific amusement, has grown into an im-
portant branch of astronomical science. It has now
joined hands with spectroscopy to make it probable
that in most cases the variations of light in a star are
due to changes in its constitution produced by in-
visible planets revolving round it.

All these results naturally involve a great increase
in the number of men who are devoting themselves
to astronomical research. When we study the work
of this small army of investigators, and compare the
possibilities of the field they are exploring with what
has been done in the past, we feel that astronomy,
although the oldest of the sciences in years, is reach-
ing a stage of vigorous youth, and that the twentieth
century will open up views of the universe of which
quite possibly we, at its beginning, have no conception.

A mere survey of what has been done in the vari-
ous lines we have mentioned would be far from giving
an idea of the real significance of the advance we are
considering. Cataloguing the stars, estimating their
magnitudes, recording and comparing their spectra,

i 4 REVIEW OF RECENT PROGRESS

and determining their motions might be considered
as, after all, barren of results of the highest human
interest. When we know the exact position of every
star in the heavens, the direction in which it is mov-
ing, and the character of its spectral lines, how much
wiser are we ?

What could hardly have been foreseen fifty years
ago, is that these various classes of results are now
made to combine and converge upon the greatest
problem which the mind of man has ever attempted
to grasp that of the structure of the universe. The
study of variable stars has suddenly fallen into line,
so to speak, so that now it is uniting itself to the
study of all the other celestial objects, to give us at
least a faint conception of what the solution of this
problem may be.

One of the principal objects of the present work is
to make a comparison of these various researches,
and discuss the views respecting the constitution of
the stars individually, as well as of the universe as
a whole, to which they lead us. But there are a
number of details to be considered singly before we
can combine results in this way. Our early chapters
will, therefore, be devoted to the special features and
individual problems of stellar astronomy which have
occupied the minds of astronomers from the begin-
ning of their work to the present time. Keeping
these details in mind, we can profitably proceed to the
consideration of the general conclusions to be drawn
from them.

CHAPTER II

MAGNITUDES OF THE STARS

And one star differeth from another star in glory. PAUL.

TH E apparent brightness of a star, as we see it from
the earth, depends upon two causes its intrin-
sic brilliancy, or the quantity of light which it actually
emits, and its distance from us. It follows that if all
the stars were of equal intrinsic brightness we could
determine their relative distances by measuring the re-
spective amounts of light which we receive from them.
The quantity of light in such a case varies inversely
as the square of the distance. This will be seen by
the figure, where S represents the position of a star,

regarded as a luminous point, while A and B B B B are
screens placed at such distances that each will re-
ceive the same amount of light from the star. If the

16 MAGNITUDES OF THE STARS

larger screen is twice as far as the screen A, its sides
must be twice as long in order that it shall receive
all the light that would fall on A. In this case, its
surface will be four times the surface of A. It is
then evident that each quarter of the surface
marked B will receive one-fourth as much light as
the surface A. Thus, an eye or a telescope in the
position B will receive from the star one-fourth as
much light as in the position A, and the star will
seem one-fourth as bright.

The fact is, however, that the stars are very un-
equal in their actual brightness, and in consequence
the apparent magnitude of a star gives us no clue
to its distance. Among the nearer of the stars are
some scarcely, if at all, visible to the naked eye,
while among the brighter ones are several whose
distances are immeasurably great. A remarkable ex-
ample is that of Canopus, the second brightest star
in the heavens.

For these reasons astronomers are obliged to con-
tent themselves, in the first place, with determina-
tions of the actual amount of light that the various
stars send to us, or their apparent brilliancy, without
regard to their distance or actual brilliancy. The
ancient astronomers divided all the stars they could
see into six classes, the number expressing the appar-
ent brightness being called the magnitude of the star.
The brightest ones, numbering in all about fourteen,
were said to be of the first magnitude. The fifty
next in brightness were said to be of the second mag-
nitude. Three times as many, an order fainter, were

MAGNITUDES OF THE STARS 17

of the third magnitude. The progression was con-
tinued up to the sixth magnitude, which included
those which were barely visible.

As the stars are actually of every degree of appar-
ent brilliancy, no sharp line of demarkation could be
drawn between those of one magnitude and those
of the magnitude next higher. Hence, different ob-
servers made different estimates, some calling a star
of the second magnitude which others would call of
the first, and designating as of the third magnitude one
which others would call of the second. It is there-
fore impossible to state, with absolute numerical
precision, what number of stars should be regarded
as of one magnitude and what of another.

An idea of the magnitude of a star can be readily
gained by the casual observer. Looking at the
heavens on almost any cloudless evening, we may
assume that the two, three, or more brightest stars
which we see are of the first magnitude. As ex-
amples of those of the second magnitude, may be
taken the five brightest stars of the Dipper, the Pole
Star, and the brighter stars of Cassiopeia. Some or
all of these objects can be seen on any clear night of
the year in our latitude. Stars of the third magni-
tude are so numerous that it is difficult to select any
one for comparison. The brightest star of the Plei-
ades is really of this magnitude, but it does not
appear so in consequence of the five other stars by
which it is surrounded. At a distance of 15 from
the Pole Star, Beta Ursa Minoris is always visible, and
may be distinguished by being slightly redder than

i8 MAGNITUDES OF THE STARS

the Pole Star ; it lies between two fainter stars, the
brighter of which is of the third and the other of the
fourth magnitude. The five readily visible but fainter
stars of the Pleiades are about of the fourth magni-
tude. Of the fifth magnitude are the faintest stars
which are easily visible to the naked eye, while the
sixth comprises those which are barely visible with
good eyes.

Modern astronomers, while adhering to the general

system which has come down to them from ancient

times, have sought to give it greater defin-

Modern & .- o &

Conception iteness. Careful study showed that the
of actual amount of light corresponding to the

e ' different magnitudes varied nearly in geo-
metrical progression from one magnitude to another,
a conclusion which accords with the well-known psy-
chological law that the intensity of sensation varies
by equal amounts when the exciting cause varies
in geometrical progression. It was found that an
average star of the fifth magnitude gave between two
and three times as much light as an average one
of the sixth ; one of the fourth gave between two and
three times as much light as one of the fifth ; and so
on to the second. In the case of the first magnitude,
the diversity is so great that it is scarcely possible to
fix an average ratio. Sirius, for example, is really
six times as bright as Altair, which is commonly
taken as a standard for a first-magnitude star. To
give precision to their estimates, modern astronomers
are gradually seeking to lay the subject of magnitudes
on an exact basis by defining a change of one unit in

MODERN CONCEPTION OF MAGNITUDE 19

the magnitude as corresponding to an increase of
about two and one-half times in the amount of light.
If the practice of separating the visible stars into
only six orders of magnitude were continued without
change, we should still have the anomaly of including
in one class stars of markedly different degrees of
brightness. Some more than twice as bright as
others would be designated as of the same magni-
tude. Hence, to give quantitative exactness to the
results, a magnitude is regarded as a quantity which
may have any value whatever, and may be expressed
by decimals tenths or even hundredths. Thus, we
may have stars of magnitude 5.0, 5.1, 5.2, etc., or we
may even subdivide yet further and speak of stars
having magnitudes 5.11, 5.12, etc. Unfortunately,
however, there is as yet no way known of determin-
ing the amount of light received from a star except
by an estimate of its effect upon the eye. Two stars
are regarded as equal when they appear to the eye of
equal brilliancy. In such a case the judgment is very
uncertain. Hence, observers have endeavoured to
give greater precision to it by the use of photo-
meters, instruments for measuring quantities of
light. But even with this instrument the observer
must depend upon an estimated equality of light as
judged by the eye. The light from one star is in-
creased or diminished in a known proportion until it
appears equal to that of another star, which may be
an artificial one produced by the flame of a candle.
The proportion of increase or diminution shows the
difference of magnitude between the two stars.

20 MAGNITUDES OF THE STARS

As we proceed to place the subject of photometric
measures of star-light on this precise basis we find
the problem to be a complex one. In the first place,
not all the rays which come from a star are visible to
our eyes as light. But all the radiance, visible or
invisible, may be absorbed by a dark surface, and will
then show its effect by heating that surface. The
most perfect measure of the radiance of a star would
therefore be the amount of heat which it conveys,
because this expresses what is going on in the body
better than the amount of visible light can do. But
unfortunately the heating effect of the rays from a
star is below what can be measured by an instrument.
We are therefore obliged to abandon any thought of
determining the total amount of radiation and con-
fine ourselves to that portion which we call light.

Here, when we aim at precision, we find that light,
as we understand it, is properly measured only by its
effect on the optic nerve, and there is no way of
measuring this effect except by estimation. Thus, all
the photometer can do is to give us the means of in-
creasing or diminishing the light from one star, so
that we can make it equal by estimation to that from
some other star or source of light.

The difficulty of reaching strict results in this way
is increased by the fact that the stars differ in color.
Effect of Two lights can be estimated as equal with
Colour on greater precision when they are of the same
Magnitude. co j our t j lan w h e n their colours are different.
An additional source of uncertainty is brought in by
what is known as the Purkinje phenomenon, after

PHO TO GRAPH 1C MA GNITUDES 2 1

the physicist who first observed it. He found that if
we took two lights of equal apparent brightness, the
one red and the other green, and then increased or
diminished them in the same proportion, they would
no longer appear equal. In other words, the geomet-
rical axiom that halves or quarters of equal quantities
are themselves equal, does not apply to the effect
of light on the eye. When the lights are diminished
the green will look brighter than the red. If we increase
them in the same proportion, the red will look brighter
than the green. In other words, the red light will, to
our vision, increase or fade away more rapidly with a
given amount of change than the green light will.

It is found in recent times that this law of change
does not extend progressively through all spectral
colours. It is true that as we pass from the red to the
violet end of the spectrum the yellow fades away less
rapidly with a given diminution than does the red, and
the green still less rapidly than the yellow. But when
we pass from the green to the blue, it is said that the
latter does not fade out quite so fast as the green.

One obvious conclusion from all this is that two stars
of different colours which look equal to the naked eye
will not look equal in the telescope. The red or yellow
star will look relatively brighter in a telescope ; the
green or bluish one relatively brighter to the naked eye.

In recent times stars have been photographed on a
large scale. Their magnitudes can then be photo-
determined by the effect of the light on the graphic
photographic plate, the impression of the
star, as seen in a microscope, being larger and more

22 MAGNITUDES OF THE STARS

intense as the star is brighter. But the magnitude thus
determined is not proportional to the apparent bright-
ness as seen by the eye, because the photographic
effect of blue light is much greater than that of red
light having the same apparent brightness. In fact,
the difference is so great that, with the chemicals for-
merly used, red light was almost without photographic
effect. Even now, what we measure in taking the
photograph of a star is almost entirely the light in the
more refrangible portions of the spectrum. It appears
therefore that when a blue and a yellow star, equally
bright to the naked eye, are photographed, the impres-
sion made on the negative by the blue star will be
greater than that made by the yellow one. A distinc-
tion is therefore recognised between photographic and
visual magnitudes. The bluer the star, the brighter
will be its photographic as compared with its visual
magnitude.

The photographic magnitudes of the stars are now
being investigated and catalogued on a scale even
larger than that on which we have studied the visual
magnitudes. Yet we have to admit the non-corre-
spondence of the two systems. The most that can be
done is to bring about the best attainable agree-
ment between them in the general average of all the
stars.

Fortunately the differences between the colours of
the stars are by no means so great as those between
the colours of natural objects around us. All the stars
radiate light of all colours ; and although the colouring
is quite appreciable by the eye, it is not so great as it

SURVEYS OF THE HEAVENS 23

would have been were the variations in colour as wide
as in the case of terrestrial objects.

Two comprehensive surveys of the heavens, in-
tended to determine as accurately as possible the mag-
nitudes of all the brighter stars, have s urveys O f
recently been undertaken. One of these is the Heavens
the Harvard photometry, commenced by Professor
Pickering at the Harvard Observatory, and now ex-
tended to the southern hemisphere by the aid of the
branch establishment at Arequipa, Peru.

The instrument designed by Professor Pickering for
his purpose is termed a meridian photometer, and is
so arranged that the observer can see in the field of
his telescope a reflected image of the Pole Star, and,
at *he same time, the image of some other star while
it is passing the meridian. By a polarising apparatus
the image of the star to be measured is made to appear
of equal brightness with that of the Pole Star, and the
position of a Nicol prism, which brings out this equal-
ity, shows the ratio between the magnitudes of the two
^stars.

The other survey, with the same object, is now being
made at the Potsdam Astrophysical Observatory, near
Berlin. In the photometer used by the German as-
tronomers the image of one star is compared with an
artificial star formed by the flame of a candle. The
work is performed in a more elaborate way than at the
Harvard Observatory, and in consequence only that
part of the heavens extending from the equator to 40
north declination has been completed and published.
A comparison of the results of the German astrono-

24 MAGNITUDES OF THE STARS

mers with those of Professor Pickering shows a curious
difference depending on the colour of the star. In the
case of the reddest stars, the estimates are found to
be in fairly close agreement, Pickering's being a little
the fainter. But in the case of the white or bluish
stars, the estimates of the German astronomers are
more than one-fourth of a magnitude greater than
those of Pickering. This corresponds to a change
of nearly one-fourth in the brightness. Whether this
difference is to be regarded as purely psychological,
or as due to the instruments used, is an interesting
question which has not yet been settled. It is diffi-
cult to conceive how different instruments should give
results so different. On the one hand, the compar-
isons made by the Germans make it difficult to accept
the view that the difference is due purely to the per-
sonality of the observers. There are two German
observers, Drs. Miillerand Kempf, whose results agree
with each other exactly. On the other hand, Pritch-
ard, at Oxford, made quite an extensive photometric
survey, using an instrument by which the light of one
star was cut down by a wedge-shaped dark glass,
whereby any gradation of light could be produced.
A comparison shows that the results of Pritchard agree
substantially with those of Pickering. It is quite pos-
sible that the Purkinje phenomenon maybe the cause
of the difference, the source of which is eminently
worthy of investigation.

It must not be supposed from this that such estim-
ates are of no value for scientific purposes. Very
important conclusions, based on great numbers of

THE LIGHT-RATIO 25

stars, may be drawn even from these uncertain quan-
tities. Yet, it can hardly be doubted that if the light
of a star could be measured from time to time to its
thousandth part, conclusions of yet greater value and
interest might be drawn from the measures.

We have said that in our modern system the aim
has been to so designate the magnitudes of the stars
that a series of magnitudes in arithmetical progression
shall correspond to quantities of light ranging in
geometrical progression. We have also said that a
change of one unit of magnitude corresponds to a
multiplication or division of the light by about 2.5.
On any scale of magnitude this factor of multiplica-
tion is called the light-ratio of the scale. In recent
times, after much discussion of the subject and many
comparisons of photometric measures with estimates
made in the old-fashioned way, there is a general
agreement among observers to fix the light-ratio at
the number whose logarithm is 0.4. This is such that
an increase of five units in the number expressing the
magnitude corresponds to a division of the light by'
one hundred. If, for example, we take a standard star
of magnitude i and another of magnitude 6, the first
would be one hundred times as bright as the second.
This corresponds to a light-ratio slightly greater
than 2.5.

When this scale is adopted, the series of magnitudes
may extend indefinitely in both directions so that to
every apparent brightness there will be a certain mag-
nitude. For example, if we assign the magnitude
i.o to a certain star, taken as a standard, which

26 MAGNITUDES OF THE STARS

would formerly have been called a star of the first
magnitude, then a star a little more than 2.5 times as
bright would be of a magnitude one less in number,
that is, of magnitude O. The one next brighter in the
series would be of magnitude i. So great is the di-
versity in the brightness of the stars formerly called of
the first magnitude that Sirius is yet brighter than
the star just supposed, the number expressing its
magnitude being- 1.4.

This suggests what we may regard as one of the
capital questions in celestial photometry. There
being no limit to the extent of the photometric scale,
stellar what would be the stellar magnitude of the
Magnitude sun as we see it when expressed in this way
of the Sun. Qn t k e sca j e p Such a number is readily de-
rivable when we know the ratio between the light of
the sun and that of a star of known magnitude. Many
attempts have been made by observers to obtain this
ratio ; but the problem is one of great difficulty, and
the results have been extremely discordant. Amongst
them there are three which seem less liable to error
than others : those of Wollaston, Bond, and Zollner.
Their results .for the stellar magnitude of the sun are
as follows :

Wollaston 26.6

Bond -25.8

Zollner 26.6

Of these, Zollner's seems to be the best, and may,
therefore, in taking the mean, be entitled to double
weight. The result will then be :

Stellar magnitude of sun 26.4

STELLAR MAGNITUDE OF THE SUN 27

From this number may be readily computed the
ratio of sunlight to that of a star of any given magni-
tude. We thus find :

The sun gives us :

10,000,000,000 times the light of Sirius.
91,000,000,000 times the light^of a star of magnitude i.
9,100,000,000,000 times the light of a star of magnitude 6.

The square roots of these numbers show the num-
ber of times we should increase the actual distance of
the sun in order that it might shine as a star of the
corresponding magnitude. These numbers and the
corresponding parallax are as follows :

Sirius; Dista
Mag. i

" 2

" 3 "
4 "

" 5 "
" 6

These parallaxes are those that the sun would have
if placed at such a distance as to shine with the
brightness indicated in the first column. They are
generally larger than those of stars -of the corre-
sponding magnitudes, from which we conclude that the
sun is smaller than the brighter of the stars.

IOO,OOO

Parallax = 2".o6

302,000

o".68

479,000

"-43

759,000

o".2 7

1,202,000

o r .i 7

1,906,000

O^.II

3,020,000

o /r .o 7

CHAPTER III

CONSTELLATION AND STAR NAMES

Now came still evening on, and twilight grey
Had in her sober livery all things clad.

. now glowed the firmament
With living sapphires ; Hesperus that led
The starry host rode brightest. MILTON.

IT is strongly recommended to the reader to study
the constellations for himself. If he desires to feel
all the sublimity associated with them, he must not
be satisfied with the hurried glance or occasional sur-
vey to which one commonly confines himself in his
evening walk. What he should do is, on a clear and
moonless summer evening, to escape from his usual
surroundings, and go to a place, whether field or
housetop, where there is nothing to obstruct his
vision, or disturb the current of his thoughts. There
he must recline on his back, so as to take in as much
as possible of the starry vault at one view. One
doing this for the first time will be surprised at the
magnificence of the spectacle. As he looks upon the
" universal frame " and reflects that it has stood as he
now sees it through ages compared with which the
whole period of human history is but a fleeting

STUDY OF THE CONSTELLATIONS 29

moment, the mind will be filled with a consciousness
of infinity and eternity which never before entered it.
Other sights become stale from custom, but this can
never lose its relish. It can be enjoyed without
knowing the name of a constellation, but is more
impressive when one reflects that the eyes of man
have gazed upon and studied it ever since our race
appeared on earth.

In ancient times the practice was adopted of im-
agining the figures of heroes and animals to be so
outlined in the heavens as to include in each figure a
large group of the brighter stars. In a few cases
some vague resemblance may be traced between the
configurations of the stars and the features of the
object they are supposed to represent ; in general,
however, the object chosen seems quite arbitrary.
One animal or man could be fitted in as well as
another. There is no historic record as to the time
when the constellations were mapped out, or of the
process by which the outlines were traced. The
names of heroes, such as Perseus, Cepheus, Hercules,
etc., intermingled with the names of goddesses, show
that the time was probably during the heroic age.
No maps are extant showing exactly how each figure
was placed in the constellation ; but in the catalogue
of stars given by Ptolemy in his Almagest, the posi-
tions of particular stars on the supposed body of the
hero, goddess, or animal are designated. For exam-
ple, Aldebaran is said to have formed the eye of the
Bull. Two stars marked the right and left shoulders
of Orion, and a small cluster marked the position of

30 CON STELLA TIONS AND STAR NAMES

his head. A row of three stars in a horizontal line
showed his belt, three stars in a vertical line below
them his sword. From these statements the position
of the figure can be reproduced with a fair degree of
certainty.

In the well-known constellation Ursa Major, the
Great Bear, familiarly known as " the Dipper," three
stars form the tail of the animal, and four others
a part of his body. This formation is not unnatural,
yet the figure of a dipper fits the stars much better
than that of a bear. In Cassiopeia, which is on the
opposite side of the pole from the Dipper, the brighter
stars may easily be imagined to form a chair in which
a lady may be seated. As a general rule, however,
the resemblances of the stars to the figure are so
vague that the latter might be interchanged to any
extent without detracting from their appropriate-
ness.

In any case, it was impossible so to arrange the
figures that they should cover the entire heavens ;
blank spaces were inevitably left in which stars might
be found. In order to include every star in some
constellation, the figures have been nearly ignored by
modern astronomers, and the heavens have been
divided up, by somewhat irregular lines, into patches,
each of which contains the entire figure as recognised
by ancient astronomers. But all are not agreed as
to the exact outlines of these extended constellations,
and, accordingly, a star is sometimes placed in one
constellation by one astronomer and in another con-
stellation by another.

THE SOUTHERN CONSTELLATIONS 31

The confusion thus arising is especially great in
the southern hemisphere, where it has been intensified
by the subdivision of one of the old con-
stellations. The ancient constellation Argo Southern
covered so large a region of the heavens, Consteiia-
and included so many conspicuous stars,
that it was divided into four, representing various
parts of a ship the sail, the poop, the prow, and the
hull.

Dr. Gould, while director of the Cordoba Observa-
tory, during the years 1870 to 1880, constructed the
Uranometria Argentina, in which all the stars visible
to the naked eye from the south pole to a parallel of
declination ten degrees north of the celestial equator
were catalogued and mapped. He made a revision
of the boundaries of each constellation in such a way
as to introduce greater regularity. The rule gener-
ally followed was that the boundaries should, so far
as possible, run in either an east-and-west or a north-
and-south direction on the celestial sphere. They
were so drawn that the smallest possible change
should be made in the notation of the conspicuous
stars ; that is, the rule was that, if possible, each
bright star should be in the same constellation as
before. The question whether this new division shall
replace the ancient one is one on which no consensus
of view has yet been reached by astronomers. Sim-
plicity is undoubtedly introduced by Gould's arrange-
ment ; yet, in the course of time, owing to precession,
the lines on the sphere which now run north and
south or east and west will no longer do so, but will

32 CONSTELLATIONS AND STAR NAMES

deviate almost to any extent. The only advantage
then remaining will be that the bounding lines will
generally be arcs of great circles.

When the heavens began to be carefully studied,
two or three centuries ago, new constellations were
introduced by Hevelius and other astronomers to fill
the vacant spaces left by the ancient ones of Ptolemy.
To some of these rather fantastic names were given ;
the Bull of Poniatowski, for example. Some of these
new additions have been retained to the present time,
but in other cases the space occupied by the proposed
new constellation was filled up by extending the
boundaries of the older ones.

At the present time the astronomical world, by
common consent, recognises eighty-nine constellations
in the entire heavens. In this enumeration Argo is
not counted, but its four subdivisions are taken as
separate constellations.

A glance at the heavens will make it evident that
the problem of designating a star in such a way as to
Naming distinguish it from all its neighbours must
the Stars. De a difficult one. If such be the case with
the comparatively small number of stars visible to the
naked eye, how must it be with the vast number that
can be seen only with the telescope ? In the case of
the great mass of telescopic stars we have no method
of designation except by the position of the star and
its magnitude ; but with the brighter stars, and, in-
deed, with all that have been catalogued, other means
of identification are available.

It is but natural to give a special name to a con-

NAMING THE STARS 33

spicuous star. That this was done in very early
antiquity we know by the allusion to Arcturus in the
Book of Job. At least two such names, Castor and
Pollux, have come down to us from classical antiquity,
but most of the special names given to the stars in
modern times are corruptions of certain Arabic desig-
nations. As an example we may mention Aldebaran,
a corruption of A I Dabaran The Follower. There
is, however, a tendency to replace these special names
by a designation of the stars on a system devised by
Bayer early in the seventeenth century.

This system of naming stars is quite analogous to
our system of designating persons by a family name
and a Christian name. The family name of a star is
that, of the constellation to which it belongs. The
Christian name is a letter of the Greek or Roman
alphabet or a number. As any number of men in
different families may have the same Christian name,,
so the same letter or number may be assigned to stars
in any number of constellations without confusion.

The work of Bayer was published under the title of
Uranometria, of which the first edition appeared in
1 60 1. This work consists mainly of maps of the stars.
In marking the stars with letters on the map, the rule
followed seems to have been to give the brighter
stars the earlier letters in the alphabet. Were this
system followed absolutely, the brightest star should
always be called Alpha ; the next in order Beta, etc.
But this is not always the case. Thus in the constella-
tion Gemtnz,\he brightest star is Pollux, which is marked
Beta, while Alpha is the second brightest. What sys-

34 CONSTELLATION AND STAR NAMES

tern, if any, Bayer adopted in detail has been a subject
of discussion, but does not appear to have been satis-
factorily made out. Quite likely Bayer himself did not
attempt accurate observations on the brightness of the
stars, but followed the indications given by Ptolemy
or the Arabian astronomers. As the number of stars
to be named in several constellations exceeds the
number of letters in the Greek alphabet, Bayer had
recourse, after the Greek alphabet was exhausted, to
letters of the Roman alphabet. In this case the letter
A was used as a capital, in order, doubtless, that it
should not be confounded with the Greek a. In other
cases small italics are used. In several catalogues
since Bayer, new italic letters have been added by
various astronomers. Sometimes these have met with
general acceptance, and sometimes not.

Flamsteed was the first Astronomer Royal of Eng-
land, and observed at Greenwich from 1666 to 1715.
Among his principal works is a catalogue of stars in
which the positions are given with greater accuracy
than had been attained by his predecessors. He
slightly altered the Bayer system by introducing
numbers instead of Greek letters. This had the ad-
vantage that there was no limit to the number of stars
which could be designated in each constellation. He
assigned numbers to all the brighter stars in the order
of their right ascension, irrespective of the letters
used by Bayer. These numbers are extensively used
.to the present day, and will doubtless continue to be
the principal designations of the stars to which they
refer. It is very common in our modern catalogues

NAMING THE STARS 35

to give both the Bayer letter and the Flamsteed
number in the case of Bayer stars.

The catalogues by Flamsteed do not include quite
all the stars visible to the naked eye ; but various
uranometries have been published which were intended
to include all such stars. In such cases the designations
now used frequently correspond to the numbers given
in the uranometries of Bode, Argelander, and Heis.

In recent times these uranometries have been sup-
plemented by censuses of the stars, which are intended
to include all the stars to the ninth or tenth magni-
tude. I shall speak of these in the next section ; at
present it will suffice to say that stars are very gener-
ally designated by their place in such a census.

There is still here and there some confusion both as
to the boundaries of the constellations and as to the
names of a few of the stars in them. I have already
remarked that, in drawing the imaginary boundaries
on a star map, as representing the celestial sphere,
different astronomers have placed the lines differently.
One of the regions in which this is especially true is
in the neighbourhood of the north pole, where some
astronomers place stars in the constellation Cepheus
which others place in Ursa Minor. Hence in the
Bayer system the same star may have different names
in different catalogues. Again, in extending the
names or numbers, some astronomers use names
which others do not regard as authoritative. The re-
mapping of the southern hemisphere by Dr. Gould
changed the boundaries of most of the southern con-
stellations in a way already mentioned.

36 CON STELLA TION AND STAR NAMES

I have spoken of the subdivision of the great con-
stellation A rgo into four separate ones. Bayer having
assigned to the principal stars in this constellation the
Greek letters alpha, beta, gamma, etc., the general
practice among astronomers since the subdivision has
been to continue the designation of the stars thus
marked as belonging to the constellation Argo. Thus,
for example, we have Alpha Argus, which after the
subdivision belonged to the constellation Carina. The
variable star Eta Argus also belongs to the constella-
tion Carina. But in the case of stars not marked by
Bayer, the names were assigned according to the sub-
divided constellations, Vela, Carina, etc. Confusing
though this proceeding may appear to be, it is not pro-
ductive of serious trouble. The main point is that the
same star should always have the same name in suc-
cessive catalogues. Still, however, it has recently
become quite common to ignore the constellation
Argo altogether and use only the names of its sub-
divisions. The reader must therefore be on his guard
against any mistake arising in this way in the study
of astronomical literature.

In star catalogues the position of a star in the heav-
ens is sometimes given in connection with its name.
In this case the confusion arising from the same star
having different names may be avoided, since a star
can always be identified by its right ascension and
declination. The fact is that, so far as mere identifi-
cation is concerned, nothing but the statement of a
star's position is really necessary. Unfortunately, the
position constantly changes through the precession of

NAMING THE STARS 37

the equinoxes, so that this designation of a star is a
variable quantity. Hence the special names which we
have described are the most convenient to use in the
case of well-known stars. In other cases a star is
designated by its number in some well-known cata-
logue. But even here different astronomers choose
different catalogues, so that there are still different
designations for the same star. The case is one in
which uniformity of practice is unattainable.

CHAPTER IV

CATALOGUING AND NUMBERING THE STARS

Canst thou bind the sweet influences of Pleiades, or loose the bands of
Orion ? Canst thou bring forth Mazzaroth in his season ? Or canst thou guide
Arcturus with his sons? JOB.

AC AT A LOG U E or list of stars is a work giving for
each star listed its magnitude and its position on
the celestial sphere, with such other particulars as may
be necessary to attain the object of the catalogue. If
the latter includes only the more conspicuous stars, it
is common to add the name of each star that has one ;
if none is recognised, the constellation to which the
star belongs is frequently given.

The position of a star on the celestial sphere is de-
fined by its right ascension and declination. These
Ri ht As- correspond to the longitude and latitude of
cension and places on the earth in the following way :
Decimation. i ma gj ne a pl ane passing through the centre
of the earth and coinciding with its equator, to
extend out so as to intersect the celestial sphere. The
line of intersection will be a great circle of the celes-
tial sphere, called the celestial equator. The axis of
the earth, being also indefinitely extended in both the

RIGHT ASCENSION AND DECLINA TION 39

north and the south directions, will meet the celestial
sphere in two opposite points, known as the north
and south celestial poles. The equator will then be
a great circle 90 from each pole. Then as meridians
are drawn from pole to pole on the earth, cutting the
equator at different points, so imaginary meridians are
conceived as drawn from pole to pole on the celestial
sphere. Corresponding to parallels of latitude on
the earth we have parallels of declination on the celes-
tial sphere. These are parallel to the equator, and
become smaller and smaller as we approach either pole.
The correspondence of the terrestrial and celestial cir-
cles is this :

To latitude on the earth's surface corresponds declin-
ation in the heavens.

To longitude on the earth corresponds right ascen-
sion in the heavens.

A little study of this system will show that the zenith
of any point on the earth's surface is always in a de-
clination equal to the latitude of the place. For ex-
ample, for an observer in Philadelphia, in 40 latitude,
the parallel of 40 north declination will always pass
through his zenith, and a star of that declination will,
in the course of its diurnal motion, also pass through
his zenith.

So also to an observer on the equator the celestial
equator always passes through the zenith and through
the east and west points of the horizon.

In the case of the right ascension, the relation be-
tween the terrestrial and celestial spheres is not con-
stant, because of the diurnal motion, which keeps the

40 CATALOGUING AND NUMBERING

terrestrial meridians in constant revolution relative to
the celestial meridians. Allowing for this motion,
however, the system is the same. As we have on the
earth's surface a prime meridian passing from pole to
pole through the Greenwich Observatory, so in the
heavens a prime meridian passes from one celestial
pole to the other through the vernal equinox. Then
to define the right ascension of any star we imagine a
great circle passing from pole to pole through the star,
as we imagine one to pass from pole to pole through
a city on the earth of which we wish to designate the
longitude. The actual angle which this meridian
makes with the prime meridian is the right ascension
of the star, as the corresponding angle is the longi-
tude of the city on the earth's surface.

There is, however, a difference in the unit of angu-
lar measurement commonly used for right ascensions
in the heavens and longitude on the earth. In as-
tronomical practice, right ascension is very generally
expressed by hours, twenty-four of which make a com-
plete circle, corresponding to the apparent revolution
of the celestial sphere in twenty-four hours. The rea-
son of this is that astronomers determine right ascen-
sion by the time shown by a clock so regulated
as to read oh. om. os. when the vernal equinox
crosses the meridian. The hour-hand of this clock
makes a revolution through twenty-four hours during
the time that the earth makes one revolution on its
axis, and thus returns to oh. o m. o s. when the
vernal equinox again crosses the meridian. A clock
thus regulated is said to show sidereal time. Then

ANCIENT AND MEDIEVAL CATALOGUES 41

the right ascension of any star is equal to the sidereal
time at which it crosses the meridian of any point on
the earth's surface. Right ascension thus designated
in time may be changed to degrees and minutes by
multiplying by 15. Thus, one hour is equal to 15 ;
one minute of time is equal to 15' of arc, and one
second of time to 15" of arc.

It may be remarked that in astronomical practice
terrestrial longitudes are also expressed in time, the
longitude of a place being designated by the number of
hours it may be east or west of Greenwich. Thus,
Washington is said to be 5h. 8m. 155. west of Green-
wich. This, however, is not important for our present
purpose.

The first astronomer who attempted to make a
catalogue of all the known stars is supposed to be
Hipparchus, who flourished about i^o B.C.

. . r . i rr Ancient and

There is an unverified tradition to the effect Medieval
that he undertook this work in conse- Catalogues

F , F . of Stars.

quence of the appearance of a new star in

the heavens, and a desire to leave on record, for the

use of posterity, such information respecting the

heavens in his time that any changes which might

take place in them could be detected. This catalogue

has not come down to us at least not in its original

form.

Ptolemy, the celebrated author of the Almagest,
flourished A.D. 150. His great work contains the
earliest catalogue of stars 'which we have. There
seems to be a certain probability that this catalogue
may either be that of Hipparchus adopted by Ptolemy

42 CATALOGUING AND NUMBERING

unchanged, or may be largely derived from Hip-
parchus. This, however, is little more than a sur-
mise, due to the fact that Ptolemy does not seem to
have been a great observer, but based his theories
very largely on the observations of his predecessors.
The actual number of stars which it contains is 1030.
The positions of these are given in longitude and
latitude, and are also described by their places in the
figure of the constellation to which each may belong.
Not unfrequently the longitude or latitude is a degree
or more in error, showing that the instruments with
which the position was determined were of rather
rough construction.

So far as the writer is aware, no attempt to make a
new catalogue of the stars is found until the tenth
century. Then arose the Persian astronomer, Abd-
Al-Rahman Al-Sufi, commonly known as Al-Sufi,
who was born A.D. 903 and lived until 986. Nothing
is known of his life except that he was a man cele-
brated for his learning, especially in astronomy. His
only work on the latter subject which has come down
to us is a description of the fixed stars, which was
translated from the Arabic by Schjellerup and pub-
lished in 1874 by the St. Petersburg Academy of
Science. This work is based mainly on the catalogue
of Ptolemy, all the stars of which he claimed to have
carefully examined. But he did not add any new
stars to Ptolemy's list, nor, it would seem, did he at-
tempt to redetermine their positions. He simply
used the longitudes and latitudes of Ptolemy, the
former being increased by 12 42' on account of the

ANCIENT AND MEDIEVAL CATALOGUES 43

precession during the interval between his time and
that to which Ptolemy's catalogue was reduced. The
translator says of his work that it gives a description
of the starry heavens at the time of the author and is
worthy of the highest confidence. The main body
of the work consists of a detailed description of each
constellation, mentioning the positions and appear-
ances of the stars which it contains. Here we find the
Arabic names of the stars, which were not, however,
used as proper names, but seem rather to have been
Arabic words representing some real or supposed pe-
culiarity of the separate stars, or arbitarily applied to
them.

Four centuries later arose the celebrated Ulugh
Beigh, grandson of Tamerlane, who reigned at Sam-
arcand in the middle of the fifteenth century. Baily
says of him :

" Ulugh Beigh was not only a warlike and powerful monarch,
but also an eminent promoter of the sciences and of learned men.
During his father's lifetime he had attracted to his capital all the
most celebrated astronomers from different parts of the world ; he
erected there an immense college and observatory, in which above
a hundred persons were constantly occupied in the pursuits of
science, and caused instruments to be constructed of a better
form and greater dimensions than any that had hitherto been used
for making astronomical observations."

His fate was one which so enlightened a promoter
of learning little deserved : he was assassinated by
the order of his own son, who desired to succeed him
on his throne, and, in order to make his position the.
more secure, also put his only brother to death. A

44 CATALOGUING AND NUMBERING

catalogue of the stars bears the name of this monarch ;
he is supposed to have made many or most of the
observations on which it is founded. Posterity will
be likely to suppose that a sovereign used the eyes
of others more than his own in making the observa-
tions. However this may be, his catalogue seems to
have been the first in which the positions of the stars
given by Ptolemy were carefully revised. He found
that there were twenty-seven of Ptolemy's stars too
far south to be visible at Samarcand, and that eight
others, although diligently looked after, could not be
discovered. It is curious that, like Al-Sufi, he does
not seem to have added any new stars to Ptolemy's
list.

Next in the order of time comes the work of Bayer,
whose method of naming the stars has already been
described. The main feature of his work consists in
maps of all the constellations. Previous to his time,
celestial globes, made especially for the use of the
navigator, took the place of maps of the stars. The
first edition of this book was published in 1601, and
is distinguished by the fact that a list of stars in each
constellation is printed on the backs of the maps.
Bayer did not confine himself to the northern hemi-
sphere, but extended his list over the whole celestial
sphere, from the north to the south pole.

The catalogue of the celebrated Tycho Brahe, pre-
pared toward the end of the sixteenth century, though
of great historic value, is of no special interest to the
general reader at the present time. A supplement to
it, continuing its list of stars to the south pole, was

MODERN CATALOGUES OF STARS 45

published by Halley, who made the necessary observa-
tions during a journey to St. Helena in 1677.

The catalogue of Hevelius, published in 1690, offers
no feature of special interest, except the addition of
several new constellations, which he placed between
those already known. Having the aid of the tele-
scope, he was able to include in his catalogue stars
which had been invisible to his predecessors.

Modern catalogues of the stars may be divided into
two classes : Those which include only stars of a
special class, or stars of which the observer Modern
sought to determine the position or magni- Catalogues
tude with all attainable precision ; and cata- ' stars,
logues intended to include all the stars in any given
region of the heavens, down to some fixed order
of magnitude. It may appear remarkable that no at-
tempt of the latter sort was seriously made until more
than two centuries after the telescope had been pointed
at the heavens by Galileo. A reason for the absence
of such an attempt will be seen in the vast number of
stars shown by the telescope, the difficulty of stopping
at any given point, and the seeming impossibility of
assigning positions to hundreds of thousands of stars.
The latter difficulty was overcome by the improved
methods of observation devised in modern times.

Catalogues intended to be complete down to some
given magnitude are of two classes : Those which
include only the stars visible to the naked eye, or
with a small opera-glass, and those which take in all
the stars to the Qth or loth magnitude.

Those of the first class are mostly published in con-

46 CATALOGUING AND NUMBERING

nection with star maps, and are sometimes called
" uranometries." For that portion of the sky visible
in our latitudes the best work of this kind is Heis's
Atlas Coelestis, which extends to magnitude 6.3.

About the middle of the nineteenth century the cel-
ebrated Argelander commenced the work of actually
cataloguing all the stars of the northern celestial hemi-
sphere to magnitude 9^. This work was termed a
Durchmusterung of the northern heavens, a term
which has been introduced into astronomy generally
to designate a catalogue in which all the stars down
to the 9th or loth magnitude are supposed to be
mustered, as if a census of them were taken. The
work fills three quarto volumes and contains more
than 324,000 stars, between the north pole and 2 of
south declination, of each of which the magnitude
and the right ascension and declination are given.
This work was extended by Schonfeld, Argelander's
assistant and successor, to 22 of south declination.

In the latitudes in which the great observatories of
the northern hemisphere are situated, that part of the
celestial sphere within 40 or 50 of the south pole
always remains below the horizon. Above this in-
visible region a belt of somewhat indefinite breadth,
10 or more, can be only imperfectly observed, owing
to the nearness of the stars to the horizon, and the
brevity of the period between their rising and setting.
Up to the middle of the nineteenth century, the few
observatories situated in the southern hemisphere
were too ill-endowed to permit of their undertaking a
complete census of their part of the sky.

THOME 'S D URCHMUSTER UNG 47

The first considerable work emanating from the
Cordoba Observatory, under Gould, was the Urano-
metria Argentina, already mentioned, which com-
prised a catalogue of all the stars down to the 7th
magnitude from the south pole to 10 of north de-
clination. Another work, which was not issued until
after Dr. Gould's death, was devoted to photographs
of southern clusters of stars.

The work of Argelander is being continued at the
Cordoba Observatory as a Durchmusterung of the
southern heavens. It commences at 22 of south de-
clination, where Schonfeld's work ended, and is to be
continued to the south pole. This work is still in-
complete, but three volumes have been published by
Thome, extending to 51 of south declination. It is
expected that the fourth is approaching completion.
This catalogue is, in one point at least, more com-
plete than that of Argelander and Schonfeld, as it
contains all the stars down to the tenth magnitude-
The three volumes give the positions and magnitudes
of no less than 489,827 stars, nearly 175,000 more
than the catalogue of Argelander gives for the entire
northern hemisphere. If the remaining part of the
heavens, from 42 to the south pole, is equally rich,
it will contain about 350,000 stars, and the entire
work will comprise more than 800,000 stars.

The Royal Observatory of the Cape of Good Hope,
under the able and energetic direction of Dr. David
Gill, has carried out a work of the same kind, which
is remarkable for being based on photography. The
history of this work is of great interest. In 1882

48 CATALOGUING AND NUMBERING

Gill secured the aid of a photographer at the Cape of
Good Hope to take pictures of the brilliant comet
of that year, with a large camera. On developing
the pictures the remarkable discovery was made that
not only all the stars visible to the naked eye, but
telescopic stars down to the ninth or tenth magnitude
were also found on the negatives. This remarkable
result suggested to Gill that here was a new and
simple method of cataloguing the stars. It was only
necessary to photograph the heavens and then meas-
ure the positions of the stars on the glass negatives,
which could be done with much greater ease and cer-
tainty than measures could be made on the positions
of the actual stars, which were in constant apparent
motion.

As soon as the necessary arrangements could be
made and the necessary instruments devised and put
The Cape mto successful operation, Gill proceeded to
Durchmus- the work of photographing the entire south-
terung. em h eavens f rom !8 of south declination to

the celestial pole. The results of this work are found
in the Cape Photographic Durchmusterung, a work in
three quarto volumes, in which the astronomers of all
future time will find a permanent record of the south-
ern heavens towards the end of the nineteenth century.
The actual work of taking the photographs extended
from 1 88 7 to 1 89 1 . This, however, was far from being
the most difficult part of the enterprise. The more
arduous task of measuring the positions of a half-
million of stars on the negatives, and determining the
magnitude of each, was undertaken by Professor J.

THE CAPE DURCHMUSTERUNG 49

C. Kapteyn, of the University of Groningen, Holland,
and brought to a successful completion in the year
1899^

What the work gives is, in the first place, the mag-
nitude and approximate position of every star photo-
graphed. The determining of the magnitude of a
star from its photograph is an important and delicate
question. There is no difficulty in determining, from
the diameter of the image of the star as seen in the
microscope, what its photographic magnitude was at
the time of the exposure, as compared with other
stars on the same plate. But can we rely upon simi-
lar photographic magnitudes on different plates corre-
sponding to similar brightnesses of the stars ? In the
opinion of Gill and Kapteyn we cannot. The trans-
parency of the air varies from night to night, and on
a very clear night the same star will give a stronger
image than it will when the air is thick. Besides,
slightly different instruments were used in the course
of the work. For these reasons a scale of magnitude
was determined on each plate by comparing the pho-
tographic intensity of the images of a number of stars
with the magnitudes as observed with the eye by vari-
ous observers. Thus on each plate the magnitude
was reduced to a visual scale.

It does not follow from this that the magnitudes

1 This work of Kapteyn offers a remarkable example of the spirit which ani-
mates the born investigator of the heavens. Although the work was officially
that of the British Government, the years of toil devoted to it were, as the
writer understands, expended without other compensation than the consciousness
of making a noble contribution to knowledge, and the appreciation of his fel-
low astronomers of this and future generations.
4

50 CATALOGUING AND NUMBERING

are visual, and not photographic. It is still true that
a blue star will give a much stronger photographic
image than a red star of equal visual brightness. In
a general way, it may be said that the category in-
cludes all the stars to very nearly the tenth magnitude,
and on most of the plates stars of 10.5 were included.
In fact, now and then is found a star of the eleventh
magnitude.

A feature of the work which adds greatly to its
value is a careful and exhaustive comparison of its
results with previous catalogues of the stars. When
a star is found in any other catalogue the latter
is indicated. Most interesting is a complete list
of catalogued stars which ought to be on the
photographic negatives, but were not found there.
Every such case was exhaustively investigated.
Sometimes the star was variable, sometimes it was
so red in colour that it failed to impress itself
on the plate, sometimes there were errors in the
catalogue.

The great enterprise of making a photographic map
of the heavens, now being carried on as an interna-
tional enterprise, having its headquarters at Paris, is
yet wider in its scope than the works we have just
described. One point of difference is that it is in-
tended to include all the stars, however faint, that
admit of being photographed with the instruments in
use. The latter are constructed on a uniform plan,
the aperture of each being 34 centimetres, or 13.4
inches, and the focal length 343 centimetres. Two sets
of plates are taken, one to include all the stars that the

NUMBERING THE STARS 51

instrument will photograph, and the other only to
take in those to the eleventh magnitude. Of the lat-
ter it is intended to prepare a catalogue. Some por-
tions of the German and English catalogues have
already been published, and their results will be made
use of in the course of the present work.

Closely connected with the work of cataloguing
the stars is that of enumerating them. In view of
what may possibly be associated with any Numbering
one star planets with intellectual beings the stars,
inhabiting them the question how many stars there
are in the heavens is one of perennial interest. But
beyond the general statement we have already made,
this question does not admit of even an approximate,
answer. The question which we should be able to
answer is this: How many stars are there of each
distinguishable magnitude? How many of the first
magnitude, of the second, of the third, and so on to
the smallest that have been estimated ? Even in this
form we cannot answer the question in a way which
is at the same time precise and satisfactory. One
magnitude merges into another by insensible grada-
tions, so that no two observers will agree as to
where the line should be drawn between them. The
difficulty is enhanced by the modern system very
necessary, it is true of regarding magnitude as a
continuously varying quantity and estimating it with
all possible precision. In adjusting the new system
to the old one, it may be assumed that an average
star of any given magnitude on the old system would
be designated by the corresponding number on the

52 CATALOGUING AND NUMBERING

new system. For example, an average star of the
fourth magnitude would be called 4.0 ; one of the fifth,
5.0, etc. Then the brightest stars which formerly
were called of the fourth magnitude, would now be, if
the estimate were carried to hundredths, 3.50, while
the faintest would be 4.50. What were formerly called
stars of the fifth magnitude would range from 4.50 to
5.50, and so on. But we meet with a difficulty when
we come to the sixth magnitude. On the modern sys-
tem, magnitude 6.0 represents the faintest star visible
to the naked eye ; but the stars formerly included
in this class would, on the average, be somewhat
brighter than this, because none could be catalogued
except those so visible.

The most complete enumeration of the lucid stars
by magnitudes has been made by Pickering (Annals
of the Harvard Observatory, vol. xiv.). The stars
were classified by half-magnitudes, calling

M. M.

Mag. 2.0 all from 1.75 to 2.25
" 2.5 " " 2.25 to 2.75, etc.

For the northern stars, Pickering used the Harvard
Photometry ; for the southern, Gould's Uranometria
Number Argentina. A zone from the equator to 30
of stars, south declination is common to both ; for this
zone I use Gould. The number of each class in the
entire sky, north and south of the celestial equator, is
as follows:

NUMBER OF STARS

Mag.
i

2.0
2-5

3-o
3-5
4.0

4-5
5-0

5-5
6.0

Northern Southern
Hemisphere. Hemisphere.
Pickering. Gould.

114

228

45
787
789

15
24

126

234

426

681

1189

Total.
23
32
4i

135

240

462

876
1468
1978

Sum 2509 2824 5333

It would seem from this that the number of lucid
stars in the southern celestial hemisphere is 315
greater than in the northern. But this arises wholly
from a seemingly greater number of stars of magni-
tude 6. In the zone o to 30 S., Pickering has 214
stars of this class fewer than Gould. Hence it is not
likely that there is really any greater richness of the
southern sky.

The total number of lucid stars is thus found to be
5333. But it is not likely that stars of magnitudes
6.1 and 6.2 should be included in this class, though
this is done in the above table. From a careful
study and comparison of the same data from Picker-
ing and Gould, Schiaparelli numerated the stars to
magnitude 6.0. He found :

North pole to 30 S. 3113 stars

30 S. to south pole 1190

Total lucid stars 4303

54 CATALOGUING AND NUMBERING

For most purposes a classification by entire magni-
tudes is more instructive than one by half-magnitudes.
From the third magnitude downward we may assume
that forty per cent, of the stars of each half-magni-
tude belong to the magnitude next above, and sixty
per cent, to that next below. We thus find that of

Total.
Mag. o and i there are 21 stars 21

52
157

506
1740

73
230

736

2476
7647

Here it is to be remarked that under magnitude 6
are included many other than the lucid stars, namely,
all down to magnitude 6.4. The last column gives
the entire number of stars down to each order of
magnitude.

It will be remarked that the number of stars, of
each order is between three and four times that of
the order next brighter. How far does this law ex-
tend ? Argelander's Durchmusterung, which is sup-
posed to include all stars to magnitude 9.5, gives
315,039 stars for the northern hemisphere, from
which it would be inferred that the whole sky con-
tains 630,000 stars to the ninth magnitude. Com-
paring this with the number, 764.7, of stars to the
magnitude 6.5, we see that it is fortyfold, so that it
would require a ratio of about 3.5 from each mag-
nitude to the next lower. But it is now found that
Argelander's list contains, in the greater part of the
heavens, all the stars to the tenth magnitude.

NUMBER OF STARS 55

On the other hand, Thome's Cordoba Durchmus-
terung gives 340,380 stars between the parallels 22
and 42. This is 0.14725 of the whole sky, so
that, on Thome's scale of magnitude, there are about
2,311,000 stars to the tenth magnitude in the sky.
This is more than three times the Argelander num-
ber to the ninth magnitude. There is, therefore, no
evidence of any falling off in the ratio of increase up
to the tenth magnitude.

CHAPTER V

THE SPECTRA OF THE STARS

No unregarded star

Contracts its light
Into so small a character,

Removed far from our humane sight,

But if we steadfast looke

We shall discerne
In it, as in some holy booke,

How man may heavenly knowledge learne.

HABINGTON.

THE principles on which spectrum analysis rests
can be stated so concisely that I shall set them
forth for the special use of such readers as may not
be entirely familiar with the subject. Every-

Pnnciples i i r i

O f one knows that when the rays of the sun

Spectrum p ass through a triangular prism of glass or

Analysis. , , ,

other transparent substance they are un-
equally refracted, and thus separated into rays of
different colours. These colours are not distinct, but
each runs into the other by insensible gradations, from
deep crimson through red, scarlet, orange, yellow,
green, and blue to a faint violet.

This result is due to the fact that the light of the
sun is made up of an indiscriminate mixture of rays

SPECTRUM ANALYSIS

of an infinite number of wave-lengths, or, in simpler
language, of an infinite number of tints of colour,
since to every wave-length corresponds a definite
tint. Such a spreading out of elementary colours
in the form of a visible sheet is called a spectritm.
By the spectrum of an incandescent object is meant
the spectrum formed by the light emitted by the
object when passed through a refracting prism or
otherwise separated into its elementary colours. The
interest and value which attach to the study of spectra
arise from the fact that different bodies give different
kinds of spectra, according to their constitution, their
temperature, and the substances of which they are
composed. In this manner it is possible, by a study
of the spectrum of a body, to reach certain inferences
respecting its constitution.

In order that such a study should lead to a definite
conclusion, we must recall that to each special shade
of colour corresponds a definite position in the spec-
trum. That is to say, there is a special kind of light
having a certain wave-length and therefore a certain
shade which will be refracted through a certain fixed
angle, and will therefore fall into a definite position
in the spectrum. This position is, for every possible
kind of light, expressed by a number indicating its
wave-length.

If we form a spectrum with the light emitted by an
ordinary incandescent body, a gaslight for example,
we shall find the series of colours to be unbroken from
one end of the spectrum to the other. That is to
say, there will be light in every part of the spectrum.

58 THE SPECTRA OF THE STARS

Such a spectrum is said to be continuous. But if we
form the spectrum by means of sunlight, we shall
find the spectrum to be crossed by a great number of
more or less dark lines. This shows that in the
spectrum of the sun light of certain definite wave-
lengths is wholly or partly wanting. This fact has
been observed for more than a century, but its true
significance was not seen until a comparatively recent
time.

If, instead of using the light of the sun, we form a
spectrum with the light emitted by an incandescent
Spectrum gas, say hydrogen made luminous by the
Analysis, electric spark, we shall find that the spec-
trum consists only of a limited number of separate
bright lines, of various colours. This shows that
such a gas, instead of emitting light of all wave-
lengths, as an incandescent solid body does, princi-
pally emits light of certain definite wave-lengths.

It is also found that if we pass the light of an incan-
descent body through a sufficiently large mass of gas
cooler than the body, the spectrum, instead of being
entirely continuous, will be crossed with dark lines
like that of the sun. This shows that light of certain
wave-lengths is absorbed by the gas. A comparison
of these dark lines with the bright lines emitted by
the same gas when incandescent led Kirchhoff to the
discovery of the following fundamental principle :

Every gas, when cold, absorbs the same rays of light
which it emits when incandescent.

An immediate inference from this law is that the
dark lines seen in the spectrum of the sun are caused

SPECTR UM ANAL YSIS 59

by the passage of the light through gases either around
the sun or forming the atmosphere of the earth. A
second inference is that we can determine what these
gases are by comparing the position of the dark lines
with that of the bright lines produced by different
gases when they are made incandescent. Hence
arose the possibility of spectrum analysis, a method
which has been applied with such success to the
study of the heavenly bodies.

So far as the general constitution of bodies is con-
cerned, the canons of spectrum analysis are these :

Firstly, when a spectrum is formed of distinct
bright lines, the light which forms it is emitted by a
transparent mass of glowing gas.

Secondly, when a spectrum is entirely continuous
the light emanates either from an incandescent solid,
from a body composed of solid particles, which may
be ever so small, or from a mass of incandescent gas
so large and dense as not to be transparent through
and through.

Thirdly, when the spectrum is continuous, except
that it is crossed by fine dark lines, the body emitting
the light is surrounded by an atmosphere formed of
gases cooler than itself. The chemical constitution
of these gases can be determined by the position of
the lines.

Fourthly, if, as is frequently the case, a spectrum is
composed of an irregular succession of bright and
shaded portions, the body is probably a gaseous mass
under great pressure.

It will be seen from the preceding statement that

THE SPECTRA OF THE STARS

a mass of gas so large as not to be transparent may
not be distinguishable from a solid body. It is
therefore not strictly correct to say, as is sometimes
done, that an incandescent gas always gives a spec-
trum of bright lines. It will give such a spectrum
only when it is transparent through and through. 1

A gaseous mass, so large as to be opaque, would, if
it were of the same temperature inside and out, give
a continuous spectrum, without any dark lines. But
the laws of temperature in such a mass show that it
will be cooler at the surface than in the interior.
This cooler envelope will absorb the rays emanating
from the interior, as in the case when the latter is
solid. We conclude, therefore, that the fact that the
great majority of stars show a spectrum like that
of the sun, namely, a continuous one crossed by dark
lines, does not throw any light on the question
whether the matter composing the body of the star is
in a solid, liquid, or gaseous state. The fact is that
the most plausible theories of the constitution of the
sun lead to the conclusion that its interior mass is
really gaseous. Only the photosphere may be to
a greater or less extent solid or liquid. The dark
lines that we see in the solar spectrum are produced

1 As this principle is not universally understood, it may be well to remark
that it results immediately from Kirchhoff slaw of the proportionality between
the radiating and absorbing powers of all bodies for light of each separate
wave-length. When a body, even if gaseous in form, is of such great size and
density that light of no colour can pass entirely through it, then the consequent
absorption by the body of light of all colours shows that throughout the region
where the absorption occurs there must be an emission of light of these same
colours. Thus light from all parts of the spectrum will be emitted by the
entire mass.

DESCRIPTION OF THE SPECTRUM 61

by the absorption of a comparatively thin and cool
layer of gas resting upon the photosphere. Analogy
as well as the general similarity of the spectra lead
us to believe that the constitution of most of the stars
is similar to that of the sun.

The visible spectrum, as commonly described, term-
inates with the red at one end and the violet at the
other. But the termination is by no means Description
sharp at either end. Especially is this the of the
case with the violet, where, if extraneous light s P ectrum -
be shut off, a faint extension known as the ultra-violet,
to which no definite limit can be assigned, will become
visible. Moreover, it is found that the heating effect
does not terminate with the red end of the spectrum,
but that if a sensitive thermometer be held in the
seeming darkness beyond the red end a heating effect
is produced. It is also found that a photographic
effect is produced by rays scarcely, if at all, visible in
the ultra-violet.

These three different effects were formerly at-
tributed to three different kinds of rays, those of
heat, those of light, and those which, affecting the
photographic plate, were called chemical or actinic
rays. But it is now known that heat, light, and pho-
tographic effects are all due to one and the same
agency, which we may call radiance. The radiance
from an incandescent body like the sun may be of
all wave-lengths ; at least we can set no definite limit
to the wave-length. These lengths may be expressed
in millionths of a millimetre, or, as is now more
commonly done, in ten millionths. This measure is

62 THE SPECTRA OF THE STARS

sometimes called the tenth-metre, meaning the metre
divided by the tenth power of ten. To give a general
idea of wave-length we remark that near the brightest
part of the spectrum the wave-length is 5000 tenth-
metres or 500 millionths of a millimetre, the latter
being nearly ^ F of our inch. The wave-length in
question is v therefore about 5-0 ^or ^ an mcn - As we
pass toward the violet end of the spectrum, commonly
called the upper end, this wave-length diminishes ; as
we pass toward the lower or red end it increases. As
we approach wave-length 7500, the effect on the eye
as light gradually dies away with a sensation of very
deep red ; below that point only the heat effect is
produced, except that with certain chemicals a faint
photographic effect may still be obtained.

The more refrangible parts of the spectrum are now
studied almost entirely by photography. The astro-
physicist can photograph not only the visible spec-
trum at pleasure, but the higher parts of the spectra
of bodies even when so faint as to be invisible to the
eye. The photograph has the additional advantage
that it forms a permanent record which can be
measured and studied at pleasure.

The farthest exploration into the ultra-violet region
has been made by Dr. V. Schumann, who has exam-
ined it up to W. L. 1620. The higher region is very
rich in lines, of which he found more than six hundred,
separated into fifteen groups. As we approach its
limit the air becomes opaque to radiation. A layer
of one millimetre in thickness was found to absorb all
the radiance shorter than 1 700.

DESCRIPTION OF THE SPECTRUM 63

The strongest dark lines of the spectra were studied
and laid down by Wollaston about 1800. He desig-
nated the strongest by the capital letters A, B, C, D,
E, and F, to which some small letters were subse-
quently added. As the exploration of the spectrum
extended into the violet additional letters were added.
It has been found convenient in recent times to re-
place some of those letters by symbols expressing the
substance which produces the line. Thus, the line
which Wollaston called C, being produced by hydro-
gen, is now frequently called Ha. The other lines
produced by this substance are designated as H/2,
H r , etc.

Extensive maps of the solar spectrum have been
published, of which that of Rowland surpasses all others
in the completeness of its details. The number of spec-
tral lines as found on this map mount high into the
thousands, so that the great mass of them can be desig-
nated only by their wave-length. Thus the line C or
Ha may be designated as 6561.7. Maps or tables of
the spectra of the various chemical elements are found
in special treaties on the subject.

While some substances, notably the lightest and
most permanent gases, have few lines in their respect-
ive spectra, in other substances the lines are very nu-
merous. The metal which gives the richest spectrum
is iron. Thalen has recorded not less than 1200 lines
in its spectrum between wave-lengths 4000 and 7600.

It is now found that the spectra of most substances
vary with the physical condition of the substance in
such a way that detection may become doubtful or

64 THE SPECTRA OF THE STARS

difficult. The general rule is that, when a gas is sub-
jected to pressure, the lines, if dark, become blacker
and broader, being sometimes changed into bands
with more or less ill-defined borders. Commonly the
line broadens only on one side, thus leading to a
displacement of its apparent position with the press-
ure. Not less than three distinct spectra have been
found as due to argon. These changes have not,
up to the present time, been expressed by any uni-
form and general law. It is not alone the thickness
of the lines which changes ; it frequently happens
that a line visible under one condition will disappear
under another, while a second will be better seen.
These seeming anomalies may sometimes make our
conclusions from the spectral analysis of the heavenly
bodies uncertain ; but it may be hoped that when
they are fully understood, they will give us more
precise knowledge than we yet possess of the exact
physical constitution of these bodies.

A complete map of the spectrum is too full of
detail to well serve the purpose of the general reader
or student. We therefore give on the opposite page
a plan of the visible spectrum, giving the wave-
lengths, the arrangement of colours, and a few of the
stronger lines with the substances to which they are
due. It must not, however, be supposed that the solar
spectrum with its lines is so simple as might appear
from this plan. For the most part, what are drawn
and lettered as lines really consist of groups of lines
of different degrees of intensity. Whether they shall
appear as a simple ill-defined line or a group depends

SPECTR

WAVE
LENGTH

LINE AND DESIGNATION

39
40
4 I
42-
43

46
47
48

54-

55(

66
67
68
69

70
71
72

73
74
75<
76

SUBSTANCE.
OR ORIGIN

ULTRA VIOLET

1 pc

Hor H6---
h or HP

\ / 1 s^. i r^ ~r-

VI OLc T

Rl 1 IF

LJ LU l_
Tnr Hfi

GREEN

00-

GREENISH YELLOW
YELLOW

Di P'

00-

ORANGE.

Cx- API p-p

oo-

C or Hc{

BRIGHT RED

B-

DEEP RED

00-

PARK RED

CALCIUM

CALCIUM, HYDROGEN

HYDROGEN

IRON
HYDROGEN

HYDROGEN

NEBULAR LINE

NEBULAR LINE.

MAGNESIUM
CALCIUM

SODIUM

HYDROGEN
AQUEOUS VAPOR

Aqueous VAPOR

AQUEOUS VAPOR

66 THE SPECTRA OF THE STARS

largely on the resolving power of the spectroscope.
With every increase of power new lines are brought
out. It will also be seen from the photographs
which we reproduce that the spectra of the heavenly
bodies, whether stars or sun, do not consist of uni-
form sheets of light crossed by dark lines, but that
one part runs into another with slight and nearly
imperceptible gradations of shade. These are due
partly to innumerable lines not visible singly, and
partly to the varying and irregular absorption to
which the light has been subject.

Particularly irregular is the absorption produced by
the aqueous vapour of the atmosphere. The strong-
est lines and groups of lines in the red, notably those
between A and B, as well as irregular shadings in the
bright parts of the spectrum, are due to the absorp-
tion of this agent.

It thus happens that the individual Wollaston lines
cannot as a general rule be considered as each due
to some one substance, most of them being composed
of a number of lines produced by different substances
whose lines chance to fall very close together.

In connection with the lines and the wave-lengths
we have also named the spectral colours. One of
these shades into the other so gradually that no pre-
cise line of demarkation can be drawn. In fact, the
change of colour is continuous from one end of the
spectrum to the other. The red, green, blue, and
violet are the only colours which, to the eye, seem
unchanged through any perceptible space in their
central portions.

CLASSIFICATION OF STELLAR SPECTRA 67

Different authorities, and perhaps different eyes,
may therefore assign different boundaries to the col-
ours. For these reasons we have not attempted to
draw any demarkations of the colours, but have simply
shown the central parts of those colours which are
best marked.

Quite possibly different eyes may have slightly
different impressions of the spectral colours. To those
of the writer, the yellow of the spectrum is in no way
comparable in depth and intensity with the yellow of
such flowers as the buttercup. The shading from a
tinge of red on the one side to a tinge of green on
the other takes place without what seems like a pure
bright yellow.

When the spectra of thousands of stars were re-
corded for study, such a variety was found that some
system of classification was necessary. The
commencement of such a system was made tion of
by Secchi in 1863. It was based on the stellar
observed relation between the colour of a
star and the general character of its spectrum.

Arranging the stars in a regular series, from blue
in tint through white to red, it was found that the
number and character of the spectral lines varied in a
corresponding way. The blue stars, like Sirius, Vega,
and Alpha Aquilse, had the F lines strong, as well as
the two violet lines H, but had otherwise only ex-
tremely fine lines. On the other hand, the red stars,
like Alpha Orionis and Alpha Scorpii, show spectra
with several broad bands. Secchi was thus led to
recognise three types of spectra, as follows :

EXAMPLES OF STELLAR SPECTRA

CLASSIFICATION OF STELLAR SPECTRA 69

The first type is that of the white or slightly blue
stars, like Sirius, Vega, Altair, Rigel, etc. The typi-
cal spectrum of these stars shows all seven spectral
colours, interrupted by four strong, dark lines, one in
the red, one in the bluish green, and the two others
in the violet. All four of these lines belong to hy-
drogen. Their marked peculiarity is their breadth,
which shows that the absorbing layer is of consider-
able thickness, or is subjected to a great pressure.
Besides these broad rays, fine metallic rays are found
in the brighter stars of this type. Secchi considers
that this is the most numerous type of all, half the
stars which he studied belonging to it.

The second type is that of the somewhat yellow
stars, like Capella, Pollux, Arcturus, Procyon, etc.
The most striking feature of the spectrum of these
stars is its resemblance to that of our sun. Like the
latter, it is crossed by very fine and close black rays.
It would seem that the more the star inclines toward
red, the broader these rays become and the easier it
is to distinguish them. We give a figure showing
the remarkable agreement between the spectrum of
Capella, which may be taken as an example of the
type, and that of the sun.

The spectra of the third type, belonging mostly to
the red stars, are composed of a double system of
nebulous bands and dark^lines. The latter are funda-
mentally the same as in the second type, the broad,
nebulous bands being an addition to the spectrum.
Alpha Herculis may be taken as an example of this
type.

7 o THE SPECTRA OF THE STARS

It is to be remarked that, in these progressive
types, the brilliancy of the more refrangible end of
the spectrum continually diminishes relatively to that
of the red end. To this is due the gradations of
colour in the stars.

To these three types Secchi subsequently added a
fourth, given by a comparatively few stars of a deep
red colour. The spectra of this class consist princi-
pally of three bright bands, which are separated by
dark intervals. The brightest is in the green ; a very
faint one is in the blue ; the third is in the yel-
low and red, and is divided up into a number of
others.

To these types a fifth v/as subsequently added by
Wolf and Rayet, of the Paris Observatory. The
spectra of this class show a singular mixture of bright
lines and dark bands, as if three different spectra
were combined, one continuous, one an absorption
spectrum, and one an emission spectrum from glowing
gas. Less than a hundred stars of this type have
been discovered. A very remarkable peculiarity,
which we shall discuss hereafter, is that they are
nearly all situated very near the central line of the
Milky Way.

Vogel proposed a modification of Secchi's classi-
fication, by subdividing each of his three types into
two or three others, and including the Wolf-Rayet
stars under the second type. His definitions are as
follows :

Type I is distinguished by the intensity of the
light in the more refrangible end of the spectrum, the

CLASSIFICATION OF STELLAR SPECTRA 71

blue and violet. The type may be divided into three
subdivisions, designated a, b, and c :

In la the metallic lines are very faint, while the
hydrogen lines are distinguished by their breadth and
strength.

In \b the hydrogen lines are wanting.

In \c the lines of hydrogen and helium both show
as bright lines. Stars showing this spectrum are now
known as helium stars.

According to Vogel, the spectra of type II are dis-
tinguished by having the metallic lines well marked
and the more refrangible end of the spectrum much
fainter than in the case of type I. He recognises two
subdivisions :

In lla the metallic lines are very numerous, es-
pecially in the yellow and green. The hydrogen
lines are strong, but not so striking as in la.

In lib are found dark lines, bright lines, and faint
bands. In this subdivision he includes the Wolf-
Rayet stars, more generally classified as of the fifth
type.

The distinguishing mark of the third type is that,
besides dark lines, there are numerous dark bands in
all parts of the spectrum, and the more refrangible
end of the latter is almost wanting. There are two
subdivisions of this type :

In Ilia the broad bands nearest the violet end are
sharp, dark, and well defined, while those near the red
end are ill defined and faint. In \\\b the bands near
the red end are sharp and well defined ; those toward
the violet, faint and ill defined. The character of the

72 THE SPECTRA OF THE STARS

bands is therefore the reverse of that in subdivi-
sion a.

This classification of Vogel is still generally followed
in Germany and elsewhere. It is found, however,
that there are star spectra of types intermediate to all
these defined. Moreover, in each type the individual
differences are so considerable that there is no well-
defined limit to the number of classes that may be
recognised. Other designations frequently occur in
literature. The stars of type II are sometimes
termed Capellan stars, or solar stars. The stars
which show the lines of helium are known as helium
stars.

A classification far more minute than either of the
preceding was made by Miss Antonio C. Maury, of
the Harvard Observatory, and has been adopted in
the Draper Memorial work of that institution. 1 The
classification is too extended for us to give more than
its principal features. In the main it recognises a
regular progression in the character of the spectra.
The principal feature is the addition of an extended
type called the Orion type, because the stars show-
ing it abound in the constellation Orion, though not
confined to it. It is marked principally by what are
called Orion lines, which include most of the lines of
hydrogen, and nearly one hundred others. Few or
none of the latter can be recognised as solar lines,
nor can they certainly be ascribed to any known sub-
stances. The peculiar feature of the type is that the
Orion lines are strong and numerous, declining in the

1 Annals Harvard Observatory, vol. xxviii., No. i.

RES UL TS OF SPECTR UM ANAL YSIS 73

later groups. The hydrogen lines are of moderate
intensity, inclining toward those of the first type. Of
the two main calcium lines, K is often, and H gener-
ally, absent.

This Orion type is divided into five groups : type
I into five, types II and III each into four. Besides
these there are several intermediate groups, and
a group each for the fourth and fifth types, the
whole number of such groups being twenty-two.
Each group is still further subdivided into classes.

There are many star spectra which cannot be in-
cluded in any of the classes we have described. Up
to the present time these are generally described as
stars of peculiar spectra.

As the present chapter is confined to the more
general side of the subject, we shall not attempt any
description of special spectra. These, especially the
peculiar spectra of the nebulae, of new stars, of vari-
able stars, etc., will be referred to, so far as necessary,
in the chapters relating to those objects.

The most interesting conclusion drawn from ob-
servations with the spectroscope is that the stars are
composed, in the main, of elements similar p esu i ts O f
to those found in our sun. As the latter Spectrum
contains most of the elements found on the Anal y sis -
earth and few or no others, we may say that earth
and stars seem to be all made out of like matter.
It is, however, not yet easy to decide to what extent
elements unknown on the earth exist in the heavens.
It would scarcely be safe to assume that, because
the line of some terrestial substance is found in the

74 THE SPECTRA OF THE STARS

spectrum of a star, it is produced by that substance.
It is quite possible that an unknown substance might
show a line in appreciably the same position as that
of some substance known to us. The evidence be-
comes conclusive only in the case of those elements
of which the spectral lines are so numerous that when
they all coincide with lines given by a star there can
be no doubt of the identity.

CHAPTER VI
PROPER MOTIONS OF THE STARS

I 'm constant as the Northern Star,

Of whose true-fixed and vesting quality

There is no fellow in the firmament. SHAKESPEARE.

WE may assume that the stars are all in motion.
It is true that only a comparatively small
number of stars have been actually seen to be in
motion ; but as some motion exists in nearly every
case where observations would permit of its being de-
termined, we may assume the rule to be universal.
Moreover, if a star were at rest at any time it would
be set in motion by the attraction of other stars.

In dealing with the subject, the astronomer com-
monly expresses the motion in angular measurement,
as so many seconds per year or per century. The
keenest eye would not, without telescopic aid, be able
to distinguish between two stars whose apparent dis-
tance is less than 2' or 120" of arc. The pair of stars
known as Epsilon Lyrse are over 3' apart ; yet to ord-
inary vision they appear as a single star. To ap-
preciate what i" of arc means we must conceive that
the distance between these two stars is divided by
200. Yet this minute space is easily distinguished
and accurately measured by the aid of a telescope of
ordinary power.

76 PROPER MOTIONS OF THE STARS

Statements of the motion from different points of
view illustrate in a striking way the vast distance of
Apparent tne stars an ^ tne power of modern telescopic
and Real research. If Hipparchus or Ptolemy should
Motions. r j ge f rom hj s s l ee p of two thousand years

- nay, if the earliest priests of Babylon should come
to life again and view the heavens, they would not
perceive any change to have taken place in the relat-
ive positions of the stars. The general configurations
of the constellations would be exactly that to which
they were accustomed. Had they been exact ob-
servers they might notice a slight change in the
position of Arcturus; but not in that of any other star.

Slow as the angular motion is, our telescopic
power in the course of a few years makes its detection
frequently possible in the case of Arcturus even in a
few weeks. As accurate determinations of posi-
tions of the stars have been made only during a
century and a half, no motions can be positively
determined except those which would become evi-
dent to telescopic vision in that period. Only
about three thousand stars have been accurately ob-
served so long as this. In the large majority of cases
the interval of observation is so short or the motion
so slow that nothing can be asserted respecting the
law of the motion.

Contrast these apparently slow motions with the
actual motions. Swift indeed are these when meas. '
ured by terrestrial standards. Arcturus has been
moving ever since the time of Job at the rate of
probably more than two hundred miles per second

APPARENT AND REAL MOTIONS 77

possibly three hundred miles. Generally, however,
the motion is much smaller, ranging from an imper-
ceptible quantity up to forty miles a second.

The great mass of stars seem to move only a few
seconds per century, but there are some whose mo-
tions are exceptionally rapid. >The general rule is
that the brighter stars have the largest proper motions.^
This is what we should expect, because in the gen-
eral average they are nearer to us, and therefore their
motion will subtend the greatest angle to the eye.
But this rule is only one of majorities. As a matter
of fact, the stars of largest proper motion happen to
be low in the scale of magnitude. It happens thus
because the number of stars of smaller magnitudes
is so much greater than that of the brighter ones
that their very small proportion of large proper
motions exceeds in actual number those among the
brighter stars.

The discovery of the star of greatest known proper
motion was made by Kapteyn, of Groningen, in 1897,
co-operating with Gill and Innes, of the Cape Ob-
servatory. While examining the photographs of the
stars made at this institution, Kapteyn was surprised
to notice the impression of a star of the eighth magni-
tude which at first could not be found in any cata-
logue^. " Eirt^ on comparing different star lists and
diftererf^phot'ograpris it soon became evident that the
>star^'had been previously seen or photographed, but
always in different positions. An examination of the
observed positions at various times showed that the
star had a more rapid proper motion than any other

PROPER MOTIONS OF THE STARS

yet known. Yet, great though this motion is, it would
require nearly 150,000 years for the star to make a
complete circuit of the heavens if it moved round the
sun uniformly at its present rate.

The following is a list of the annual proper mo-
tions of nine stars exceeding 4". We add the po-
sitions and magnitudes of the stars.

STAR

POSITION

MAG.

PROP.
MOT.

DEC.

Z C q h 24.-} .

5
ii

21
IO
21
II

7
47
59

2
58
56

-45-0
+38.4
-36.4
-37-8
+38.2
+44-3
-57-2
+44-0
- 7.8

8.5
6.4
7-1
8.5
4-8
7-3
4-8
8.7
4-5

8.70
7.04
7.OO
6.07
5-2O
4.76

4.68
4.41
4.06

Groomb 1830

La.ca.ille Q352 . .

Cord 32 416

6 1 Cygni

LI. 21 185

LI 21 258

o 2 Eridani

The fact that the stars move suggests a very nat-
ural analogy to the solar system. In the latter a
Moving number of planets revolve round the sun
Systems as their centre, each planet continually de-
of stars, scribing the same orbit, while the various
planets have different velocities. Around several of
the planets revolve one or more satellites. Were
civilised men ephemeral, observing the planets and
satellites only for a few minutes, these bodies would
be described as having proper motions of their own,
as we find the stars to have. May it not then be
that the stars also form a system ; that each star
is moving in a fixed orbit, performing a revolution
around some far-distant centre in a period which ma)

MOVING SYSTEMS OF STARS 79

be hundreds of thousands or hundreds of millions of
years ? May it not be that there are systems of stars
in which each star revolves around a centre of its own
while all these systems are in revolution around a
single centre ?

This thought has been entertained by more than
one contemplative astronomer. Lambert's magnifi-
cent conception of system upon system will be
described hereafter. Madler thought that he had
obtained evidence of the revolution of the stars
around Alcyone, the brightest of the Pleiades, as
a centre. But, as the proper motions of the stars
are more carefully studied and their motion and
direction more exactly ascertained, it becomes very
clear that when considered on a large scale these con-
ceptions are never realised in the actual universe as a
whole. But there are isolated cases of systems of
stars which are shown to be in some way connected
by their having a common proper motion. We shall
mention some of the more notable cases.

The Pleiades are found to move together with such
exactness that up to the present time no difference in
their proper motions has been detected. This is true
not only of the six stars which we readily see with
the naked eye, but of a much larger number of fainter
ones made known by the telescope. It is an interest-
ing fact, however, that a few stars apparently within
the group do not partake of this motion, from which
it may be inferred that they do not belong to the
system. But there must be some motion among
themselves, else the stars would ultimately fall to-

8o PROPER MOTIONS OF THE STARS

gether by their mutual attraction. The amount and
nature of this motion cannot, however, be ascertained
except by centuries of observation.

Another example of the same sort is seen in five
out of the seven stars of Ursa Major, or The Dipper.
The stars are those lettered /? ? y, # ? , and 6. All five
have a proper motion in R. A. of nearly 8" per cent-
ury, while in declination the movements are some-
times positive and sometimes negative ; that is to
say, some of the stars are lessening their distance
from the pole, while others are increasing it. But
when we project the motions on a map we find
that the actual direction is very nearly the same for
all five stars, and the reason why some move slightly
to the north and others slightly to the south is due to
the divergence of the circles of right ascension. It is
worthy of remark that the community of motion is
also shown by spectroscopic observations of the
radial motions described below.

The five stars in question are all of the second
magnitude except Delta, which is of the third. It is
a curious fact that no fainter stars than these five
have been found to belong to the system.

From a study of these motions Hoffler has con-
cluded that the five stars lie nearly in the same plane
and have an equal motion in one and the same direc-
tion. From this hypothesis he has made a determin-
ation of their relative and actual distances. The
result reached in this way cannot yet, however, be
regarded as conclusive.

There are three stars in Cassiopeia, Beta, Eta, and

RADIAL MOTIONS OF THE STARS 81

Mu, each having a large proper motion in so nearly
the same direction that it is difficult to avoid at least
a suspicion of some relation between them. The
angular motions are, however, so far from equal that
we cannot regard the relation as established.

In the constellation Taurus, between Aldebaran
and the Pleiades, most of the stars which have been
accurately determined seem to have a motion which
is positive in R. A. and negative in declination. But
these motions are not equal, as they should be if the
stars belonged to one system, and we cannot draw any
definite conclusion from them. They show a phenom-
enon which Proctor very aptly designated as star-drift.

Another curious case is that of A Ophiuchi and a
smaHer star of the seventh magnitude, about 14' from
it, having an equal proper motion, showing the two
to form a connected system.

The systems we have just described comprise stars
situated so far apart that, but for their common mo-
tion, we should not have suspected any relation be-
tween them. The community of origin which their
connection indicates is of great interest and import-
ance, but this subject belongs to a later chapter.

No achievement of modern science is more remark-
able than the measurement of the velocity with which
stars are moving to or from us. This is ef-

Radial

fected by means of the spectroscope through Motions
a comparison of the position of the spectral of the
lines produced by the absorption of any sub-
stance in the atmosphere of the star with the corre-
sponding lines produced by the same substance on

82 PROPER MOTIONS OF THE STARS

the earth. The principle on which the method de-
pends may be illustrated by the analogous case of
sound. It is a familiar fact that if we stand alongside
a railway while a locomotive is passing us at full
speed and at the same time blowing a whistle, the
pitch of the note which we hear from the whistle is
higher as the engine is approaching than after ^t
passes. The reason is that the pitch of a sound de-
pends upon the number of sound-beats per second.

Now, we may consider the waves which form light,
when they strike our apparatus, as beats in the ethe-
real medium which follow each other with extraerdin-
ary rapidity, millions of millions in a second, moving
forward with a definite velocity of more than 186,000
miles a second. Each spectral line produced by a
chemical element shows that that element, when in-
candescent, beats the ether a certain number of times
in a second. These beats are transmitted as waves.
Since the velocity is the same whether the number of
beats per second is less or greater, it follows that, if
the body is in motion in the direction in which it
emits the light, the beats will be closer together than if
it is at rest ; if moving away they will be farther apart.
The fundamental fact on which this result depends is
that the velocity of the light-beat through the ether
is independent of the motion of the body causing the

A B X

O .......

beat To show the result, let A be a luminous body

RADIAL MOTIONS OF THE STARS 83

at rest ; let the seven dots to the right of A be the
crests of seven waves or beats, the first of which, at
the end of a certain time, has reached X. The wave-
length will then be one-seventh the distance A X.
Now, suppose A in motion toward X with such speed
that when the first beat has reached X, A has reached
the point B. Then the seven beats made by A while
the first beat is travelling from A to X, and A travel-
ling from A to B, will be crowded into the space B X,
so that each wave will be one-seventh shorter than
before. In other words, the wave-lengths of the light
emitted by any moving body will be less or greater
according as the .motion is in the direction in which
its light is transmitted, or in the opposite. direction.

The position of a ray in the spectrum depends
solely on the wave-length of the light. It follows
that the rays produced by any substance will be dis-
placed toward the blue or red end of the spectrum,
according as the body emitting or absorbing the rays
is moving towards or from us. This method of deter-
mining the motions of bodies to or from us has been
perfected by photographing the spectrum of a star, or
other heavenly body, side by side with that of a ter-
restrial substance rendered incandescent in the tube
of a telescope. The rays of this substance pass
through the same spectroscope as those from the
star, so that, if the wave-lengths of the lines produced
by the substance were the same as those found in
the star spectrum, the two lines would correspond
in position. The minute difference found on the
photographic plate is the measure of the velocity

8 4

PROPER MOTIONS OF THE STARS

of the star in the line of sight called its radial
motion.

SPECTROGRAM OF POLARIS TAKEN BY CAMPBELL AT THE LICK OBSERVATORY
The bright cross-lines are those of the comparison-spectrum of iron

These measures require apparatus and manipulation
of extraordinary delicacy, in order to avoid every pos-
sible source of error. The displacement of the lines
produced by the motion is in fact so minute that great
skill is required to make it evident, unless in excep-
tional cases.

It will be seen that the conclusion as to radial mo-
tion depends on the hypothesis that the position of
any ray produced by a substance is affected by no
cause but the motion of the substance. How and

RADIAL MOTIONS OF THE STARS 85

when this hypothesis may fail is a very important
question. It is found, for example, that the position
of a spectral ray may be altered by compressing the
gas emitting or absorbing the ray ; and it may be in-
quired whether the results for motion in the line of
sight may not be vitiated by the absorbing atmo-
sphere of the star being under heavy pressure, thus
displacing the absorption line.

To this it may be replied that, in any case, the
outer layers of the atmosphere, through which the
light must last pass, are not underpressure. How far
the inner portions may produce an absorption spec-
trum we cannot discuss at present, but it does not
seem likely that serious errors are thus introduced in
many cases.

In the measures made by Vogel at Potsdam the
substance used for comparison was generally hydro-
gen, the lines of this substance being frequently very
sharp in the spectrum of the stars. The spectrum of
iron can also be used for comparison. The stars
measured by Vogel are forty-seven in number, all
brighter than the third magnitude, this being about
the limit which his instrument could reach. Out of
his forty-seven stars he found four to be affected with
a periodic inequality and therefore to belong to the
class of binary systems to be described in a subsequent
chapter.

About 1892 Belopolsky of Pulkova continued Vo-
gel's work with a much larger instrument, detecting
several other periodic motions. One of his most in-
teresting discoveries was a periodic motion in the star

86 PROPER MOTIONS OF THE STARS

Eta Aquilae corresponding in period to the variations
of its light. He also detected in Castor a variation
with a period of about three days. Another of his
discoveries was the very rapid motion of seventy kilo-
metres per second in the motion of Zeta Herculis.
This, however, is exceeded by the motion of eighty-
seven kilometres which Campbell discovered in a
star of Cepheus. Large though these motions are,
they fall much below those that belong to Arcturus
and 1830 Groombridge.

THE MILLS SPECTROQRAPH OF THE LICK OBSERVATORY

During the last few years another step forward has
been made by Campbell of the Lick Observatory
with the Mills spectrograph. 1 In order to reach

1 It may be. remarked in this connection that Mr. D. O. Mills, the donor of
this instrument, was one of the original trustees charged by Mr. Lick in 1874
with the construction of his Observatory.

MOTION OF THE SUN 87

fainter stars than ever before, a longer exposure of the
photographic plate was necessary. A difficulty is met
with in the prolonged exposure, owing to the change
of temperature of the apparatus, which alters the re-
fracting power of the prisms. This difficulty was
obviated by protecting the apparatus from such
changes. With this great increase in photographic
power and time of exposure it is now possible to
photograph the spectra of stars down to the 6th or
7th magnitude. But it is not all stars that can thus
be measured, because, in many cases, the spectral lines
of the star are not sufficiently sharp and well defined.

When a star is found to be seemingly in motion,
as described in the last section, we may ascribe the
phenomenon to a motion either of the star The Motion
itself or of the observer. In fact no motion of the Sun -
can be determined or defined except by reference to
some body supposed to be at rest. In the case of any
one star, we may equally well suppose the star to be
at rest and the observer in motion, or the contrary.
Or we may suppose both to have such motions that the
difference of the two shall represent the apparent
movement of the star. Hence our actual result in the
case of each separate star is a relation between the
motion of the star and the motion of the sun.

I say the motion of the sun and not of the earth,
because, although the observer is actually on.the earth,
yet the latter never leaves the neighbourhood of the
sun, and, as a matter of fact, the ultimate result in the
long run must be a motion relative to the sun itself, as
if we made our observations from that body. The

88 PROPER MOTIONS OF THE STARS

question then arises whether there is any criterion for
determining how much of the apparent motion of any
given star should be attributed to the star itself and
how much to a motion of the sun in the opposite
direction.

If we should find that the stars, in consequence of
their proper motions, all appeared to move in the
same direction, we would naturally assume that they
were at rest and the sun in motion. A conclusion of
this sort was first reached by Herschel, who observed
that among the stars having notable proper motions
there was a general tendency to move from the direc-
tion of the constellation Hercules, which is in the
.northern hemisphere, towards the opposite constella-
tion Argo, in the southern hemisphere.

Acting on this suggestion, succeeding astronomers
have adopted the practice of considering the general
average of all the stars, or a position which we may
regard as their common centre of gravity, to be at
rest, and then determining the motion of the sun with
respect to this centre. Here we encounter the diffi-
culty that we cannot make any absolute determina-
tion of the position of such a centre. The latj
will vary according to what particular stars
able to include in our estimate. What we can 1
to take all the stars which appear to have a proper
motion, and determine the general direction of that
motion. This gives us a certain point in the heavens
toward which the solar system is travelling, and which
is now called the solar apex, or " the apex of the solar
way."

MOTION OF THE SUN 89

The apparent motion of the stars away from the
apex, and due to this motion of the solar system, is
now called their parallactic motion, to distinguish it
from the actual motion of the star itself.

The interest which attaches to the position of the
solar apex has led a great number of investigators to
determine it. Owing to the rather indefinite charac-
ter of the material of investigation, the uncertainty of
the proper motions, and the additions constantly made
to the number of stars which are available for the
purpose in view, different investigators have reached
different results. Until quite recently, the general
conclusion was that the solar apex was situated some-
where in the constellation Hercules. But the general
trend of recent research has been to place it in or near
the adjoining constellation Lyra. This change has
arisen mainly from including a larger number of stars,
whose motions were determined with greater accuracy.

Former investigators based their conclusions en-
tirely on stars having considerable proper motions,
these being, in general, the nearer to us. The fact
is, however, that it is better to include stars having a
small proper motion, because the advantage of their
great number more than counterbalances the disad-
vantage of their distance.

The conclusions reached by some recent investigat-
ors of the position of the solar apex are as follows :
We call A the right ascension of the apex ; D its
declination.

Prof. Lewis Boss, from 273 stars of large proper
motion, found :

90 PROPER MOTIONS OF THE STARS

A=28 3 . 3 ; D=44.i.

If he excluded the motions of 26 stars which. exceeded
40" per century the result was

^A = 288. 7 ; D = S i . 5 .

A comparison 6^ these numbers shows how much the
result depends on the special stars selected. By
leaving out 26 stars the apex is changed by 5 in R.
A. and 7 in declination.

It is to be remarked that the stars used by Boss
are all contained in a belt four degrees wide, extend-
ing from i to 5 north of the equator.

Dr. Oscar Stumpe, of Berlin, made a list of 996
stars having proper motions between 16" and 128"
per century. He divided them into three groups,
the first including those between 16" and 32" ; the
second between 32" and 64" ; the third between 64"
and 128". The number of stars in each group and
the position of the apex derived from them are as
follows :

Gr. I, 551 stars ; A = 28 7 . 4 ; D = +45.o

II, 339 282.2 43 . 5

III, 106 28o. 2 33.5

Porter, of Cincinnati, made a determination from a
yet larger list of stars with results of the same gen-
eral character.

These determinations have the advantage that the
stars are scattered over the entire heavens, the south-
ern as well as the northern ones. The difference of
more than 10 between the position derived from
stars with the largest proper motions, and from the
other stars, is remarkable.

MOTION OF THE SUN 91

The present writer, in a determination of the pre-
cessional motion, incidentally determined the solar
motion from 2527 stars contained in Bradley's Cata-
logue which had small proper motions, and from
about 600 more having larger proper motions. Of
the latter the declinations only were used. The re-
sults were :

From small motions : A 274. 2 ; D = -{-31. 2
From large motions : 276. 9 3i-4

Quite recently Campbell has made a determination
of the position of apex from the radial motions of 280
stars, mostly measured by himself. The result is :

A= 2 7 7 . 5

D = +20.0

From all these results it would seem that the most
likely apex of the solar motion is toward a point in

Right Ascension, 280
Declination, 35 north

This point is situated in the constellation Lyra,
about 4 from the first-magnitude star Vega. The
uncertainty of the result is as much as this difference,
4 or 5 at least. We may therefore state the con-
clusion in this form :

The apex of the solar motion is in the general direc-
tion of the constellation Lyra, and perhaps near the
star Vega, the brightest of that constellation.

It must be admitted that the wide difference be-
tween the positions of the apex from large and from
small proper motions, as found by Porter, Boss, and
Stumpe, requires explanation. Since the apparent

92 PROPER MOTIONS OF THE STARS

motions of the stars are less the greater their dis-
tance, these results, if accepted as real, would lead to
the conclusion that the position of the solar apex
derived from stars near to us was much farther south
than when derived from more distant stars. This,
again, would indicate that our sun is one of a cluster
or group of stars having, in the general average, a
different proper motion from the more distant stars.
But this conclusion is not to be accepted as real until
the subject has been more fully investigated. The
result may depend on the selection of the stars ; and
there is, as yet, no general agreement among investigat-
ors as to the best way of making the determination.

The next question which arises is that of the ve-
locity of the solar motion. The data for this de-
termination are more meagre and doubtful than those
for the direction of the motion. The most obvious
and direct method is to determine the parallactic
motion of the stars of known parallax. Regarding
any star 90 from the apex of the solar motion as in
a state of absolute rest, we have the obvious rule that
the quotient of its parallactic motion during any
period, say a century, divided by its parallax, gives
the solar motion during that period, in units of the
earth's distance from the sun. In fact, by a motion
of the sun through one such unit, the star would have
an apparent motion in the opposite direction equal to
its annual parallax. If 'the star is not 90 from the
apex we can easily reduce its observed parallactic
motion by dividing it by the sine of its actual dis-
tance from the apex.

MOTION OF THE SUN 93

Since every star has, presumably, a proper motion
of its own, we can draw no conclusion from the
apparent motion of any one star, owing to the impos-
sibility of distinguishing its actual from its parallactic
motion. We should, therefore, base our conclusion
on the mean result from a great number of stars,
whose average position or centre of mass we might
assume to be at rest. Here we meet the difficulty
that the stars measured for parallax are generally
those having a proper motion away from the apex.
This will make the result derived in this way too
large.

A second method is based on measures of the
motion of stars in the line of sight. A star at rest
in the direction of the solar apex would be apparently
moving towards us with a velocity equal to that of
the solar motion. Assuming the centre of mass of
all the stars observed to be at rest, we should get the
solar motion from the mean of all. In the investiga-
tion just referred to, Campbell has derived the ve-
locity, 19.89 kilometres per second, with a probable
error of 1.52 kilometres. A speed of 19 kilometres
per second would carry our system over almost ex-
actly four radii of the earth's orbit in a year, and
we may regard this as the most likely value of the
speed in question.

CHAPTER VII

VARIABLE STARS

And the moist star . . .
Was sick almost to doomsday with eclipse. SHAKESPEARE.

IT is a curious fact that the ancient astronomers,
notwithstanding the care with which they ob-
served the heavens, never noticed that any of the
stars changed in brightness. The earliest record of
such an observation dates from 1596, when the peri-
odical disappearance of Omicron Ceti was noticed.
After this, nearly two centuries elapsed before another
case of variability in a star was recorded. During
the first half of the nineteenth century Argelander so
systematised the study of variable stars as to make it
a new branch of astronomy. In recent years it has
become of capital interest and importance through
the development of spectroscopic research.

Students who are interested in the subject will find
the most complete information attainable in the cata-
logues of variable stars published from time to time
by Chandler in the Astronomical Journal. His third
catalogue, which appeared in 1896, comprises more
than three hundred stars whose variability has been

CLASSES OF VARIABLE STARS 95

well established, while there is always a long list of
''suspected variables "-whose cases are still to be
tried. The number to be included in the established
list is continually increasing at such a rate that it is
impossible to state it with any approximation to ex-
actness. The possibility of such a statement has
been yet further curtailed by the recent discovery at
the Harvard Observatory that certain clusters of stars
contain an extraordinary proportion of variables.
Altogether at the time of the latest publication, 509
such stars were found in twenty-three clusters. The
total number of these objects in clusters, therefore,
exceeds the number known in the rest of the sky.
They will be described more fully in a subsequent
chapter. For the present we are obliged to leave
this rich field out of consideration and confine our
study to the isolated variable stars which are found
in every region of the heavens.

Variable stars are of several classes, which, how-
ever, run into each other by gradations so slight that
a sharp separation cannot always be made between
them. Yet there are distinguishing features, each of
which marks so considerable a number of these stars
as to show some radical difference in the causes
on which the variations depend.

We have first to distinguish the two great classes
of irregular and periodic stars. The irregular ones
increase and diminish in so fitful a way that no law of
their change can be laid down. To this class belong
the so-called " new stars," which at various periods in
history have blazed out in the heavens, and then in

96 VARIABLE STARS

a few weeks or months have again faded away. It is
a remarkable fact that no star of the latter class has
ever been known to blaze out more than once.
This fact distinguishes new stars from other irregu-
larly variable ones.

Periodic stars are those which go through a regular
cycle of changes in a definite interval of time, so that,
Periods after a certain number of days, sometimes
of Variable of hours, the star returns to the same bright-
Stars, ness. But even in the case of periodic
stars, it is found that the period is more or less vari-
able, and in special cases the amount of the variation
is such that it cannot always be said whether we
should call a star periodic or irregular.

The periodic stars show wide differences, both in
the length of the period and in the character of the
changes they undergo. In most cases they increase
rapidly in brightness during a few days or weeks, and
then slowly fade away, to go through the same
changes again at the end of the period. Some stars
are distinguished more especially by their maxima,
or periods of greatest brightness, while others are
more sharply marked by minima, or periods of least
brightness. In some cases there are two unequal
maxima or minima in the course of a period.

Chandler's third catalogue of variable stars gives
the periods of 280 of these objects, which seem to
have been fairly well made out. Mr. A. W. Roberts
has added an important number of southern stars in
a list found in the Astronomical Journal, xxi., p. 84. A
classification of these periods, as to their length, will

PERIODS OF VARIABLE STARS

be interesting. The first set of numbers in the fol-
lowing table, headed C., are the periods of Chandler's
catalogue, the next, headed R., are the additional
periods given by Roberts. There are of periods

Beti

veen 50 ai

100

150

200
250
300
350
400
450
500
550
600

id 100 da
150
200
250
309
350
400

500
550
600
6^0

. 20

... 44

Sum.

73 Sts

irs.

49
50

It will be seen from this that, leaving out the cases
of very short period, the greater number of the
periods fall between 300 and 400 days. From this
value the number falls off in both directions. Only
four periods exceed 500 days, and of these the long-
est is 610 days. We infer from this that there is
something in the constitution of these stars, or in the
causes on which their variation depends, which limits
the period. This limitation establishes a well-marked
distinction between the periodic stars and the irreg-
ular variables to be hereafter described.

Returning to the upper end of the scale, the con-
trast between the great number of stars less than
50 days, and the small number between 50 and 100
seems to show that we have here a sharp line of
distinction between stars of long and those of short
period. But when we examine the matter in detail
we find that the statistics of the periods do not

9 8

VARIABLE STARS

enable us to draw any such line. Among isolated
stars about ten periods are less than one day, and the
number of this class known to us is continually in-
creasing. Forty or fifty are between one and ten
days, and from this point upwards they are scattered
with a fair approach to equality up to a period of 100
days. There is, however, a possible distinction,
which we shall develop presently.

The law of change in a variable star is represented
to the eye by a curve in the following way : We
Light- draw a straight horizontal line A X to re-
curve present the time. A series of equidistant

of a Star. p O i ntS) ^ ^ ^ ^ etc ^ on t hj s J me w {\\ re _

present moments of time. One of the spaces, a, b,
etc., may represent an hour, a day, or a month, accord-

' d

t
}

f ,,<

+*'"'

*~"

ing to the rapidity of change. We take a to represent
the initial moment, and erect an ordinate, a d , of such
length as to represent the brightness of the star on
some convenient scale at this moment. At the second
moment, b, which may be an hour or a day later, we
erect another ordinate, b b' , representing the brightness
at this moment. We continue this process as long
as may be required. Then we draw a curve, repre-
sented by the dotted line, through the ends of all the

TYPES OF VARIABLE STARS 99

ordinates. In the case of a periodic star it is only
necessary to draw the curve through a single period,
since its continuation will be a repetition of its form
for any one period.

We readily see that if a star does not vary, all the
ordinates will be of equal length, and the curve will
be a horizontal straight line. Moreover, the curve
will take this form through any portion of time dur-
ing which the light of the star is constant.

There are three of the periodic stars plainly visible
to the naked eye at maximum, of which Types of
the variations are so wide that they may Variable
easily be noticed by anyone who looks for stars<
them at the right times, and knows how to find the
stars.- These stars are :

Omicron Ceti, called also Mira Ceti.
Beta Persei, or Algol.
Beta Lyre.

It happens that each of these stars exemplifies a
certain type or law of variation.

On August 13, 1596, David Fabricius noticed a
star in the constellation Cetus which was not found
in any catalogue. Bayer, in his Uranomet- The Ceti
ria, of which the first edition was published T 7P e -
in 1 60 1, marked the star Omicron, but said nothing
about the fact that it was visible only at certain times.
Fabricius observed the star from time to time until
1609, but he does not appear to have fully and accur-
ately recognised its periodicity. But so extraordin-
ary an object could not fail to command the attention
of astronomers, and the fact was soon established that

ioo VARIABLE STARS

the star appeared at intervals of about eleven months,
gradually fading out of sight after a few weeks of
visibility. Observations of more or less accuracy
having been made for more than two centuries, the
following facts respecting it have been brought to
light :

Its variations are somewhat irregular. Sometimes,
when at its brightest, it rises nearly or quite to the
second magnitude. This was the case in October,
1898, when it was about as bright as Alpha Ceti. At
other times its maximum brightness scarcely exceeds
the fifth magnitude. No law has yet been discovered
by which it can be predicted whether it will attain
one degree of brightness or another at maximum.

Its minima are also different. Sometimes it sinks
only to the eighth magnitude ; at other times to the
ninth or lower. In either case it is invisible to the
naked eye.

As with other stars of this kind, it brightens up
more rapidly than it fades away. It takes a few
weeks from the time it becomes visible to reach its
greatest brightness, whatever that may be. It gener-
ally retains this brightness for two or three weeks,
then fades away, gradually at first, afterwards more
rapidly. The whole time of visibility will, therefore,
be two or three months. Of course, it can be seen
with a telescope at any time.

The period also is different in a somewhat irregular
way. If we calculate when the star ought to be at its
greatest brightness on the supposition that the inter-
vals between the maxima ought to be equal, we shall

THE ALGOL TYPE 101

find that sometimes the maximum will be thirty or
forty days early and at other times thirty or forty
days late. These early or late maxima follow each
other year after year, with a certain amount of
regularity as regards the progression, though no de-
finable law can be laid down to govern them. Thus,
during the period from 1782 to 1800 it was from
thirteen to twenty-four days late. In 1812 it was
thirty-nine days late. From 1845 to : ^5 6 lt was on
the average about a month too early. Several recent
maxima, notably those from 1895 to 1898, again oc-
curred late. Formulae have been constructed to show
these changes, but there is no certainty that they ex-
press the actual law of the case. Indeed, the proba-
bility seems to be that there is no invariable law that
we can discover to govern it.

Argelander fixed the length of the period at 331.9
days. More recently, Chandler fixed it at 331.6 days.
It would seem, therefore, to have been somewhat
shorter in recent times. It was at its maximum to-
ward the end of October, 1898. We may therefore
expect that future maxima will occur in June, 1902 ;
May, 1903; April, 1904; March, 1905, and so on,
about a month earlier each year. During the few
years following 1903 the maxima will probably not be
visible, owing to the star being near conjunction with
the sun at the times of their occurrence.

The star Algol, or Beta Persei, as it is commonly
called in astronomical language, may, in The Algol
northern latitudes, be seen on almost any Type-
night of the year. In the early summer we should

102 VARIABLE STARS

probably see it only after midnight, in the north-east.
In late winter it would be seen in the north-west.
From August until January one can find it at some
time in the evening by becoming acquainted with the
constellations. It is nearly of the second magnitude.
One might look at it a score of times without seeing
that it varied in brilliancy. But at certain stated in-
tervals, somewhat less than three days, it fades away
to nearly the fourth magnitude for a few hours, and
then slowly recovers its light. This fact was first dis-
covered by Goodrick in 1783, since which time the
variations have been carefully followed. The law of
variation thus defined is expressed by a curve of the
following form :

The idea that what we see in the star is a partial
eclipse caused by a dark body revolving round it, was
naturally suggested even to the earliest observers. But
it was impossible to test this theory until recent times.
Careful observation showed changes in the period be-
tween the eclipses, which, although not conclusive
against the theory, might have seemed to make it
somewhat unlikely. The application of the spectro-
scope to the determination of radial motions enabled
Vogel, of Potsdam, in 1889, to set the question at
rest. His method of reasoning and proceeding was
this:

If the fading out which we see is really due to an
eclipse by a dark body, that body must be nearly or

THE ALGOL TYPE 103

quite as large as the star itself, else it could not cut
off so much of its light. In this case, it is probably
nearly as massive as the star itself, and therefore
would affect the motion of the star. Both bodies
would, in fact, revolve around their common centre
of gravity. Therefore when, after the dark body has
passed in front of the star, it has made one-fourth of
a revolution, which would require about seventeen
hours, the star would be moving towards us. Again,
seventeen hours before the eclipse, it ought to be
moving away from us.

The measurement of six photographs of the spec-
trum, of which four were taken before the eclipses
and two afterward, gives the following results :

Before eclipses : Velocity from the sun equals 39 km. per
second.

After eclipses : Velocity toward the sun equals 47 km. per
second.

These results show that the hypothesis in question
is a true one, and afforded the first conclusive evid-
ence of a dark body revolving around a distant star.
A study of the law of diminution and recovery of the
light during the eclipse, combined with the preceding
motions, enabled Vogel to make an approximate es-
timate of the size of the orbit and of the two bodies.
The star itself is somewhat more than a million of
miles in diameter ; the dark companion a little less.
The latter is about the size of our sun. Their dis-
tance apart is somewhat more than three millions
of miles ; the respective masses are about one-half

104 VARIABLE STARS

and one-fourth that of the sun. These results, though
numerically rather uncertain, are probably near
enough to the truth to show us what an interesting
system we here have to deal with. We can say with
entire certainty that the size and mass of the dark
body exceed those of any planet of our system, even
Jupiter, several hundredfold.

The period of the star is also subject to variations
of a somewhat singular character. These have been
attributed by Chandler to a motion of the whole sys-
tem around a third body, itself invisible. This theory
is, however, still to be proved. Quite likely the planet
which causes the eclipse is not the only one which
revolves around this star., The latter may be the
centre of a system like our solar system, and the other
planets may, by their action, cause changes in the
motion of the body that produces the eclipses. The
most singular feature of the change is that it seems
to have taken place quite rapidly about 1840. The
motion was nearly uniform up to near this date ; then
it changed, and again remained nearly uniform until
1890. Since then not enough of observations have
been published to test the laws of change conclus-
ively.

It is found that several other stars vary in the same
way as Algol ; that is to say, they are invariable in
brightness during the greater part of the time, but
fade away for a few hours at regular intervals. This
is a kind of variation which it is most difficult to dis-
cover, because it will be overlooked unless the ob-
server happens to notice the star during the time

THE ALGOL TYPE 105

when an eclipse is in progress, and is thoroughly
aware of its previous brightness. One might observe
a star of this kind very accurately a score of times,
without hitting upon the right moment. On the
principle that like effects are due to like causes, we
are justified in concluding that in the cases of all
stars of this type, the eclipses are caused by the revol-
ution of a dark body round the principal star.

A feature of all the Algol variables is the shortness
of the periods. The longest period is less than five
days, while three are less than one day. This is a
result that we might expect from the nature of the
case. The nearer a dark planet is to the star, the
more likely it will be to hide its light from an ob-
server at a great distance. If, for example, the
planet Jupiter were nearly as large as the sun, the
chances would be hundreds to one against the plane
of the orbit being so nearly in the line of a distant
observer that the latter would ever see an eclipse of
the sun by the planet. But if the planet were close
to the sun, the chances might increase to one in ten,
and yet further to almost any extent, according to the
nearness of the two bodies.

Still, we cannot set any definite limit to the period
of stars of this type ; all we can say is that, as the
period we seek for increases, the number of stars
varying in that period must diminish. This follows
not only from the reason just given, but from the
fact that the longer the interval that separates the
partial eclipses of a star of the Algol type, the less
likely they are to be detected.

106 VARIABLE STARS

The star Beta Lyrae shows variations quite differ-
ent in their nature from those of Algol, yet having a
The certain analogy to them. Anyone who looks

Beta Lyrae at the constellation Lyra a few nights in
Type * succession, and compares Beta with Gamma,
a star of nearly the same brightness in its neighbour-
hood, will see that while on some evenings the stars
are of equal brightness, on others Beta will be fainter
by perhaps an entire magnitude.

A careful examination of these variations shows us
a very remarkable feature. On a preliminary study,
the period will seem to be six and one-half days.
But, comparing the alternate minima, we shall find
them unequal. Hence the actual period is thirteen
days. In this period there are two unequal minima,
separated by equal maxima. That is to say, the
partial eclipses at intervals of six and one-half days
are not equal. At the alternate minima the star
is half as bright again as at the intermediate minima.

It is impossible to explain such a change as this
merely by the interposition of a dark body, and this
for two reasons. Instead of remaining invariable
between the minima, the variation is continuous dur-
ing the whole period, like the rising and falling of
a tide. Moreover, the inequality of the alternating
minima is against the theory.

Pickering, however, found from the doubling of
the spectral lines that there were two stars revolving
round each other. Then Prof. G. W. Myers, of
Indiana, worked out a very elaborate mathematical
theory to explain the variations, which is not less

THE BETA LYR^E TYPE 107

remarkable for its ingenuity than for the curious na-
ture of the system it brings to light. His conclusions
are these :

Beta Lyrae consists of two bodies, gaseous in their
nature, which revolve round each other, so hear to-
gether as to be almost in contact. They are of
unequal size. Both are self-luminous. By their
mutual attraction they are drawn out into ellipsoids.
The smaller body is much brighter than the other.
When we see the two bodies laterally, they are at
their brightest. As they revolve, however, we see
them more and more end on, and thus the light
diminishes. At a certain point one begins to cover
the other and hide its light. Thus the combined
light continues to diminish until the two bodies move
across our line of sight. Then we have a minimum.
At one minimum, however, the smaller and brighter
of the two bodies is projected upon the larger one,
and thus increases its apparent brilliancy. At the
other minimum, it is hiding behind the other, and
therefore we see the light of the larger one alone.

This theory receives additional confirmation from
the fact, shown by the spectroscope, that these stars
are either wholly gaseous, or at least have self-lumin-
ous atmospheres. Some of Professor Myers's conclu-
sions respecting the magnitudes are summarised as
follows :

The larger body is about 0.4 as bright as the
smaller.

The flattening of the ellipsoidal masses is about
0.17.

io8 VARIABLE STARS

The distance of centres is about i-J- the semi-major
axis of the larger star, or about 50,000,000 kilometres
(say 30,000,000 miles).

The mass of the larger body is about twice that of
the smaller, and 9^- times the mass of the sun.

The mean density of the system is a little less than
that of air. 1

It should be remarked that these numbers rest on
spectroscopic results which need further confirmation.
They are therefore liable to be changed by subse-
quent investigation. What is most remarkable is
that we have here to deal with a case to which we
have no analogy in our solar system, and which we
should never have suspected, had it not been for
observations of this star.

The gap between the variable stars of the Algol
type and those of the Beta Lyrae type is at the pre-
sent time being filled by new discoveries in such a
way as to make a sharp distinction of the two classes
difficult. It is characteristic of the Algol type proper
that the partial eclipses are due to the interposition
of a dark planet revolving round the bright star. But
suppose that we have two nearly equal stars, A and
B, both bright, revolving round their common centre
of gravity in a plane passing near our system. Then
A will eclipse B, and, half a revolution later, B will
eclipse A, and so on in alternation. But when the
stars are equal we may have no way of deciding
which is being eclipsed, and thus we shall have a star
of the Algol type so far as the law of variation is

1 Astrophysical Journal, vol. vii., January, 1898.

THE BETA LYR^E TYPE log

concerned, yet, as a matter of fact, belonging rather
to the Beta Lyrse type. If the velocity in the line of
sight could be measured, the question would be set-
tled at once. But only the brightest stars can, so far,
be thus measured, so that the spectroscope cannot
help us in the majority of cases.

The most interesting case of this kind yet brought
to light is that of Y Cygni. The variability of
this star, ordinarily of the fourth magnitude, was dis-
covered by Chandler in December, 1886. The min-
ima occurred at intervals of three days. But in the
following summer he found an apparent period of
i d, 12 h., the alternate minima being invisible be-
cause they occurred during daylight, or when the
star -was below the horizon. With this period the
times of minima during the summer of 1888 were
predicted.

It was then found that the times of the alternate
minima, which, as we have just said, were the only
ones visible during any one season, did not corre-
spond to the prediction. The period seemed to have
greatly changed. Afterward, it seemed to return to
its old value. After puzzling changes of this sort, the
tangle was at length unravelled by Duner, of Lund,
who showed that the alternate periods were unequal.
The intervals between minima were i d. 9 h., i d.
15 h., i do 9 h., i d. 15 h., and so on, indefinitely.

This law once established, the cause of the anom-
aly became evident. Two bright stars revolve round
their common centre of gravity in a period of nearly
three days. Each eclipses the other in alternation.

no VARIABLE STARS

The orbit is eccentric, and, in consequence, one half
of it is described in a less time than the other half.
If we could distinguish the two stars by telescopic
vision, and note their relative positions at the four
cardinal points of their orbit, we should see the pair
alternately single and double, as shown in the follow-
ing diagram :

A B

Position (i), stars at pericentre *

Interval, 16 hours.

Position (2), A eclipses B

Interval 19 hours.

B A

Position (3), stars at apocentre * *

Interval, 20 hours.

Position (4), B eclipses A . . *

Interval 17 hours.

A B
Position ( i ) is repeated

* *

U Pegasi is a star which proved as perplexing as
Y Cygni. It was first supposed to be of the Algol
type, with a period of about two days. Then it was
found that a number of minima occurred during this
period, and that the actual interval between them was
only a few hours. The great difficulty in the case arises
from the minuteness of the variation, which is but
little more than half a magnitude between the ex-
tremes. The observations of Wendell, at the Harvard
Observatory, with the polarising photometer, enabled
Pickering to reach a conclusion which, though it may
still be open to some doubt, seems to be the most
likely yet attainable. The star is of the Beta Lyrae

THE BETA LYR^E TYPE

type; its complete period is 8 hours 59 minutes 41
seconds, or 19 seconds less than 9 hours ; during
this period it passes through two equal maxima, each
of magnitude 9.3, and two unequal minima, 9.76 and
9.9, alternately.

t^/t ^ ^ 4^ 5^ 6^ 7^ 8^ ^

9.2

^9.3
^9.4
59.5
'9.6
|&7
9.8
^9.9
10.0

V J

LIGHT-CURVE OF U PEQASI, OF THE BETA LYR/E TYPE.

The difference of brightness of these minima, 0.14
mag., is less than the errors which ordinarily affect meas-
ures of a star's magnitude with the best photometers.
Some scepticism has, therefore, been felt as to the
reality of the difference ; which, if it does not exist,
would reduce the periodic time below 4^- hours, the
shortest yet known. But Pickering holds that, in
observations of this kind upon a single star, the
precision is such that the reality of the difference,
small though it be, is beyond serious doubt.

Taking Pickering's law of change as a basis, Myers
has represented the light-curve of U Pegasi on a
theory similar to that which he constructed for Beta
Lyrae. His conclusion is that, in the present case, the
two bodies which form the visible star are in actual
contact. A remarkable historic feature of the case -is

ii2 VARIABLE STARS

that Poincare has recently investigated, by purely
mathematical methods, the possible forms of revolving
fluid masses in a condition of equilibrium, bringing out
a number of such forms previously unknown. One of
these, which he calls the apioidal form, consists of two
bodies joined into one, and it is this which Myers
finds for U Pegasi.

Quite similar to these two cases is that of Z
Herculis. This star, ordinarily of the seventh mag-
nitude, was found, at Potsdam, in 1894, to diminish
by about one magnitude. Repeated observations
elsewhere indicate a period of very nearly four days.
Actually it is now found to be only ten minutes less
than four days. The result was that during any one
season of observation the minima occur at nearly the
same hour every night or day. To an observer
situated in such longitude that they occur during the
day, they would, of course, be invisible.

Continued observations then showed a secondary
minimum, occurring about half-way between the
principal minima hitherto observed. It was then
found that these secondary minima really occur some
two hours earlier than the mid-moment, so that the one
interval would be between forty-six and forty-seven
hours and the other between forty-nine and fifty.
The time which it takes the star to lose its light and
regain it again is about ten hours. More recent ob-
servations, however, do not show this inequality, so
that there is probably a rapid motion of the pericentre
of the orbit.

It will be seen that this star combines the Algol

THE BETA LYR^E TYPE 113

and Beta Lyrae types. It is an Algol star in that its
light remains constant between the eclipses. It is of the
Beta Lyrae type in the alternate minima being unequal.
Duner subjected the observations of this star to a very
careful discussion. His conclusion is as follows :

Z Herculis consists of two stars of equal size, one of which is
twice as bright as the other. These stars revolve around their
common centre of gravity in an elliptic orbit whose semiaxis
major is six times the diameter of the stars. The plane of the
orbit passes through the sun ; the eccentricity is 0.2475, and the
line of apsides is inclined at an angle of 4 to the line of sight
{Astrophysical Journal, vol. i.).

From a careful study, Seliger and Hartwig derived
the following particulars respecting this system :

Diameter of principal star, 15,000,000 kilometres.

smaller 12,000,000

Mass of the larger star, 172 times sun's mass.
Mass of the smaller star, 84 times sun's mass.
Distance of centres, 45,000,000 kilometres.
Time of revolution, 3 d. 23 h. 49 m. 32.7 s.

It must be added that the data for these extra-
ordinary numbers are rather slender and partly
hypothetical.

Beta Lyrae is always of the same brightness at the
same hour of its period, and Algol has always the
same magnitude at minimum. It is true that the length
of the period varies slowly in the case of these stars.
But this may arise from the action of other invisible
bodies revolving around the visible stars. This general
uniformity is in accord with the theory which attributes
the apparent variations to the various aspects in which
we see one and the same pair of revolving stars.

ii4 VARIABLE STARS

Another variable star showing some unique features
is Eta Aquilae. What gives it special interest is that
Variation of spectroscopic observations of its radial mo-
Eta Aquilae. tion show it to have a dark body revolving
round it in a very eccentric orbit, and in the same
time as the period of variation. It might therefore be
supposed that we have here a star of the Algol or
Beta Lyrae type. But such is not the case. There is
nothing in the law of variation to suggest an eclipsing
of the bright star, nor does it seem that the variations
can readily be represented by the varying aspects of
any revolving system.

The orbit of this star has been exhaustively investi-
gated by Wright from Campbell's observations of the
radial motion. The laws of change in the system are
shown by the curves below, which are reproduced, in
great part, from Wright's paper in the Astrophysical
Journal.

ML*

-I-ZO
+ 15
-HO
4- 5

-5
-10
.-]$
.-20

*./

Coi

-A.

20
15"
+ JO
5

-5
-/O

ft**

l w *" 3" ** * 6" 7'

LK3HT- AND VELOCITY-CURVES OF > AQUILyC COMPARED.

RADIAL MOTIONS 115

The lower curve is the light-curve of the star during
a period of 7.167 days. Starting from a maximum
of 3.5 mag., it sinks, in the course of 5 days, to a
minimum of 4.7 m. It was found by Schwab that the
diminution is not progressive, but that a secondary
maximum of 3.8 m. is reached at the end of the second
day. After reaching the principal minimum it rises
rapidly to the principal maximum in 2\ days.

The upper curve shows the radial velocity of the
star during the period of variation. It will be seen
that the epoch of greatest negative velocity, which, re-
ferred to the centre of mass of the system, is 16.2 km.
per second, occurs at the time of maximum brightness.
The greatest positive velocity, 23.9 km., occurs during
the sixth day of the period, just after the time of
minimum brightness.

Finally, the moments of inferior and superior con-
junction of the dark body with the bright one are
neither of them an epoch of minimum brightness,
which takes place half-way between the two.

The case of Delta Cephei is not dissimilar to that
of Eta Aquilae. This star is regularly variable in a
period of 5.366 days. Its magnitude at maximum
is 3.7 ; at minimum 4.9. It was found by Belopolsky
to be a spectroscopic binary with a period the
same as that of its variation of the light. He finds
that, as in the case of the other star, there appears
to be nothing in the nature of an eclipse. The
orbit is, however, very eccentric. The epoch of
minimum is one day earlier than that of perihelion
passage.

n6 VARIABLE STARS

Its slight variation, as in the case of Eta Aquilae, is
much more rapid during the increase than during the
decrease. From Schur's table it seems that the whole
time of rise, from minimum to maximum, is 1.6 d.,
which is less than one-third the entire period. More-
over, the larger part of this change takes place in less
than a day.

A classification of variable stars, based on the
period of variation and the law of change, was pro-
Ciassifica- Psed by Pickering. It does not, however,
tionofVari- seem that a hard-and-fast line can yet be
able stars. drawn between different types and classes
of these bodies, one type running into another, as we
have found in the case of the Algol and Beta Lyrae
types. Yet the discovery of the cause of the variation
in these types makes it likely that a division into four
great classes, dependent on the cause of variation, is
possible. These classes are :

(i) Stars, or systems appearing to us as a single
star, of which the apparent variability arises solely or
mainly from the rotation of the system as a whole, or
from the revolution of its components around each
other. In this case the variations of light are purely
the effect of perspective, arising from the various as-
pects which the system presents to us during the
revolution of its components. There is no real varia-
tion either in the constitution of the star or in the
actual amount of light which it emits. If we could
change our point of view so that the plane of the orbit
of an Algol star no longer passed near our system, the
star would cease to appear variable. Under the same

CLASSIFICA TION 1 1 7

circumstances the apparent variations of a star of the
Beta Lyrae type would be smaller than they are, and
would disappear entirely if the axis of rotation were
directed toward our system. The stars of this class
are also distinguished by the uniformity and regularity
with which they go through their cycle of change.

(2) The second class comprises stars in which the
changes of light are real and arise from some cycle of
change going on in the star, but -which may be due to
the action of an external body. This class may be
divided into two or three subclasses, as has been done
by Pickering, depending on the length of the period
and the character of the variation. But it does not
appear that we can yet sharply define the subdivision,
because, as already stated, one class runs into the
other by insensible gradations. Perhaps the best de-
fined class is that of the Omicron Ceti type. There
are certain general laws, of variation and irregu-
larities of brightness which stars of this class go
through. Starting from the time of the minimum, the
increase of light-is at first very slow. It grows more
and more rapid as the maximum is approached, near
which there may be as great an increase in two or three
days as there formerly was in a month. The diminu-
tion of light is generally slower than the increase. The
magnitude at corresponding times in different periods
may be very different. Thus, as we have already re-
marked, Omicron Ceti is ten times as bright at some
maxima as it is at others. The periods also, so far as
they have been made out, vary more widely than those
of stars of the other types. The most remarkable

1 1 8 VARIABLE STARS

feature of this type is found in its spectrum. Nearly
all these stars have spectra of the third type in which
the hydrogen lines are bright at the time of maximum.
So well defined is this peculiarity that stars are
recognised as variable at the Harvard Observatory
merely by this feature of the spectrum.

From what has been said, it will be seen that, al-
though a sharp line cannot be drawn, there seems to
be some distinction between the stars of short and
long periods. The number of stars which have been
known to belong to the first class is quite small, only
about fifteen all told. On the other hand, there are
still left some stars having a period less than ten days,
which are otherwise not distinguishable from the
Omicron Ceti type.

The discovery that Delta Cephei and Eta Aquilae
have dark bodies revolving around them in a period
equal to that of the variation of light, suggests the
idea that in perhaps all this class of stars the variations
of light are due to the varying action of a revolving
planet as it moves around in a very eccentric orbit.

The periodic stars of short period which have not
been recognised as of the Algol or Beta Lyrae type
form an interesting subject of study. Although the
separation between them and the stars of long period
is not sharp, it seems likely to have some element of
reality in it. But no conclusions on the subject can
be reached until the light-curves of a large number of
them are carefully drawn ; and this requires an
amount of patient and accurate observation which can-
not be carried out for years to come.

SPECTRA 119

(3) The third class comprises stars subject to small
and irregular but frequently recurring fluctuations of
light. The range of variation is commonly only a
fraction of a magnitude. The following are the most
noteworthy examples of this class :

of Cassiopeae, range in mag. 2.2 to 2.8
p Persei, " " " 3.4 " 4.2

tfOrionis, " " " i.o " 1.4

a Herculis, " " " 4.6 " 5.4 ,
/* Cephei, " " " 4.0 " 5.0
ft Pegasi, " " " 2.2 " 2.7

(4) The fourth class are the " novae," or new stars,
which, so far as is known, blaze out but once in history.
They will be described in the next chapter.

It might be supposed that the changes in the light
of the variable stars, at least in those cases where they
are not caused by a mere partial eclipsing spectra
of the star, would be accompanied by wide of Variable
changes in their spectra, following some de- stars,

finable law. Many studies have been made on this
subject, but it is difficult to formulate any general con-
clusion from them. The investigation is a difficult one,
because the most interesting cases are those in which
the diminution of light at minimum is very great, and
the spectrum cannot be well studied. The star Omi-
cron Ceti has perhaps been more carefully studied from
this point of view than any other. Campbell found that
near the time of maximum, the bright hydrogen linec
Hy was very strong and overexposed on all the
plates. He found that two minutes sufficed to obtain
an impression of this line, at a stage of brightness

I2O

VARIABLE STARS

when an hour is wanted for the rest of the spectrum.
Under the same circumstances, the line Htf is triple.
The central component of this triple system is much
stronger than the two others, which are about equal.
As the spectrum grows fainter, the components
occupy nearly the position of certain iron lines, but
nothing definite can be ascertained about them.

SPECTRUM OF O CETI NEAR THE MAXIMUM OF 1897, PHOTOGRAPHED LY FATHER
SIDGREAVES AT THE STONYHURST COLLEGE OBSERVATORY.

The question whether certain stars vary in colour
without materially changing their brightness has some-
Suspected times been raised. This was at one time
y*" 3 ! 10 ! 18 supposed to be the case with one of the

in the Colour ri

ofstars. stars of Ursa Major. This suspected vari-
ation has not, however, been confirmed, and it does
not seem likely that any such changes take place in
the colour of stars not otherwise variable.

CHANGES OF COLOUR 121

All the variations we have hitherto considered take
place with such rapidity that they can be observed by

comparisons embracing but a short interval ,

** . Possible Sc-

ot time a few days or months at the out- C uiar Varia-

side. A somewhat different question of tions in the

11 i /v TV/T Brightness

great importance is still lett open. May not of stars
individual stars be subject to a slow varia-
tion either in their colour or their brightness, which are
sensible in the course of only one generation of men,
but admit of being brought out by a comparison of the
brightness of the stars at widely distant epochs ? Is
it certain that, in the case of stars which we do not
recognise as variable, no change has taken place since
the time of Hipparchus and Ptolemy ? This question
has been investigated by C. S. Pierce and others.
The conclusion reached is that no real evidence of any
change can be gathered. The discrepancies are no
greater than might arise from errors of estimates.

There is, however, an aspect of the question which is
of great interest and has been much discussed in re-
cent times. In several ancient writings the colour of
Sirius is described as red. This fact would, at first
sight, appear to afford very strong evidence that,
within historic times, the colour of the brightest star in
the heavens has actually changed from red to bluish
white.

Two recent writers have examined the evidence on
this subject most exhaustively and reached opposite
conclusions. The first of these was Prof. T. J. J.
See, who collated a great number of cases in which
Sirius was mentioned by ancient writers as red or fiery,

122 VARIABLE STARS

and thus concluded that the evidence was in favour of
a red colour in former times. Shortly afterwards,
Schiaparelli examined the evidence with equal care
and thoroughness and reached an opposite conclusion,
showing that the terms used by the ancient authors
which might have indicated redness of colour were
susceptible of other interpretations ; they might mean
fiery, blazing, etc., as well as red in colour, and were
therefore probably suggested by the extraordinary
brightness of Sirius and the strangeness with which it
twinkled when near the horizon. In this position a
star not only twinkles, but changes its colour rapidly.
This change is not sensible in the case of a faint star,
but if one watches Sirius when on the horizon, it will
be seen that it not only changes in appearance, but
seems to blaze forth in different colours.

It seems to the writer that this conclusion of
Schiaparelli is the more likely of the two. From what
we know of the constitution of the stars, a change in
the colour of one of these bodies in so short a period of
time as that embraced by history is so improbable as
to require much stronger proofs than any that can be
adduced from ancient writers. In addition to the
possible vagueness or errors of the original writers,
we have to bear in mind the possible mistakes or
misinterpretations of the copyists who reproduced
the manuscripts.

CHAPTER VIII

NEW STARS

It may be glorious to write

Thoughts that shall glad the two or three

High souls, like those far stars that come in sight

Once in a century. LOWELL

THE stars considered in the preceding chapter go
through their changes of light in a limited and
generally more or less regular period, so that a predic-
tion of their brightness at future epochs is in most
cases possible. They are distinguished by the re-
markable fact, pointed out at the beginning of the
chapter, that the period seems to be limited, none so
long as two years being yet known.

New stars, or " Novae " as they are frequently
called, are distinguished from the irregularly variable
stars already described by their blazing forth, so far
as is yet known, only once in the period of their his-
tory.

The limitation of the period seems to form a well-
marked distinction between periodic stars and the
irregularly variable ones now to be considered, and
to indicate some radical difference in the cause of
variability.

123

i2 4 NEW STARS

The most remarkable among these stars is un-
doubtedly Eta Argus, which, though now invisible to
the naked eye, was, at various times between 1830 and
1850, of the first magnitude. It falls so closely on a
line between the new or temporary stars and those
which are irregularly variable that it may form a
distinct class. Being in 58 of south declination it
is not visible except in latitudes south of 32. For
this reason it could not be made a subject of ob-
servation in northern European countries. Of the
greatest interest is the question whether it was
visible in early historic times. On this question no
decisive evidence can be gathered. The catalogues
of Ptolemy and Ulugh Beigh are among the earlier
authorities which we consult on the subject. Much
confusion, however, is found in the data to be consult-
ed. In Halma's edition of Ptolemy 's catalogue, two
stars in the constellation Argo are marked as having
the Bayer letter Eta. But neither of these is near the
position of the star under consideration. In fact,
Ptolemy's constellation Argo seems scarcely to ex-
tend as far east as the point in question. The same
remark applies to the mediaeval catalogue of Ulugh
Beigh. The only conclusion we can draw on the
subject is that the star was probably not so conspicu-
ous in early historic times as to excite the attention
of observers.

On Bayer's charts, published about 1600, there is
a star marked Eta, but this is nowhere near the place
of the modern Eta, nor is there any star shown in the
position of the latter. The fact appears to be that

ETA ARGUS 125

Bayer's maps of this constellation are so erroneous that
little correspondence can be found between his figures
and the heavens, and the certain identification of any
particular star scarcely seems possible, except in the
case of Canopus and possibly a few other bright ones.
Near the position of the modern Eta are several small
stars marked d, but from what has been said we have
no reason to identify these with the star in question.
The first authentic observation of the star is found
in Halley's catalogue, made at St. Helena in 1677,
where it appears as of the fourth magnitude. The next
observation is by Lacaille, who observed it at the Cape
of Good Hope about 1750. In the catalogue at the
end of his Ccelum Australe Stelliferum, the star is
given as of the second magnitude ; but in the original
observations it is marked of magnitude 2.3. It may
be added that Lacaille was the first one to assign
the symbol Eta. From a remark at the end of the
catalogue, it seems that he assigned these symbols in
accordance with Bayer only when the Bayer stars
could be identified, but it would seem that there
could have been few such identifications in Argo. In
catalogues made between the years 1822 and 1832
it still appears as of the second magnitude ; whether
this magnitude was an independent one or merely
taken from Lacaille may be an open question, but
we cannot suppose that the variation from Lacaille's
estimate was at all striking. A traveller named
Birchell noted it as of the first magnitude in 1827,
but this seems doubtful in view of the records of
other observers.

126 NEW STARS

Our next authority on the subject is Sir John
Herschel, who, during his residence at the Cape of
Good Hope, in 1834, noted Eta Argus as of mag-
nitude between first and second. It remained with-
out exciting any suspicion of change to near the end
of 1837. In December of this year Herschel's as-
tonishment was excited by the appearance of " a new
candidate for distinction among the very bright stars
of the first magnitude, in a part of the heavens with
which being perfectly familiar, I was certain that no
such brilliant object had before been seen." This was
soon found to be identical with Eta Argus, of which the
light had nearly trebled. It decidedly surpassed Pro-
cyon, Alpha Orionis, and even Rigel, which was nearest
to it. It continued to increase until the beginning of
January, 1838, when it was equal to Alpha Centauri.
Then it began slowly to fade, but on April i4th, which
seems to have been the date of Herschel's last observa-
tion, it was still about equal to Aldebaran, and therefore
of the first magnitude. It seems to have blazed up
again, according to the testimony of observers, in
1843, when it was fully as bright as Canopus, and
could not therefore have been far below Sirius. It
fluctuated during the following ten years, and then
began to fade away slowly. In 1868 it was estimated
by Mr. Tebbut as only of the sixth magnitude, and
gradually disappeared from vision by the naked eye
in the year following. During the last fifteen or
twenty years it has generally been of the seventh
magnitude, or fainter, and there is no evidence of any
approaching renewal of its bright stage of half a

NEW STARS 127

century ago. I quote the following list of deter-
minations from Mr. R. T. A. Innes (M. N. R. A. S.,
lix., 570.)

Year 1886. 2 Mag. 7.60 (Finlay)

1896. 4 7.58 (Innes)

1897. 2 " 7.60 (See)

1899. 5 " 7.71 (Innes)

We now pass to the class of new or temporary
stars properly so called. A distinguishing feature of
a star of this class is that it blazes up, so far as is
known, only once in the period of its history, then
gradually fades away to its former magnitude, which
it commonly retains with, so far as is yet known,
little or no subsequent variation.

It was formerly supposed that stars of this class
were new creations which went out of existence after
a span of life which would have been brief even for
a human being, much less for a star. It is hardly
necessary to say that such a view as this can find
no place in modern science.

Miss Clerke, in her System of the Stars, gives a list
of ten such stars which appeared between B.C. 134
and the end of the fifteenth century. Accepting all
these as real there would be an average of one such
star in about 160 years. In the few cases where
the duration of the appearance is given it varies
from three weeks to eight months. The following
list of such stars which have appeared since 1500
is compiled from the circulars of the Harvard Ob-
servatory :

128

NEW STARS.

YEAR.

CONSTELLA-
TION.

POSITIO

N, IQOO.

MAG.

DISCOVERER.

R. A.

DEC.

H. M.

1572. .

Cassiopeia.

o. 19.2

+63 36'

Br.

Tycho.

1600.

Cygnus.

2O.I4.I

+37 43

Jan son.

1604.

Ophiuchus.

17.24.6

21 24

Br.

Kepler.

1670.

Vulpecula.

19-43-5

4-27 4

Anthelm.

1848. .

Ophiuchus.

I6.53-9

12 44

Hind.

1860. .

Scorpius.

I6.II.I

22 44

Auvvers.

1866. .

Corona Bor .

IS-55-3

-j-26 12

Birmingham.

1876. .

Cygnus

21.37.8

+ 42 23

Schmidt.

1885 .

Andromeda.

0.37.2

+40 43

Hartwig.

1887. .

Perseus.

I-55- 1

+56 15

Fleming.

189 i. .

Auriga.

5- 2 5.6

+ 30 22

Anderson.

1893, .

Norma.

15.22.2

50 I 4

Fleming.

1895. .

Carina.

ii. 3.9

61 24

Fleming.

1895.

Centaurus.

13-34-3

-31

Fleming.

1898. .

Sagittarius.

18.56.2

-13 8

Fleming.

1901.

Perseus.

3.22

4-44 o

Anderson.

Among all these the first, sometimes called Tycho's
Star, was the most brilliant. It was first noticed on No-
vember 7, I572, 1 by Lindaeur at Winterthur. It was
first seen by Tycho Brahe four days later, when it
had attained the first magnitude. It continued to
increase in brilliancy, at length becoming equal to
Venus and visible in full daylight. In December it
began to diminish, faded gradually away, and finally
disappeared from view in May. As the telescope
was then unknown, it was impossible to follow it
further.

During the period of its visibility Tycho not only
made all the observations he was able to on its ap-
pearance, but measured its position relative to
other stars, It is now found that a star of magni-

1 System of Stars, page 97.

NEW STARS 129

tude 10.5 is situated within a minute of the posi-
tion derived from Tycho's observations. In view of
this fact there is a strong presumption that this is
the star. It has therefore been watched occasionally
to detect evidences of variability, but, although some
change was strongly suspected by Hind, it does not
appear that observations upon it have been made
systematically enough to establish any actual change
at the present time.

Of Janson's Star of 1600 little is known; a star
called P Cygni is supposed to be identical with it, but
on what authority I do not know.

The star of 1604 in Ophiuchus has a history not
unlike that of Tycho. It was first seen in October,
when it had attained the first magnitude. In a few
days it became as bright as Jupiter, but began to fall
off during the winter. It seems to have been re-
markable for its duration, having been visible to the
naked eye during the whole year 1605. Early in
1606 it disappeared from view. A very full history
of this star has been left by Kepler.

Nearly two centuries now elapse before we have
any record of another appearance of the kind. On
April 28, 1848, Mr. Hind, then in charge of a private
observatory in London, noticed a star of between the
fourth and fifth magnitude where none had been
seen April 5th. For some days it seems to have fluctu-
ated between the fifth and sixth magnitudes. Soon
it began to diminish and fade away year after year
until it sank to magnitude 12.5, at which it seems to
have remained for more than thirty years.

130 NEW STARS

The Auwers Star of 1860 was discovered in the
cluster Messier 80. It only reached the seventh
magnitude, soon faded away, and has not since been
recognised. It is mainly of interest in connection
with the recent discovery at the Harvard Observatory
of great numbers of variable stars in clusters.

The star T Cororiae, which appeared in May, 1866,
attained the greatest brilliancy of any new star since
that of Kepler, having been nearly or quite of the
second magnitude. One of the most interesting
questions connected with it is the rapidity with which
such a star may blaze up, a question which is not yet
fully settled. The facts on record are that on the
1 2th and i3th of May it was remarked independently
by at least five observers in Europe and America.
On May i2th Schmidt of Athens, who was scanning
the heavens, asserts in the most positive manner that
the star could not have been visible without his
having noticed it. If we accept this negative testi-
mony as conclusive the star must have risen from
some low magnitude, probably fainter than the fifth,
to the second, within a few hours.

The star is of special interest as the first of which
the light could be analysed with the spectroscope.
This was done by Mr. Huggins on the first evening
after he received notice of the strange object. He
found the spectrum to be a singularly composite one,
leading to the conclusion that two distinct spectra
were superimposed, and that the light had emanated
from two different sources, each forming its own
spectrum. The principal spectrum was analogous

NEW STARS 131

to that of the sun. It indicated light emitted by an
incandescent photosphere which suffers partial ab-
sorption by passing through a vaporous atmosphere.
Beginning at the red end of the spectrum the first
dark line was a little more refrangible than the hydro-
gen line C. Next came a shaded group of lines,
then a faint line coincident with D. In the higher
regions of the spectrum, the lines were stronger and
extended as far as the spectrum could be traced.

The second spectrum was composed of five bright
lines. One of these seemed to coincide with line C ;
still brighter was one coinciding with F, then two
fainter lines. The fifth bright line was near G. All
the bright lines were much more apparent than the
continuous spectrum. It would follow that the gas
which emitted them must have had a temperature
higher than that of the stellar photosphere from
which the light forming the other spectrum emanated.

Mr. Huggins compared the spectrum of the star
with that of hydrogen. It seemed quite apparent
that two of the brighter lines were entirely co-
incident with the lines C and F of hydrogen. The
conclusion, therefore, was that the great brilliancy of
the star was due to an outburst of incandescent
hydrogen, giving rise to a volume of flame of such
magnitude as to be visible at the vast distance of our
system.

The star faded away with great rapidity. In
twelve days it fell from the second to the eighth
magnitude, so that no opportunity was afforded for a
continuous study of its spectrum.

132 NEW STARS

The stars which have subsequently appeared have
naturally been studied by a greater number of ob-
servers and with much detail. Among them Nova
Aurigae, which appeared in February, 1892, long
held the first place, on account of the length of time
during which it remained bright enough for favourable
examination. A citation of the observations and re-
searches would fill a small volume. Within our limited
space we can only summarise the principal conclusions
of Campbell, Sidgreaves, and Vogel.

The star was first noticed by Dr. Anderson, a
diligent watcher of the heavens, at Edinburgh about
the end of January, 1892. As it has been in some
noteworthy cases since, the region occupied by the
star was found to have been photographed at the
Harvard Observatory before the star was noticed by
Dr. Anderson. On November 2, 1891, the star was
not shown on a plate where those of the eleventh mag-
nitude were impressed. On December ist it would
have been shown had it been brighter than the sixth
magnitude. The first plate on which it was found
bore the date December i6th, when the magnitude
was the sixth. Two days previously it was invisible
on a plate taken at a European observatory. It must
therefore have blazed up within a period of two or
three days. It seemed to vary from night to night
at least the magnitudes assigned by the observers
were very different. Early in March it began to
fade rapidly. By the middle of the month it had
sunk to the eighth magnitude, and, by the end, to the
twelfth. For several months it was supposed to

NOVA AURIGA 133

have sunk almost out of sight, as the minutest object
visible in the most powerful telescopes. But in
August new interest was excited by its again blazing
up to the ninth magnitude. From this time it seems
to have fluctuated in a very irregular way for nearly
a year before it finally sunk into its former in-
significance.

Its spectrum was of course photographed by every
astronomer who had the means of doing so. Lock-

SPECTRUM OF NOVA AURIQ/E PHOTOGRAPHED BY CAMPBELL

yer and Huggins in England, Vogel in Germany,
and Campbell at Mount Hamilton are the investi-
gators on whom we shall mainly depend. Lockyer
found that all the lines in the spectrum were broad,
although they showed perfectly sharp in the spectrum
of Arcturus. There was no falling off of intensity
at the edges of the bright lines. The hydrogen lines
and the K line of calcium were very bright and accom-
panied by dark lines on their more refrangible sides.
As Campbell had the best optical means for photo-
graphing the spectrum, we reproduce one of his

.134 NEW STARS

photographs, taken on February 28th. It is accom-
panied by an intensity curve, showing the intensity of
the light in the various parts of the spectrum by the
length of the ordinate with greater accuracy than it
can be inferred from the figure of the spectrum. The
numbers on the spectrum are the wave-lengths in
millionths of a millimetre.

The apparent superposition of at least two spectra,
one continuous with dark lines, the other consisting
of bright lines, was noticed both by Campbell and
Vogel. The latter found the spectrum to extend far
into the violet, showing many bright and broad lines,
among which the whole range of hydrogen lines were
especially noticeable ; but on the more refrangible
side most of these were broad, dark lines, whose
distances from the bright lines increased in going
toward the violet in proportion to the increasing
dispersion of the prism, and whose identity with the
bright lines is thereby established. On February
2Oth Vogel compared the spectrum with that of hy-
drogen, showing with seeming certainty that this
element was principally concerned in forming the
spectrum. The main difference was that the lines
were bright in the spectrum of the star and were per-
ceptibly brighter and more sharply defined on the
side toward the violet than on that toward the red.
Besides being three or four times brighter than the
lines of hydrogen, they were displaced strongly toward
the red, showing a rapid motion away from the earth.
On the other end the dark lines which accompanied
the bright ones were so much displaced toward the

NOVA AURIGA 135

violet that they could be readily distinguished. A
remarkable fact noticed by Vogel was that a number
of the lines coincided with those of the sun's chromo-
sphere as catalogued by Young.

On March igth the continuous spectrum was very
faint and fell off rapidly beyond F. The latter was
now the brightest line in the spectrum, but several
were occasionally glimpsed in the green.

After the star again brightened up in September
there was a change in the spectrum, which now con-
sisted principally of a bright line in the green and
a faint continuous spectrum. This continued without
change until March, 1893. The lines coincided with
the brighter ones in the spectrum of the nebulae, but
there was also a very faint continuous spectrum. It
was noted by other observers that the spectrum now
became identical with that of a planetary nebula.

The remarkable opposite displacement of the lines
during the early period of the star's visibility is shown
in the following condensed summary of the results of
Vogel's measures: Taking the first four bright lines
of hydrogen and calcium the following velocities
away from the earth were derived from the four
lines :

K .......... 243 kilometres per second

H .......... 265

H 5a ........ 402

H v ......... 457

It will be seen that the calcium lines agree fairly
well in giving a motion of 250 kilometres, while the
hydrogen lines, especially H , give a considerably

136 NEW STARS

larger motion, the mean of the two being 430 kilo-
metres per second.

Very different was it with the accompanying dark-
line spectrum. The two hydrogen lines agreed in
giving a motion toward the earth of about 780 kilo-
metres per second. The difference of these two
results is enormous, more than 600 English miles
per second.

The problem of reconciling these rapid motions
with any easily conceivable constitution of the body
or bodies was no easy one, and the proposed so-
lutions can hardly be considered as better than
speculations. The view most generally received
was that two bodies had suddenly approached very
closely together, perhaps come into collision, and
then separated. While this view is by no means
impossible, it is far from being established. The
great change in the character of the spectrum, while
not conclusive against it, certainly seems to throw
difficulties in the way of its reception. The history
of the star leaves us in great doubt on the question
whether, even if the displacement of the lines was
due to a rapid motion, the latter was the integral
motion of a body. It might have been only that
of an incandescent gas escaping from under press-
ure, in a direction from our system, in fact, an erup-
tion of hydrogen and calcium vapours. If these
vapours, after cooling, fell back again in such a way
as to cut off the light of the brighter region be-
yond, they would absorb the dark lines and give the
spectrum of a dark body moving toward us.

CAUSE OF NEW STARS 137

The most recent investigations showing to what
changes the form, position, and brightness of spectral
lines are subject through changes in the physical
condition of the bodies which emit the light lead to
great caution in attributing the displacement of
broadened lines in any spectrum to motion.

The fact that these objects blaze up only once
in their history shows that the phenomenon is due
to some cataclysm of a rather extraordinary kind.
The first and most interesting question raised by this
fact is whether one star is more likely to be subject
to such a cataclysm than another. If new stars were
known to vary, or to have any special kind of spec-
trum before their sudden outburst, we should know
that the latter was a catastrophe to which only a
particular kind of star is subject. If we could find
no peculiarity in the spectrum of the star we should
conclude that the catastrophe was due to some ex-
ternal cause. But unfortunately we have thus far
no record of any new star before its appearance
except, in a very few cases, its position in the heavens.
It is true that the star may be studied after it has
settled down again, but if the catastrophe was due to
an external cause, we have no reason to suppose that
it had relapsed to its former condition. Quite likely
the cataclysm might have made a permanent change
in its constitution.

Perhaps the most natural theory at first sight is
that the outburst is due to a collision. It seems
probable that stars like our sun, which are in a state
of considerable condensation, have somewhat the

138 NEW STARS

character of masses of gas confined under enormous
pressure, as if they were hollow globes of highly
heated and compressed gas. We do not mean by this
that the shell is solid ; what is possible is that it is
composed of divided matter probably denser than
the gases below, and compressing the latter by its
weight rather than by its tension. If, by the fall of
a foreign body, an opening is suddenly made in the
shell, the interior gases will burst forth. What mag-
nitude the outburst might assume it is impossible
to say, and cautious thinkers will decline to accept
this or any other solution until we have had more ex-
perience on the subject.

A general fact that seems supported by the most
recent observations is that after their outbursts of
light these bodies settle down to a nebular condition.
This was the case with Nova Aurigae, and the recent
Nova Aquilae of 1900. Campbell found the spec-
trum of the latter to consist of extremely faint con-
tinuous light in the green, and three bright bands in
the positions of the three nebular lines.

On the night of February 21-22, 1901, Dr. Ander-
son of Edinborough noticed a previously unknown
The New star ^ magnitude 2. 7, in the constellation
star of 1901 Perseus. In the course of the next two
m Perseus. ^ avs ^ i ncreasec [ so rapidly as to become

about the third brightest star in the sky, being a
little brighter than Capella. Then it began slowly
to fade away. Early in March it was again of the
third magnitude, and before the middle of April had
dropped to the fifth.

NOVA PER SET 139

It seems to have blazed out with extraordinary
rapidity. It happened most fortunately that the
region had been photographed at the Harvard Ob-
servatory several times during the month of Febru-
ary, the last photograph having been taken on the
iQth. The plate showed stars as faint as the eleventh
magnitude. It must therefore have risen from some
magnitude below the eleventh to the first within
about three days. This difference corresponds to an
increase of the light ten thousandfold.

Its spectrum shows the mixture of dark and bright
bands characteristic of new stars. But, in the begin-
ning, Campbell found that the sodium lines were faint
and dark. He was thus enabled to determine the
radial velocity of the star, which was six kilometres
per second away from the sun.

Nova Persei, as the star will hereafter be called, is
the brightest new star that has been recorded since
the time of Kepler. But it is not impossible that,
before the heavens were so carefully watched by ob-
servers, such an object might have reached an equal
degree of brightness without exciting notice. The
complete history of this star cannot yet be written,
and there is no reason to suppose that it will differ
very widely from that of Nova Aurigae. Indeed on
June 25, 1901 Professor Pickering reported that its
spectrum had been gradually changing into that of a
gaseous nebula.

CHAPTER IX
THE PARALLAXES OF THE STARS

These mathematic men have thoughts that march
From sphere to sphere and measure out the blue
Of infinite space like roods of garden ground.

BLACKIE.

IT needs only the most elementary conceptions of
space, direction, and motion to see that, as the
earth makes its vast swing from one extremity of its
orbit to the other, the stars, being fixed, must have an
apparent swing in the opposite direction. The seem-
ing absence of such a swing was in all ages before our
own one of the great stumbling-blocks of astronomy.
It was the base on which Ptolemy erected his proof
that the earth was immovable in the centre of the
celestial sphere. It was felt by Copernicus to be a
great difficulty in the reception of his system. It led
Tycho Brahe to suggest a grotesque combination of
the Ptolemaic and Copernican systems, in which the
earth was the centre of motion, round which the sun ;
revolved, carrying the planets with it.

With every improvement in their instruments, as-
tronomers sought to detect the annual swing of the
stars. Each time that increased accuracy in observa-

140

THE PARALLAXES OF THE STARS 141

tions failed to show it, the difficulty in the way of the
Copernican system was heightened. How deep the
feeling on the subject is shown by the enthusiastic
title, Copernicus Triumphans, given by Horrebow to
the paper in which, from observations by Roemer, he
claimed to have detected the swing. But, ^alas,
critical examination showed that the supposed in-
equality was produced by the varying effect of the
warmth of the day and the cold of the night upon
the rate of the clock used by the observer, and not by
the motion of the earth.

Hooke, a contemporary of Newton, published an
attempt to determine the parallax of the stars, under
the title An Attempt to Prove the Motion of the Earth,
but Jiis work was as great a failure as that of his pre-
decessors. Had it not been that the proofs of the
Copernican system had accumulated until they became
irresistible, these repeated attempts might have led
men to think that perhaps, after all, Ptolemy and the
ancients were somehow in the right.

The difficulty was magnified by the philosophic
views of the period. It was supposed that Nature
must economise in the use of space as farmer would
in the use of valuable land. The ancient astronomers
correctly placed the sphere of the stars outside that of
the planets, but did not suppose it far outside. That
Nature would squander her resources by leaving a
vacant space hundreds of thousands of times the ex-
tent of the solar system was supposed contrary to all
probability. The actual infinity of space ; the con-
sideration, that one had only to enlarge his conceptions

1 42 THE PARALLAXES OF THE STARS

a little to see spaces a thousand times the size of the
solar system look as insignificant as the region of a
few yards round a grain of sand, does not seem to
have occurred to anyone.

Considerations drawn from photometry were also
lost sight of, because that art was still undeveloped.
Kepler saw that the sun might well be of the nature of
a star ; in fact, that the stars were probably suns.
Had he and his contemporaries known that the light of
the sun was more than ten thousand million times that
of a bright star, they would have seen that if placed
at one hundred thousand times its present distance
the sun would still shine as a bright star. If, then, the
stars are as bright as the sun, they must be one hun-
dred thousand times as far away, and their annual
parallax would then have been too small for detection
w r ith the instruments of the time. Such considerations
as this would have removed the real difficulty.

The efforts todiscover stellar parallax were,of course,
still continued. Bradley, about 1740, made observa-
tions on Gamma Draconis, which passed the meridian
near his zenith, with an instrument of an accuracy be-
fore unequalled. He thus detected an annual swing
of 20" on each side of the mean. But this swing did
not have the right phase to be due to the motion of
the earth ; the star appeared at one or the other ex-
tremity of its swing when it should have been at the
middle point, and vice versa. What he saw was really
the effect of aberration, depending on the ratio of the
velocity of the earth in its orbit to the velocity of light.
It proved the motion of the earth, but in a different

FIRST MEASURES OF PARALLAX 143

way from what was expected. All that Bradley could
prove was that the distances of the stars must be
hundreds of thousands of times that of the sun.

An introductory remark on the use of the word
parallax may preface a statement of the results of re-
searches now to be considered.

In a general way, the change of apparent direction
of an object arising from a change in the position of
an observer is termed parallel x. More especially, the
parallax of a star is the difference of its direction as
seen from the sun and from that point of the earth's
orbit from which the apparent direction will be
changed by the greatest amount. It is equal to the
angle subtended by the radius of the earth's orbit, as
seen from the star. The simplest conception of an arc
of one second is reached by thinking of it as the angle
subtended by a short line at a distance of 206,265
times its length. To say that a star has a parallax of
i" would therefore be the same thing as saying that it
was at a distance of 206,265 times that of the earth
from the sun. A parallax of one-half a second implies
a distance twice as great ; one of one-third, three
times as great. A parallax of o."2o implies a distance
of more than a million times that of our unit of
measure.

The first conclusive result as to the extreme min-
uteness of the parallax of the brighter stars was
reached by Struve, at Dorpat, about 1830. FirstMeas _
In the high latitude of Dorpat the right uresof
ascension of a star within 45 of the pole Parallax -
can be determined with great precision, not only at

i 4 4 THE PARALLAXES OF THE STARS

the moment of its transit over the meridian, but also
at transit over the meridian below the pole, which
occurs twelve hours later. He, therefore, selected a
large group of stars which could be observed twice
daily in this way at certain times of the year, and
made continuous observations on them through the
year. It was not possible, by this method, to cer-
tainly detect the parallax of any one star. What was
aimed at was to determine the limit of the average
parallax of all the stars thus observed. The con-
clusion reached was that this limit could not exceed
one-tenth of a second and that the average distance
of the group could not, therefore, be much less than
two million times the distance of the sun. If, per-
chance, some stars were nearer than this, others were
more distant.

By a singular coincidence, success in detecting stel-
lar parallax was reached by three independent inves-
tigators almost at the same time, observing three
different stars.

To Bessel is commonly assigned the credit of hav-
ing first actually determined the parallax of a star
with such certainty as to place the result beyond
question. The star having the most rapid proper
motion on the celestial sphere, so far as known to
Bessel, was 61 Cygni, which is, however, only of the
fifth magnitude. This rapid motion indicated that it
was probably among the stars nearest to us, much
nearer, in fact, than the faint stars by which it is
surrounded.

After several futile attempts, he undertook a series

FIRST MEASURES OF PARALLAX 145

of measurements, the best in his power to make, with
a heliometer, in August, 1837, and continued them
until October, 1838. The object was to determine,
night after night, the position of 61 Cygni relative to
certain small stars in its neighbourhood. Then he and
his assistant, Sluter, made a second series, which was
continued until 1840. All these observations showed
conclusively that the star had a parallax of about

o"-35-

While Bessel was making these observations, Struve,
at Dorpat, made a similar attempt upon Alpha Lyree.
This star, in the high northern latitude of Dorpat,
could be accurately observed throughout almost the
entire year. It is one of the brightest stars of the
northern heavens and has a proper motion. There
was, therefore, reason to believe it among the nearest of
the stars. The observations of Struve extended from
1835 to August, 1838, and were, therefore, almost
simultaneous with the observations made by Bessel
on 6 1 Cygni. He concluded that the parallax of
Alpha Lyrae was about one-fourth of a second. Sub-
sequent investigations have, however, made it proba-
ble that this result was about double the true value of
the parallax.

The third successful attempt was made by Hender-
son, of England, astronomer at the Cape of Good
Hope. He found from meridian observations that
the star Alpha Centauri had a parallax of about i".
This is a double star of the first magnitude which,
being only 30 from the south celestial pole, never
rises in our latitudes. Its nearness to us was indicated

I 4 6 THE PARALLAXES OF THE STARS

not only by its magnitude, but also by its con-
siderable proper motion. Although subsequent in-
vestigation has shown the parallax of this body to
be less than that found by Henderson, it is, up to
the time of writing, the nearest star whose distance
has been ascertained.

The great difficulty of detecting an annual change
in the direction of a star amounting to only a fraction
of a second will be obvious to the reader. He will
be still more impressed with it if, looking through a
powerful telescope at any star, he sees how it flickers
in consequence of the continual motions going on in
the air through which it is seen, and considers how
difficult it must be to fix any point of reference from
which to measure the change of direction.

The latter is the capital difficulty in measuring the
parallax. How shall we know that a star has changed
its direction by a fraction of a second in the course of
six months ? There must be for this purpose some
standard direction from which we can measure.

The most certain of these standard directions is
that of the earth's axis of rotation. It is true that
this direction varies in the course of the year, but the
amount of the variation is known with great precision,
so that it can be properly allowed for in the reduction
of the observations. The angle between the direc-
tion of a star and that of the earth's axis, the latter
direction being represented by the celestial pole, can
be measured with our meridian instruments. It is, in
fact, the north polar distance of the star, or the com-
plement of its declination. If, therefore, the astrono-

MODERN METHODS 147

mer could measure the declination of a star with
great precision throughout the entire year, he would
be able to determine its parallax by a comparison of
the measures. But it is found impossible in practice
to make measures of so long an arc with the neces-
sary precision. The uncertain and changing effect of
the varying seasons and different temperatures of day
and night upon the air and the instrument quite masks
the parallax in all ordinary cases. After several at-
tempts with the finest instruments, handled with the
utmost skill, to determine stellar parallax from the de-
clinations of the stars, the method has been practically
abandoned.

The method now practised is that of relative paral-
lax. - By this method the standard direction is that
of a small star apparently alongside one Modem
whose parallax is to be measured, but, pre- Methods.
sumably, so much farther away that it may be regarded
as having no parallax. In this assumption lies the
weak point of the method. Can we be sure that the
smaller stars are really without appreciable parallax ?
The latest researches make it probable that we can.
It is now considered quite safe to assume that the
small stars without proper motion are so far away that
their parallax is insensible.

Until recent times it was generally supposed that
the magnitude of the stars afforded the best index to
their relative distances. If the stars were of the
same intrinsic brilliancy, the amount of light received
from them would, as already pointed out, have been
inversely as the square of the distance. Although

148 THE PARALLAXES OF THE STARS

there was no reason to suppose that any such equality
really existed, it would still remain true that, in the gen-
eral average, the brighter stars must be nearer to
us than the fainter ones. But when the proper
motions of stars came to be investigated, it was found
that the amount of this motion afforded a better index
to the distance than the magnitude did. The diversity
of actual or linear motion is not so wide as that of
absolute brilliancy. Stars have, therefore, in recent
times, been selected for parallax very largely on ac-
count of their proper motion, without respect to their
brightness.

Ever since the time of Bessel the experience of
practical astronomers has tended toward the conclu-
sion that the best instrument for delicate measure-
ments like these is the heliometer. This is an
equatorial telescope of which the object-glass is
divided along a diameter into two semicircles, which
can slide along each other. Each half of the object-
glass forms a separate image of any star at which the
telescope may be pointed. By sliding the two halves
along each other, the images can be brought together
or separated to any extent. If there are two stars in
proximity, the image of one star made by one-half of
the glass can be brought into coincidence with that
of the other star made by the other half. The sliding of
the two halves to bring about this coincidence affords
a scale of measurement for the angular distance of the
two stars.

The most noteworthy forward steps in improving
the heliometer are due to the celebrated instrument-

MODERN METHODS 149

makers of Hamburg, the Messrs. Repsold, aided by
the suggestions of Dr. David Gill, astronomer at the
Cape of Good Hope. The latter, in connection with
his coadjutor, Elkin, made an equally important step
in the art of managing the instrument and hence in de-
terming the parallax of stars. The best results yet at-
tained are those of these two observers, and of Peter,
of Germany.

Yet more recently, Kapteyn, of Holland, has ap-
plied what has seemed to be the unpromising method
of differences of right ascension observed with a
meridian circle. This method has also been applied
by Flint, at Madison, Wis. Through the skill of these
observers, as well as that of Brunnow and Ball, in ap-
plying the equatorial telescope to the same purposes,
the parallaxes of nearly one hundred stars have been
measured with greater or less precision.

A rival method to that of the heliometer has been
discovered in the photographic telescope. The plan
of this instrument, and its application to such pur-
poses as this, are extremely simple. We point a tele-
scope at a star and set the clock-work going, so that the
telescope shall remain pointed as exactly as possible in
the direction of the star. We place a sensitised plate
in the focus and leave it long enough to form an
image both of the particular star in view and of all the
stars around it. The plate being developed, we have
a permanent record of the relative positions of the
stars which can be measured with a suitable instru-
ment at the observer's leisure. The advantage of the
method consists in the great number of stars which

150 THE PARALLAXES OF THE STARS

may be examined for parallax, and in the rapidity with
which the work can be done.

The earliest photographs which have been utilised
in this way are those made by Rutherfurd in New
York during the years 1860 to 1875. The plates taken
by him have been measured and discussed principally
by Reesand Jacoby, of Columbia University. Before
their work was done, however, Pritchard, of Oxford,
applied the method and published results in the case
of a number of stars.

One of the pressing wants of astronomy at the
present time is a parallactic survey of the heavens for
the purpose of discovering all the stars whose parallax
exceeds some definable limit, sayo". i. Such a survey
is possible by photography, and by that only. A
commencement, which may serve as an example of one
way of conducting the survey, has been made by
Kapteyn on photographic negatives taken by Donner
at Helsingfors.

These plates cover a square in the Milky Way
about two degrees on the side, extending from 34
50' in declination to 36 50', and from 2oh. im. in R.
A. to 2oh. lorn. 245. Three plates were used, on
each of which the image of each star is formed twelve
times. Three of the twelve impressions were made at
the epoch of maximum parallactic displacement, six at
the minimum six months later, and three at the fol-
lowing maximum. The parallaxes found on the plates
can only be relative to the general mean of all the
other stars, and must therefore be negative as often as
positive. The following positive parallaxes, amount-

MODERN METHODS 151

ing to o".i, came out with some consistency from the
measures :

Star, B. D., 3972 Mag. 8.6 R. A. 2oh. 2m. os. Dec. +35. 5 Par.-|-o".ir

Star, B. D., 3883 Mag. 7.1 R. A. 2oh. 2m. 35. Dec. +36. i Par.-f-o".i8

Star, B. D.,4003 Mag. 9.2 R. A. 2oh. 4m. 585. Dec. +35. 4 Par.-fo".io

Star, B. D.,3959 Mag. 7.0 R. A. 2oh. gm. 145. Dec. +36. 3 Par.-fo".io

Against these are to be set negative parallaxes of
o".O9, o".o8, and several a little smaller, which are
certainly unreal,

The presumption in favour of the actuality of one or
more of the above ppsitive values, which is created by
their excess over the negative values, is offset by r the
following considerations : The area of the entire sky
is more than 40,000 square degrees, or 10,000 times
the area covered by the Helsingfors plates. We can-
not well suppose that there are 1000 stars in the sky
with a parallax of o". 10 or more without violating all
the probabilities of the case. The probabilities are
therefore against even one star with such a parallax
being found on those plates. Yet the cases of these
four stars are worthy of further examination, if any of
them are found to have a sensible proper motion.

On an entirely different plan is a survey recently
concluded by Chase with the Yale heliometer. It in-
cludes such stars having an annual proper motion of
o".5O or more as had not already been measured for
parallax. The results, in statistical form, are these :

2 stars have parallaxes between -f- o".2o and -\- o" .25.

6 stars have parallaxes between + o". 15 and -f- o".2o.
ii stars have parallaxes between -j- o".io and -f- o".i5.
24 stars have parallaxes between -}- ".05 and -f- o".io.
34 stars have parallaxes between o".oo and -j- o".o5.

152 THE PARALLAXES OF THE STARS

8 stars have parallaxes between o".o5 and o".oo.
5 stars have parallaxes between o".io and o",o5.
2 stars have parallaxes between o".i5 and o".io.

92, total number of stars.

It will be understood that the negative parallaxes
found for fifteen of these stars are the result of errors
of observation. Assuming that an equal number of
the smaller positive values are due to the same cause,
and substracting these thirty stars from the total
number, we shall have sixty-two s. tars left of which the
parallax is real and generally amounts to 0^.05 more
or less. The two values approximating to o".25 seem
open to little doubt. We might say the same of the
six next in the list. The first two belong to the stars
54 Piscium and Weisse, i7h., 322.

A table of all the well-determined parallaxes of
stars which the author has been able to find in astro-
nomical literature will be found in the Appendix to
the present work.

CHAPTER X

SYSTEMS OF STARS

and other suns perhaps,

With their attendant moons thou wilt descry,

Communicating male and female light,

Which two great sexes animate the world. MILTON.

SIR WILLIAM HERSCHEL was the first to
notice that many stars which, to the unaided
vision, seemed single, were really composed of two
stars in close proximity to each other. The first quest-
ion to arise in such a case would be whether the
proximity is real or whether it is only apparent, arising
from the two stars being in the same line from our
system. This question was speedily settled .by more
than one consideration. If there were no real con-
nection between any two stars, the chances would be
very much against their lying so nearly in the same
line from us as they are seen to do in the case of double
stars. Out of five thousand stars scattered at random
over the celestial vault the chances would be
against more than three or four being so close
together that the naked eye could not separate them,
and would be hundreds to one against any two being
as close as the components of the closer double stars

153

154 SYSTEMS OF STARS

revealed by the telescope. The conclusion that the
proximity is in nearly all cases real is also proved by
the two stars of a pair moving together or revolving
round each other.

Altogether there is no doubt that in the case of the
brighter stars all that seem double in the telescope are
really companions. But when we come to the thou-
sands or millions of telescopic stars, there may be some
cases in which the two stars of a pair have no real
connection and are really at very different distances
from us. The stars of such a pair are called " opti-
cally double." They have no especial interest for us
and need not be further considered in the present work.

After Herschel, the first astronomer to search for
double stars on a large scale was Wilhelm Struve, the
celebrated astronomer of Dorpat. So thorough was
his work in this field that he may fairly be regarded as
the founder of a new branch of astronomy. Armed
with what was, at that time (1815-35), a remarkable
refracting telescope, he made a careful search of that
part of the sky visible at Dorpat, with a view of dis-
covering all the double stars within reach of his instru-
ment. The angular distance apart of the components
and the direction of the fainter from the brighter star
were repeatedly measured with all attainable precision.
The fine folio volume, Mensurtz Micrometriccz, in
which his results were published and discussed, must
long hold its place as a standard work of reference on
the subject.

Struve had a host of worthy successors, of whom we
can name only a few. Sir John Herschel was rather

DOUBLE STARS

'55

a contemporary than a successor. His most notable
work on double stars was done during his expedition
to the Cape of Good Hope, where he discovered a
great number of these objects in the southern heav-
ens with the great telescope at his command. Her-
schel, South, and Dawes, of England, were among
the greatest English observers about the middle of the
century. Otto Struve, son of Wilhelm, continued his
father's work with zeal and success at Pulkowa. Later
one of the most industrious observers was Dembowski,
of Italy. During the last thirty years one of the most
successful cultivators of double-star astronomy has
been Burnham, of Chicago. He is to-day the leading
authority on the subject. Enthusiasm, untiring in-
dustry, and wonderful keenness of vision have com-
bined to secure him this position.

Let P be the principal star and C the companion.
Let N S be a north and south
line through P, or an arc of the
celestial meridian, the direction
N being north and S south from
the star P.

Then, the angle N P C is called
the position-angle of the pair. It
is counted round the circle from
o to 360. The angle drawn in
the figure is nearly 1 20. Were
the companion C in the direction
S the position-angle would be 180; to the right of
P it would be 270; to the right of N it would be
between 270 and 360.

156 SYSTEMS OF STARS

The distance is the angle P C between the compon-
ents which is expressed in seconds of arc.

The following definitions and explanations will be
useful to the general reader. The two stars of a pair
are called its components. The lesser is called the
companion of the brighter. To separate a pair means
to distinguish the two stars of the pair. The particu-
lars which the careful observer of a double star should
record are the position-angle and distance of the com-
ponents and their respective magnitudes. To these
Struve added their colours ; but this has not gen-
erally been done.

We cannot set any well-defined limit to the range
of distance. The general rule is that the greater the
distance beyond a few seconds the less the interest
that attaches to a double star, partly because the ob-
servation of distant pairs offers no difficulty, partly
because of the increasing possibility that the compon-
ents have no physical connection, and so form only
an optically double star. With every increase of
telescopic power so many closer and closer pairs are
found that we cannot set any limit to the number of
stars that may have companions. It is therefore to
the closer pairs that the attention of astronomers is
more especially directed.

The difficulty of seeing a star as double, or, in the
familiar language of observers, of "separating" the
components, arises from two sources, the proximity of
the companion to the principal star, and the difference
in magnitude between the two. It was only in rare
cases that Struve could separate a pair as close as

BINARY SYSTEMS 157

half a second. Now Burnham finds pairs whose dis-
tance is less than one-quarter of a second ; indeed the
limit of a tenth of a second is being approached. It
goes without saying that a very minute companion to
a bright star may, when the distance is small, be lost
in the rays of its brighter neighbour. For all these
reasons no estimate can be made of the actual number
of double stars in the heavens. With every increase
of telescopic power and observing skill more difficult
pairs are being found, without any indication of a
limit.

The great interest which attaches to double stars
arises from the proof which they afford that the law
of gravitation extends to the stars. Struve, by com-
paring his own observations with each other, or with
those of Herschel, found that many of the pairs
which he measured were in relative motion ; the posi-
tion-angle progressively changing from year to year,
and sometimes the distance also. The lesser star was
therefore revolving round the greater, or, to speak
with more precision, both were revolving round their
common centre of gravity. To such a pair the name
binary system is now applied.

There can be no reasonable doubt that the two
components of all physically connected double stars
revolve round each other. If they did not their
mutual gravitation would bring them together and
fuse them into a single mass. We are therefore justi-
fied in considering all double stars as binary systems,
except those which are merely optically double. For
reasons already set forth, the pairs of the latter class

158 SYSTEMS OF STARS

which are near together must be very few in number ;
indeed, there are probably none among the close
double stars whose brightest component can be seen
optically by the naked eye.

The time of revolution of the binary systems is so
long that there are only about fifty cases in which it
has yet been determined with any certainty. Leav-
ing out the " spectroscopic binaries," to be hereafter
described, the shortest period yet fully established
is eleven years. In only a small minority of cases
is the period less than a century. In the large
majority either no motion at all has yet been de-
tected, or it is so slow as to indicate that the period
must be several centuries, perhaps several thousand
years.

There is great difficulty in determining the period
with precision until the stars have been observed
through nearly a revolution, owing to the number of
elements, seven in all, that fix the orbit, and the diffi-
culty of making the measures of position-angle and
distance with precision. It thus happens that many
of the orbits of binary systems which have been com-
puted and published have no sound basis. Two cases
in point may be mentioned.

The first-magnitude star Castor or Alpha Gemino-
rum is seen to be double with quite a small telescope.
The components are in relative motion. Owing to the
interesting character of the pair it has been well ob-
served, and a number of orbits have been computed.
The periodic times found by the computers have a
wide range. The fact is, nothing is known of the

BINARY SYSTEMS 159

period except that it is to be measured by centuries,
perhaps by thousands of years.

The history of 61 Cygni, a star ever memorable
from being the first of which the parallax was determ-
mined, is quite similar. Although, since accurate ob-
servations have been made on it, the ^components
have moved through an apparent angle of 30, the ob-
servations barely suffice to show a very slight curva-
ture in the path which the two bodies are describing
round each other. Whether the period is to be
measured by centuries or by thousands of years can-
not be determined for many years to come.

In his work on the Evolution of the Stellar Systems,
Prof. T. J. J. See has investigated the orbits of forty
double stars having the shortest periods. There are
twenty-eight periods of less than one hundred years.

In considering the orbits of binary systems we must
distinguish between the actual and the apparent orbit.
The former is the orbit as it would appear to an ob-
server looking at it from a direction perpendicular to
its plane. This orbit, like that of a planet or comet
moving round the sun, is an ellipse, having the princi-
pal star in its focus. The point nearest the latter is
called the periastron, or pericentre, and corresponds
to the perihelion of a planetary orbit. The point
most distant from the principal star is the apocentre.
It is opposite the pericentre and corresponds to the
aphelion of a planetary orbit. The law of motion is
here the same as in the case of a body of the solar sys-
tem ; the radius vector joining the two bodies sweeps
over equal areas in equal times.

160 SYSTEMS OF STARS

The apparent orbit is the orbit as it appears to us.
It differs from the actual orbit because we see it from
a more or less oblique direction. In some cases the
plane of the orbit passes near our system. Then to
us the orbit will appear as a straight line and the
small star will seem to swing from one side of the
large one to the other like a pendulum, though the ac-
tual orbit may differ little from a circle. In some
cases there may be two pet icentres and two apocentres
to the apparent orbit. This will be the case when a
nearly circular orbit is seen at a considerable
obliquity.

It is a remarkable and interesting fact that the law
of areas holds good in the apparent as in the actual
orbit. This is because all parts of the plane of the
orbit are seen at the same angle, so that the obliquity
of vision diminishes all the equal areas in the same
proportion and thus leaves them equal.

The two most interesting binary systems are those
of Sirius and Procyon. In the case of each the exist-
Bin r ence and orbit of the companion were in-

Systems of ferred from the motions of the principal
Sirius and s t ar before the companion had been seen.
Before the middle of the century it was
found that Sirius did not move with the uniform
proper motion which characterises the stars in general ;
and the inequality of its motion was attributed to the
attraction of an unseen satellite. Later Auwers, from
an exhaustive investigation of all the observations of
the star, placed the inequality beyond doubt and
determined the elements of the orbit of the otherwise

SIRIUS AND PROCYON 161

unknown satellite. Before his final work was pub-
lished the satellite was discovered by Alvan G. Clark,
of Cambridgeport, Mass., son and successor of the
first and greatest American maker of telescopes. Ad-
ditional interest was imparted to the discovery by the
fact that it was made in testing a newly constructed
telescope, the largest refractor that had been made up
to that time. The discoverer was, at the time, un-
aware of the work of Peters and Auwers demonstrat-
ing the existence of the satellite. The latter was,
however, in the direction predicted by Auwers, and a
few years of observation showed that it was moving in
fairly close accordance with the prediction.

The orbit as seen from the earth is very eccentric,
the greatest distance of the satellite from the star
being about ten seconds, the least less than three
seconds. Owing to the brilliant light of Sirius the
satellite is quite invisible, even in the most powerful
telescopes, when nearest its primary. This was the
case in the years 1890-92 and will again be the case
about 1940, when another revolution will be completed.

The history of Procyon is remarkably similar. An
inequality of its motion was suspected by Peters, but
not proved. Auwers showed from observations that
it described an orbit seemingly circular, having a radius
of about i". There could be no doubt that this
motion must be due to the revolution of a satellite, but
the latter long evaded discovery, though carefully
searched for with the new telescopes which were from
time to time brought into use. At length in 1895
Schaeberle found the long-looked-for object with the

l62

SYSTEMS OF STARS

1835

36-inch telescope of the Lick Observatory. It was
nearly in the direction predicted by Auwers, and a
year's observation by Schaeberle, Barnard, and others
showed that it was revolving in accordance with the
theory.

If the conclusion of Auwers that the apparent orbit
of the principal star is circular were correct, the dis-
tance of the satellite should always be the same. It

would then be equally easy
to see at all times. The
fact that neither Burnham
nor Barnard ever succeed-
ed in seeing the object
with the Lick telescope
would then be difficult to
account for. The fact is,
however, that the periodic
motion of Procyon is so
small that a considerable
eccentricity might exist
without being detected by
observations. The prob-
ability is, therefore, that
the apparent orbit is
markedly eccentric and
that the satellite was
nearer the primary during the years 1878-92 than it
was when discovered.

One very curious feature, common to both of these
systems, is that the mass of each satellite, as compared
with that of its primary, is out of all proportion to its

fio.E.

1669

APPARENT ORBIT OF a CENTAURI, BY
PROFESSOR SEE

TRIPLE AND MULTIPLE SYSTEMS

163

brightness. The remarkable conclusions to be drawn
from this fact will be discussed in a subsequent chapter.

The system of Alpha Centauri is interesting from the
shortness of the period, the brightness of the stars, and
the fact that it is the nearest star to us, so far as
known. We reproduce a diagram of the apparent
orbit from Dr. See's work. The period of revolution
found by Dr. See is eighty-one years. The major
axis of the apparent orbit is 32" ; the minor axis 6".

Special interest attaches to binary systems of short
period. Omitting Capella, which will be described
later, it does not seem that a well-established period
of less than eleven years is known, though several are
suspected. Among the pairs of which the period of
revolution is the shortest are these :

K Pegasi : R. A. =2ih. 4001. Dec.=

<? Equulei : =2ih. lorn.

/3 883 : " = 4 h. 45m.

% Sagittarii : " = i8h. 56111.

p Argus : " = yh. 47111.

85 Pegasi: " =23!!. 57111.

Shorter periods than these have been suspected in
the cases of * Pegasi and ft 883. Dr. See considers
that the period of ft 883 is only five and one-half
years, but the extreme difficulty of the observations
still leaves room for question.

Systems of three or more stars so close together that
there must be a physical connection between Triple and
them are quite numerous. There is every Multiple
variety of such systems. Sometimes a small s y stems -
companion of a brighter star is found to be itself

YEARS

+ 2SIl'

Period =11. 42

+ 937' (
- 3 i'

" =15-80
" =18.85

" =22.00

+ 26 34 '

" =24.00

164 SYSTEMS OF STARS

double. A curious case of this sort is that of Gamma
Andromedae. This object was observed and measured
by Struve as an ordinary double star, of which the com-
panion was much smaller than the principal star.
Some years later Alvan Clark found that this com-
panion was itself a close double star, of which the
components, separated by about i", were nearly equal.
Moreover, it was soon found that these components re-
volved round each other in a period not yet accurately
determined, but probably less than a century. Thus
we have a binary system revolving round a central
star as the earth and moon revolve round the sun.

In most triple systems there is no such regularity as
this. The magnitudes and relative positions of the
components are so varied that no general description
is possible. Stars of every degree of brightness are
combined in every way. Observations on these sys-
tems extend over so short an interval that we have no
data for determining the laws of motion that may pre-
vail in any but one or two of the simplest cases. They
are, in all probability, too complicated to admit of
profitable mathematical investigation. There is,
therefore, little more of interest to be said about them.

There is a very notable multiple system known as
the Trapezium of Orion from the fact that it is com-
posed of four stars. They are so close together as to
appear like a single star to the naked eye, but may be
well separated in the smallest telescope. There are
also two other very faint stars, each of which seems to
be a companion of one of the bright ones. This
system is situated in the great nebula of Orion, to be

s-
tems.

SPECTROSCOPIC BINAR Y S Y STEMS, 1 65

described in the next chapter, a circumstance which
has made it one of the most interesting objects to ob-
servers. No motion has yet been certainly detected
among the components.

Among the many striking results of recent astro-
nomical research it would be difficult to name any
more epoch-making than the discovery that

r s , ... Spectro-

great numbers of the stars have invisible scopic

dark bodies revolving round them of a mass Binary Sy
comparable with their own. The existence
of these revolving bodies is made known not only by
their eclipsing the star, as explained in the chapter on
Variable Stars, but by their producing a periodic
change in the radial motion of the star. How this
motion is determined by means of the spectroscope
has been briefly set forth in a former chapter. As a
general rule the motion is uniform in the case of each
star. We have described in a former chapter the
periodic character of the radial motion of Algol, dis-
covered by Vogel. This was followed by the discovery
that Alpha Virginis, though not variable, was affected
by a similar inequality of the radial motion, having a
period of four days and nineteen minutes. The
velocity of the star in its apparent orbit is very great,
about ninety-one kilometres, or fifty-six English
miles, per second. It follows that the radius of the
orbit is some three million miles. The mass of the in-
visible companion must, therefore, be very great.

A new form of binary system was thus brought out,
which, from the method of discovery, was called the
spectroscopic binary system. But there is really no line

166 SYSTEMS OF STARS

to be drawn between these and other binary systems.
We have seen that as telescopic power is increased,
closer and closer binary systems are constantly being
found. We naturally infer that there is no limit to
the proximity of the pairs of stars of such systems, and
that innumerable stars may have satellites, planets, or
companion stars so close or so faint as to elude our
powers of observation.

The actual orbit of such a system cannot be determ-
ined with the spectroscope, because only one com-
ponent of the motion, that in the direction of the
earth, can be observed. In the case of an orbit of
which the plane was perpendicular to the line of sight

from the earth to the
star the spectroscope
could give us no infor-
mation as to the mo-

RADIAL MOTION OF A BINARY SYSTEM fo^. The mOtlOn tO

or from the earth would be invariable. To show the
result of the orbit's being seen obliquely, let E be the
earth and A S be the plane of the orbit seen edgewise.
Drop the perpendicular A M upon the line of sight.
Then, while the star is moving from S to A the spec-
troscope will measure the motion as if it took place
from S to M. Since S M is less than A S, the measured
velocity will always be less than the actual velocity,
except in the rare case when the motion of the star is
directed toward the earth. Since the spectroscope
can give us no information as to the inclination under
which we see the orbit, it follows that the actual
orbital velocities of the spectroscopic binaries must

SPECTROSCOPIC BINARY SYSTEMS 167

remain unknown. We can only say that they cannot
be less, but may be greater to any extent, than that
shown by our measures.

If the components of a spectroscopic binary system
do not differ greatly in brightness, its character may be
detected without actually measuring the radial veloc-
ities. Since the motion is shown by a displacement of
the spectral lines, and since in any binary system the
two components must always move in opposite direc-
tions, it follows that the displacements of the spectral
lines of the two stars will be in opposite directions.
Hence, when one of the stars, say A, is moving
towards us, and the other, say D, from us, all the
spectral lines common to the two will appear double,
the lines made by A being displaced toward the blue
end of the spectrum and those by B toward the red
end. After half a revolution the motion will be re-
versed and the lines will again be double ; only the
lines of star A will now be on the red side of the
others. Between these two phases will be one in
which the radial velocities of the two stars are the
same ; the lines will then appear single.

The first star of which the binary character was
detected in this way is Xi- Ursae Majoris. The
discovery was made at the Harvard Observatory.

The perfection of the spectroscopic method is of so
recent date that only binary systems of comparatively
short period have so far been certainly detected.
It is quite likely that nearly all double stars so bright
that their spectrum can be accurately measured for
the purpose of radial motion will eventually be

168 SYSTEMS OF STARS

investigated with the spectroscope. But, so far, there
has been no time to determine an orbit of long period
from the radial motion. There has therefore been a
wide gap between the shortest period of a visual
binary system and the longest of a spectroscopic
binary.

Quite recently, however, this gap has been filled in a
remarkable way. Early in 1900 it was found by
Campbell, and independently by Newall, at Cam-
bridge, that Capella was a spectroscopic binary in
whose spectrum two types were superimposed. There
was first the regular spectrum of the second type, of-
fering a remarkable resemblance to that of our sun ;
superimposed on this was a second spectrum similar to
that of Procyon. Between the lines of these two
spectra a relative motion was found with a period of
104 days.

With the new 28-inch telescope of the Greenwich
Observatory the observers have been able to see the
duplicity of Capella and, measuring the position-angle
from time to time, found a period substantially the
same as that derived from the radial motions. The
components were too close together to admit of their
distance being accurately measured. The best estim-
ates that could be made placed it at less than one
tenth of a second, probably about o".o8. This is
about equal to the parallax of the star, as measured by
Elkin. The two stars did not seem to differ much in
brightness. The conclusion to be drawn is that the
actual distance of the components is not very different
from the distance between the earth and sun. The

STAR-CLUSTERS 169

fact that they revolve in less than one-third the time
that our earth does shows that the combined mass of
the two bodies must be about ten times that of the
sun.

It is very remarkable in this connection that the ob-
servations at Greenwich have not, so far, been con-
firmed at Mount Hamilton, where the telescope is
more powerful and the conditions of seeing supposed
to be of the best, nor at the Yerkes Observatory.

A star-cluster is a bunch or collection of stars
separated from the great mass of stars which stud the
heavens. The Pleiades, or " Seven Stars" star-

as they are familiarly called, form a cluster clusters
of which six of the components are easily seen by the
naked eye while five others may be distinguished by a
good eye without a telescope.

About 1780 Michell, of England, raised the quest-
ion whether, supposing the stars visible to the naked
eye to be scattered over the sky at random, there
would be a reasonable possibility that those of the
Pleiades would all fall within so small a space as that
filled by the constellation. His correct conclusion
was in the negative. It follows that this cluster does
not consist of disconnected stars at various distances,
which happen to be nearly in a line from our system,
but is really a collection of stars by itself. Besides
the stars visible to the naked eye, the Pleiades com-
prise a great number of telescopic stars, of which
about sixty have been catalogued and their relative
positions determined. The principal star of the clus-
ter is Alcyone or Eta Tauri, which is of the third

OF THE

UNIVERSITY

170 SYSTEMS OF STARS

magnitude. The five which come next in the order of
brightness are not very unequal, being all between the
fourth and fifth magnitudes. Six are near the sixth
magnitude. The remainder, so far as catalogued,
range from the seventh to the ninth.

In this case there is a fairly good method of dis-
tinguishing between a star which belongs to the
cluster and one which probably lies beyond it. This
test is afforded by the proper motion. We have
stated in Chapter VI that all the stars of the group
have a common proper motion in the same direction.
The amount of this motion is about 7" per century.
The first accurate measures made on the relative posi-
tions of the stars of the cluster were those of Bessel,
about 1830. In recent years several observers have
made yet more accurate determinations. The most
thorough recent discussion is by Elkin. One result
of his'work is that there is as yet no certain evidence
of any relative motion among the stars of the group.
They all move on together with their common motion
of 7" per century, as if they were a single mass.

A closer cluster, which is plainly visible to the
naked eye and looks like a cloudy patch of light, is
Praesepe in the constellation Cancer. It is very well
seen in the early evenings of winter and spring. Al-
though there is nothing in the naked-eye view to
suggest a star, it is found on telescopic examination
that the individual stars do not fall far below the
limit of visibility, several being of about the seventh
magnitude.

Another notable cluster of the same general nature

STAR-CL USTERS

171

is that in Perseus. This constellation is situated in
the Milky Way, not far from its region of nearest ap-

THE GREAT CLUSTER IN HERCULES, AS PHOTOGRAPHED WITH THE
CROSSLEY REFLECTOR OF THE LICK OBSERVATORY

proach to the pole. In the figure of the constellation
the cluster forms the handle of the hero's sword. It
may be seen in the evening during almost any season

172 SYSTEMS OF STARS.

except summer. To the naked eye it seems more
diffused and star-like than Praesepe ; in fact, it has two
distinct centres of condensation, so that it may be con-
sidered as a double cluster.

The two clusters last described may be resolved
into stars with the smallest telescopes. But in the
case of most of these objects the individual stars are
so faint that the most powerful instruments scarcely
suffice to bring them out. One of the most remark-
able clusters in the northern heavens is that of Her-
cules. To the naked eye it is but a faint and
insignificant patch, which would be noticed only by a
careful observer, but in a large telescope it is seen
to be one of the most interesting objects in the
heavens. Near the border the individual stars can be
readily distinguished, but they grow continually
thicker toward the centre, where, even in a telescope
of two feet aperture, the observer can see only a
patch of light, which is, however, as he scans it, sug-
gestive of the countless stars that must there be
collected. By the aid of photography, Professor
Pickering nearly succeeded in the complete resolution
of this cluster, and Keeler was even more successful
with the Crossley reflector of the Lick Observatory.

In many cases the central portions of these objects
are so condensed that they cannot be visually resolved
into their separate stars, even with the most power-
ful telescopes. A closer approach to complete resol-
ution has been made by photography. We reproduce
photographs of two noted clusters which show their
appearance in a powerful telescope.

STAR-CLUSTERS. 173

The cluster which, according to Pickering, may be
called the finest in the sky, is Omega Centauri. It lies
just within the border of the Milky Way, in right as-
cension i3h. 2O.8m., and declination 46 47'. There
are no bright stars near. To the naked eye it appears
as a hazy star of the fourth magnitude. Its actual ex-
treme diameter is about 40'. The brightest individual
stars within this region are between the eighth and
ninth magnitudes. Over six thousand have been
counted on one of the photographs, and the whole
number is much greater. (See Figure on page 1 75.)

The most remarkable and suggestive feature of the
principal clusters is the number of variable stars
which they contain. This feature has been brought
out by the photographs taken at the Harvard Observ-
atory and at its branch station in Arequipa. The
count of stars and the detection of the variables was
very largely made by Professor Bailey, who for sev-
eral years past has been in charge of the Arequipa
station.

The results of his examination of the photographs
are given in the table below. 1 In this table, the first
number is that of the new general catalogue of
Dreyer. The second column gives the usual designa-
tion of the cluster, generally its number in Messier's
list. The next two columns give the position re-
ferred to the equinox of 1900. Next follows the
approximate number of stars examined. The other
columns are sufficiently explained by their headings.

1 Harvard College Observatory Circular No. jj.

SYSTEMS OF STARS.
VARIABLE STARS IN CLUSTERS

DESIGNATION.

POSITION 1900

R. A. DEC.

NO STARS
EX-
AMINRD

AREA
EX-
AMINED.

NO.
OF
VAR.

PROPORTION.

h. m. '

sq.min.

FRACT;

J. liN.

104 47 Tucanse

o 19.6 72 38

2OOO

1257

()

.OO3

333

362

o 58.9 71 23

675

.O2I

(869
{.884

2 12.0 +56 41 )

2 15.4 -(-56 39 f

1050

10800

.001

1050

1904 Messier 79

5 20.1 24 37

2OO

.025

OOQ-l

70 /i

O 1 A

J^VJ

4755 ^ Crucis

1 U ^ LJ . \J 2 J Q\J

12 47 7 ^O J.8

/ *t

c c c

J 1 4

1 T/1

. (J(JU
c\f\r\

5139 ca-Centauri

L ^ *\ 1 1 Dv T-

13 20.8 46 47

JJ J

3000

J X 4
1257

125

.UvXJ

.042^

5272 Messier 3

13 37.6 +28 53

900

1257

132

.147

5904 Messier 5

15 13.5 + 2 27

900

1257

.094

5986

15 39-5 37 26

289

314

.003

289

6093 Messier 80

16 i i. i 22 44

145

.014

6205 Messier 13

16 38.1 +36 39

1000

177

.002

500

6266 Messier 62

16 54.9 29 58

9 60

218

26 .027

6397

17 32.5 53 37

487

218

2 ! .OO4

244

6626 Messier 28

.18 18.4 24 55

9OO

9 .010

100

6656 Messier 22

18 30.3 23 59

1550

218

.010

6723

18 52.8 36 46

9 00

.018

6752

19 2.0 60 8

600

218

.002

600

6809 Messier 55

19 33-7 31 10

440

218

.'005

220

7078 Messier 15

21 25.2 +11 44

900

1257

.057

7089 Messier 2

21 28.3 i 16

600

218

.017

7099 Messier 30

21 34.7 23 38

275

218

.on

19050

20-380

509

It will be seen from this table that the pro-
portion of variables is very different in different clus-
ters. In the double cluster 869-884, only one has
been found among a thousand stars. The richest in
variables is Messier 3, in which one variable has
been detected among every seven stars. It might be
suspected that the closer and more condensed the
cluster the greater the proportion of variables. This,
however, does not hold universally true. In the
great cluster of Hercules only two variables are
found among a thousand stars.

STAR-CLUSTERS. 175

Very remarkable, at least in the case of Omega
Centauri, is the shortness of the period of the variables.
Out of 125 found, 98 have periods less than twenty-

THE CLUSTER > CENTAURI, PHOTOGRAPHED BY GILL AT THE CAPE OBSERVATORY.

four hours. On the subject of the law of variation
in these cases, Pickering says :

"The light curves of the ninety-eight stars whose periods are
less than twenty-four hours may be divided into four classes. The
first is well represented by No. 74. The period of this star is
i2h. 4111. 3. and the range in brightness two magnitudes. Probably

1 76 SYSTEMS OF STARS,

the change in brightness is continuous. The increase of light is
very rapid, occupying not more than one-fifth of the whole period.
In some cases, possibly in this star, the light remains constant for
a short time at minimum. In most cases, however, the change in
brightness seems to be continuous. The simple type shown by
No. 74 is more prevalent in this cluster than any other. There
are, nevertheless, several stars, as No. 7, where there is a more or
less well marked secondary maximum. The period of this star is
2d. nh. 5im. and the range in brightness one and a half magni-
tudes. The light curve is similar to that of well-known short-
period variables, as Delta Cephei and Eta Aquilae. Another class
may be represented by No. 126, in which the range is less than a
magnitude and the times of increase and decrease are about equal.
The period is 8h. i2m. 3. No. 24 may perhaps be referred to as
a fourth type. The range is about seven-tenths of a magnitude
and the period is nh. 5m. 7. Apparently about 65 per cent, of
the whole period is occupied by the increase of the light. This
very slow rate of increase is especially striking from the fact that
in many cases in this cluster the increase is extremely rapid,
probably not more than 10 per cent, of the whole period. In one
case, No. 45, having a period of 14!!. 8m., the rise from minimum
to maximum, a change of two magnitudes, takes place in about
one hour, and in certain cases, chiefly owing to the necessary
duration of a photographic exposure, there is no proof at present
that the rise is not much more rapid."

The periods of 63 of the 85 variables in Messier 5
have been determined by Professor Bailey. Their most
remarkable feature is the approach of a majority of
them to half a day. Of the number, 39, or more than
three-fifths, are contained between the limits loh.
48m. and i5h.

The regularity in the period of these stars is re-
markable. Several have been studied during more
than a thousand, and one during more than five

STAR-CLUSTERS. 177

thousand, periods without irregularities manifesting
themselves.

It may be added that this regularity of the period,
taken in connection with the case of Eta Aquilae, al-
ready mentioned, affords a strong presumption that
the variations in the light of these stars are in some
way connected with the revolution of bodies round
them, or of one star round another. Yet it is certain
that the types are not of the Algol class and that the
changes are not due merely to one star eclipsing an-
other. That such condensed clusters should have a
great number of close binary systems is natural, al-
most unavoidable, we might suppose. It is probable
that among the stars in general, single stars are the ex-
ception rather than the rule. If such be the case, the
rule should hold yet more strongly among the stars of
a condensed cluster.

Perhaps the most important problem connected
with clusters is the mutual gravitation of their com-
ponent stars. Where thousands of stars are con-
densed into a space so small, what prevents them from
all falling together into one confused mass ? Are they
really doing so, and will they ultimately form a single
body ? These are questions which can be satisfac-
torily answered only by centuries of observation ; they
must, therefore, be left to the astronomers of the
future.

CHAPTER XI

NEBULA

Some tumultuous cloud
Instinct with fire and nitre.

MILTON.

THE first nebula, properly so called, to be detected
by an astronomical observer was that of Orion.
Huyghens, in his Sy sterna Saturnium, gives a rude
drawing of this object, with the following description :

" There is one phenomenon among the fixed stars worthy of
mention which, so far as I know, has hitherto been noticed by no
one, and, indeed, cannot be well observed except with large tele-
scopes. In the sword of Orion are three stars quite close to-
gether. In 1656, as I chanced to be viewing the middle one -of
these with the telescope, instead of a single star, twelve showed
themselves (a not uncommon circumstance). Three of these al-
most touched each other, and, with four others, shone through a
nebula, so that the space around them seemed far brighter than
the rest of the heavens, which was entirely clear, and appeared
quite black, the effect being that of an opening in the sky,
through which a brighter region was visible."

For a century after Huyghens made this observa-
tion it does not appear that these objects received
special attention from astronomers. The first to ob-
serve them systematically on a large scale was Sir

178

NEBULA 179

Wm. Herschel, whose vast researches naturally em-
braced them in their scope. His telescopes, large
though they were, were not of good defining power
and, in consequence, Herschel found it impossible to
draw a certain line in all cases between nebulae and
clusters. At his time it was indeed a question whether
all these bodies might not be clusters. This question
Herschel, with his usual sagacity, correctly answered
in the negative. Up to the time of the spectroscope,
all that astronomers could do with nebulae was to dis-
cover, catalogue, and describe them.

Several catalogues of these objects have been pub-
lished. The one long established as a standard is the
General Catalogue of Nebula and Clusters, by Sir John
Herschel. With each object Herschel gave a con-
densed description. Recently Herschel's catalogue
has been superseded by the general catalogue of
Dreyer, based upon it and published in the Memoirs
of the Royal Astronomical Society.

Some of the more conspicuous of these objects are
worthy of being individually mentioned. At the head
of all must be placed the great nebula of Orion.
This is plainly visible to the naked eye and can be seen
without difficulty whenever the constellation is visible.
Note the three bright stars lying nearly in an east
and west line and forming the belt of the warrior.
South of these will be seen three fainter ones, hang-
ing below the belt, as it were, and forming the sword.
To a keen eye, which sharply defines the stars, the
middle star will appear hazy. It is the nebula in
question. Its character will be strongly brought out

i8q NEBULA

by the smallest telescope, even by an opera-glass.
Drawings of it have been made by numerous astron-
omers, the comparison of which has given rise to the
question whether the object is variable. It cannot be
said that this question is yet decided ; but the best
opinion would probably be in the negative. In recent
times the improvements of the photographic process

THE GREAT NEBULA OF ORION, AS PHOTOGRAPHED BY A. A. COMMON, F.R.S.,
WITH HIS FOUR-FOOT REFLECTOR

have led to the representation of the object by photo-
graphy. A photograph made by Mr. A. A. Common,
F.R.S., with a reflecting telescope, gives so excellent
an impression of the object that by his consent we re-
produce it.

The most remarkable feature connected with the

NEBULAE

181

nebula of Orion is the so-called Trapezium, already
described. That these four stars form a system by
themselves cannot be doubted. The darkness of the
nebula immediately around them suggests that they
were formed at the expense of the nebulous mass.

Great interest has recently been excited in the spiral
form of certain nebulae. The great spiral nebula M.
51 in Canes Venatici has long been known. We re-
produce a photograph of this object and another. It
is found by recent studies at the Lick Observatory
that a spiral form can be detected in a great number
of these objects by careful examination.

THE GREAT SPIRAL NEBULA M. 51, AS PHOTOGRAPHED WITH THE
CROSSLEY REFLECTOR AT THE LICK OBSERVATORY

1 82 NEBULAE

Another striking feature of numerous nebulae is
their varied and fantastic forms, of which we give a
number of examples. The " Triphid nebula," figured
in our frontispiece, is a noted one in this respect.

The great nebula of Andromeda is second only to
that of Orion. It also is plainly visible to the naked
eye and can be more readily recognised as a nebula

THE GREAT NEBULA OF ANDROMEDA, PHOTOGRAPHED BY
DR. ISAAC ROBERTS, F.R.S.

NEBULA 183

than can the other. It has frequently been mistaken
for a comet. Seen through a telescope of high power,
its aspect is singular, as if a concealed light were
seen shining through horn or semi-transparent glass.

Another nebula which, though not conspicuous to
the naked eye, has attracted much attention from as-
tronomers, is known, from the figure of one of its
branches, as the Omega nebula. Sir John Herschel,
who first described this object in detail, says of it :
" The figure is nearly that of the Greek capital
Omega, somewhat distorted and very unequally
bright." From one base of the letter extends out to
the east a long branch with a hook at the end, which
in most of the drawings is more conspicuous than the
portion included in the Omega. The drawings, how-
ever, vary so much that the question has been raised
whether changes have not taken place in the object.
As in other cases, this question is one which it is not
yet possible to decide. The appearance of such ob-
jects varies so much with the aperture of the telescope
and the conditions of vision that it is not easy to de-
cide whether the apparent change may not be due to
these causes. It is curious that in a recent photo-
graph, the Omega element of it, if I may use the
term, is far less conspicuous than in the older draw-
ings, and is, in fact, scarcely recognisable.

Among the most curious of the nebulae are the
annular ones, which, as the term implies, have the
form of a ring. It should be remarked that in such
cases the interior of the ring is not generally entirely
black, but is" filled with nebulous light. We may,

184 NEBULA

therefore, define these objects as nebulae which are
brighter round their circumference than in the centre.
The most striking of the annular nebulae is that of
Lyra. It may easily be found from being situated
about half-way between the stars Beta and Gamma.
Although it is visible in a medium telescope, it
requires a powerful one to bring out its peculiar feat-
ures in a striking way. Recently it has been photo-
graphed by Keeler with the Crossley reflector of the
Lick Observatory, who found that the best general
impression was made with an exposure of only ten
minutes.

The ring, as shown by Keeler's photograph, has a
quite complicated structure. It seems to be made up
of several narrower bright rings, interlacing somewhat
irregularly, the spaces between them being filled with
fainter nebulosity. One of these rings forms the
outer boundary of the preceding end of the main
ring. Sweeping around to the north end of the
minor axis, it becomes very bright, perhaps by super-
position on the broader main ring of the nebula at this
place. It crosses this ring obliquely, forming the
brightest part of the whole nebula, and then forms the
inner boundary of the main ellipse toward its follow-
ing end. The remaining part of the ring is not so
easily traced, as several other rings interlace on the
south end of the ellipse.

The central star of this nebula has excited some in-
terest. Its light seems to have a special actinic
power, as the star is more conspicuous on the photo-
graphs than to the eye.

NEBULA 185

There are several other annular nebulae which are
fainter than that of Lyra. The one best visible in our
latitudes is known as H IV. 13, or 4565 of Dreyer's
catalogue. It is situated in the constellation Cygnus,
which adjoins Lyra. Both Herschel and Lord Rosse
have made drawings of it. It was photographed by
Keeler with the Crossley reflector on the nights of
August 9 and 10, 1899, with exposures of one and two
hours, respectively. Keeler states that the nebula, as
shown by these photographs, " is an elliptical, nearly
circular ring, not quite regular in outline, pretty
sharply defined at the outer edge." The outside dimen-
sions are :

Major axis 42". 5

Minor axis 40. "5

Position angle of major axis 32.

The nebula has a nucleus with a star exactly in the
center. This is very conspicuous on a photograph,
but barely if at all visible with a 36-inch reflector.

Another curious class of nebulae are designated as
planetary, on account of their form. These consist of
minute, round disks of light, having somewhat the ap-
pearance of a planet. The appellation was suggested
by this appearance. These objects are for the most
part faint and difficult.

It is impossible to estimate the number of nebulae
in the heavens. New ones have from time to time
been discovered, located, and described by many ob-
servers during the last thirty years. Among these

1 86 NEBULA

Lewis Swift is worthy of special mention as one of the
most successful discoverers of these objects.

NEBULOUS MASS IN CYQNUS, INCLUDING H. V. 14 AND H. 2093,
PHOTOGRAPHED AT THE LICK OBSERVATORY

But in recent times photography has gone far to-
ward replacing the eye in this field. On photographing
the sky near the galactic pole with the Crossley reflec-
tor, Keeler found no less than seven of these objects
in a space of about one-half a square degree. He there-

NEBULAE 187

fore estimates the whole number in the heavens
capable of being photographed at several hundred
thousand. It may be assumed that only a moderate
fraction of these are visible to the eye, even aided by
the largest telescopes.

Among the most singular of these objects are large
diffused nebulae, sometimes extending through a re-
gion of several degrees. A number of these were
discovered by Herschel. Barnard, W. H. Pickering,
and others have photographed these for us. One of
the most remarkable of them winds around in the
constellation Orion in such a way that at first sight one
might be disposed to inquire whether the impression
on the photographic plate might not have been the re-
sult of some defect in the apparatus or some reflection
of the light of the neighbouring stars, which is so apt
to occur in these delicate photographic operations.
But its existence happens to be completely confirmed
by independent testimony. It was first detected by
W. H. Pickering and afterwards independently by
Barnard.

A curious fact connected with the distribution of
nebulae over the sky is that it is in a certain sense the
reverse of that of the stars. The latter are vastly
more numerous in the regions near the Milky Way
and fewer in number near the poles of that belt. But
the reverse is the case with the nebulae proper. They
are least numerous in the Milky Way and increase in
number as we go from it in either direction. Precisely
what this signifies one would not at the present time
be able to say. Perhaps the most obvious suggestion

1 88 NEBULAE

would be that in these two opposite nebulous regions
the nebulae have not yet condensed into stars. This,
however, would be a purely speculative explanation.

On the other hand, star-clusters are more numerous
in the galactic region. This, however, is little more
than saying that in the regions where the stars are so
much more numerous than elsewhere many of them
naturally tend to collect in clusters. It is, however, a
curious fact that, so far as has yet been noticed, the
large diffused nebulae which we have mentioned are
more numerous in or near the Milky Way. If this
tendency is established it will mark a curious distinc-
tion between them and the smaller nebulae.

The most interesting question connected with these
objects is that of their physical constitution. When,
about 1866, the spectroscope was first applied to as-
tronomical investigation by Huggins he found that
the light of the great nebula of Orion formed a spec-
trum of bright lines, thus showing the object to be
gaseous. This was soon found to be true of the ne-
bulae generally. There is, however, a very curious
exception in the case of the great nebula of Androm-
eda. This object gives a more or less continuous
spectrum. The bright lines in the spectrum of a ne-
bula are seldom or never more than four in number.
The wave-lengths are 4341, 4861, 4957, 5004. The
first of these is the violet, is very faint, and visible only
in the brightest nebulae. The last is the brightest,
and in faint nebulae is the only one that can be dis-
tinguished. None of these lines can be certainly
identified with those of any terrestrial substance.

NEBULAE 189

The supposed matter which produces them has,
therefore, been called nebulmn.

Beyond the general fact that the light of a nebula
does not come from solid matter, but from matter of
a gaseous or other attenuated form, we have no cer-
tain knowledge of the physical constitution of these
bodies. Certain features of their constitution can,
however, be established with a fair approach to accu-
racy. Not only the spectroscopic evidence of bright
lines but the aspect of the objects themselves show
that they are transparent through and through. This
is remarkable when taken in connection with their in-
conceivable size. Leaving out the large diffused
nebulae which we have mentioned, these objects are
frequently several minutes in diameter. Of their dis-
tance we know nothing, except that they are probably
situated in the distant stellar regions. Their parallax
can be but a small fraction of a second. We shall
probably err greatly in excess if we assume that it
varies between one-hundredth and one-tenth of a
second. To assign this parallax is the same thing as
saying that at the distance of the nebulae the dimen-
sions of the earth's orbit would show a diameter which
might range between one-fiftieth and one-fifth of a
second, while that of Neptune would be more or less
than one second. Great numbers of these objects
are, therefore, thousands of times the dimensions of
the earth's orbit, and probably most of them are thou-
sands of times the dimensions of the whole solar
system. That they should be completely trans-
parent through such enormous dimensions shows

190 NEBULA

their extreme tenuity. Were our solar system placed
in the midst of one of them, it is probable that we
should not be able to find any evidence of its existence.

A form of matter so different from any that can be
found or produced on the surface of the earth can
hardly be explained by our ordinary views of matter.
A theory has, however, been propounded by Sir Nor-
man Lockyer, so ingenious as to be at least worthy of
mention. It is that these objects are vast collections
of meteorites in rapid motion relatively to each other,
which come into constant collision. Their velocity is
such that at each collision heat and light are produced.
In the language of our progenitors, who in the ab-
sence of matches used flint and steel, they " strike fire "
against each other. The idea of such a process orig-
inated with Prof. P. G. Tait, in an attempt to explain
the tail of a comet, but it was elaborated and devel-
oped by Mr. Lockyer in his work on the Meteor itic
Theory.

The objections to this theory seem insuperable. A
velocity so great, at such a distance from the centre
of the nebulae, would be incompatible with the extreme
tenuity of these objects. Every time that two meteors
came into collision they would lose velocity, and, there-
fore, if the mass was sufficient to hold them from flying
through space, would rapidly fall toward a common
centre. The amount of light produced by the collision
of two such objects is only a minute fraction of the en-
ergy lost. The meteors which fall on the earth are most-
ly of iron, and, were the theory true, numerous lines of
iron should be most conspicuous in the spectrum.

CHAPTER XII

CONSTITUTION OF THE STARS

Doubt thou the stars are fire. SHAKESPEARE.

THE spectroscope shows that, although the consti-
tution of the stars offers an infinite variety of de-
tail, we may say, in a general way, that these bodies
are suns. It would, perhaps, be more correct to say
that the sun is one of the stars and does not differ es-
sentially from them in its constitution. The problems
of the physical constitution of the sun and stars may,
therefore, be regarded as one, all these being bodies
of the same general nature, consisting of vast masses
of incandescent matter at so exalted a temperature
as to shine by their own light.

This similarity in general constitution does not,
however, preclude very great differences in detail.
The spectra of the stars show that hardly Diversities
any two are exactly alike in the substances among

of which they are composed, and in the the stars *
temperature and density of these substances. Most
remarkable is the diversity of their actual luminosities
or the amount of light and heat which they individu-
ally emit. The whole tendency of recent research
has been to accentuate this diversity. It was once

191

192 CONSTITUTION OF THE STARS

supposed that the brighter stars must all be among the
nearer ones to us. But as parallaxes were measured
with greater and greater accuracy, it became more and
more certain that this is not always the case.

The last step in this direction has been taken by Gill
in his measures of the parallaxes of the southern stars
of the first magnitude. Of two at least, Canopus and
Rigel, the parallaxes are so small as to elude certain
detection. Most extraordinary is the case of Canopus,
the second brightest star in the heavens. A long-con-
tinued series of measures, sufficient to make evident a
parallax of one hundredth of a second, converged to a
value of o".ooo ! Canopus is doubtless situated among
the small stars of the eighth magnitude around it, of
which we have every reason to believe the parallax to
be only a few thousandths of a second. In all likeli-
hood, it is more than ten thousand times as bright as
the sun. A planet as near to it as we are to the sun
would become red hot under its radiation.

At the other extreme we have the minute stars of
large proper motion whose parallaxes have been meas-
ured. These seem to be of only about one-fiftieth
the brightness of the sun. It therefore seems certain
that some stars emit hundreds of thousands nay,
millions of times as much light as others.

It has long been known that the mean density of the
sun is only one-fourth that of the earth, and, there-
Masses and f re > I GSS than half as much again as that of
Densities of water. In a few cases an approximate es-
the stars. timate of the density of stars may be made.
The method by which this is done can be rigorously

MASSES AND DENSITIES OF THE STARS 193

set forth only by the use of algebraic formulae, but a
general idea of it can be obtained without the use of
that mode of expression.

Let us set forth in advance an extension of Kepler's
third law, which applies to every case of two bodies re-
volving around each other by their mutual gravitation
The law in question, as stated by Kepler, is that the
cubes of the mean distances of the planets are propor-
tional to the squares of their times of revolution. If we
suppose the mean distances to be expressed in terms of
the earth's mean distance from the sun as a unit of
length, and if we take the year as the unit of time,
then the law may be expressed by saying that the
cubes of the mean distances will be equal to the
squares of the periods. For example, the mean dis-
tance of Jupiter is thus expressed as 5.2. If we take
the cube of this, which is about 140, and then extract
the square root of it, we shall have n.8, which is the
period of revolution of Jupiter around the sun ex-
pressed in years. If we cube 9.5, the mean distance
of Saturn, we shall have the square of a little more
than 29, which is Saturn's time of revolution.

We may also express the law by saying that if we
divide the cube of the mean distance of any planet by
the square of its periodic time we shall always get i
as a quotient.

The theory of gravitation and the elementary
principles of force and motion show that a similar rule
is true in the case of any two bodies revolving around
each other in virtue of their mutual gravitation. If we
divide the cube of their mean distance apart by the

194 CONSTITUTION OF THE STARS

square of their time of revolution, we shall get a
quotient which will not indeed be i, but which will
be a number expressing the combined mass of the two
bodies. If one body is so small that we leave its mass
out of consideration, then the quotient will express the
mass of the larger body. If the latter has several
minute satellites moving around it, the quotients will
be equal, as in the case of the sun, and will express
the mass of this central body. If, as in the case we
have supposed, we take the year as a unit of time and
the distance of the earth from the sun as a unit of
length, the quotient will express the mass of the cen-
tral body in terms of the mass of the sun. It is thus
that the masses of the planets are determined from the
periodic times and distances of their satellites, and the
masses of binary systems from their mean distance
apart and their periods. To express the general law
by a formula we put

a, the mean distance apart of the two bodies, or the
semi-major axis of their relative orbit in terms of the
earth's mean distance from the sun ;

P, their periodic time ;

M, their combined mass in terms of the sun's mass
as unity.

Then we shall have :

Another conclusion we draw is that if we know the
time of revolution and the radius of the orbit of any
binary system, we can determine what the time of

MASSES AND DENSITIES OF THE STARS 195

revolution would be if the radius of the orbit had
some standard length, say unity. To do this we have
only to divide the actual period by the cube of the
square root of the actual radius of the orbit.

We cannot determine the dimensions of a binary
system unless we know its distance from us. But
there is a remarkable law which, so far as I know,
was first announced by Pickering, by virtue of which
we can determine a certain relation between the sur-
face brilliancy and the density of a binary system
without knowing its distance.

Let us suppose a number of bodies of the same con-
stitution and temperature as the sun models of the
latter we may say differing from it only in size. To
fix the ideas, we shall suppose two such bodies, one
having twice the diameter of the other. Being of the
same brilliancy, we suppose them to emit the same
amount of light per unit of surface. The larger body,
having four times the surface of the smaller, will then
emit four times as much light. The volumes being
proportional to the cubes of their diameters, it will
have eight times its volume. The densities being
supposed equal, it will have eight times the mass.

Suppose that each has a satellite revolving around
it, of which the size is proportional to that of its pri-
mary, as shown in the figure, and that the orbit of the
satellite of the larger body is twice the radius of that
of the smaller one. Calling the radius of the nearer
satellite i, that of the more distant one will then be 2
The cube of this number is 8. It follows from the ex
tension of Kepler's third law, which we have cited

196 CONSTITUTION OF THE STARS

that the times of revolution of the two satellities will
be the same. Thus the two bodies, A and B, with
their satellites, a and b, form two binary systems whose
proportions and whose periods are the same, only the
linear dimensions of B are all double those of A. In
other words, we shall have a pair of binary systems
which will look alike in every respect, only one will
have double the dimensions and eight times the mass
of the other.

TWO BINARY SYSTEMS ON THE SAME MODEL, ONE HAVING TWICE THE
LINEAR DIMENSIONS OF THE OTHER

Now, let us suppose the larger system to be placed
twice as far away from us as the smaller. The two
will then appear of the same size, and, if stars, will ap-
pear of the same brightness, while the two orbits will
have the same apparent dimensions. In a word, the
two systems will appear alike when examined with
the telescope, and the periodic times will be equal.

Near the end of the second chapter we have given
a little table showing the magnitude that the sun
would appear to us to have were it placed at dif-
ferent distances among the stars. The parallaxes we

MASSES AND DENSITIES OF THE STARS 197

have there given are simply the apparent angles
which would be subtended by the radius of the
earth's orbit at different distances. It follows that,
were the stars all of similar constitution to the sun,
the numbers given in the last column of the table re-
ferred to would, in all cases, express the apparent dis-
tance from the star of a companion, having a time of
revolution of one year. From this we may easily
show what would be the time of revolution of any
binary system of which the companions were separated
by i", if the stars were of the same constitution as the
sun.

Periods of binary systems whose components are separated by i" and
whose constitution is the same as that of the sun.

Period, Annual

Mag. Years. Motion.

I . .8 200

2 3-5 102

3 7-o 51

4 14-1 25

5 28.1 13

6 56.0 6

7 112. 3.2

8 223. 1.6

It will be seen that the periods are very nearly
doubled for each diminution of the brilliancy of the
star by one magnitude. Moreover, the value of the
photometric ratio for two consecutive magnitudes is a
little uncertain, so that we may, without adding to the
error of our results, suppose the period to be exactly
doubled for each addition of unity to the magnitude.
A computation of the period for any magnitude, m, may
be made with all necessary precision by the formula :

198 CONSTITUTION OF THE STARS

P=0 y .88 X 2m;
or, log. P=9.944 + 0.30*.

It will now be of interest to compare the results of
this theory with the observed periods of binary sys-
tems with a view to comparing their constitution with
that of our sun. There are, however, two difficulties
in the way of doing this with precision.

The first difficulty is that there are very few binary
systems of which the apparent dimensions of the orbits
and the periods are known with any approach to ex-
actness. This would not be a serious matter were it
not that the systems of short, and, therefore, known,
periods belong to a special class, that having the
greatest density. Hence, when we derive our results
from such systems we shall be making a biassed selec-
tion from this particular class of stars.

The next difficulty is that the theory which we have
set forth assumes the mass of the satellite either to be
very small compared with that of the star, or the two
bodies to be of the same constitution. If we apply
the theory to systems in which this is not the case, the
results which we shall get will be, in a certain way,
those corresponding to the mean of the two compo-
nents. Were it a question of masses, we should get
with entire precision the sum of the masses of the two
bodies. The best we can do, therefore, is to suppose
the two companions fused into one having the com-
bined brilliancy of the two. Then, if the result is too
small for one, it will be too large for the other.

To show the method of proceeding, I have taken

MASSES AND DENSITIES OF THE STARS 199

the six systems of shortest period found in Dr. See's
Researches on Stellar Evolution. The principal
numbers are shown in the table below.

The first column, a", after the name of the star,
gives the apparent semi-major axis of the orbit in
seconds of arc. The next column gives the period in
years. Column Mag. gives the apparent magnitude
which the system would have were the two bodies
fused into one. Column P' gives the period in years
as it would be were the radius of the orbit equal to
one second. It is formed by dividing the actual
period by a 11 *. The next column gives the period as
it would be were the stars of similar constitution to
the sun. The last column gives the square of the
ratio of the two periods, which, if the stars had the
same surface brilliancy as the sun, would express
the ratio of density of the stars to that of the sun.
Actually, it gives the product : Density X brilliancy *.

PER.

MAG.

SUN'S

PER.

STAR'S

DENSITY.

H Pegasi

O .4.2

Years.
114.

4.2

Years.
41. Q

Years.

16 2

O 1C

& Equulei

o .4.$

1 1.4.

4.6

^7.8

2 I O

w.x^

O ?!

Sagittarii

o .60

18.8

2.O

22.7

6.7

o 04

F9 Argus

o .6c

22.O

I.*!

42.0

-2Q.7

O GO

42 Comae
ft Delphini

o .64
o 67

25-6

27 7

4-4

2 7

50.0

CO 4

i8.5

114

O.I4

o c i

W O *

The numbers in the last column being all less than
unity, it follows that either these stars are much less
dense than the sun or they are of much greater sur-
face brilliancy. Moreover, these stars belong to a

200 CONSTITUTION OF THE STARS

selected list in which the numbers of the last column
are larger than the average.

To form some idea of the result of a selection from
the stars in general, we may assume that the average
of all the measured distances between the components
of a number of binary systems is equal to the average
radius of their orbits, and that the observed annual
motion is equal to the mean motion of the companion
in its orbit. Taking a number of cases of this sort, I
find that the number corresponding to the last num-
ber of the preceding table would be little more than
one-thousandth.

A very remarkable case is that of Zeta Orionis.
This star, in the belt of Orion, is of the second mag-
nitude. It has a minute companion at a distance of
2". 5. Were it a model of the sun, a companion at
this apparent distance should perform its revolution in
fourteen years. But, as a matter of fact, the motion
is so slow that even now, after fifty years of observa-
tion, it cannot be determined with any precision. It
is probably less than o. i in a year. The number ex-
pressing the comparison of the density and surface
brilliancy of this star with those of the sun is probably
less than .0001.

The general conclusion to be drawn is obvious.
The stars in general are not models of our sun, but
have a much smaller mass in proportion to the light
they give than our sun has. They must, therefore,
have either a less density or a greater surface
brilliancy.

We may now inquire whether such extreme differ-

MASSES AND DENSITIES OF THE STARS 201

ences of surface brilliancy or of density are more
likely. The brilliancy of a star depends primarily,
not on its temperature throughout, but on that of
some region near or upon its surface. The tempera-
ture of this surface cannot be kept up except by con-
tinual convection currents from the interior to the
surface. We are, therefore, to regard the amount of
light emitted by a star not merely as indicating tem-
perature, but as limited by the quantity of matter
which, impeded by friction, can come up to the surface,
and there cool off and afterwards sink down again.
This again depends very largely on internal friction,
and is limited by that. Owing to this limitation, we
cannot attribute the difference in question wholly to
surface brilliancy. We must conclude that at least
the brighter stars are, in general, composed of matter
much less dense than that of the sun. Many of them
are probably even less dense than air and in nearly all
cases the density is far less than that of any known
liquid.

An ingenious application of the mechanical
principle we have laid down has been made independ-
ently by Mr. A. W. Roberts, of South Africa, and Mr.
H. N. Russell, of Princeton, in another way. If we
only knew the relation between the diameters of the
two companions of a binary system, and its dimensions,
we could decide how much of the difference in ques-
tion is due to density and how much to surface bril-
liancy. Now this may be approximately done in the
case of variable stars of the Algol and Beta Lyrse
types. If, as is probably the most common case, the

202 CONSTITUTION OF THE STARS

passage of the stars over each other is nearly cen-
tral, the ratio of their diameter to the radius of the
orbit may be determined by comparing the duration
of the eclipse with the time of revolution. This was
one of the fundamental data used by Myers in his
work on Beta Lyrae, of which we have quoted the re-
sults. Without going into reasoning or technical de-
tails at length, we may give the results reached by
Roberts and Russell in the case of the Algol variables.

For the variable star X Carinae, Roberts finds, as a
superior limit for the density of the star and its com-
panion, one-fourth the density of the sun. It may be
less than this is, to any extent.

In the case of S Velorum the superior limits of den-
sity are :

Bright star 0.61

Companion 0.03

In the case of RS Sagittarii the upper limits of den-
sity are o. 16 and 0.21.

It is possible, in the mean of a number of cases like
these, to estimate the general average amount by
which the densities fall below the limits here given.
Roberts's final conclusion is that the average density
of the Algol variables and their eclipsing companions
is about one-eighth that of the sun.

The work of Russell was carried through at the
same time as that of Roberts, and quite independ-
ently of his. It appeared at the same time. 1 His
formulae and methods were different, though they

1 Astrophysical Journal, vol. x, no. 5.

MASSES AND DENSITIES OF THE STARS 203

rested on similar fundamental principles. Taking the
density of the sun as unity, he computes the superior
limit of density for 12 variables, based on their periods
and the duration of their partial eclipses. The
greatest limit is in the case of Z Herculis and is 0.728.
The least is in the case of S Cancri and is 0.035.
The average is about 0.2. As the actual density may
be less than the limit by an indefinite amount,
the general conclusion from his work may be re-
garded as the same with that from the work of
Roberts.

The results of the preceding theory are independ-
ent of the parallax of the stars. They, therefore, give
us no knowledge as to the mass of a binary system.
To determine this we must know its parallax, from
which we can determine the actual dimensions of the
orbit when its apparent dimensions are known. Then
the formula already given will give the actual mass of
the system in terms of the sun's mass.

There are only six binary systems of which both the
orbit, and the parallax are known. These are shown
in the table below. Here the first two columns after
the stars named give the semi-major axis of the orbit
and the measured parallax. The quotient of the first
number by the second is the actual mean radius of
the orbits in terms of the earth's distance from the sun
as unity. This is given in the third column, after
which follow the period and the resulting combined
mass of the system. The last column shows the
actual amount of light emitted by the system, com-
pared with that emitted by the sun.

2O4

CONSTITUTION OF THE STARS

PAR.

PERIOD.

MASS.

LIGHT.

TI Cassiopiae ....

8 21

o 20

4.1 O

y-
igs.8

i 8

I O

Sirius

8 03

o 37

21.7

S2.2

2 7

32 O

Procyon

3 oo

Q. 3O

IO.O

4O.O

0.6

8 s

ot Centauri

17.70

0.7=;

23.6

81.1

2.O

1.7

70 Ophiuchi

4. ^ ^

O IQ

24 O

884

i 8

O 7

8s Pesasi

J J

o 80

x y

O OS

17 8

24. O

2 2

w o

Even in these few cases some of the numbers on
which the result depends are extremely uncertain. In
the case of Procyon, the radius of the orbit can be
only a rough estimate. In the case of 85 Pegasi.the
parallax is uncertain. In the case of Eta Cassiopiae
the elements are still doubtful.

So far as we have set forth the principles involved
in the question, we do not get separate results for the
mass of each body. The latter can be determined
only by meridian observations, showing the motion
of the brighter star around the common centre of
gravity of the two. This result has thus far been
worked out with an approximation to exactness only
in the cases of Sirius and Procyon. For these systems
we have the following masses of the companions of
these bodies in terms of the sun's mass :

Companion of Sirius . . .
Companion of Procyon

1.2
0.2

It will now be interesting to compare the bright-
ness of these bodies with that which the sun would
have if seen at their distance. In a former chapter we
showed how this could be done. The results are :

MASSES AND DENSITIES OF THE STARS 205

At the distance of Procyon the apparent magni-
tude of the sun would be 2 m .8. At the distance of
Sirius, it would be 2 m .3. Supposing the sun to be
changed in size, its density remaining unchanged,
until it had the same mass as the respective com-
panions of Procyon and Sirius, its magnitudes would
be:

For companion of Procyon 3.9

For companion of Sirius 2.9

These numbers are the magnitudes the compan-
ions would show were they models of our sun. Their
actual magnitudes cannot be estimated with great
precision, owing to the effect of the brilliancy of the
star. From the estimate of the companion of Sirius,
by Professor Pickering, its magnitude was about the
eighth. It is probable that the magnitude of the
companion of Procyon is not very different. It will
be seen that these magnitudes are very different from
those which they would have were they models of the
sun. What is very curious is that they differ in the
opposite direction from the stars in general, and
especially from their primaries. Either they have a
far less surface brilliancy than the sun or their density
is much greater. There can be no doubt that the
former rather than the latter is the case.

This great mass of the two companions as com-
pared with their brilliancy suggests the question
whether they may not shine, in part at least, by the
light of their primaries. A very little consideration
will show that this cannot be the case. To shine as

206 CONSTITUTION OF THE STARS

brightly as it does by reflected light, the diameter of
the companion of Sirius would have to be enormous,
at least one-thirtieth its distance from Sirius. More-
over, its apparent brightness would vary so widely
in different parts of its orbit that we should see it
almost as well when near Sirius as when distant from
it. The most likely cause of the great dimness is
the low temperature of the bodies.

All these results point to the conclusion that the
stars, or at least the brighter among them, are masses

of gas, enormously compressed in their in-
Gaseous *ii r i
Constitu- tenor by the gravitation or their outer parts.

tionofthe We have now to show how this result was
Stars. arrived at, at least in the case of the sun,
from different considerations, before the spectroscope
had taught us anything of the constitution of these
bodies.

We must accept, as one of the obvious conclusions
of modern science, the fact that the sun and stars
have, for untold millions of years, been radiating heat
into space. We refrain from considering the basis on
which this conclusion rests, not so much because it
must be considered unquestionable, as because the
discussion would be too long and complex for the
present work.

One of the great problems of modern science has
been to ascertain the source of this heat. Before
the theory of energy was developed this problem
suggested no difficulty. In the time of Newton, Kant
and even of La Place and Herschel, no reason was
known why the stars should not shine forever without

GASEOUS CONSTITUTION OF THE STARS 207

change. Now we know that when a body radiates
heat, that heat is really an entity termed energy, of
\vhich the supply is necessarily limited. Kelvin com-
pared the case of a star radiating heat to that of a
ship of war belching forth shells from her batteries.
We know that if the firing is kept up, the supply of
ammunition must at some time be exhausted. Have
we any means of determining how long the store of
energy in sun or star will suffice for its radiation ?

We know that the substances which mainly com-
pose the sun and stars are similar to those which
compose our earth. We know the capacity for heat
of these substances, and we also have determined how
much heat the sun radiates annually. From these
data, it is found by a simple calculation that the
.temperature of the sun would be lowered annually by
more than two degrees Fahrenheit, if its capacity for
heat were the same as that of water. If this capacity
were only that of the substances which compose the
great body of the earth, the lowering of temperature
would be from 5 to 10 annually. Evidently, there-
fore, the actual heat of the sun would only suffice for
a few thousand years' radiation, if not in some way re-
plenished.

When the difficulty was first attacked, it was sup-
posed that the supply might be kept up by meteors
falling into the sun. We know that in the region
round the sun, and, in fact, in the whole solar
system, are countless minute meteors, some of which
may from time to time strike the sun. The amount
of heat that would be produced by the loss of energy

208 CONSTITUTION OF THE STARS

suffered by a meteor moving many hundred miles a
second would be enormously greater than that which
would be produced by combustion. But critical ex-
amination shows that this theory cannot have any
possible basis. Apart from the fact that it could at
best be only a temporary device, there seems to be no
possibility that meteors sufficient in mass can move
round the sun or fall into it. Shooting stars show that
our earth encounters millions of little meteors every
day; but the heat produced by the collisions is ab-
solutely insignificant.

It was then shown by Kelvin and Helmholtz that
the sun might radiate the present amount of heat for
several millions of years simply from the fund of
energy collected by the contraction of its volume
through the mutual gravitation of its parts. As the sun
cools it contracts ; the fall of its substance toward the
centre, produced by this contraction, generates energy,
which energy is constantly turned into heat. The
amount of contraction necessary to keep up the
present supply maybe roughly computed ; it amounts
in round numbers to 220 feet a year, or four miles in
a century.

Accepting this view, it will almost necessarily fol-
low that the great body of the sun must be of gaseous
constitution. Were it solid, its surface would rapidly
cool off, since the heat radiated would have to be con-
ducted from the interior. Then, the loss of heat no
longer going on at the same rate, the contraction also
would stop and the generation of heat to supply the
radiation would cease. Even were the sun a liquid,

GASEOUS CONSTITUTION OF THE STARS 209

currents of liquid matter could scarcely convey to the
surface a sufficient amount of heated matter to supply
the enormous radiation. Thus the reason of the case
combines with observation of the density of the sun
to show that its interior must be -regarded as gaseous
rather than solid or liquid.

A difficult matter, however, presents itself. The
density of the sun is greater than we ordinarily see in
gases, being, as we have remarked, even greater than
the density of water. The explanation of this
difficulty is very simple : the gaseous interior is sub-
ject to compression by its superficial portions. The
gravitation on the surface being twenty-seven
times what it is on the earth, the pressure increases
twenty-seven times as fast when we go towards the
centre as it does on the earth. We should not have
to go very far within its body to find a pressure of
millions of tons on the square inch. Under such
pressure and at such an enormous temperature
as must there prevail, the distinction between a gas
and a liquid is lost ; the substance retains the
elasticity of a gas, while assuming the density of a
liquid.

It does not follow, however, that the visible surface
of the sun is a gas, pure and simple. The sudden
cooling which a mass of gaseous matter undergoes on
reaching the surface may liquefy it or even change it
into a solid. But, in either case, the sudden contrac-
tion which it thus undergoes makes it heavier and it
sinks down again to be remelted in the great furnace
below. It may well be, therefore, that the description

210 CONSTITUTION OF THE STARS

of the sun as a vast bubble is nearly true. It maybe
added that all we have said about the sun may very
well be supposed true of the stars. We have now to
consider the law of change as a sun or star contracts
through the loss of heat suffered by its radiation into
space.

This subject was very exhaustively developed by
Ritter some years since. 1 It is not practicable to give
even an abstract of Ritter's results in the present work,
especially as every mathematical investigation of the
subject must either rest on hypotheses more or less
uncertain, or must, for its application, require data
impossible to obtain. We shall, therefore, confine our-
selves to a brief outline of the main points of the sub-
ject. A fundamental proposition of the whole theory
is Lane's law of gaseous attraction, which is as follows :

When a spherical mass of incandescent gas contracts
through the loss of its heat by radiation into space, its
temperature continually becomes higher as long as the
gaseous condition is retained.

The demonstration of this law is simple enough to
be understood by anyone well acquainted with ele-
mentary mechanics and physics, and it will also fur-
nish the basis for our consideration of the subject.

We begin by some considerations on the condition
of a mass of gas held together by the mutual at-
traction of its parts. This attraction results in a
certain hydrostatic pressure, capable of being ex-
pressed as so many pounds or tons per unit of sur-
face, say a square inch. This pressure at any point

1 Wiedemann's Annalen der Physik u. Chemie, 1878 to 1883, etc.

INCREASING TEMPERATURE OF THE STARS 211

is equal to the weight of a column of the gas having
a section of one square inch and extending from the
point in question to the surface. It is a law of at-
traction, in a sphere of which the density is the same
at equal distances from its centre, that if we suppose
an interior sphere concentric with the body, the at-
traction, of all the matter outside that interior sphere,
on any point within it, is equal in every direction,
and, therefore, is completely neutralised. A point is,
therefore, drawn towards the centre only by the
attraction of matter inside the sphere on the surface
of which it lies.

At every point in the interior the hydrostatic pres-
sure must be balanced by the elastic force of the gas.
In the case of any one gas this force is proportional
to the product of the density into the absolute tem-
perature. This condition of equilibrium must be
satisfied at every point throughout the mass.

Let the two circles in the figure represent gaseous
globes of the kind supposed. The larger, A, repre-
sents the globe in a certain condition of its evolution ;
the smaller, B, its condition after its volume has

2i2 CONSTITUTION OF THE STAItS

contracted to one-half. The temperature in each
case will necessarily increase from the surface to the
centre. The law of this increase is incapable of
accurate expression, but is not necessary for our
present purpose.

Let the inner circle, C D, represent a spherical
shell of the matter forming the body, situated any-
where in the interior of the mass, but concentric
with it. Let E F be the corresponding shell after
the contraction has taken place. The case will then
be as follows :

The two shells will by hypothesis have the same
quantity of matter, both in their own substance and
throughout their interior.

In case B, the central attraction, being as the in-
verse square of the distance from the centre, will be
four times as great for each unit of matter in the
shell.

This force of attraction, tending to compress the
shell, is, in case B, exerted on a surface one quarter
as great, because the surface of a shell is proportional
to the square of its diameter.

Hence the hydrostatic pressure per unit of surface
is sixteen times as great in case B as in case A.

The elastic force of the gas, if the two bodies were
at the same temperature, would be eight times as
great in case B as in case A, being inversely as the
volume.

The hydrostatic pressure being sixteen times as
great, while the elastic force to counterbalance it is
only eight times as great, no equilibrium would be

INCREASING TEMPERATURE OF THE STARS 213

possible. To make it possible, the absolute tempera-
ture of the gas must be doubled, in order that the
elastic force shall balance the pressure. The tem-
perature of the spherical surface E F will therefore
be double that of the surface C D.

That a mass can become hotter through cooling,
may, at first sight, seem paradoxical. We shall,
therefore, cite a result which is strictly analogous.
If the motion of a comet is hindered by a resisting
medium, the comet will continually move faster.
The reason of this is that the first effect of the
medium is to diminish the velocity of the object.
Through this diminution of velocity, the comet falls
towards the sun. The increase of velocity caused by
the fall more than counterbalances the diminution
produced by the resistance. The result is that the
comet takes up a more and more rapid motion, as it
gradually approaches the sun, in consequence of the
resistance it suffers. In the same way, when a gas-
eous celestial body cools, the fall of its mass towards
the centre changes an amount of energy greater than
that radiated away from a potential to an actual
form.

The critical reader will see a weak point in this
reasoning, which it is necessary to consider. What
we have really shown is that if the mass, being in
equilibrium when it has the volume A, has to remain
in equilibrium when it is reduced to the volume B,
then its temperature must be doubled. But we have
not proved that its temperature actually will be
doubled by the fall. In fact, it cannot be doubled

2i 4 CONSTITUTION OF THE STARS

unless the energy generated by the fall of the super-
ficial portions towards the centre is sufficient to
double the absolute amount of heat. Whether this
will be the case depends on a variety of circum-
stances, including the mass of the body, and the capac-
ity of its substance for heat. If we are to proceed
with mathematical rigour, it is, therefore, necessary to
determine in any given case whether this condition is
fulfilled. Let us suppose that in any particular case
the mass is so small or the capacity for heat so con-
siderable that the temperature is not doubled by the
contraction. Then the contraction will go on further
and further, until the mass becomes a solid. But
in this case let us reverse the process. The body
being supposed nearly in a state of equilibrium in
position A, let the elastic force be slightly in excess.
Then the gas will expand. In order that it shall be re-
duced to a state of equilibrium by expansion, its tem-
perature must diminish according to the same law
that it would increase if it contracted. When its di-
ameter doubles, its temperature should be reduced to
one-half or less by the expansion, in order that the
equilibrium shall subsist. But, in the case supposed,
the temperature is not reduced so much as this.
Hence, it is too high for equilibrium by a still greater
amount and the expansion must go on indefinitely.
Thus, in the case supposed, the hypothetical equili-
brium of the body is unstable. In other words, no
such body is possible.

This conclusion is of fundamental importance. It
shows that the possible mass of a star must have an

TEMPERA TURES OF DIFFERENT STARS 215

inferior limit, depending on the quantity of matter it
contains, its elasticity under given circumstances, and
its capacity for heat. It is certain that any small mass
of gas, taken into celestial space and left to itself,
would not be kept together by the mutual attraction
of its parts, but would merely expand into indefinite
space. Possibly this might be true of the earth, if it
were gaseous. The computation would not be a
difficult one to make, but I have not made it.

In what precedes, we have supposed a single mass
to contract. But our study of the relations of tem-
perature and pressure in the two masses assumes no
relationship between them, except that of equality.
Let us now consider any two gaseous bodies, A and
B, and suppose that the body B, instead of having
the same mass as A, is another body with a different
mass.

Since the mass B may be of various sizes, according
to the amount of contraction it has undergone, let us
begin by supposing it to have the same volume as A,
but twice the mass of A. We have then to inquire
what must be its temperature in order that it may be
in equilibrium. We have first to inquire into the hy-
drostatic pressure at any point of the interior. Refer-
ring to either of the bodies in the figure of p. 211,
a spherical shell like CD will now, in the case of
the more massive body, have double the mass of the
corresponding shell of A. The attraction will also
be doubled, because the diameter of the spherical
shell is the same, while the amount of matter within
it is twice as great. Hence the hydrostatic pressure

216 CONSTITUTION OF THE STARS

per unit of surface will be four times as great, or will
vary as the square of the density. The elasticity at
equal temperatures being proportional to the density,
it follows that, were the temperature the same in the
two masses, the elasticity would be double in the
case of mass B ; whereas, to balance the hydrostatic
pressure, it should be quadrupled. The temperature
of B must, therefore, be twice as great as that of A.
It follows that in the case of stars of equal volume,
but of different masses, the temperature must be pro-
portional to the mass or density.

But how will it be if we suppose the density of the
two bodies to be the same, and, therefore, the mass
to be proportional to the volume? In this case the
attraction at a given point will be proportional to the
diameter of the body. If, then, we suppose one body
to have twice the diameter of the other, but to be of
the same density, it follows that at corresponding
points of the interior, the hydrostatic pressure will be
twice as great in the larger body. The density being
the same, it follows that the temperature must be
twice as high in order that equilibrium may be main-
tained. It follows that the stars of the greatest mass
will be at the highest temperature, unless their volume
is so great that their density is less than that of the
smaller stars.

CHAPTER XIII
STELLAR EVOLUTION

As yet this world was not, and Chaos wild

Reigned where these heavens now roll, where earth now rests.

MILTON.

Und Stiirme brausen um die Wette
Vom Meer aufs Land vom Land aufs Meer
Und bilden wiithend eine Kette
Der tiefsten Wirkung ringsumher.

GOETHE.

IT follows from the theory set forth in the last
chapter that the stars are not of fixed constitu-
tion, but are all going through a progressive change
cooling off and contracting into a smaller volume.
If we accept this result, we find ourselves face to face
with an unsolvable enigma, How did the evolution of
the stars begin ? To show the principle involved in
the question, I shall make use of an illustration drawn
from another work. An inquiring person, wandering
around in what he supposes to be a deserted building,
finds a clock running. If he knows nothing about
the construction of the clock, or the force necessary
to keep it in motion, he may fancy that it has been
running for an indefinite time just as he sees it, and
that it will continue to run until the material of which

217

218 STELLAR EVOLUTION

it is made shall wear out. But if he is acquainted
with the laws of mechanics, he will know that this is
impossible, because the continued movement of the
pendulum involves a constant expenditure of energy.
If he studies the construction of the clock, he will
find the source of this energy in the slow falling of a
weight suspended by a cord which acts upon a train of
wheels. Watching the motions, he will see that the
scape-wheel acting on the pendulum moves very per-
ceptibly every second, while he must watch the next
wheel for several seconds to see any motion. If the
time at his disposal is limited, he will not be able to
see any motion at all in the weight. But an examina-
tion of the machinery will show him that the weight
must be falling at a certain rate, and he can compute
that at the end of a certain time the weight will reach
the bottom, and the clock will stop. He can also see
that there must have been a point from above which
the weight could .never have fallen. Knowing the
rate of fall, he can compute how long the weight occu-
pied in falling from this point. His final conclusion
will be that the clock must in some way have been
wound up and set in motion by an external force a
certain number of hours or days before his inspection,
and must be again wound up by such a force unless it
is to stop.

If we accept the theory that the heat of the stars is
kept up by their slow contraction we must think of the
universe of stars as of a clock which is running down.
As we can see by the eye of reason that the weight of
the clock was higher yesterday than it is to-day, so we

STELLAR EVOLUTION 219

can compute that the stars must have been larger in
former times, and that there must have been some
finite and computable period when they were all
nebulae. Not even a nebula can give light without a
progressive change of some sort. Hence, within a cer-
tain finite period the nebulae themselves must have be-
gun to shine. How did they begin ? This is the un-
solvable question.

The process of stellar evolution may be discussed
without considering this question. Accepting as a
fact, or at least as a working hypothesis, that the stars
are contracting, we find a remarkable consistency in
the results. Year by year laws are established and
more definite conclusions reached. It is now possible
to speak of the respective ages of stars as they go
through their progressive course of changes. This
subject has been so profoundly studied and so fully
developed by Sir William and Lady Huggins that I
shall depend largely on their work in briefly setting it
forth. 1 At the same time, in an attempt to condense
the substance of many folio pages into so short a space,
one can hardly hope to be entirely successful in giving
merely the views of the original author. The follow-
ing may, therefore, be regarded as partly the views of
Sir William Huggins, condensed and arranged in the
order in which they present themselves to the writer's
mind, and partly those of the writer himself.

There is an infinite diversity among the spectra of
the stars ; scarcely two are exactly alike in all their de-
tails. But the larger number of these spectra, when

1 Publications of Sir William Huggins's Observatory, vol. i., London, 1899.

220 STELLAR EVOLUTION

carefully compared, may be made to fall in line, thus
forming a series in which the passage of one spectrum
into the next in order is so gradual as to indicate that
the actual differences represent, in the main, successive
epochs of star life rather than so many fundamental
differences of chemical constitution. Each star may
be considered to go through a series of changes an-
alogous to those of a human being from birth to old
age. In its infancy a star is simply a nebulous mass ;
it gradually condenses into a smaller volume, growing
hotter, as set forth >in the last chapter, until a stage of
maximum temperature is reached, when it begins to
cool off. Of the duration of its life we cannot form
an accurate estimate. We can only say that it is cer-
tainly to be reckoned by millions and probably by tens
of millions or even hundreds of millions of years. We
thus have in the heavens stars ranging through the
whole series from the earliest infancy to old age.
How shall we distinguish the order of development ?
Mainly by their colours and their spectra. In its first
stage the star is of a bluish white. It gradually passes
through white into yellow and red. Sir William gives
the following series of stars as an example of the suc-
cessive stages of development :

Sirius ; a Lyrae.
a Ursse Majoris.
OL Virginis.
a Aquilae.
Rigel.
a Cygni.

Capella ; the sun.

LIFE HISTORY OF A STAR 221

Arcturus.
Aldebaran.
a Orionis.

The length of the life of a star has no fixed limit ; it
depends entirely on the mass. The larger the mass,
the longer the life ; hence a small star may pass from
infancy to old age many times more rapidly than a
large one.

At the same time, up to at least the yellow stage,
the star continually grows hotter as it condenses. A
difficulty may here suggest itself in reconciling this
order with a -well-known physical fact. As a radiating
body increases in temperature, its color changes from
red through yellow to white, and the average wave-
length of its light continually diminishes. We see a
familiar example of this in the case of iron, which
when heated is first red in color and then goes
through the changes we have mentioned. The ordi-
nary incandescent electric light is yellow, the arc light,
the most intense that we can produce by artificial
means, is white. When the spectrum of a body thus
increasing in temperature is watched, the limit is found
to pass gradually from the red toward the violet end.
It would seem, therefore, that the hotter stars should
be the white ones and the cooler the yellow or red
ones.

There are, however, two circumstances to be con-
sidered in connection with the contracting star. In the
first place, the light which we receive from a star does
not emanate from its hottest interior, bu(Rom a re-
gion either upon or, in most cases, near its surface. It

222 STELLAR EVOLUTION

is, therefore, the temperature of this region which de-
termines the colour of the light. In the next place,
part of the light is absorbed by passing through the
cooler atmosphere surrounding the star. It is only
the light which escapes through this atmosphere that
we actually see.

In the case of the sun all the light which it sends
forth comes from a comparatively shallow bounding
layer, the photosphere. The most careful telescopic
examination shows no depth to this layer, which
would rapidly cool off were it not for convection cur-
rents bringing up heated matter from the interior.
It might be supposed that such a current would result
in the surface being kept at nearly as high a tempera-
ture as the interior ; but, as a matter of fact, the
opposite is the case. As the volume of gas rises, it
expands from the diminished pressure and it is thus
cooled in the very act of coming to the surface, as
well as by the rapid radiation when it reaches the
surface.

In the case of younger stars, there is probably no
photosphere, properly so called. The light which
they emit comes from a considerable distance in the
interior. Here the effect of gravity comes into play.
The more the star condenses, the greater is gravity at
its surface ; hence the more rapidly does the density
of the gas increase from the surface toward the in-
terior. In the case of the sun, the density of any
gas which may immediately surround the photosphere
must be doubled every mile or two of its depth until
we reach the photosphere. But if the sun were many

LIFE HISTORY OF A STAR 223

times its present diameter, this increase would be
very much slower. Hence, when the volume is very
great the increase of density is comparatively slow ;
there being no well-defined photosphere, the light
reaches us from a much greater depth from the in-
terior than it does at a later stage.

The gradual passing of a white star into one of the
solar type is marked by alterations in its spectrum.
These alterations are especially seen in the behaviour
of the lines of hydrogen, calcium, magnesium, and
iron. The lines of hydrogen change from broad to
thin ; those of calcium constantly become stronger.

Of the greatest interest is the question, At what
stage does the temperature of the star reach its maxi-
mum and the body begin to cool ? Has our sun
reached this stage ? This is a question to which,
owing to the complexity of the conditions, it is im-
possible to give a precise answer. It seems probable,
however, that the highest temperature is reached in
about the stage of our sun. Accepting Sir William
Huggins's view, the reason the light is not then bluest
is that it suffers a strong selective absorption by the
gases surrounding the photosphere. We know this
to be the case with the sun. According to Vogel, the
removal of the sun's atmosphere would make its
light two-and-a-half times as bright at the blue-violet
end of the spectrum.

The general fact that every star has a life history
that this history will ultimately come to an end
that it must have had a beginning in time is indi-
cated by so great a number of concurring facts that

224 STELLAR EVOLUTION

no one who has most profoundly studied the subject
can have serious doubts upon it. Yet there are some
unsolved mysteries connected with the case, which
might justify a waiting for further evidence, coupled
with a certain degree of scepticism. Of the questions
connected with the case the most serious one is raised
by the geologists.

On the theory set forth in the last chapter, that
the radiant energy sent out is balanced by the con-
tinual loss of potential energy due to the contraction,
the age of the sun can be at least approximately esti-
mated. About twenty millions of years is the limit
of time during which it could possibly have radiated
anything like its present amount of energy. But this
conclusion is directly at variance with that of geology.
The age of the earth has been approximately esti-
mated from a great variety of geological phenomena,
the concurring result being that stratification and
other geological processes must have been going on
for hundreds nay, thousands of millions of years.
This result is in direct conflict with the only physical
theory which can account for the solar heat.

The nebulae offer a similar difficulty. Their ex-
treme tenuity and their seemingly almost unmaterial
structure appear inadequate to account for any such
mutual gravitation of their parts as would result in
the generation of the flood of energy which they are
constantly radiating. What we see must, therefore,
suggest at least the possibility that all shining heav-
enly bodies have connected with them some source
of energy of which science can, as yet, render no

STELLAR EVOLUTION 225

account. Facts are accumulating which converge to
the view that forms of substance exist which are
neither matter nor ether, but something between the
two perhaps primeval substance from which matter
itself was evolved. In this ethereal substance is stored
an almost exhaustless supply of energy, the with-
drawal of which results in the condensation of the
substance into matter. More than this it seems hard
to say until we have either seen the nebulae contract-
ing in volume, or have made such estimates of their
probable masses that we can compute the amount of
contraction they must undergo to maintain the supply
of energy.

CHAPTER XIV

THE STRUCTURE OF THE HEAVENS

He who through vast immensity can pierce,

See worlds on worlds compose one universe,

Observe how system into system runs,

What other planets circle other suns,

What varied being peoples every star,

May tell why Heaven has made us as we are. POPE.

THE problem of the structure and duration of the
universe is the most far-reaching with which the
mind has to deal. Its solution may be regarded as
the ultimate object of stellar astronomy, the possibil-
bility of reaching which has occupied the minds of
thinkers since the beginning of civilisation. Before
our time the problem could be considered only from
the imaginative or the speculative point of view.
Although we can to-day attack it to a limited extent
by scientific methods, it must be admitted that we
have scarcely taken more than the first step toward
the actual solution. We can do little more than
state the questions involved, and show what light, if
any, science is able to throw upon the possible
answers.

First, we may inquire as to the extent of the
universe of stars. Are the latter scattered through

226

SS THE UNIVERSE INFINITE? 227

infinite space, so that those we see are merely that
portion of an infinite collection which happens to be
within reach of our telescopes, or are all the stars
contained within a certain limited space ? In the
latter case, have our telescopes yet penetrated to the
boundary in any direction ? In other words, as, by
the aid of increasing telescopic power, we see fainter
and fainter stars, are these fainter stars at greater
distances than those before known, or are they smal-
ler stars contained within the same limits as those we
already know ? Otherwise stated, do we see stars
on the boundary of the universe ?

Secondly, granting the universe to be finite, what
is the arrangement of the stars in space ? Especially,
what is the relation of the galaxy to the other stars ?
In what sense, if any, can the stars be said to form a
permanent system ? Do the stars which form the
Milky Way belong to a different system from the
other stars, or are the latter a part of one universal
system ?

Thirdly, what is the duration of the universe in
time ? Is it fitted to last for ever in its present form,
or does it contain within itself the seeds of dissolu-
tion ? Must it, in the course of time, in we know
not how many millions of ages, be transformed into
something very different from what it now is ? This
question is intimately associated with the question
whether the stars form a system. If they do, we
may suppose that system to be permanent in its
general features ; if not, we must look further for our
conclusion.

228 STRUCTURE OF THE HEAVENS

The first and third of these questions will be
recognised by students of Kant as substantially those
raised by the great philosopher in the form of anti-
nomies. Kant attempted to show that both the
propositions and their opposites could be proved or
disproved by reasoning equally valid in either case.
The doctrine that the universe is infinite in duration
and that it is finite in duration are both, according to
him, equally susceptible of disproof. To his reason-
ing on both points the scientific philosopher of to-
day will object that it seeks to prove or disprove, a
priori, propositions which are matters of fact, of
which the truth can be therefore settled only by an
appeal to observation. The more correct view is
that afterward set forth by Sir William Hamilton,
that it is equally impossible for us to conceive of in-"
finite space (or time), or of space (or time) coming to
an end. But this inability merely grows out of the
limitations of our mental power, and gives us no clue
to the actual universe. So far as the questions are
concerned with the latter, no answer is valid unless
based on careful observation. Our reasoning must
have facts to start from before a valid conclusion can
be reached.

The first question we have to attack is that of the
extent of the universe. In its immediate and practi-
cal form, it is whether the smallest stars that we see
are at the boundary of a system, or whether more
and more lie beyond to an infinite extent. This
question we are not yet ready to answer with any
approach to certainty. Indeed, from the very nature

IS THE UNIVERSE INFINITE? 229

of the case, the answer must remain somewhat in-
definite. If the collection of stars which forms the
Milky Way be really finite, we may not yet be able
to see its limit. If we do see its limit, there may yet
be, for aught we know, other systems and other
galaxies, scattered through infinite space, which must
for ever elude our powers of vision. Quite likely the
boundary of the system may be somewhat indefinite,
the stars gradually thinning out as we go farther and
farther, so that no definite limit can be assigned. If
all stars are of the same average brightness as those
we see, all that lie beyond a certain distance must
evade observation, at least as individual stars, for the
simple reason that they are too far off to be visible
in our telescopes.

There is a law of optics which throws some light
on the question. Suppose the stars to be scattered
through infinite space in such a way that every great
portion of $pace is, in the general average, about
equally rich in stars. Then imagine that, at some
great distance, say that of the average stars of the
sixth magnitude, we describe a sphere having its
centre in our system. Outside this sphere, describe
another one, having a radius greater by a certain
quantity, which we may call S. Outside that let there
be another of a radius yet greater by S, and so on
indefinitely. Thus we shall have an endless succes-
sion of concentric spherical shells, eaqh of the same
thickness, S. The volume of each of these regions
will be nearly proportional to the square of the diame-
ters of the spheres which bound it. Hence, supposing

2 30 STRUCTURE OF THE HEAVENS

an equal distribution of the stars, each of the
regions will contain a number of stars increasing as
the square of the radius of the region. Since the
amount of light which we receive from each individ-
ual star is as the inverse square of its distance, it
follows that the sum-total of the light received from
each of these spherical shells will be equal. Thus,
as we include sphere after sphere, we add equal
amounts of light without limit. The result of the suc-
cessive addition of these equal quantities, increasing
without limit, would be that if the system of stars
extended out indefinitely the whole heavens would
be filled with a blaze of light as bright as the sun.

Now, as a matter of fact, such is very far from
being the case. It follows that infinite space is not
occupied by the stars. At best there can only be"
collections of stars at great distances apart.

The nearest approximation to such an appearance
as that described is the faint, diffused light of the
Milky Way. But so large a fraction of this illumin-
ation comes from the stars which we actually see in
the telescope that it is impossible to say whether any
visible illumination results from masses of stars too
faint to be individually seen. Whether the cloud-like
impressions which Barnard has found on long-ex-
posed photographs of the Milky Way are produced
by countless distant stars, too faint to impress
themselves individually even upon the most sensitive
photographic plate, is a question which cannot yet
be answered. But even if we should answer it in
the affirmative, the extreme faintness of the light

76 1 THE UNIVERSE INFINITE! 231

shows that the stars which produce it are not scat-
tered through infinite space ; but that, although they
may extend much beyond the limits of the visible stars,
they thin out very rapidly. The evidence, therefore,
seems to be against the hypothesis that the stars we
see form part of an infinitely extended universe.

But there are two limitations to this conclusion.
It rests upon the hypothesis that light is never lost
in its passage to any distance, however great. This
hypothesis is in accordance with our modern theories
of physics, yet it cannot be regarded as an established
fact for all space^even if true for the distances of the
visible stars. | About half a century ago Struve pro-
pounded the contrary hypothesis that the light of
the more distant stars suffers an extinction in its
passage to us. But this had no other basis than the
hypothesis that the stars were equally thick out to
the farthest limits at which we could see them. It
might be said that he assumed an infinite universe,
and, from the fact that he did not see the evi-
dence of infinity, concluded that light was lost.
The hypothesis of a limited universe and no ex-
tinction of light, while not absolutely proved, must
be regarded as the one to be accepted until further
investigation shall prove its unsoundness.

The second limitation arises from the possible
structure of an infinite universe. The mathematical
reader will easily see that the conclusion that an in-
finite universe of stars would fill the heavens with a
blaze of light, rests upon the hypothesis that every
region of space of some great but finite extent is, on

232 STRUCTURE OF THE HEAVENS

the average, occupied by at least one star. In other
words, the hypothesis is that, if we divide the total
number of the stars by the number of cubic miles of
space, we shall have a finite quotient. But an infin-
ite universe can be imagined which does not fill this
condition. Such will be the case with one con-
structed on the celebrated hypothesis of Lambert, pro-
pounded in the latter part of the eighteenth century.
This author was an eminent mathematician who
seems to have been nearly unique in combining the
mathematical and the speculative sides of astronomy.
He assumed a universe constructed on an extension
of the plan of the solar system. The smallest sys-
tem of bodies is composed of a planet with its sat-
ellites. We see a number of such systems, designated
as the Terrestrial, the Martian (Mars and its sat-
ellites), the Jovian (Jupiter and its satellites), etc., all
revolving round the sun, and thus forming one
greater system, the solar system. Lambert extended
the idea by supposing that a number of solar systems,
each formed of a star with its revolving planets and
satellites, were grouped into a yet greater system.
A number of such groups form the great system
which we call the galaxy, and which comprises all
the stars we can see with the telescope. The more
distant clusters may be other galaxies. All these
systems again may revolve around some distant
centre, and so on to an indefinite extent. Such a
universe, how far so ever it might extend, would not
fill the heavens with a blaze of light, and the more
distant galaxies might remain for ever invisible to us.

SS THE UNIVERSE INFINITE? 233

But modern developments show that there is no
scientific basis for this conception, attractive though
it be by its grandeur.

So far as our present light goes, we must conclude
that, although we are unable to set absolute bounds
to the universe, yet the great mass of stars is in-
cluded within a limited space the extent of which we
have as yet no evidence. Outside of this space there
may be scattered stars or invisible systems. But if
these systems exist, they are distinct from our own.

The second question, that of the arrangement of
the stars in space, is one on which it is equally diffi-
cult to propound a definite general conclusion. So
far, we have only a large mass of faint indications,
based on researches which cannot be satisfactorily
completed until great additions are made to our fund
of knowledge.

A century ago Sir William Herschel reached the
conclusion that our universe was composed of a com-
paratively thin but widely extended stratum of stars.
To introduce a familiar object, its figure was that of
a large, thin grindstone, our solar system being near
the centre. Considering only the general aspect of
the heavens, this conclusion was plausible. Suppose
a mass of a million of stars scattered through a space
of this form. It is evident that an observer in the
centre, when he looked through the side of the stratum,
would see few stars. The latter would become more
and more numerous as he directed his vision toward
the circumference of the stratum. In other words,
assuming the universe to have this form, we should

234

STRUCTURE OF THE HEAVENS

see a uniform, cloud-like arch spanning the heavens
a galaxy in fact.

This view of the figure of the universe was also
adopted by Struve, who was, the writer believes, the
first astronomer after Herschel to make investigations
which can be regarded as constituting an important
addition to thought on the subject. To a certain ex-
tent we may regard the hypothesis as incontestable.
The great mass of the visible stars is undoubtedly
contained within such a figure as is here supposed.

To show this let Fig. i represent a cross section of
the heavens at right angles to the Milky Way, the

solar system being in the centre. It is an observed
fact that the stars are vastly more numerous in
the galactic regions G G than in the regions P P.
Hence, if we suppose the stars equally scattered, they
must extend much farther out in G G than in P P. If
they extend as far in the one direction as in the other,
then they must be more crowded in the galactic belt.
It will still remain true that the greater number of the
stars are included in the flat region G G P P, those out-
side this stratum being comparatively few in number.
But we cannot assume that this hypothesis of the
form of the universe affords the basis for a satisfactory

FORM OF THE UNIVERSE 235

conception of its arrangement. Were it the whole
truth, the stars would be uniformly dense along the
whole course of the Milky Way. Now, it is a familiar
fact that this is not the case. The Milky Way is not
a uniformly illuminated belt, but a chain of irregular
cloud-like aggregations of stars. Starting from this
fact as a basis, our best course is to examine the most
plausible hypotheses we can make as to the distribu-
tion of the stars which do not belong to the galaxy,
and see which agrees best with observation.

Let figure 2 represent a section of the galactic
ring or belt in its own plane, with the sun near the

x J* * ^ ' ~*

N %

f i c ; * *; i

\ : iiv '.A

H- N / J?*

L; B!

/ I

r I

-' /

v*v ^*i* *

x ;3.%v . ^'S* \ !;U

FlG.2. Flc . 3 .

centre, S. To an observer at a vast distance in the
direction of either pole of the galaxy, 1 the latter would
appear of this form. Let Fig. 3 represent a cross

1 Regarding the galaxy as a belt spanning the heavens, the central line of
which is a great circle, the poles of the galaxy are the two opposite points in the
heavens everywhere 90 from this great circle. Their direction is that of the
two ends of the axle of the grindstone, as seen by an observer in the centre,
while the galaxy would be the circumference of the stone

236 STRUCTURE OF THE HEAVENS

section as viewed by an observer in the plane of the gal-
axy at a great distance outside of it. How would the
stars that do not belong to the galaxy be situated ?
We may make three hypotheses :

1. That they are situated in a sphere (A B) as large
as the galaxy itself. Then the whole universe of
stars would be spherical in outline, and the galaxy
would be a dense belt of stars girdling the sphere.

2. The remaining stars may still be contained in a
spherical space (K L), of which the diameter is much
less than that of the galactic girdle. In this case our
sun would be one of a central agglomeration of stars,
lying in or near the plane of the galaxy.

3. The non-galactic stars may be equally scattered
throughout a flat region (M N P Q), of the grindstone
form. This would correspond to the hypothesis of
Herschel and Struve.

There is no likelihood that either of these hypotheses
is true in all the geometric simplicity with which
I have expressed it. Stars are doubtless scat-
tered to some extent through the whole region M N
P Q, and it is not likely that they are confined within
limits defined by any geometrical figure. The most
that can be done is to determine to which of the
three figures the mutual arrangement most nearly
corresponds.

The simplest test is that of the third hypothesis as
compared with the other two. If the third hypo-
thesis be true, then we should see the fewest stars
in the direction of the poles of the galaxy ; and the
number in any given portion of the celestial sphere,

FORM OF THE UNIVERSE 237

say one square degree, should continually increase,
slowly at first, more rapidly afterwards, as we went
from the poles toward the circumference of the
galaxy. At a distance of 60 from the poles and
30 from the central line or circumference we should
see perhaps twice as many stars per square degree
a.s near the poles.

Were it possible to determine the distance of a
star as readily as we do its direction, the problem of
the distribution of the stars in space would be at
once solved. This not being the case, we must first
study the apparent arrangement of the stars with
respect to the galaxy, with a view to afterward draw-
ing such conclusions as we can in regard to their
distance.

CHAPTER XV

APPARENT DISTRIBUTION OF THE STARS
IN THE SKY

Zwei Dingen erfiillen das Gemuth mit immer neuer und zunehmender
Bewunderung und Erfurcht, je ofter und anhaltender sichdas Nachdenkting
damit beschaftigt . der bestirnte Himmel tiber mir und das moralische
Gesetz in mir. KANT.

OUR question now is, How are the stars, as we
see them, distributed over the sky ? We know
in a general way that there are vastly more stars
round the belt of the Milky Way than in the re-
mainder of the heavens. But we wish to know in
detail what the law of increase is from the poles of
the galaxy to the belt itself.

In considering any question of the number of stars
in a particular region of the heavens, we are met by
a fundamental difficulty. We can set no limit to
the minuteness of stars, and the number will depend
upon the magnitude of those which we include in
our count. As already remarked, there are, at least
up to a certain limit, three or four times as many
stars of each magnitude as of the magnitude next
brighter. Now, trie smallest stars that can be seen,
or that may be included in any count, vary greatly

238

DISTRIBUTION OF LUCID STARS 239

with the power of the instrument used in making the
count. If we had any one catalogue, extending over
the whole celestial sphere, and made on an absolutely
uniform plan, so that we knew it included all the
stars down to some given magnitude, and no others,
it would answer our immediate purpose. If, however,
one catalogue including the stars in a certain part of
the sky should extend only to the ninth, magnitude,
while another, covering another part, should extend
to the tenth, we should be led quite astray in assum-
ing that the number of stars in the two catalogues
expressed the star density in the regions which they
covered. The one would show three or four times
as many stars as the other, even though the actual
density in the two cases were the same.

If we could be certain, in any one case, just what
the limit of magnitude was for any catalogue, or if
the magnitudes in different catalogues always cor-
responded to absolutely the same brightness of the
star, this difficulty would be obviated. But this is
the case only with that limited number of stars whose
brightness has been photometrically measured. In
all other cases our count must be more or less un-
certain. One illustration of this will suffice :

I have already remarked that in making the pho-
tographic census of the southern heavens, Gill and
Kapteyn did not assume that stars of which the
images were equally intense on different plates were
actually of the same magnitude. Each plate was
assumed to have a scale of its own, which was fixed by
comparing the intensity of the photographic impres-

2 4 o APPARENT DISTRIBUTION OF STARS

sions of those stars whose magnitudes had been
previously determined with these determinations, and
thus forming as it were a separate scale for each
plate. But, in forming the catalogue from the inter-
national photographic chart of the heavens, it is
assumed that the photographs taken with telescopes
of the same aperture, in which the plates are exposed
for five minutes, will all correspond, and that the
smallest stars found on the plates will be of the
eleventh magnitude.

In the case of the lucid stars this difficulty does
not arise, because the photometric estimates are on .a
Distribution sufficiently exact and uniform scale to
of the Lucid enable us to make a count, which shall be
Stars. nearly correct, of all the stars down to, say,
magnitude 6.0 or some limit not differing greatly,
from this. Several studies of the distribution of these
stars have been made ; one by Gould in the Urano-
metria Argentina, one by Schiaparelli, and another
by Pickering. The counts of Gould and Schiaparelli,
the former having special reference to the Milky
Way, are best adapted to our purpose. The most
striking result of these studies is that the condensa-
tion in the Milky Way seems to commence with the
brightest stars. A little consideration will show that
we cannot, with any probability, look for such a con-
densation in the case of stars near to us. Whatever
form we assign to the stellar universe, we shall expect
the stars immediately around us to be equally dis-
tributed in every direction. Not until we approach
the boundary of the universe in one direction, or some

DISTRIBUTION OF LUCID STARS 241

great masses like those of the galaxy in another
direction, should we expect marked condensation
round the galactic belt. Of course we might imagine
even the nearest stars to be most numerous in the
direction round the galactic circle. But this would
imply an extremely unlikely arrangement, our system
being as it were at the point of a conical region
richer in stars than the region around it. It is clear
that if such were the case for one point, it could not
be true if our sun were placed anywhere except at
this particular point. Such an arrangement of the
stars round us is outside of all reasonable probability.
Independent evidence of the equal distribution of the
nearer stars will hereafter be found in the proper
motions. If, then, the nearer stars are equally dis-
tributed round us, and only distant ones can show
a condensation toward the Milky Way, it follows that
among the distant stars are some of the brightest in
the heavens, a fact which we have already shown to
follow from other considerations.

As we have to study the distribution of the stars
with respect to the galaxy, the precise position of the
latter enters into our problem. There is no difficulty
in mapping out its general course by unaided eye
observations of the heavens or a study of maps of the
stars. Looking at the heavens, we shall readily see
that it crosses the equator at two opposite points ; the
one east of the constellation Orion, between 6h. and
7h. of right ascension ; the other at the opposite point,
in Aquila, between i8h. and igh. It makes a con-
siderable angle with the equator, somewhat more than

242 APPARENT DISTRIBUTION OF STARS

60. Consequently it passes within 30 of either
celestial pole. The point nearest of approach to the
north pole is in the constellation Cassiopeia.

Its position can readily be determined by noting
the general course of its brighter portions on a map
of the stars, and then determining, by inspection or
otherwise, the circle which will run most nearly
through those portions. It is thus found that the
position is nearly always near a great circle of
the sphere. From the very nature of the case the
position of this circle will be a little indefinite, and
probably the estimates made of it have been based
more on inspection than on computation. The fol-
lowing positions have been assigned to the pole of
the galaxy :

Gould R. A. = i2h. 4im. Dec. = + 27 21'

Herschel, W . . . . " " i 2 h. 29111. " " +31 30'

Seeliger " " i 2 h. 49111. " " + 27 30'

Argelander " " i 2 h. 4om. " "+28 5'

The author, with the assistance of Mr. Wm. T. Car-
rigan, has made an independent determination by find-
ing the great circle which will pass nearest to some
40 of the brightest regions of the galaxy. The result
is different according as we include or omit the diver-
gent branch toward the west between Cygnus and
Aquila. Including the branch, the position of the
galactic pole is,

R. A. = i2h. 44m. Dec. = 26 48'
Excluding the branch it is,

R. A. = i2h. 5im. Dec. = 27 12'

DISTRIBUTION OF LUCID STARS 243

Very remarkable is the fact, first pointed out by Sir
J. Herschel, and more fully developed by Gould, that
a belt of bright stars encircles the heavens but does
not exactly coincide with the Milky Way. It inter-
sects the galaxy at the points nearest the celestial
poles, one node being near the Southern Cross and
the other in Cassiopeia. This belt includes the
brightest stars in a number of constellations, from
Canis Major through the southern region of the
heavens and back to Scorpius. In the northern
heavens the brightest stars in Orion, Taurus, Cas-
siopeia, Cygnus, and Lyra belong to it. It would not
be safe, however, to assume that the existence of
this belt results from anything but the chance dis-
tribution of the few bright stars which form it. In
order to reach a definite conclusion bearing on the
structure of the heavens, it is advisable to consider the
distribution of the lucid stars as a whole.

Dr. Gould found that the stars brighter than the
fourth magnitude are arranged more symmetrically
relatively to the belt of bright stars we have just de-
scribed than to the galactic circle. This and other facts
suggested to him the existence of a small cluster within
which our sun is eccentrically situated, and which is
itself not far from the middle plane of the galaxy.
This cluster appears to be of a flattened shape and to
consist of somewhat more than 400 stars of magni-
tudes ranging from the first to the seventh. Since
Gould wrote, the extreme inequality in the intrinsic
brightness of the stars has been brought to light and
seems to weaken his explanation of the fact.

244 APPARENT DISTRIBUTION OF STARS

A very thorough study of the subject, but without
considering the galaxy, has also been made by
Schiaparelli. The work is based on the photometric
measures of Pickering and the Uranometria Argen-

STAR-DENSITY OF THE NORTHERN HZMISPHERE

Una of Gould. One of its valuable features is a series
of planispheres, showing in a visible form the star
density in every region of the heavens for stars of
various magnitudes. We reproduce on a reduced scale
two of these planispheres. They were constructed by
Schiaparelli in the following way : The entire sky

DISTRIBUTION OF LUCID STARS

245

was divided into 36 zones by parallels of declination
5 apart. Each zone was divided into spherical
trapezia by hour-circles taken at intervals of 5 from
the equator up to 50 of north or south declination ;

STAR-DENSITY OF THE SOUTHERN HEMISPHERE

of 10 from 50 to 60 ; of 1 5 from 60 to 80 ; of 45 from
80 to 85, while the circle within 5 of the pole was
divided into four regions. In this way 1800 areas,
not excessively different from each other, were formed.
The star-density, as it actually is, might be indicated

246 APPARENT DISTRIBUTION OF STARS

by the number of stars of these regions. As a matter
of fact, however, the density obtained in this way
would vary too rapidly from one area to the adjoining
one, owing to the accidental irregularities of distribu-
tion of the stars. An adjustment was, therefore, made
by rinding in the case of each area the number of
stars contained in i /2OO of the entire sphere, includ-
ing the region itself and those immediately around it.
The number thus obtained was considered as giving
the density for the central region. The total number
of stars being 4303, the mean number in i / 200 of the
whole sphere is 21.5, and the mean in each area is 10.4.

The numbers on the planisphere given in each area
express the star density of the region, or the number
of stars per 100 square degrees, expressed generally to
the nearest unit, the half-unit being sometimes added/

A study of the reproduction which we give will
show how fairly well the Milky Way may be traced
out round the sky by the tendency of those stars
visible to the naked eye to agglomerate near its course.
In other words, were the cloud-forms which make up
the Milky Way invisible to us, we should still be able
to mark out its course by the crowding of the lucid
stars toward it. Asa matter of interest, I have traced
out the central line of the darker shaded portions of the
planispheres as if they were the galaxy itself. The
nearest great circle to the course of this line was then
found to have its pole in the following position :

R. A.; i2h. 1 8m.
Dec. + 27.

This estimate was made without having at the time

DISTRIBUTION OF FAINTER STARS 247

any recollection of the position of the galaxy given by
other authorities. Compared with the positions given
in the last chapter by Gould and Seeliger, it will be
seen that the deviation is only 5 in right ascension >
while the declinations are almost exactly similar.
We infer that the circle of condensation found in
this way makes an angle with the galaxy of less
than 5.

The most thorough study of the distribution of the
great mass of stars relative to the galactic plane has
been made by Seeliger in a series of papers Dis t ribu tion
presented to the Munich Academy from oftheFaint-
1884 to 1898. The data on which they are er Stars,
based are the following :

1. The Bonner Durchmusterungoi Argelander and
Schonfeld, described in our third chapter. The two
works under this title are supposed to include all the
stars to the ninth magnitude, from the north pole to
24 of south declination. But there are some incon-
sistencies in the limit of magnitude which we shall
hereafter mention.

2. The " star gauges " of the two Herschels. These
consisted simply in counts of the number of stars visi-
ble in the field of view of the telescope when the lat-
ter was directed toward various regions of the sky.
Sir William Herschel's gauges were partly published
in the Philosophical Transactions. A number of un-
published ones were found among his papers by
H olden and printed in the publications of the Wash-
burn Observatory, vol. ii. The younger Herschel,
during his expedition to the Cape of Good Hope,

248 APPARENT DISTRIBUTION OF STARS

continued the work in those southern regions of the
sky which could not be seen in England.

3. A count of the stars by Celoria, of Milan, in a
zone from the equator to 6 N. Dec., extending round
the heavens.

From what has been said, the first question to oc-
cupy our attention is that of the distribution of the
stars with reference to the galactic plane, or, rather,
the great circle forming the central line of the Milky
Way.

The whole sky is divided by Seeliger into nine
zones or regions, each 20 in breadth, by small circles
parallel to the galactic circle. Region I. is a circle of
20 radius, whose centre is the north galactic pole.
Round this central circle is a zone 20 in breadth,
called zone II. Continuing the division, it will be
seen that zone V. is the central one of the Milky Way,
extending 10 on each side of the galactic circle. VI.
is the zone next south of the galaxy, and so on to IX.,
which is the circle 40 in diameter round the south
galactic pole.

The condensed result of the work is shown in the
following table.

Column " Area " shows the number of square de-
grees in each region, so far as included in the survey.
It will be remarked that the catalogues in question do
not include the whole sky, as they stop at 24 S.Dec.

Column " Stars " shows the number of stars to
magnitude 9.0 found in each area.

Column " Density " is the quotient of the number of
stars by the area, and is, therefore, the mean number

DISTRIBUTION OF FAINTER STARS 249

of stars per square degree in each region. In the last
column these numbers are corrected, for certain anom-
alies in the magnitudes given by the catalogues, so as
to reduce them to a common standard.

Area. Corrected

Region. Degrees. Stars. Density. Density.

I i,398.7 4,277 3- 6 2.78

II 3,!46.9 I0 , l8 5 3- 2 4 3-3

III 5,126.6 19,488 3.80 3.54

IV 4,589-8 24,492 5.34 5.32

V 4,519.5 33,267 7-36 8.17

VI 3,97i-5 23,580 5.94 6.07

VII... 2,954.4 11,790 3.99 3.71

VIII i,79- 6 6 ,375 3-56 3.21

IX 468.2 1,644 3-5 1 3-i4

A study of the last two columns is decisive of one
of the fundamental questions already raised. The
star-density in the several regions increases continu-
ously from each pole (regions I. and IX.) to the
galaxy itself. If the latter were a simple ring of stars
surrounding a spherical system of stars, the star-
density would be about the same in regions I., II.,
and III., and also in VII., VIII., and IX., but would
suddenly increase in IV. and VI. as the boundary of
the ring was approached. Instead of such being the
case, the numbers 2.78, 3.03, and 3.54 in the north,
and 3.14, 3.21, and 3.71 in the south, show a progres-
sive increase from the galactic pole toward the galaxy
itself.

The conclusion to be drawn is a fundamental one.
The universe, or, at least, the denser portions of it,
is really flattened between the galactic poles, as sup-

250 APPARENT DISTRIBUTION OF STARS

posed by Herschel and Struve. In the language of
Seeliger : " The Milky Way is no merely local phe-
nomenon, but is closely connected with the entire
constitution of our stellar system."

This conclusion is strengthened by a study of the
data given by Celoria. It will be remarked that the
zone counted by this astronomer cuts the Milky Way
diagonally at an angle of about 62, and, therefore,
does not take in either of its poles. Consequently,
regions I. and IX. are both left out. For the re-
maining seven regions the results are shown as fol-
lows : We show first the area, in square degrees, of
each of the regions, II. to VIII., included in Celoria's
zone. Then follows in the next column the number
of stars counted by Celoria, and, in the third, the
number enumerated in the Durchmusterung, in these
portions of each region. The quotients show the
star-density, or the mean number of stars per square
degree, recorded by each authority :

Area. Number of Stars. Star-Density.

Region. Degrees. Cel. D. M. Cel. D. M.

II 44-4 2 7,35 2 J ' 2 3 6 7- 6 3-4

III 284.6 22,551 932 79.3 3.28

IV 254.6 29,469 1,488 115.7 5.83

V... 284.6 41,820 1,833 146.9 6.44

VI 284.6 3 T ,76 M7 2 1 1 1-4 5- 22

VII 329.5 25,618 1,342 77.7 4.07

VIII 314.5 22,264 1,184 708 3.77

It will be seen that the law of increasing star-density
from near the galactic pole to the galaxy itself is
of the same general character in the two cases. The

DISTRIBUTION OF FAINTER STARS 251

number of stars counted by Celoria is generally be-
tween 1 8 and 25 times the number in the Durch-
musterung.

An important point to be attended to hereafter is
that the star-density of the Milky Way itself, as
found by Celoria and the authors of the Durch-
musterung, is between two or three times that near
the galactic poles. Very different is the result de-
rived from the Herschelian gauges, which is this :

Region....!. II. III. IV. V. VI. VII. VIII. IX.
Density.. . 107 154 281 560 2019 672 261 154 in

From the gauges of the Herschels it follows that
the galactic star-density is nearly 20 times that near
the galactic poles. At these poles the Herschels
counted only about 50 per cent, more stars than Celoria.
In the galaxy itself they counted 14 for every one by
Celoria. There is little doubt as to the principal
cause of this discrepancy. The observations by the
first two authorities were made with smaller telescopes
than that of Herschel, and they failed to count all the
visible stars of the Milky Way. The recent compari-
sons of the Durchmusterung with the heavens, mostly
made since Seeliger worked out the results we have
given, show that the limit of magnitude to which this
list extends is far from uniform, and varies with the
star-density. In regions poor in stars, all of the
latter to the tenth magnitude are listed ; in the richer
regions of the galaxy the list stops, we may suppose,
with the ninth magnitude, or even brighter. Yet, in
all cases, the faintest stars listed are classed as of

252 APPARENT DISTRIBUTION OF STARS

magnitude 9.5. Thus a ninth-magnitude star in the
galaxy, according to the Durckmusterung, is markedly
brighter than one of this magnitude elsewhere.

Having found that the stars of every magnitude
show a tendency to crowd toward the region of the
Distribu- Milky Way, the question arises whether this
tionofthe is true of those stars which have a sensible
in^Sensr P r P er niotion. Kapteyn has examined this
bie Proper question in the case of the Bradley stars.
Motion. j_[j s conclusion is that those having a con-
siderable proper motion, say more than 5" per cent-
ury, are nearly equally distributed over the sky, but
that when we include those having a small proper
motion, we see a continually increasing tendency to
crowd toward the galactic plane.

It seems to the writer that the uncertainty as to
the smaller proper motions of the Bradley stars ren-
ders this result quite unreliable. To reach a more
definite conclusion, we must base our work on lists
of proper motions which are as nearly complete
within their limits as it is possible to make them.
Such lists have been made by Auwers and Boss, their
work being based on their observations of zones of
stars for the catalogue of the Astronomische Gesell-
schaft. The zone observed by Auwers was that be-
tween 15 and 20 of N. Dec.; while Boss's was
between i and 5. To speak more exactly, the
limits were from 14 50' to 20 10' and o 50' to 5
10', each zone of observation overlapping 10' on the
adjoining one. Thus the actual breadths were 5 20'
and 4 20'. Within these respective limits, Auwers,

PROPER-MOTION STARS

253

by a comparison with previous observations, found
1300 stars having an appreciable proper motion, and
Boss 295. But Boss's list is confined to stars having
a motion of at least 10"; of such the list of Auwers
contains 431. The number of square degrees in the
two zones is 1556 and 1830, respectively. The cor-
responding number of stars with proper motions ex-
tending 10" is for each 100 square degrees :

In Boss's zone, 18.9.
In Atiwers's zone, 23.9.

The question whether the greater richness of
nearly 25 per cent, in Auwers's zone is real is one
to which it is not easy to give a conclusive answer.
The probability, however, seems to be that it is
mainly due to the greater richness of the material
on which Auwers's proper motions are based. Hap-
pily, the question is not essential in the present
discussion.

We now examine the question of the respective
richness of proper-motion stars in this way :

Each of these zones cuts the galaxy at a consider-
able angle in two opposite regions. Each zone, as a
matter of course, has a far greater richness of stars
per unit of surface in the two galactic regions than
in the intermediate regions. We, therefore, divide
each zone in four strips, two including the galactic
regions and two the intermediate regions. The
boundaries are somewhat indefinite ; we have fixed
them by the richness of the total number of stars.
For the galactic strips we take in Boss's zone the

254 APPARENT DISTRIBUTION OF STARS

strip between 5h. and 8h. of R. A. and that between
1 7h. and 2oh. Each of these strips being 3)1. in
length, the two together comprise one quarter the
total surface of the zone. If the proper-motion stars
crowd towards the galaxy like others do, then the
numbers in the galactic region should be proportional
to the total number observed in the region. But
if they are equally distributed, then there should be
only one quarter as many in the galactic region as in
the other regions.

In the case of Boss's zone, the total number of
stars observed, and of those having a proper motion,
found in the four regions described, are as follows :

Star-
Total Number Proper Density
Observed. Motions, per hour.

Galactic strip, 5h. to 8h. 1,614 2 4 8

Galactic strip, i yh. to 2oh i,34 36 12

Intermediate strip, 8h. to i yh 2,458 124 12

Intermediate strip, 2oh. to 5h 2,831 in 12

The last column contains the average number of
proper-motion stars per hour in each of the four strips.
There is evidently no excess of richness in the galactic
strips, but rather a deficiency in the strip near 6h.,
which we may regard as accidental.

In the case of Auwers's zone, the galactic strips
are those between 5h. and 8h., and again between i8L
and 2 ih. Here, as in the other case, the galactic strips
include one quarter of the whole area. But, owing
to the greater richness of the sky, they include nearly
forty per cent, of the whole number of stars. Then,
if the-proper motion stars are equally distributed, one-

STARS WITH PROPER MOTION 255

quarter should be found in the galactic regions, and
if they are proportional to the number of stars ob-
served, forty per cent, should be within these regions.
Grouping the regions outside the galaxy together, as
we need not distinguish between them, the result is

as follows :

Star

Stars Proper Density

Observed. Motions, per hour.

Galactic strip, 5h. to 8h 1,797 155 52

Galactic strip, i8h. to 2ih 1,984 202 67

Outside the galaxy 6,008 901 50

We see that in the galactic strip from 5h. to 8h.
there is contained almost exactly one-eighth the
whole number of proper-motion stars. That is, in
this region the stars are no thicker than elsewhere.
In the region from i8h. to 2ih. there is an excess
of 45 stars having proper motions, or 15 per hour.
Whether this excess is real may well be doubted. It is
scarcely, if at all, greater than might be the result of
accidental inequalities of distribution. Were the
proper-motion stars proportional to the whole num-
ber, there ought to be 240 within the strip. The actual
number is 38 less than this.

It is to be remembered that Auwers's proper mo-
tions are not limited to a definite magnitude, as were
Boss's, but that he looked for all stars having a sensi-
ble proper motion. The question, what proper mo-
tion would be sensible, is a somewhat indefinite one,
depending very largely on the data. It may, there-
fore, well be that the small excess of 45 found within
this strip is due to the fact that more stars were

256 APPARENT DISTRIBUTION OF STARS

observed and investigated, and, therefore, more proper
motions found. Besides this, some uncertainty may
exist as to the reality of the minuter proper motions.

The conclusion is interesting and important. If we
should blot out from the sky all the stars having no
proper motion large enough to be detected, we should
find remaining stars of all magnitudes ; but they
would be scattered almost uniformly over the sky, and
show little or no tendency to crowd toward the galaxy,
unless, perhaps, in the region near igh. of R. A.

From this again it follows that the stars belonging
to the galaxy lie farther away than those whose
proper motions can be detected.

Pickering found that the stars of the fifth spectral
type, or of Vogel's class II b, are mostly distributed
Distribution a l on g" the central line of the Milky Way. An"
of Fifth-type exception occurs in the case of a group situ-
stars ' ate in the " Magellanic clouds," a cloud-like

mass of small stars too far south to be visible in our
latitudes, and detached from the main course of the
Milky Way itself. The total number of the stars in
question is 91, of which 70 are in the Milky Way and
21 in the Magellanic clouds.

An interesting question now is whether the 70
stars along the Milky Way are arranged independently
of the latter, or belong to its agglomerations. In the
latter case we should expect to find most of the stars
in the densest portions of the galaxy ; in the former
case they would be arranged independently of the
galactic masses.

The actual distribution is not decidedly in favour of

FIFTH-TYPE STARS 257

either view. Groups of the stars are found here and
there in the densest spots of the galaxy ; but there
are also a number in the very darkest regions of the
central line. The mean distance of the 70 stars
from the central galactic circle is 2. 6 ; the mean dis-
tance of 42 of the brightest regions of the galaxy
from the same circle is 2. 3. The central circle which
passes most nearly through the 71 stars has its pole
in the position

R. A. = i8h. 44m., Dec. = + 26. 6
The coincidence of this with the galactic circle is very
close, the deviation being only a quarter of a degree.
Most curious is the unequal distribution of these
stars around the galactic circle. Starting from the
point where this circle crosses the equator near i8h.
4om. of R. A., and going toward the north there are

In the first quadrant 15 stars
" " second " 3 "
" " third " 21 "
" " fourth " 31 "

Thus there are 18 stars in the first semicircle against
52 in the second. They are sometimes bunched to-
gether ; thus in R. A. loh. and Dec. 60 there are
i3h. of the stars in a region 5 square.

CHAPTER XVI
THE CLUSTERING OF THE STARS

The stars in deep amaze

Stand fixed in steadfast gaze,

Bending one way their precious influence

And will not take their flight

For all the morning light

Or Lucifer that often warned them thence.

A STUDY of Schiaparelli's planispheres, found in
the last chapter, shows that some regions of the
heavens are especially rich in lucid stars and others
especially poor.

Neither telescope nor planisphere is necessary to
show that many of those stars are collected in clusters.
That the Pleiades form a group of stars by itself is
clear from the consideration that six stars so bright
would not fall so close together by accident. This
conclusion is confirmed by their common proper mo-
tion, different from that of the stars around them.
The singular collection of bright stars which form
Orion, the most brilliant constellation in the heavens,
and the little group called Coma Berenices the Hair
of Berenice also suggest the problem of the possible
connection of the stars which form them.

The question we now propose to consider is whether
these clusters include within their limits an important

258

SMALL STARS IN THE PLEIADES 259

number of the small stars seen in the same direction.
If they and all the small stars which they contain
within their actual limits were removed from the sky,
would important gaps be left ? The significance of
this question will be readily seen. If important gaps
would be left, it would follow that a large proportion
of the stars which we see in the direction of the
clusters really belong to the latter, and that, therefore,
most of the stars would be contained within a limited
region. The clusters which we shall especially study
from this point of view are the Pleiades, Coma Bere-
nices, Praesepe, and Orion.

The Pleiades. -In the case of this cluster the ques-
tion was investigated by Professor Bailey, by means
of a Harvard photograph 2 square, having Alcyone
near its centre. It was divided into 144 squares,
each 10' on a side. The brighter stars of the cluster
were included within 42 of these squares. The
count of stars gave the results :

Within cluster : 1012 stars, or 24 per square.
Without cluster : 2960 stars, or 29 per square.

It therefore seems that the portion of the heavens
covered by the cluster is actually poorer in stars than
the region around it.

Two opposite conclusions might be suggested by
this fact. Assuming that the difference is due to the
presence of the cluster, we might suppose that the
latter was formed of material that otherwise would
have gone into numerous smaller stars. Accepting
this view, it would follow that the material in ques-
tion was a sheet so thin that the thickness of the

2 6o THE CLUSTERING OF THE STARS

space filled by the cluster was an important fraction
of that occupied by the stars. In other words, one
fifth of the stars of the region would be contained in
a thin sheet. This result seems too unlikely to be ac-
cepted. The other and more likely conclusion is that
the number of very minute stars included in the cluster
is no greater than that in the surrounding regions,
and that the lesser number in the region is to be
regarded as accidental.

Coma Berenices. This cluster, which may be seen
east, south, or west of the zenith on a spring or summer
evening, contains seven stars visible to the naked eye,
each of the fifth magnitude. It may be considered as
comprised within the limits I2h. 1301. and I2h. 25111. of
R. A., and 25 to 29 of declination, an area of io.5.
The existence of seven lucid stars within so small an
area suggests that they belong together, and may have
smaller stars belonging to the group, making the
star-density of this area greater than that of the sky
in general.

The question whether there is any corresponding
excess of richness in the fainter stars will be decided by
a count of those contained in Graham's section of the
A. G. Catalogue, which extends to the ninth magni-
tude. Within the area above defined this catalogue
gives 71 stars. Subtracting the 7 lucid stars, we have
64 small stars left within the area. To the same belt of
declination 336 stars are listed in the twelfth hour of
R. A., giving an average of 67 stars to an area equal
to that of the cluster. The small stars are, therefore,
no thicker within the area of the cluster than around

SMALL STARS IN ORION 261

it. It may be added that the seven lucid stars do not
seem to have any common proper motion, so that
their proximity is probably an accident.

Pr&sepe* This object, situate in the constellation
Cancer, appears to the naked eye as a patch of
nebulous light. It is actually a condensed group of
stars, of which the brightest are of the seventh mag-
nitude. The stars of the ninth magnitude included
within the area of the group probably belong, for the
most part, to it, but they are too few to serve as the
base for any positive conclusion.

Orion. I find by measurement and count that a
circle 20 in diameter, comprising the brightest stars
of this constellation, contains 80 stars to magnitude
6.3. Of these, 6 are of the first or second, leaving 74
from the third to the sixth. The resulting richness
is 24 to 100 square degrees, about the average richness
along the borders of the galaxy. It follows that this
remarkable collection of bright stars has no unusual
collection of faint stars associated with it.

A very natural inquiry is whether the bright stars
in Orion have any common proper motion, indicating
that they form a system by themselves. The answer
is shown in the following statement of the proper
motions in a century :

Proper Motions.

Star. Mag. R. A. Dec.

// //

Rigel i -|-o.i o.o

rf Or ion is 3 +0.1 0.3

y Orionis 2 o 6 1.7

ft Orionis 2 o.o 0.2

262 THE CLUSTERING OF THE STARS

Proper Motions.

Star. Mag. R. A. Dec.

// //

Orionis 2 o.o +-i

<? Orionis 2 o.o 1.4

# Orionis 2 -f-o.i 0.3

a Orionis i +3.0 +0.9

For the most part these motions are too small to
be placed beyond doubt, even by all the observations
hitherto made. In the case of Alpha Orionis the
motion is established ; in those of Gamma and Zeta it
is more or less probable, but not at all certain ; in all
the other cases it is too small to be measured.

This minuteness of the motion makes it probable
that these stars are very distant from us, an inference
which is confirmed by the smallness of their parallaxes.
The careful and long-continued measures of Gill show
no parallax to Rigel, while Elkin finds one of only
o".02 to Alpha Orionis.

The general conclusion from our examination is
this : The agglomeration of the brighter stars into clus-
ters does not, in the cases where it is noticeable to the
eye, extend to the fainter stars.

Let us now study the question on the opposite side.
Schiaparelli's planispheres show regions of great pau-
city in lucid stars ; is there in these regions any paucity
of telescopic stars 1

The two regions of greatest paucity are near the
equator ; one extends through the hour o of R. A. ;
the other from I2h. 2om. to I2h. 40111. The richness
of these and of the adjoining regions may be inferred
from Boss's zone of the A. G. Catalogue, including a

REGIONS SPARSE IN STARS 263

belt from i to 5 of declination. The number of stars
observed by Boss in each hour from 2$h. to 3h. is as

follows :

In 23!}. : 271 stars.
In oh. : 293 stars.
In ih. : 299 stars.
In 2h. : 295 stars.

^/These numbers show no paucity in the hour o, and
no excess in the hour 2, which is much richer in lucid
stars than the hour o.

In the strip from I2h. 2om. to I2h. 40111. the cata-
logue contains 78 stars, a richness of 234 to the hour.
In the hour preceding there are 211 stars ; in that fol-
lowing, 225. There is, therefore, no paucity in the
strip in question.

We conclude from all this that the separate stars of
a cluster do not range through a scale of brightness so
wide as the stars in general, and that they are limited
in number. The numerous small stars seen in the
same direction have no connection with them. But
we shall see that this rule does not apply to the clus-
ters of the galaxy.

CHAPTER XVII
THE STRUCTURE OF THE MILKY WAY

A broad and ample road whose dust is gold,
And pavement stars, as stars to thee appear
Seen in the galaxy, that milky way
Which nightly as a circling zone thou seest
Powdered with stars. MILTON.

THE most salient problems suggested by the ap-
pearance of the Milky Way are to be approached
on lines quite similar to those followed in the last chap-
ter. We begin with a description of this wonderful ob-
ject as it appears to the observer. It can be seen
through some part of its course at some hour on any
clear night of the year, and in the evening of any
season except that of early summer. In consequence
of its obliquity to the equator, its apparent posi-
tion on the celestial sphere, as seen in our latitude,
goes through a daily change with the diurnal
rotation of the earth. In the language of technical
astronomy, every day at i2h. of sidereal time, it
makes so small an angle with the horizon as to be
scarcely visible. If the air is very clear, we might
see a portion of it skirting the northern horizon.
This position occurs during the evenings of early

264

DESCRIPTION OF THE MILKY WAY 265

summer. At oh. of sidereal time, which during
autumn and early winter fall in the evening, it
passes nearly through our zenith, from east to
west, and can, therefore, then best be seen. We
begin with the portion which will be visible in the late
summer or early autumn. We can then trace its
course southward from Cassiopeia in the northwest.
It passes a little east of the zenith down to Sagittarius,
near the south horizon. This portion of the belt is
remarkable for its diversity of structure and the in-
tensity of the brighter regions.

In Cassiopeia it shows nothing remarkable ; but
above this constellation, in Cepheus, we notice in the
midst of the brighter region a nearly circular and
comparatively dark patch several degrees in di-
ameter. A little farther along we notice a similar
elongated patch in Cygnus lying across the course of
the belt. In this region the brighter portions are of
great breadth, more than 20.

In Cygnus begins the most remarkable feature of
the Milky Way, the great bifurcation. Faintly visi-
ble near the zenith, as we trace it towards the south,
we see it grow more and more distinct, until we reach
the constellation Aquila, near the equator. Between
Cygnus and Aquila the western branch seems to be
the brighter and better marked of the two, and might,
therefore, be taken for the main branch. About
Aquila the two appear equal, but south of this con-
stellation we see the western branch diverge yet
farther toward the west, leaving the gap between it
and the eastern yet broader and more distinct than

266 THE STRUCTURE OF THE MILKY WAY

before. This branch finally terminates in the constel-
lation Ophiuchus, while the eastern branch, growing
narrower, can still be followed toward the south.

Between the equator and the southern horizon we
have the brightest and most irregular regions of all.
Several round, bright patches of greater or less in-
tensity are projected on a background sometimes
moderately bright and sometimes quite dark. If the
night is quite clear and moonless we shall see that,
after a vacant stretch, the western branch seems to
recommence just about the constellation Scorpius.
In this constellation we have again a bifurcation, a
dark region between two bright ones.

This is about as far as the object can be well traced
in our middle latitudes. From a point of view nearer
to the equator it can be traced through its whole ex-
tent. South of Scorpius and Sagittarius it becomes
broad, faint, and diffused through the constellations of
Norma and Circinus. It reaches its farthest south-
ern limit in the Southern Cross, where it becomes
narrower and. better defined. The most remarkable
feature here is the "coal sack," a dark opening of
elliptical shape in the central line of the stream.
West and north of this, in the constellation Argo, is
the broadest and most diffused part of the whole
stream, the breadth reaching fully 30. Here we again
reach the portion which rises above our horizon.

Returning now to our starting-point, we shall
notice that, as we make our observations later and
later in the autumn, the southern part, which we have
been mostly studying, is seen night by night lower

THE STRUCTURE OF THE MILKY WAY 267

down in the west, while new regions are coming into
view in the north-east and east. These regions rise
earlier every evening, and, if we continue our ob-
servations to a later hour, we shall see more and
more of them above the eastern or south-eastern
horizon. By midwinter Cassiopeia will be seen in
the north-west, and we can readily trace the course of
the galaxy from that constellation in the opposite
direction from that which we have been following.
South of Cassiopeia we see, near the central line, the
well-known cluster forming the sword-handle of
Perseus. Farther south the belt grows narrower and
fainter ; although the irregularities of structure con-
tinue, they are far less striking than on the other
side. On a moonlight evening it will scarcely be
visible at all. If the moon is absent and the air clear
we shall see that it grows slightly brighter toward the
southern horizon, near which will be the narrowest
part of its entire course. Below is the broad and
diffused region in Argo already mentioned.

One conclusion from the inequalities of structure
which we have described will be quite obvious. The
Milky Way is something more than the result of the
general tendency of the stars to increase in number
as we approach its central line. There must be large
local aggregations of stars, because, as we have al-
ready pointed out, there cannot be such diversity of
structure shown in a view of a very widely stretched
stratum of stars.

When, instead of a naked-eye view of the belt, we
study the photographs of the Milky Way, we find

PHOTOGRAPH SHOWING STRUCTURE OF THE MILKY WAY, BY BARNARD.

268

THE STRUCTURE OF THE MILKY WAY 269

this evidence of clustering to grow still stronger. It
is seen very strikingly in the photograph by Bar-
nard showing the singular rifts in the Milky Way in
the constellation Ophiuchus. Yet more singular are
three small openings very close together in the con-
stellation Aquila, the positions of which are :

(1) R. A. = iQh. 35.om.; Dec. = + 10 17'.

(2) " = i 9 h. 36.5111.; " = + 10 37'-

(3) = i9h- 37.2m.; = -f 11 2'.

The fundamental question which we meet in our
further study of this subject is : At what magnitude
do these agglomerations of stars begin ? Admitting,
as we must, that they are local, are they composed
altogether of faint stars, or do they also include
the brighter stars within their limits ? We consider
this question in a way quite similar to that in which
we discussed the clustering of the stars in the last
chapter. We mark oujt on a map of the Milky
Way the brightest regions that is, those which
include the densest agglomeration of very faint stars.
We also mark out the darkest regions, including
the coal sack. For this purpose I have taken the
maps found in Heis's Atlas Ccelestis for the northern
portion of the Milky Way and the Atlas of Gould's
Uranometria Argentina for the southern portion. In
order to enable anyone to repeat and verify the work
I give the position of the central part of each patch
or region studied. This serves simply for the pur-
pose of indentification. The outlines can be drawn
by anyone when the patch is identified. In the

RIFTS IN THE MILKY WAY, PHOTOGRAPHED BY BARNARD.
270

LUCID STARS IN MILKY WAY 271

third column of the table is given, approximately, the
number of square degrees in the patch as outlined.
Then follows the number of stars found on the map.
Here are included stars somewhat fainter than those
regarded as lucid. Heis maps all stars down to about
magnitude 6.2 or 6.3. Gould gives the places of all
stars to magnitude 7.

A. Number of lucid stars in certain bright regions or patches of
the Milky Way.

I. Northern portion, from Heis.

Position

of patch.

Area.

Number

R.A.

Dec.

sq. deg.

of stars.

iQh. iom.

+ 35

2oh. om.

+ 37

2oh. 2om.

+ 47

2ih. 5m.

+ 45

oh. 2om.

+ 60

2h. 2om.

+ 55

3h. 3om.

+ 36

3h. 4bm.

+ 44

Sums 277 91

II. Southern portion, from Gould

Position

Area.

R. A.

Dec.

sq. deg.

Stars.

8h. 4m.

-47

2h. 24m.

-44

loh. 35m.

-58

nh. 4om.

i6h. iom.

-53

i8h. om.

. 9

i8h. iom.

-18

i8h. 42m.

Sums 97 77

272 THE STRUCTURE OF THE MILKY WAY

B. Number of lucid stars in the darker regions or patches of the
Milky Way.

Stars.
10

12
IO
19
13

Stars.
8

5
4
16
6
5

3
3

74
1 A long narrow region between the limits defined in the first two columns.

I. Northern part, from

Heis.

Position.

Area.

R. A. De

:c.

sq. deg.

2ih. om. -f

22h. om. 4

22h. 25111. 4

. 30

oh. om. 4-

4h. om. 4"

4h. 2om. 4-

6h. i5m. 4"

6h. 1 2m. 4-

Sums

47 e

II. Southern part, from

Gould.

Position.

Area.

R. A. E

lec.

sq. deg.

yh. 22m.

7h. 28m.

8h. om.

8h. 4om.

g\\. om.

loh. om.

i2h. 4om.

i5h. lorn.

i7h. 3om.

i8h. lorn.

i8h. om.

22)

i8h. 30^-

24 1

i8h. 5om.

Sums. .

. 210

LUCID STARS IN MILKY WAY 273

To derive the best conclusions from these numbers
we must compare them with the mean star-density
for the sky in general, and for the regions near the
galactic plane. Heis has 3903 stars north of the
equator; Gould, 6755 south of it. The area of each
hemisphere is 20,626 square degrees. It will be con-
venient to express the various star-densities in terms
of 100 square degrees as the unit of area. Thus we
have the following star-densities according to the two

authorities :

His. Gould.

Star-density of the entire hemisphere 19.0 32.7

Star-density of the darker galactic regions 20.4 33.8

Star-density of the bright galactic regions 32.9 79.4

The first two pairs of numbers lead to the remark-
able and unexpected conclusion that the darker re-
gions of the Milky Way are but slightly richer in
lucid stars than the average of the whole sky ; cer-
tainly no richer than is due to the general tendency
of all the stars to crowd toward the galactic plane.
On the other hand, the bright areas are 60 per cent,
richer according to Heis, and more than 100 per
cent, richer according to Gould, than the darker
areas seen among and around them. The conclusion
is that an important fraction of the lucid stars which
we see in the same areas with the agglomerations of
the Milky Way is really in those agglomerations and
form part of them.

A study quite similar to this has been made by
Easton for the portions of the Milky Way between
Cygnus and Aquila, where the diversities of brightness

274 THE STRUCTURE OF THE MILKY WAY

are greatest. His count of the stars in the bright
and dark regions differs from that made above
principally by including all the stars of the Durch-
musterMng, which we may suppose to extend to
about the ninth magnitude. 1

He divides the regions studied into six degrees of
brightness. For our present purpose it is only ne-
cessary to consider three regions, the brightest, the
faintest, and those intermediate between the two.
Besides the count from the Durchmusterung he made
a count of the same sort from Dr. Wolf's photo-
graphs and from Herschel's gauges of the heavens.
In the following table I have reduced all his results
so as to express the number of stars in a square
degree in the three separate regions. At the top of
each column is given the authority, whether Arge-
lander, Wolf, or Herschel. Wolf had two sets of
photographs, one supposed to include all the stars to
the eleventh, the other to the twelfth magnitude.
The magnitudes included are given in the second
line. That Herschel's count extends to the fifteenth
magnitude is by no means certain ; but we can judge
from the great number of his stars that it goes con-
siderably beyond Wolf's in the faintness of the stars
included. Below this we give, in the regions A, B,
and C, which are respectively those of least, of
medium, and of greatest brightness, the number of
stars per square degree according to each of the
authorities :

1 Easton's work is given in detail in the Astronomische Nachrichten, vol.
137, and the A s trophy sic al Journal, vol. i, no. 3.

STARS IN THE MILKY WAY 275

Authority Arg. Wolf (A) Wolf(B) Herschel.

Magnitude ,..i 9 i n i 12 i 15(7)

Region A 23 72 224 405

Region B 33 134 7 6 4 4'M

Region C 48 217 1266 6920

C A 25 145 1042 6425

Ratio C : A 2. i 3.0 5.7 14.0

The vastly greater number of individual stars per
square degree in the brighter regions is what we
should expect from the studies we have made of the
lucid stars. But what is of most interest in the table
is the continual increase in the proportion of faint
stars in the separate regions. We notice that, when
we consider only the stars of the ninth magnitude,
there are twice as many in the brightest as in the
darkest portions. When we go to the eleventh mag-
nitude, as shown by Wolf's photograph A, we find
the number of stars in the brighter regions to be
threefold. When the twelfth magnitude is included
we find that there are between five and six times as
many stars in the bright regions as the dark ones.
Finally, when we come to stars from Herschel's
gauges there are fourteen times as many stars per
square degree in the brighter regions as in the dark.

At first sight this result seems to show a great dif-
ference between the clusters of stars described in the
last chapter, and the collections of the Milky Way,
in that the former include few or no faint stars, while
the latter include a greater and greater number as
we ascend in the scale of magnitude. This difference
is important as showing a vastly greater range of act-
ual brightness among the galactic stars than among

276 THE STRUCTURE OF THE MILKY WAY

those which form the scattered clusters. Allowing
for this difference, the results from the two classes
of objects can be brought to converge harmoniously
toward the same conclusion.

We have collected abundant evidence that, separate
from the accumulations of stars in the Milky Way, per-
haps extending beyond them, there is a vast collec-
tion of scattered stars, spread out in the direction of
the galactic plane, as already described, which fill the
celestial spaces in every direction. We have shown
that when, from any one area of the sky, we abstract the
stars contained in clusters, this great mass is not seri-
ously diminished. We have also collected abundant
evidence that the distances of this great mass are very
unequal ; in other words, there is no great accumula-
tion, in a superficial layer, at some one distance. The
question which now arises is whether the darker areas
which we see in the Milky Way are vacancies in this
mass. Although some of the counts seem to show
that they are, yet a general comparison leads to the
contrary conclusion. In the darkest areas of the
Milky Way, when of great extent, the stars are as
numerous as on each side of the galactic zone. Our
general conclusion is this :

If we should remove from the sky all the local aggre-
gations of stars, and also the entire collection which
forms the cloud-forms of the Milky Way, we should
have left a scattered collection, constantly increasing in
density toward the galactic belt.

CHAPTER XVIII

THE PROGRESSION IN THE NUMBER OF STARS
AS THE BRIGHTNESS DIMINISHES

Hither, as to their fountain, other stars

Repairing, in their golden urns draw light. MILTON.

WE mentioned in an earlier chapter that, when
we compare the number of stars of each suc-
cessive order of magnitude with the number of the
order next lower, we find it to be, in a general way,
between three and four times as great. The ratio in
question is so important that a special name must be
devised for it. For want of a better term, we shall
call it the star-ratio. It may easily be shown that
there must be some limit of magnitude at which the
ratio falls off. For a remarkable conclusion from
the observed ratio for the stars of the lower order of
magnitude is that the totality of light received from
each successive order goes on increasing. Photo-
metric measures show, as we have seen, that a star of
magnitude m gives very nearly 2.5 times as much
light as one of magnitude m-\-i. The number of
stars of magnitude m-\-i being, approximately from
3 to 3-75 times as great as those of magnitude m, it
follows that the total amount of light which they give

277

278 PROGRESSION IN NUMBER OF STARS

us is some 40 or 50 per cent, greater than that re-
ceived from magnitude m. Using only rough ap-
proximations, the amount of light will be about
doubled by a change of two units of magnitude ; thus
the totality of stars of the sixth magnitude gives
twice as much light as that of the fourth ; that of the
eighth twice as much light as that of the sixth ; that
of the tenth twice as much again as of the eighth,
and so on as far as accurate observations and counts
have been made.

To give numerical precision to this result, let us
take as unity the total amount of light received from
the stars of the first magnitude. The sum-total for this
and the other magnitudes, up to the tenth, will then be :

Mag. i . ............... Light = i.o

" i'.,' .............. " = 14

" 3 ................ " - 2.0

" 4 .............. " = 2.8

" 5 .............. - " - 4-0

" 6-. .............. " = 5-7

" 7 ................ " = 8.0

" 8 ................ " = 11.3

" 9 ................ " = 16.0

" 10.. " = 22.6

Total 74.8

That is, from all the stars to the tenth magnitude
combined, we have more than seventy times as much
light as from those of the first magnitude.

There must, evidently, be an end to this series, for,
were this not the case, the result would be that
which we have shown to follow if the universe were

PROGRESSION IN NUMBER OF STARS 279

infinite ; the whole heaven would shine with a blaze
of light like the sun. At what point does the rate of
increase begin to fall off ?

We are as yet unable to answer this question, be-
cause we have nothing like an accurate count of stars
above the ninth, or at most, the tenth magnitude.
All we can do is to examine the data which we have
and see what evidence can be found from them of a
diminution of the ratio.

It must be pointed out, at the outset, that the ratio
must be greater in the galactic region than it is in
other regions. This follows from the fact that the
proportion of small stars increases at a more rapid
rate in the galaxy than elsewhere. This is shown by
the comparisons we have already made of the Hersch-
elian gauges with the counts of the brighter stars.
While the galactic region is less than twice as
dense as the remaining regions for the brighter stars,
it seems to be ten times as dense for the Herschelian
stars. If we knew the limiting magnitude of the
latter, we could at once draw some numerical conclu-
sion. But unfortunately this is quite unknown. All
we know is that they were the smallest stars that
Herschel could see with his telescope.

The ratio in various regions of the heavens has
been very exhaustively investigated by Seeliger, in
the work already quoted. The bases of his inves-
tigations are the counts of stars in the Durchmus-
terung. Instead of taking the ratio for stars differing
by units of magnitude, as we have done, Seeliger
divides them according to half-magnitudes. The

2 8o PROGRESSION IN NUMBER OF STARS

reproduction of his numbers in detail would take
more space than we can here devote to the subject
and would not be of special interest to our readers.
I have, therefore, derived their general mean results
for different parts of the sky with reference to the
Milky Way and for stars of the various orders
of magnitude. The following table shows the con-
clusions :

Ratio of

Concluded

Zone.

increase.

result.

D. M.

S. D.

Diff.

2.99

3- 2 4

II.

3.00

3-49

0.49

3-25

III.

3-7

3-72

0.65

3-37

IV.

3-32

3.85

o-53

3.58

3-55

4.15

0.60

3.85

VI.

3.28

3.68

0.40

3.48

VII.

3-23

3-55

0.32

337

VIII.

3-44

3.56

0.12

3-40

IX.

3-49

3-24

In the first column we have the designation of the
zone or region of the sky, as already given.

In the second and third columns we have the mean
ratio of increase for whole magnitudes as derived
from the Durchmusterung and the Southern Durch-
musterung, respectively. It will be recalled that
region I., around the north galactic pole, is entirely
wanting in the S. D., while the adjoining regions,
II. and III., are only partially found, and that, in
like manner, the D. M. includes none of region IX.
around the south galactic pole, and but little of the
adjoining region.

SEELIGERS COUNTS OF STARS 281

It will be seen that there is a very remarkable
systematic difference between the two lists, the ratio
of the number of faint to that of bright stars being
much greater in the S. D. This difference is shown
in the fourth column. I have assumed that the two
systems are equally good, and so diminished all the
ratios of the S. D. by 0.25, and increased those of
the D. M. by the same amount. The mean of the
two corrected results was then taken, giving the
principal weight to the one or the other, according
to the number of stars on which they depend.

It will be seen that the increase of the ratio from
either galactic pole to the Milky Way itself is as
well marked as the increase of the richness of the
respective regions in stars in general. We may con-
dense the results in this way :

In the galactic zone, ratio = 3.85

In zones IV. and VI., " = 3.53

In polar zones I., II., VIII., and IX., " = 3.28

It will be recalled that zone V. is a central belt 20
broad, including the Milky Way in its limits. But
the latter, as seen by the eye, especially its brightest
portions, does not fill this zone. These portions, as
we know, comprise the irregular collection of cloud-
like masses described in the last chapter. Seeliger
has investigated the ratio within these masses, and
compared it with the stellar density, or the number
of stars per square degree. The mean results are :

In that portion of the galaxy extending from Cas-
siopeia to the equator near 6h. of R. A., ratio = 4.02.

282 PROGRESSION OF NUMBER OF STARS

In that portion from Cassiopeia in the opposite
direction to near igh. of R. A., in Aquila, ratio = 3.70.

These remarkable results are derived from the
D. M., and will be yet more striking if corrected by
half the difference between it and the S. D., as we
have done for the sky generally. They will then be
4.27 and 3.95, respectively.

As might be expected, the regions of greater star
density have generally, though not always, the higher
ratio. The highest of all is in a patch south of
Gemini, between 6h. and 7h. of R. A., and near + 5 of
declination. Here it amounts to 5.94, showing that
there are eighty-six stars of magnitude 9.0 to every
one of magnitude 6.5.

The D. M. does not stop at magnitude 9, as the
above numbers do, but extends to 9.4, while the
S. D. extends to magnitude 10. For these magni-
tudes Seeliger finds a yet higher ratio. This is,
however, to be attributed to the personal equation of
the observers, and need not be further considered.

The only available material for estimating the
ratio of increase above the ninth magnitude is found
in the Potsdam photographs for the international
chart of the heavens, which extend to magnitude n.
These are published only for a few special regions.
Five of the published plates fall in regions not far
from the galactic pole. I have made a count by
magnitudes of the 312 stars contained in these plates.
An adjustment is, however, necessary from the fact
that the minuter fractions of a magnitude could
not be precisely determined from the photographed

TOTAL LIGHT OF THE STARS 283

images. The results are practically given to fourths
of a magnitude, although expressed in tenths. But
it is found that the numbers corresponding to round
magnitudes and their halves are disproportionately
more frequent than those corresponding to the inter-
mediate fourths. For example, there are only 19
stars of magnitude 10.7 and 10.8 taken together;
while there are 49 of 10.5. Under these circum-
stances I have made an adjustment to half-mag-
nitudes by taking the stars of quarter-magnitudes
and dividing them between half-magnitudes next
higher and next lower. The number of stars of the
several magnitudes is then as follows :

Mag. Stars.

6.5

7.0 2

7-5 4

8.0 ii

8-5 15

9.0 29

9-5 33

100 39

10.5 64

n.o 115

It is difficult to derive a precise value of the star-
ratio from this table, owing to the small number of
stars of the brighter magnitudes, which are insuffi-
cient to form the first term of the ratio. Assuming,
however, that the ratio is otherwise satisfactorily de-
termined up to the ninth magnitude, we find that
there is but a slight increase from the ninth up to the
tenth. The number of the eleventh magnitude is,

284 PROGRESSION IN NUMBER OE STARS

however, nearly three times that of the tenth and
nearly double that of 10.5.

Another way to consider the subject is to compare
the total number of stars of the fainter magnitudes
with the number of lucid stars corresponding, which,
in the general average, will be found in the same
space. We may assume that near the poles of the
galaxy there is about one lucid star to every ten
square degrees. The five belts included in the
above statement cover about thirteen square degrees.
The region is, therefore, that which would contain
about one star of the sixth magnitude. An increase
of this number by somewhat more than 100 times in
the five steps from the sixth magnitude to the
eleventh would indicate a ratio somewhat less than
3 ; about 2.5. But the comparison of the photo-
graphic and visual magnitudes renders this estimate
somewhat doubtful. Besides this, it is questionable
whether we should not reckon among stars of the
eleventh magnitude those up to 11.5, which would
greatly increase the number. It is a little uncertain
whether we should regard the limit of magnitude on
the Potsdam plates as n.o or n plus some fraction
near to one half.

Altogether, our general conclusion must be that up to
the eleventh magnitude there is no marked falling off in
the ratio of increase, even near the poles of the galaxy.

I have not made a corresponding count for the
galactic region, but the great number of stars given
on the plates show, as we might expect, that there is
no diminution in the ratio of increase.

TOTAL LIGHT OF THE STARS 285

The question where the series begins to fall away
is, therefore, still an undecided one, and must remain
so until a very exact count is made of the photo-
graphs taken for the international photographic chart
of the heavens, or of the Harvard photographs.

There is also a possibility of applying a photometric
study of the sky to the question. The background of
the sky itself is by no means black. The question
to be investigated is whether a considerable fraction
of the apparently smooth and uniform light of the
nightly sky comes from countless telescopic stars,
perhaps from stars too faint to be found on the most
delicate photographs, or whether it is mostly reflected
by our atmosphere from the stars. It may seem
questionable whether the latter is the case, because
the fraction reflected in a clear atmosphere is not
supposed to exceed one tenth the total amount of
light of the stars themselves. On the other hand,
the seemingly blue colour of the sky might seem to
indicate reflected light, since the average colour of all
the stars is white rather than blue. The subject is
an extremely interesting one and requires investi-
gation before a definitive conclusion can be reached.

CHAPTER XIX

STATISTICAL STUDIES OF PROPER MOTIONS

How charming is divine philosophy,

Not harsh and crabbed as dull fools suppose,

But musical as is Apollo's lute,

And a perpetual feast of nectared sweets

Where no crude surfeit reigns. MILTON.

THE number of stars now found to have a proper
motion is sufficiently great to apply a statistical
method to their study. The principal steps in this
study have been taken by Kapteyn, who, in several
papers published during the past ten years, has shown
how important conclusions may be drawn in this way.
We must begin our subject by showing the geo-
metrical relations of the proper motion of a star, con-
sidered as an actuality in space, to the proper motion
as we see it. The motion in question is supposed to
take place in a straight line with uniform velocity.
Leaving out the rare cases of variations in the motion
due to the attraction of a revolving body, there is
nothing either in observation or theory to justify us
in assuming any deviation from this law of uniformity.
The direction of a motion has no relation to the di-
rection from the earth to the star. That is to say, it
may make any angle whatever with that direction.

286

COMPONENTS OF PROPER MOTION 287

Let E be the position of our solar system, and S
that of a star moving in the direction of a straight
line, S D. It must not be understood that the length
of this line is taken to represent the actual motion ;
the latter would be infinitesimal as compared with its

length; we

M
use it only to

show direc-
tion. We
may, however, T" " S R

use the line to COMPONENTS OF PROPER MOT.ON.

represent on

a magnified scale the actual amount of the motion
during any unit of time, say one year. It may be
divided into two components : one, S R, in the direc-
tion of the line of sight from us to the star, which for
brevity we shall call the radial line, and the other,
S M, at right angles to that line.

It must be understood that, as the term " proper
motion " is commonly used, only the component S M
can be referred to, because the radial component, S R,
does not admit of being determined by telescopic
vision. As we know from the preceding chapters, it
can in the case of the brighter stars be determined
by spectroscopic measurement of the radial motions

The visible component, S M, can also be resolved
into two perpendicular components, the one east and
west on the celestial sphere, the other north and
south. The former is the proper motion in right
ascension (the measured motion in this co-ordinate
being multiplied by the cosine of the declination

288 STATISTICAL STUDIES OF PROPER MOTION

to reduce it to a great circle), and the other is the
proper motion in declination. In star catalogues these
two motions are given, so far as practicable. Thus,
altogether, the actual motion of a star in space may be
resolved into three components : that of right ascen-
sion, that of declination, and the radial component.

An additional consideration is now to be added..
The proper motion of a star, as observed and given
in catalogues, is a motion relative to our system. It
has been shown in a former chapter that the latter
has a proper motion of its own. When account is
taken of this, and the motions are all reduced as well
as* we can to a common centre of gravity of the whole
stellar system, we conceive the observed proper mo-
tion of the star to be made up of two parts, of which
one is the actual motion of the star relative to the
common centre, and the other due to the motion of
the sun, carrying the earth with it. The direction
of the latter appears to us opposite that of the motion
of the sun. The sun's motion being directed to the
constellation Lyra, it follows that the component
in question in the case of the stars is directed toward
the opposite constellation, Argo. This component,
as we know, is termed the parallactic motion, being
dependent on the distance or parallax of the star.

As in the case of other proper motions, we may
measure the parallactic motion either in angular
measure, as so many seconds per century, or in linear
measure, as so many kilometres per second. The re-
lation of the two measures depends on the distance
of a star. The simplest conception of the relation

PAR ALL A TIC MOTION 289

may be gained by reflecting that the linear speed of
the parallactic motion must be equal to that of the
sun.

We have cited Campbell's result for the speed of
the solar motion, which is between 19 and 20 km. per
second, or 4 radii of the earth's orbit per year. Ac-
cepting this speed we shall have the following rule :

The parallax of a star lying in a direction nearly at
right angles to that of the solar motion is equal to one
fourth of its annual parallactic motion.

In the case of stars in other directions, the paral-
lactic motion for a given parallax would be less in
proportion to the sine of the angle between the direc-
tion of the star and the solar apex.

Lf the stars were at rest this rule would enable
us immediately to determine the distance of any star
by its proper motion, which would then be simply the
parallactic motion itself. Unfortunately, in the case
of any one star considered individually, there is no
way of deciding how much of its motion is proper to
itself and how much is the parallactic motion. But
when we consider the great mass of stars, it is possible
in a rough way to make a distinction between the
two motions in a general average.

The direction or motion of any particular star,
having no reference to that of the sun, is as likely to
be in the direction of one of the three components we
have described as of any other. Hence, in the aver-
age of a great number of stars we may conclude that
these components are equal.

One of the simplest applications of this law will

290 STATISTICAL STUDIES OF PROPER MOTION

enable us to compute the mean parallax of the stars
whose radial motions have been determined. As
this application is, in the present connection, made
only for the purpose of illustration, I shall confine
myself to the 47 stars of which the radial motions
have been measured by Vogel. The mean annual
proper motions of these stars, taken without any re-
gard to their signs, are :

Including Arcturus. Omitting Arcturus.

n it

In right ascension. .. 0.163 0.144

In declination - l 55 0.118

The difference of the mean motions in right ascen-
sion and declination is to be regarded as accidental.
The velocity of Arcturus is so exceptionally great
that we ought, perhaps, to leave it out in taking the
mean.

Now, the mean of the radial motions as found by
Vogel is 1 6 kilometres per second. By hypothesis
the actual motion in the radial line is in the general
average the same as in the other two directions.
We have, therefore, to determine what must be the
parallax of a star in order that, moving with a veloc-
ity of 1 6 kilometres per second, its angular proper
motion may have one of the above values. This
result is by a simple computation found to be :

// n

From the mean motion in R. A 0.049 or 0.043

From the mean motion in Dec 0.046 or 0.035

The difference of these results, which depends on

COMPONENTS OF PROPER MOTION 291

the omission or exclusion of Arcturus, shows the
amount of uncertainty of the method. Our general
conclusion, therefore, is that the mean parallax of
the Vogel stars, which may be regarded as corres-
ponding approximately to the mean parallax of all
the stars of the second magnitude, is about o".O4.

We have spoken of the two components of the
apparent motion as those in right ascension and
declination, respectively. But there is no particular
significance in the direction of these co-ordinates,
which have no relation to the heavens at large. For
some purposes it will be better to take as the two
directions in which the motions are to be resolved
that of the parallactic motion and that at right angles
to it. That is to say, taking the solar apex as a pole,
we conceive an arc of a great circle drawn upon the
celestial sphere from it to the star, and resolve the
apparent motion into two components, the one in
the direction of this arc, the other at right angles to
it. The former, which we may call the apical motion,
is affected by the parallactic motion ; the latter,
which we call the cross motion, is not, and therefore
shows the true component of the motion of the star
itself in the direction indicated.

Kapteyn has gone through the labour of resolving
all the proper motions of the Bradley stars given by
Auwers, in this way. His assumed position of the
solar apex was :

Right ascension 276 = i8h. 24m.

Declination * +34

1 This work of Kapteyn is unpublished. The author is indebted to his

292 STATISTICAL STUDIES OF PROPER MOTION

The radically new treatment in his discussion of
the distribution of the stars in space embraces three
points. The first consists in the distinction between
the spectral types of the different stars and the sepa-
rate study of the proper motions peculiar to each
type. The next point is the reference of the motions
to the solar apex. The third is the study of the re-
lations of the stars to the galactic plane.

A remarkable relation existing between the spectral
type of stars and their proper motions 1 was brought
out by these investigations. The stars of Type I.
have, in the general mean, smaller proper motions
than those of Type II. The following table is made
up from Kapteyn's work. First we give the limits
of proper motion ; then on the same line the number
of stars of the respective Types I. and II. having
proper motions within these limits :

Centennial Number of stars.

prop, motions. Type 1. Type II.

// //

o to 5 786 474

6 to 9 203 194

10 to 19 159 223

20 to 29 25 86

30 to 49 13 71

50 and more 3 58

Total 1189 1106

courtesy for a manuscript copy, with permission to use it. Kapteyn's re-
searches based on this material are contained in a series of papers communi-
cated to the Amsterdam Academy of Science. An abstract in English of one
of the earlier papers is found in Knowledge for June I, 1893.

1 The author believes that Monck, of England, independently pointed out
this relation, perhaps in advance of Kapteyn.

g, MOTIONS OF TWO SPECTRAL TYPES 293
f
It will be seen that in the case of stars having

proper motions of less than 5" per century a large
majority are of Type I. In the case of proper mo-
tions between 6" and 9" the number is nearly equal.
Between 10" and 20" there is a large majority of
Type II. Between 30" and 49" the number of Type
II. is nearly five times that of Type I. Finally, only
three stars of Type I. have proper motions exceed-
ing 50", while fifty-eight stars of Type II. have a
proper motion exceeding this limit.

We may make two hypotheses on this subject :
one, that the stars of Type II. really move more
rapidly than those of Type I. ; the other, that their
actual motion is the same, but that the stars of Type
I. are more distant stars. The last conclusion seems
much more probable, and is strengthened by the
much greater condensation of stars of Type I. toward
the Milky Way.

Let us now consider the principles by which we
may study a great collection of proper motions
statistically. There are scattered around us in the
stellar spaces, in every direction from us, a large
number of stars, each moving onward in a straight
line and in a direction which, with rare exceptions,
has nothing in common with the motion of any other
star. The velocities of the motion vary from one
star to another in a way that cannot be determined,
some moving slowly and some rapidly. Is it pos-
sible from such a maze of motions to determine any-
thing ? Certainly we cannot learn all that we wish,
yet we may learn something that will help us to

294 STATISTICAL STUDIES OF PROPER MOTION

form some idea of the respective distances of the
stars and the actual velocity of their motions. An
obvious remark is that the more distant a star the
slower it will seem to move. We must, therefore,
distinguish between the linear or actual motion of
a star, expressed as so many kilometres per second,
and its apparent or angular motion of so many
seconds per year, derived by measuring its change of
direction as we see it with our instruments.

We shall now endeavour to explain Kapteyn's
method in such a way that the reasoning shall be clear
without repeating the algebraic operations which it
inyolves. Let us conceive that the following Fig. is
drawn on the
celestial sphere
as we look up
at the heavens.
S is the direc-
tion of a star in
the sky as we
see it. Let us
also suppose

that the solar apex, situated in the constellation Lyra,
lies anywhere horizontally to the left of the star, in the
direction of the arrow-head marked Apex. Suppose
also that, were the solar system at rest, we should see
the star moving along the line S. D. Let the length of
the line S D represent the motion in some unit of time,
say, one year. Next, suppose the star at rest. Then
in consequence of the motion of the solar system, by
which we are carried toward the apex, the star would

Apex

APICAL AND CROSS MOTIONS 295

seem to be moving with its parallactic motion in the
direction S B, away from the apex. Let the length
of this line represent the parallactic motion in one
year. Then by the theory of composition of mo-
tions, the star, moving by its real motion from S to D,
and by the motion of the earth having an apparent
motion from S to B, will appear to us to move along
the diagonal S A of the parallelogram. Thus, the
line S A will represent the annual proper motion of
the star as we observe it with our instruments, and
which can be resolved into the apical motion, in the
direction S B, and its cross-motion in the direction S.

The apical motion consists of two parts, one the
parallactic motion, equal to S B ; the other real, and
due to the motion of the star itself along the line
S D, and equal to the distance of D from the line S r.

We have now to inquire how, in the case of a great
number of stars, we may distinguish between these
two parts of the apical motion.

We must make the general hypothesis that, in the
average of a great number of stars, actual motions
have no relation to the direction of our sun from the
star. Then the components of the actual motion,
S D, will in the general average have equal values,
positive and negative motions cancelling each other.
Hence, if we take the mean of a great number of
motions along the apical line it will give us the
value of S B due to the motion of the earth, and,
hence, the mean parallactic motion of all the stars
considered.

The problem now becomes one of averages. We

296 STATISTICAL STUDIES OF PROPER MOTION

wish to form at least a rude estimate of the average
speed of a star in miles or kilometres per second. To
show how this may be done let us suppose that we
observe the proper motions of a great number of
stars at some distance from the solar apex, so that
their parallactic motion shall be observable. Stumpe
and Ristenpart, the German astronomers, as well as
Kapteyn, have considered the relation between the
two motions in the following way : We divide the
stars observed into classes, taking, say, one class hav-
ing small but easily measured proper motion ; another
having a proper motion near the average, and a third,
of large proper motion. Sometimes a fourth class is
added, consisting of stars having exceptionally large
proper motions. From each of these classes we can
determine, as already shown, the average motion
from the direction of the solar apex ; that is to say,
the average parallactic motion. This will be inversely
as the average distance of the stars.

Stumpe's three classes were : I., proper motions
ranging from 16" to 32" per century; II., between
32" and 64" per century; III., between 64" and 128"
per century; IV., greater than 128". The average
of the proper motions in each class, the average of
the apparent apical motions, and the ratio of the two
are these :

Class. Prop. Mot. Par. Mot. Quotient.

// //

I. 0.23 0.142 1.6

II. 0.43 0.286 1.5

III. 0.85 0.583 1.4

IV. 2.39 2.057 i.i

AVERAGE SPEED OF A S7*AR 297

It will be seen that the ratio of the proper motion
of the star to the parallactic motion diminishes as the
former increases.

The same thing was found by Ristenpart from the
proper motions of the Berlin zone, as shown below :

Class. Prop. Mot. Par. Mot. Quotient.

n n

Small 0.128 0.061 2.1

Medium 0.197 0.109 i-8

Large 0.374 0.279 i-3

The smaller value of the quotient from stars near
to us than from the more distant stars was supposed
to lead to the conclusion that the latter had a more
rapid real motion than the former. A little thought
will show that, while this is quite true of the stars in-
cluded in the list, this does not prove it to be true for
the stars in general. We cannot, as already pointed
out, determine the motion of any star unless it ex-
ceeds a certain limit. Hence, in the case of the more
distant stars we can observe the proper motions only
of those which move most rapidly, while in the case
of the nearer ones we may have measured them all.
We should, therefore, naturally expect that the more
distant stars in our list will show too large a value of
the proper motion, for the simple reason that those
having small proper motion are not included in the
average. There is, therefore, no evidence that the
more distant stars move faster than the nearer ones.

An error in the opposite direction occurs through
the method of selecting stars of given proper motion.
We have already pointed out that in the case of any

298 STATISTICAL STUDIES OF PROPER MOTION

individual star we cannot determine how much of its
apparent apical motion may be that of the star itself,
and how much the parallactic motion arising from
the motion of the earth. What we have done is to
assume that in the case of a great number of stars
the actual apical motions will be equal, and in op-
posite directions, so as to cancel each other in the
average of a great number, leaving this average as
the parallactic motion. Now, to fix the ideas, sup-
pose that two stars have an equal apical motion, say
three radii of the earth's orbit in a year, but in opposite
directions. The apical motion of the earth being four
radii per year, it follows that the star which is mov-
ing in the same direction as the earth will have a
relative apical motion of only i, and will, therefore,
not appear in our list as a star of large proper mo-
tion. On the other hand, the star moving with equal
speed in the opposite direction will have a motion of
seven radii per year, and will, therefore, be included
among stars of considerable proper motion. Thus, a
bias occurs, in consequence of which we include many
stars having a motion away from the solar apex, while
the corresponding ones, necessary to cancel that mo-
tion, will be left out of the count. Thus, the parallactic
motion will, in the average, be too large in the case
of the stars of large apparent proper motion. Now,
this is exactly what we see in the above tables. As
we take the classes with larger and larger proper
motions, the supposed parallactic motion, which is
really the mean of the apical motions, seems to in-
crease in a yet larger degree. It is, therefore, impos-

AVERAGE SPEED OF A STAR 299

sible to determine from comparisons like these what
the exact ratio is.

This error is avoided when we do not arrange
and select the stars according to the magnitude of
their proper motions, but take a large list of stars,
determine their proper motions as best we can, and
draw our conclusions from the whole mass. This
has been done by Kapteyn in the paper already
quoted. By a process too intricate to be detailed in
the present work he has reached certain conclusions
as to the ratio of the actual motion of the sun in
space to the average motion of the stars. His defin-
itive result is :

Average speed of a star in space
= Speed of solar motion X 1.86.

This I shall call the straight-ahead motion of the
star, without regard to its direction. But the actual
motion as we see it is the straight-ahead motion, pro-
jected on the celestial sphere. The two will be equal
only in cases where there is no radial motion to or
from the earth. In all other cases the motion which
we observe will be less than the straight-ahead mo-
tion. By the process of averaging, Kapteyn finds :

Linear projected speed of a star
= Speed of solar motion X 1.46.

This projected motion, again, may be resolved into
two components at right angles to each other. It
follows that the average value of either component
will be less, than that of the projected motion. The
components may be the motions in right ascension

300 STATISTICAL STUDIES OF PROPER MOTION

or declination, or the apical motion and the motion at
right angles to it. In any case, the mean value of a
component will be :

Speed of solar motion X 0-93-

I have used Kapteyn's numbers to obtain the same
relation by a somewhat different and purely statis-
tical method.

Imagine the proper motion of a star situated nearly
at right angles to the direction of the solar motion.
Although- we cannot determine how much of its
apical motion is actual and how much is parallactic,
we can determine whether its motion, if toward the
solar apex, exceeds that of the sun. In fact, all stars
the apical component of whose motion is in the same
direction and greater than that of the sun, whatever
the distance of the star, appear to us as moving
toward the apex, a direction to which we assign a
negative algebraic sign. All stars moving more
slowly than this, or in the opposite direction from
the sun, will have apparent motions away from the
apex, which we regard as algebraic ally positive. We
can, therefore, by a simple count separate the stars
moving in the same direction as the sun, and with
greater speed, from all the others.

I have classified the stars in this way, not only as a
whole, but also with reference to their cross motion
motion at right angles to that of the sun. That is to
say, I have taken the stars whose cross motion, T,
is 2" per century or less and counted their apical-
motions as positive, negative, and zero. Then I have

AVERAGE SPEED OF A STAR

301

done the same thing with cross motions of 3" or 4",
then with cross motions ranging from 5" to 7", and
so on. All cross motions above 13" we put together. 1
The results of this work are shown, so far as described,
in the first four columns of the table below. We have
here, for the various values of r, the number of posi-
tive, negative, and zero apical-motions.

Table, showing the number of positive and negative
apical motions for different values of the crossmotion.

Values of

Apical Motions, 6

Percentage.

Pos.

Zero.

Neg.

P'.

N'.

O, 4- I, 2. .

I,0'3
360

285

215
216

261
56

425
1 60
107

52
61

V43
388

303
218
217

555
188

125

55
62

0.67
0.67
0.71
0.8o

0.78

0-33
-33
0.29

0.2O
O.22

+~i 4"

4- * to 7 .'.

+ 8 to 12

4- iv 4-

Totals

2,089

363

805

2,269

985

0.70

0.30

The first question that arises in connection with this
table is, how to count the motions that come out zero ;
that is to say, those which are too small to be certainly
observed. The most probable distribution we can
make of them is to suppose that they are equally di-
vided between positive and negative motions. I have,
therefore, added one-half of the zero motions to the
positive and one-half to the negative column, thus
getting the results given in columns P' and N'. The

1 The author should say that the greater part of the work on these countings
was done with great care and accuracy by Mrs. Arthur Brown Davis. -i-..-

302 STATISTICAL STUDIES OF PROPER MOTION

percentages of positive and negative motions thus re-
sulting are given in the last column.

We see that there is a fairly regular progression in
the percentage, depending on the value of the cross
motion. In the case of the small cross motions, which
presumably belong to the more distant stars, the per-
centage of negative apical motions is markedly greater
than it is in the case of the nearer stars which have
larger values of r $ the diminution in the number of
zero motions is still more remarkable. This arises
from the fact that in the case of the nearer stars the
apical motions are necessarily larger, whether positive
or negative.

In the preceding table all the stars were counted,
without reference to their distance from the solar
apex. The result of this will be that the mean of the
apical motions is taken as we see it projected on the
sphere, which does not correspond to the actual
motion in space except when the direction of the star
is at right angles to that of the apex. I have, there-
fore, made a second partial count, including only stars
between 60 and 120 from the apex. These stars
were selected in opposite regions of the heavens, so
as to eliminate any constant error depending on the
right ascension. The result of a count of 733 stars is :

Number of positive motions 530

" zero 50

" " negative " 153

If we proceed as before, dividing the zero motions
equally between the positive and negative ones, we
shall find the respective numbers to be 555 and 178.

AVERAGE SPEED OF A STAR

303

The percentage of negative motions is, therefore, 24.
This will still be slightly too large, owing to the
obliquity under which many of the stars were seen.
We may estimate the most likely percentage as 23.

We conclude that when the motions of all the
stars are so resolved that one component shall be
that in the direction of the apex, 23 per cent, of the
stars will be found moving towards the apex with a
greater speed than that of the sun. It may, there-
fore, be assumed that in the general average an equal
number are moving in the opposite direction with a
greater speed than that of the sun. We conclude
that the resolved motion of 46 per cent, of the stars is
greater than that of the sun, leaving 54 per cent. less.

In the absence of an exact knowledge of the rela-
tion between the magnitude and the number of
motions, we shall not be far wrong in assuming that
one-half the stars move to or from the apex with more
than the average speed, and one-half with less. Com-
paring this with the percentage found, we may con-
clude that the average motion of a star is less than
that of the sun, in the ratio 46 : 50 ; or that it is found
by multiplying the motion of the sun by the factor
0.92. This is almost exactly the number which we
have quoted from Kapteyn.

We have already stated that the actual speed of the
solar motion, still somewhat uncertain, may be esti-
mated at 20 kilometres per second, or 4 radii of the
earth's orbit in a year. For our present purposes the
latter method of expressing the velocity is the more
convenient. Multiplying this speed by the factors

304 STATISTICAL STUDIES OF PROPER MOTION

already found, we have the following results for the
average proper motions of a star in space expressed
in kilometres per second, and radii of the earth's orbit,
called R, in a year :

Straight-ahead motion 35km. = 7-4R.

Projected motion 28km. = 5.8R.

Motion in one component i8km. = 3.yR.

The motion of iQkm. or 4R. assigned to the sun is
its straight-ahead motion. This is little more than
half the average. It follows that our sun is a star of
quite small proper motion.

CHAPTER XX
THE DISTRIBUTION OF THE STARS IN SPACE

Hoc opus immensi constructum corpora mundi
Membraque naturae diversa condita forma.
^Eris atque ignis terrae pelagique jacentis,
Vis anima divina regit

MANILIUS.

WE shall now bring the lines of thought which we
have set forth in the preceding chapters to con-
verge on our main and concluding problem, that of
the distribution of the stars in space. While we can-
not reach a conclusion that can claim numerical exact-
ness, we may reach one that will give us a general
idea of the subject. The first question at which we
aim is that of the number of stars within some limit
of distance. It is as if, looking around upon an ex-
tensive landscape in an inhabited country, we wished
to estimate the average number of houses in a square
mile. On the general average, what is the radius of
the sphere occupied by a single star ? If we divide the
number of cubic miles in some immense region of
the heavens by the number of stars within that region,
what quotient should we get ? Of course, cubic miles

are not our unit of measure in such a case. It will

305

3 o6 DISTRIBUTION OF THE STARS IN SPACE

be more convenient to take as our unit of volume a
sphere of such radius that, from its centre, supposed
to be at the sun, the annual parallax of a star on the
surface would be i". The radius of this sphere would
be 206,265 times that of the earth's orbit. We may
use round numbers, consider it 200,000 of these radii,
and designate it by the letter R.

Now let us conceive drawn around the sun as a centre
concentric spheres of which the radii are R, 2R, 3R,
and so on. At the surfaces of these respective spheres
the parallax of a star would be i", half of a second,
one-third of a second, and so on. The volumes of
spheres being as the cubes of their radii, those of the
successive spheres would be proportional to the num-
bers i, 8, 27, 64, etc.

If the stars are uniformly scattered through space,
the numbers having parallaxes between the corre-
sponding limits will be in the same proportion.

The most obvious method of determining the num-
ber of stars within the celestial spaces around us is by
measurement of their parallaxes. It is possible to
reach a definite conclusion in this way only in the
case of parallaxes sufficiently large to be measured
with an approach to accuracy. In the case of a small
parallax the uncertainty of the latter may be equal to
its whole amount. In this case the star may be at
any distance outside the sphere given by its measured
parallax, or far within that sphere, so that no conclu-
sion can be drawn. It is, on the whole, useless to
consider parallaxes less than o". 10 ; even those hav-
ing this value are quite uncertain in most of the cases.

THICKNESS OF THE STARS IN SPACE 307

The data at command for our purpose are the known
individual parallaxes and the statistical summary
given by Dr. Chase as the result of his survey and
quoted in our chapter on the parallaxes of the stars.
This survey was confined to stars whose parallax was
not already measured, and it brought out no parallax
exceeding o'^o. 1

The most careful search has failed to reveal any
star with a parallax as great as i", and it is not likely
that any such exists. It is, therefore, highly probable
that the first sphere will not contain a single star
except the sun in its centre.

Within the third sphere, the parallax at the surface
of which is o".33, we may place the following four
stars :

//
ot Centauri Par. = o.75

LI. 21,185 " -4^

6 1 Cygni , " 0.39

Sirius 0.37

There are two other cases in which the parallax is
doubtful, though the measures as made bring the
stars within the sphere 3R. They are :

rj Herculis Par. =0.40

O. A. 18,609 0.35

In the case of Eta Herculis the proper motion is
so small that the presumption is strongly against so
large a parallax, and the doubtful parallax of the last

1 The results of this survey were communicated to the Astronomical and
Astrophysical Society of America toward the end of June, 1900, and published
in Science with the Proceedings of the Society.

3 o8 DISTRIBUTION OF THE STARS IN SPACE

star is so near the limit that it may be left out of the
count. The doubt in its case may be set off against
a doubt whether the parallax assigned to LI. 21,185
is not too large. We assume, therefore, that four
stars are contained within the sphere 3R, the volume
of which is 3 3 =27. This would give, in whole num-
bers, one star to 7 unit spheres of space.

When we come to smaller parallaxes we find a
great deficiency in the number measured in the South-
ern Hemisphere. The policy of Gill, under whose
direction or with whose support all the good meas-
ures in that hemisphere were made, was to make
a few very thorough determinations rather than a
general survey. Between the limits o".2o and o".33
are found :

In the Southern Hemisphere 4 meas. (Gill)

Northern " 2 " (Chase)

12 " (others)

Total 18

Of the northern results three are exactly on the
limit, o".2O, and several others are doubtful, and prob-
ably too large. The most likely number for the
Northern Hemisphere seems to be 12, and if we es-
timate an equal number for the Southern Hemisphere
we shall have 24 in all. Adding the four stars within
the sphere 3R, we shall then have a total of 28 within
the sphere 5R, of which the volume is 125. This
gives between 4 and 5 space units to a star.

Let us now consider the space between the spheres
5R and icR, including all stars whose parallax lies

THICKNESS OF THE STARS IN SPACE 309

between the limits o". 10 and o".2o. Of these the
numbers are :

Southern Hemisphere . 6 (Gill)

Northern " 15 (Chase)

15 (others)

Reasoning as before, we may assume that the
number of stars between the assigned limits is 60,
making a total of 88 within the sphere loR. The
volume of space enclosed being 1000 units, this will
give one star to 12 units of space.

How far can we rely on this number as an approxi-
mation to the actual number of stars within the tenth
sphere ? The errors in the estimate are of two
classes, those affecting the parallax itself and those
arising from a failure to include all the stars within
the sphere. The very best determinations are liable
to errors of two or three hundredths of a second, the
inferior ones to still larger errors. Thus, it may
happen that there are stars with a real parallax larger
than the limit, of which the measures fall below it
and are not included, and others smaller than the
limit, which, through the errors of measurement, are
made to come within the sphere. As we have seen
in the chapter on the parallaxes, it is quite possible that
there may be a number of stars with a measurable
parallax whose proximity we have never suspected on
account of the smallness of the proper motion. We
can only say that the nearer a star is to us the more
likely its proximity is to be detected, so that we are
much surer of the completeness of our list of large

310 DISTRIBUTION OF THE STARS IN SPACE

parallaxes than of small ones. Hence, there may
well be a number of undetermined parallaxes upon
or just above the limit o". 10.

The most likely conclusion we can draw from this
examination seems to be that in the region around
us there is one star to every 8 units of space ; or that
a sphere of radius 2R, equal to 412,500 radii of the
earth's orbit, corresponding to a parallax of 0^.50,
contains one star. This is a distance over which
light would pass in 6^- years.

We next see how far a similar result can be de-
rived from statistics of the proper motions. It seems
quite likely that nearly all proper motions exceeding
i" annually have been detected. The number known
is between 90 and 100, but it cannot be more exactly
stated because there is some doubt in the case of a
number which seem to be just about on the limit.
In this value, i", is included the effect of the parallac-
tic motion, which, on the general average, increases
the apparent proper motion of a star. To study this
effect let us call the list of 90 or more stars act-
ually found List A. Were it possible to observe the
proper motions of the stars themselves separate from
the parallactic motion, we should find that, when we
enumerate all having a proper motion of more than
i", we should add some to our List A and take away
others. The stars we should add would be those
moving in the same direction as the sun, whose
motions appear to us to be smaller than they really
are, while we should take away those moving in the
opposite direction, whose motions appear to us larger

THICKNESS OF THE STARS IN SPACE 311

than they really are. On the average, we should
take away more than we added, thus diminishing
slightly the number of stars whose motion exceeds
i". Making every allowance, we may estimate that
probably 80 stars have an actual proper motion on
the celestial sphere of i" or more. We have found
that the average linear proper motion of a star, as
projected on the sphere, is about 6 radii of the
earth's orbit annually. A star having this motion
would have to be placed at the distance 6R to have,
as seen by us, an angular motion of i". The par-
allax corresponding to the surface of this sphere is
o". 167. The volume of the sphere is 216, and accord-
ing to our estimate from the parallaxes it would con-
tain only 27 stars. Thus the proper motions seem to
give a greater density of the stars than do the meas-
ured parallaxes ; that is to say, they indicate that there
are still a large number of measurable parallaxes unde-
termined. But the fact is that the number of stars
estimated as within a given sphere by the proper
motions will be in excess, owing to the actual divers-
ity of these proper motions, which may range from o
to a value several times greater than the average.
In consequence of this, our list of stars with a proper
motion exceeding i" will contain a number lying out-
$ide the sphere 6R, but having a proper motion
larger than the average. We are also to consider
that within the sphere may actually lie stars having
a proper motion less than the average, which will,
therefore, be omitted from the list. Of the number
of omitted and added stars the latter will be the

312 DISTRIBUTION OF THE STARS IN SPACE

greater, because the volumes of spheres' increase as
the cubes of their radii. For example, the space
between the spheres 6R and gR is more than double
that within 6R, and our list will include many stars
in this space. Thus arises a discrepancy between
the parallaxes and the proper motions. 1

Let us see what the result is when we take stars of
smaller proper motion. The most definite limit which
we can set is 10" per century. We have seen that Dr.
Auwers, in his zone, found 23.9 stars per 100 square
degrees having a proper motion of 10" or more. This
ratio would give about 10,000 for the whole heavens.
The sphere corresponding to this limit of proper
motion is 6oR. On our hypothesis as to star-density
this sphere would contain 27,000 stars, nearly three
times the number derived from Auwers's work. But
it is not at all unlikely that this sphere contains three
times as many proper-motion stars as have been de-
tected. Great numbers of the more distant stars will
not have been catalogued, owing to their faintness^
because a star at the distance 6oR will shine to us
with only one per cent, the light of one at distance
6R. This corresponds to a diminution of five magni-
tudes ; that is to say, a star of the sixth magnitude

1 The principle involved in the case may be more fully stated thus : If we
take all the stars that lie within a given sphere, and determine their proper
motions and parallaxes, we shall get the correct relation between the proper
motions and parallaxes. But if we take all stars whose proper motion exceeds
a certain limit, and determine their parallaxes, the mean of these parallaxes
will be disproportionately small, owing to the omission of stars with proper
motions below the limit, but lying within the sphere of measurement. It thus
happens that the proper motions found in our Appendix II. are, in the general
average, much more than six times the parallax.

THICKNESS OF THE STARS IN SPACE 313

at distance 6R would only be of the eleventh mag-
nitude at distance 6oR, and would, therefore, not be
catalogued at all. There is, therefore, no reason for
changing our estimate of star-density, which assigns to
each star around us 8 units of volume in space.

This fact suggests another important one. Owing
to the great diversity in the absolute magnitude of
the stars, those we can observe with our telescopes
will naturally be more crowded in the neighbourhood
of our system than they will at greater distances.

Some further results as to the mean parallax of the
stars may be derived from a continuation of the statis-
tical study of the proper motions. Kapteyn's inves-
tigation in this direction includes a determination of
the mean parallactic motion of the stars of each mag-
nitude for the first and second spectral types separately.
From this he obtains the following mean parallaxes
for stars of the different magnitudes :

Mean parallaxes of stars of different magni-
tudes, and of the two principal types, as found from
their parallactic motions :

Mag. Type I. Type II.

// n

2.0 .0315 .0715

3.0 .0223 .0515

4-o .0157 .0357

5.0 .oni - 02 53

6.0 .0079 - OI 79

7.0 .0056 .0126

8.0 -0039 .0089

9.0 .0028 .0063

10.0 .0020 '45

IT.O .0014 .0032

314 DISTRIBUTION OF THE STARS IN SPACE

Using the value 4 for the solar motion, instead of 3.5, found by Kapteyn, all
these parallaxes should be diminished by one eighth of their amount.

Unfortunately, owing to the great diversity in the
absolute brightness of the stars, and the resulting
great difference in the distances of stars having the
same magnitude, these numbers can give us no idea
of the actual parallaxes. Let us take, for example,
the stars of the sixth magnitude. A few of these
are doubtless quite near to us and have a parallax
several times greater than that of the table. Exclud-
ing these from the mean, an important fraction of the
remainder, perhaps a great majority, may have a
parallax smaller than that of the table to any extent
may, in fact, be on the very confines of the
universe. 1

We get a slightly more definite result by studying
another feature of the proper motions. We may con-
sider the Bradley stars, whose motions have been in-
vestigated, as typical in the general average of stars
of the sixth magnitude. By a process of reasoning
from the statistics, of which I need not go into the
details at present, it is shown that the parallac.tic mo-
tion of a large number of these stars, probably one-
sixth of the whole, is less than r" per century. To

1 Since the present work was prepared for the press, Kapteyn has published
a number of careful and intricate researches on stellar statistics, bearing on the
subject discussed in this and the next chapter. One of these papers, forming
No. 8 of the Publications of the Astronomical Laboratory at Groningen, is "on
the mean parallax of stars of determined proper motion and magnitude " ;
another, published in the Proceedings of the Amsterdam Academy for April
2O, 1901, is "on the luminosity of the fixed stars." So far as the results
worked out in these papers bear on the problem of the extent of the universe,
the reasoning is too abstruse and the results too mathematical to be easily
presented in the present work.

THICKNESS OF THE STARS IN SPACE 315

this motion corresponds a parallax of C/.OO25, corres-
ponding" to the sphere of radius 4OoR.

The statistics of cross motions lead to a similar con-
clusion. One-half the Bradley stars have a cross
motion of less than 2". 5 per century. To this motion
would correspond a sphere of radius 2ooR and a
parallax of o".oo5. Stars at this distance must be
hundreds of times the absolute brightness of the sun
to be seen as of the sixth magnitude. Yet the con-
clusion seems unavoidable that the sphere of lucid
stars extends much beyond 4OoR.

We shall next make an estimate based on the num-
ber of the stars. All the facts we have reviewed lead
to the belief that, out to a great distance, the stars
are scattered without any great and well marked
deviation from uniformity. This belief rests upon
the remarkable equality in the number of stars in
opposite directions from us. We do not detect any
marked difference between the numbers lying round
the two opposite poles of the galaxy, nor, so far as
known, between the star density in different regions
at equal distances from the Milky Way. Accepting
this view, the question how far we must place the
boundary of a sphere in order that it may contain a
given number of stars admits of a definite answer.
We have only to extract the cube root of the num-
ber, and multiply it by 2. Consequently the sphere of
radius 2^R will contain n z stars. Thus a sphere of

Radius 4ooR will contain 8,000,000 stars
" 6ooR " " 27,000,000 "

316 DISTRIBUTION OF THE STARS IN SPACE

Radius 8ooR will contain 64,000,000 stars
" loooR " " 125,000,000 "

The minutest counts of stars that have been made,
and the photometric law shown in the beginning of
Chapter XVIII. lead us to suppose that the actual
number of non-galactic stars, visible and invisible,
probably falls within the limits of the above numbers.
We have therefore no reason to believe that, away
from the Milky Way, the stars extend far beyond
the sphere TOOoR, at whose boundary the parallax is
o".ooi, and the average proper motion of a star about
o".6 per century. But the phenomena of the Milky
Way show that around the region of the galactic belt,
there is a distance at which the law of uniform density

ceases to be true. Let
S be the sun, Ri a
portion of the surface
of the outer sphere of
uniform distribution,
and R2 and R3 two
contiguous spheres
passing through the
galactic region G, of
which the pole is in
the direction P. It
is quite certain that
Ra R 3 the star -density is
greater around G than around P. This may arise
either from the density at G being greater, or from
that at P being less than the density within the
sphere Ri. From the enormous number of stars

DISTANCE OF STARS IN THE MILKY WAY 317

collected in the galactic regions, we can scarcely doubt
that the former alternative is the correct one. But
there must be a sphere at which the second alternative
is also correct, because we find the number of stars,
even of the lucid ones, to continuously increase from
P toward G.

Can we form any idea where this difference begins,
or what is the nearest sphere which will contain an
important number of galactic stars ? A precise idea,
no ; a vague one, yes. We have seen that the
galactic agglomerations contain quite a number of
lucid stars, and that, perhaps, an eighth of these stars
are outside the sphere 4OoR. We may, therefore,
infer that the Milky Way stars lie outside this
sphere. Considerations based on the proper motions
lead us to place these stars even outside the sphere
lOOoR. It seems certain that the blue stars of the
constellation Orion have a proper motion of only a
small fraction of a second per century a few tenths
or less. Although these do not belong to the Milky
Way itself, there is reason to believe that they do
not lie beyond it, and that the proper motions of the
stars of the Milky Way are equally small. This
would place the stars of the Milky Way at a greater
distance than the probable confines of the universe in
the direction of the galactic poles.

So far as we can judge from the enumeration of
the stars in all directions, and from the aspect of the
Milky Way, our system is near the centre of the stel-
lar universe. That we are in the galactic plane itself
seems to be shown in two ways : (i) the equality in

318 DISTRIBUTION OF THE STARS IN SPACE

the counts of stars on the two sides of this plane all
.the way to its poles, and (2) the fact that the central
line of the galaxy is a great circle, which it would
not be if we viewed it from one side of its central
plane.

Our situation in the centre of the galactic circle, if
circle it be, is less easily established, because of the
irregularities of the Milky Way. The openings we
have described in its structure, and the smaller dens-
ity of the stars in the region of the constellation
Aquila, may well lead us to suppose that we are per-
haps markedly nearer to this region of its centre than
to the opposite region ; but this needs to be estab-
lished by further evidence. Not until the charts of
the International Photographic Survey of the heavens
are carefully studied dpes it seem possible to reach a
more definite conclusion than this.

One reflection may occur to the thinking reader, as
he sees these reasons for deeming our position in the
universe to be a central one. Ptolemy showed by
evidence which, from his standpoint, looked as sound
as that which we have cited that the earth was fixed
in the centre of the universe. May we not be the
victims of some fallacy, as he was ?

The following is a summary of more or less prob-
able conclusions, drawn from facts developed in the
present work :

i. The stars differ enormously in their actual lumin-
osity. Some are thousands or tens of thousands of
times more luminous than the sun ; others only one-
hundredth or one-thousandth as luminous.

SUM MAR Y OF CONCL USIONS 3 1 9

2. The more luminous stars are generally the hot-
ter, the bluer, and the rarer in their constitution..
They are, as it were, inflated masses of rare and in-
tensely incandescent gas. Hence the stars do not
differ in mass so widely as in luminosity.

3. The bluest and most luminous stars are situate
mainly in the region of the Milky Way. There is
some reason to suspect that in this region the more
densely the stars are agglomerated the larger and
more luminous they are.

4. That collection of stars which we call the uni-
verse is limited in extent. The smallest stars that
we see with the most powerful telescopes are not, for
the most part, more distant than those a grade
brighter, but are mostly stars of less luminosity,
situate in the same regions. This does not preclude
the possibility that far outside of our universe there
may be other collections of stars of which we know
nothing.

5. The boundary of our universe is probably some
what indefinite and irregular. As we approach it, the
stars may thin out gradually. The parallax at the
boundary is probably nowhere greater than o".ooi,
and may be much less. The time required for light
to pass over the corresponding interval is more than
three thousand years.

6. The universe extends farther around the girdle
of the Milky Way than toward the poles of that
girdle. But, in every direction, it extends beyond
the limit within which the proper motions of the stars
have yet been determined.

3 2o SUMMARY OF CONCLUSIONS

7. It does not yet seem possible to decide whether
the agglomerations of the Milky Way lie on the
boundary of the universe or not. The number of
lucid stars which they contain might seem to militate
against the view, though not strongly because of the
possible great luminosity of the galactic stars.

8. The total number of the stars is to be counted
by hundreds of millions.

9. Outside the galactic region the stars in general
show no tendency to collect into systems or clusters,
but are mostly scattered through space with some
approach to uniformity.

APPENDIX

In this appendix are found lists of the individual names of
certain stars, of parallaxes and large proper motions, and of spec-
troscopic binary systems.

The list of names seems to require no explanation.

List of parallaxes and proper motions.

The parallaxes in this list are derived, for the most part, from
a combination of all the investigations or authorities on the
subject. ,

A colon after a parallax indicates that it is subject to more
doubt than usual ; two colons, that it is entirely unreliable.

The numbers and letters in the column "light" are intended
to show the luminosity of the star, or the ratio of the actual
amount of light emitted from its entire surface to that emitted
from the entire surface of the sun. The numbers cannot lay any
claim to exactness, owing to the uncertainty as to the star's exact
distance from us, and are intended only to give a general idea of
the actual magnitude or luminosity of the star.

Where the letters XM are used in this column they mean that
no numerical statement is possible except that the star is thou-
sands and perhaps tens or even hundreds of thousands of times
brighter than the sun.

List of spectroscopic binary systems established to July, IQOI.

This is a list of stars for which a variability of the radial motion
supposed to be due to the action of a companion or the duplicity
of the star has been established.

The period is given in days.

The orbital velocity is the extreme deviation of the observed
orbital velocity from the mean, smoothed off where the observa-
tions are sufficiently numerous. In those cases where an orbit

321

3 22

NAMES OF STARS

has been computed from the observed velocities, the velocity
given is that derived from the elements.

It will be noted that in many cases the period and velocity are
not yet determined.

The author is indebted to Professor Campbell for most of the
particulars given in the list, and for its final revision.

/. Names of individual stars found in astronomical literature^ with
their approximate positions for 1900.

Position 1

or IQOO.

R. A.

Dec.

Achernar

<x Eridani

h m
I "34 O

57 55

Alcor

80 Ursoe Majoris

13 212

15 5 3O

Alcyone

77 Tauri

3dl 5

-\-21 48

Aldebaran

(X. Tauri . ...

40Q 2

-j-i6 18

Algenib

y Peuasi. .

O 8 I

4-i4 ^8

Algol .

ft Persei

2 17

-4-4O ^d

Alioth

Ursae Majoris .

12 4.Q 8

-L-c6 2Q

Altair

(X Aquilae

IQ 45 Q

4- 8 36

An tares

ex. Scorpii

16 2^ "\

26 1 3

Arcturus

ex. Bootis

14 1 1 T

-i IQ 42

Bellatrix

y Orionis

C TO 8

_f_ 6 16

Betelguese . .

ex. Orionis . . .

c an 8

+ 7 21,

Canopus

ex. Argus (Carinse) . .

6 21 7

52 'iS

Capella

ex. Aurigse

C Q

-1-45 54

Caph

ft Cassiopeiae

o ^.8

+ 58 36

Castor

ex. Gerninorum

7 28 2

4-^2 6

Cor Carol! ... .

ex. Canum Venaticoruni

14 %I ^

4-38 52

Deneb

ex Cygni
ft Leonis

20 38.0

I I 44 O

+44 55
4-15 8

Dubhe

ex. Urs32 Majoris

IO 57 6

4-62 17

Fomalhaut . . .

ex Piscis Australis

22 52 I

^O Q

ex. Pegasi

22 5Q 8

-4-14 4O

Mira Ceti

o Ceti

2 14 3

3 26

Mizar

Urs32 Majoris

13 IQ q

-4-cc 27

Polaris

ex Ursse Minoris

I 22.5

+88 46

Pollux

ft Geminorurn

7 3Q.2

+28 16

Procyon

7 34- 1

+ 5 2 9

ex Leonis

IO 3O

+12 27

Ricrel

ft Orionis ...

5 Q 7

8 IQ

Sirius

ex. Canis Majoris.

6 40.7

16 35

Spica

OL Virgin is

13 IQ Q

10 38

Ve^a

ex. Lyras

18 33.6

+38 41

PARALLAXES AND PROPER MOTIONS 323

//. List of parallaxes of stars and of proper motions exceeding
100" per century.

Star.

Position, 1900.

Par-
allax.

Magni-
tude.

Lumi-
nosity.

Annual Proper
Motion.

R. A.

Dec.

0=i.

R. A.

Dec.

ft Cassiopeisc.

h m
038
o 12.7
o 14.9
o 20.5
o 32.2

o 34.8
o 43.0
o 43.1
o 50.7
i 1.6

I 22.6
I 34.0

I 39.4
2 6.4
2 II. O
2 30.6
2 56.O

3 1.8
3 15.6
3 15-9
3 16.0
3 28.2
3 40.2
3 56.5
4 i-9
4 10.7
4 30.2
4 55-8
5 7-7
5 7-7
5 9-7
5 26.4
5 45-i
5 498
5 52 2
6 21.7

6 39-5
6 40.7
6 53-7
7 28.2

7 34-0

+58 36
+43 27
-65 28

-77 49
-25 19
+55 59
+57 17
+ 4 46
+60 10
+54 26
+88 46

-57 45
-16 28

-5i 19
+33 46
-1- 6 25
+6 1 20

+49 J 4
-62 58

A 1 ! 27

0.15
0.30:
0.06
0.13

0.04:
0.20

o.or.
0.14
0.06
0.04
0.31

0.14

0.04::
0.18

O.I I

0.09
o.oo

0.02
O.O6:
O.OO
O.I I

0.37

0.03:
0.20:
0.30

M
2-4

8.1

4-3
2.9
5.6

2-4
3.6

5-7
2-3
5-2

2.1

0.5
3-7
6.4
5-0

5-9
6.7
4-2

6.2

4-3
5-8
3.8

8.2

8.5
5-5

4-5
i.i

6.4

8.5

0.2
0-3

8-7
6.5
0.9

2.1
I.O

5-3
1.4

5-2

1.6
o.5

O.OI

IOOO

0.5

5
57
45

120

500
48
XM
0.7

3^
n

7
8

S.
+0.068
+0,262
+0.273
+0.703
+0. 100

+0.006

+0.143
+0.048
+0.004
+0.391
+0.136

+O.OIC
0.120
+O.225
+0.091
+0. 1 2O

+0.094
+0.133
+0.195
+0.281

+0.192

0.066

+0.053
+0.143

-(-0.014
0.148
+0.005

-{-0.040
+0.621

+0.009

0.000

+0.046
-(-0.087

-(-O.OO2
0.004
+O.OO2
+O.O02
0.037
+0.057

o 014

-0.047

n
0.18

+0-39
+1.16
+0.32
o.oo
0.03
048

-1.13

o.oo

-1-55
o.oo
0.04
+0.86
-1-0.72
-0.23

+ 1.46
-0.68
o.io
+0.65
+0.76
-fo.66

+0.02
O. 12
-1-34

o 18

Gr. 14 .

C Tucani

ft Hydri

82 B Ceti

cc Cassiopeise

t] Cassiopeiss .

147 B Piscium

y Cassiopeia

fji Cassiopeiss .

Polaris

(X Kridani . . . .

r Ceti . . .

Lac 66 1

S Trianguli

128 H J Ceti

Lac 5400 .

i Persei

C l Reticuli

C 2 Reticuli

-62 53
- 9 48

+4i 9
+35 2
+37 47
+ 17 48
6 18
- 5 52
-45 3
+45 54
- 8 19
- 3 42
80 33
+ 7 23
+44 56
-52 38
+43 4i
-16 35

+ 87 12

+32 6
+ 5 29

Eridani ,

LI 6888

LI. 7441 . .

50 Persei

o 2 Eridani

-3-44
0.19

-i. 13

-5.70
043

0.00
2.12
+ 1.09
+0.01
O.OI
+O.OI

+o 16

I. 21
O.O4
0.08
1.04

Aldebaran ......

Weisse 1189

C. Z.Vh, 243

Capella

Rigel

7t Mensae

<x Orionis

ft Aurigse

Canopus

ib 5 Aurigse

Sirius

51 H. Cephei

Castor

Procyon

3 2 4 PARALLAXES AND PROPER MOTIONS

Star.

Position, 1900.

Par-
allax.

Magni-
tude.

Lumi-
nosity
=i.

Annual Proper
Motion.

R. A.

Dec.

R. A.

Dec.

Pollux

h m

7 39-2
7 41-8
7 47-2
7 54-3
8 13.6
8 29.0
8 46.0
8 52.4
8 54-2
976
9 26.2

9 37-i
9 46.2
9 55-2
10 3.0
10 5.2
10 21.9
10 27.7
10 57-9
ii 0.5
ii 8.6
ii 14.8
ii 29.6

ii 33-5
ii 40.3

ii 41.8
ii 47.2
ii 53-0

12 4.6
12 10.0

13 7.2

13 13-2
13 40.2
13 40.7
13 56.8
14 II. I
14 32.8
14 4 6 -C
14 5L6
14 52.4

15 4-7
15 4-7

15 8.8
15 37-7
15 51-8

+28 16
-33 59
4-30 55
+29 31
12 18
-31 ii
+7i H
+48 26
+42 ii
+53 7
+52 8
+43 10
ii 49
+32 25

-f 12 27

+49 58
+49 J 9
+49 42

+36 38
+44 2

+74 i
+66 23
-32 18
+45 40
+48 14

-39 57
+38 26
-27 8
+40 49
9 44

+28 23

-17 45

+18 20
+ 15 26
-59 53
+ 19 42
60 25

-23 53
20 58

+ 54 4
-15 59
-15 54
o 58
io 36
+15 59

O.O6
0.02

o 13:

0.20
0.15
0.07
O.O6

O.O6
0.02

0.18

0. 10

0.04
0.46

O.22
0. T5
O.27:
O.O3
0.02

O.O6
0.14
O. II

0.05
0.03
0-75

O.o8

M
1.2

5-4
8.2

7.0
6.0

6.4

8-5
3-1

4-2

8.0

3-3
8.0

9-3

5-5
i-3
6.8
6.5
7-6
7.6
8-5
7.2
9.0
6.0
6.3
7.8

5.o
6.4
7-2
7-4
6.0

4-3
4.8
9.2

8-5
0.8

0.3

0.2

7.8
5-8
7-7

9-3
9.2

6.7
7-3
4.0

100

1.6

3
0.6
0.03
no

0.2

1000

0.07
0.3
0-7
0.005

O.OI

0.07
0.004

2
0.2

0.4
1.9

2 2O
IOOO

i-7

O.I

0.047

0.021
+0.058
O.O12
+0.017
0.088
0.280
0.044
-0.039
0.175
0.103
-1-0.002
+0.085
0.042
0.017
O.I4O
+0.01 1

+0.024

0.044

0.402

O IOS

O.o6
+ 1.67
-I 82
1.17
O.gq
+0.69
-0.35
0.25
O.26
O.62

0.54
-0.80
I ^O

Lac 2Q57

1,1 IC2QO. .

LI I5565..

LI. 16304

Lac. 3386 .

Fed 1384

Ursse Mai

jo Ursae Maj

Fed 1457-8 .

Ursae Maj . .

LI. 19022

\Veisse 954

-0.44

o.oo

-0.52
0.89

+0.1 1

-474
+0-95

+0.13
+0.24
+0.84
+0.03
0.28

+0.39
-5-7S
0.70
0.06

1. 01

+0.88
1.07
-i.8s
-1-47
0.03

2. CO

+0-73
0.48

-1.79
+0.48

-3-64
-3.63
-0-93
-0.34
-1.29

Regulus

Gr 1618 ....

Gr 1646

Gr 1657

LI. 21185

LI 21258

Fed. 1831

O. A. 11677.

-0.503
0.053
0.060
0.061

-0.133
+0.341
0.074
0.029
+0.005
0.060
-0.075
+0.027
+0.125
o 003
0.078

0.485
-0.066
+0.074

O.IIO

0.067
0.066

0.085
0.076

+O.O2I

Brad 1584

2 ic6i

Gr 1822

Lac 4887

Gr 1830

Lac. 4QS5. .

Gr. 1855

LI 22Q c ;d

ft Comae

61 Virginis

Auwers A. G 4999

Aron

LI 27026

43 B Librae

Fed. 2544

O. A. 14318

O. A. 14320

LI 2774.4.

LI. 28607

y Serpentis

PARALLAXES AND PROPER MOTIONS 325

Star.

Position, 1900.

Par-
allax.

Magni-
tude.

Lumi-
nosity
Q=i.

Annual Proper
Motion.

R. A.

Dec.

R. A. Dec.

h m
16 23.3
16 25.6
16 39-5
16 47.9
16 50.1
16 59.8
17 9.2
17 TO.I
17 10.9
17 ii. 6

17 12.2
17 16.9

17 20.8
17 30.2
17 37-0
18 0.4
18 4-5
18 33.6
18 41.7
18 53-1

19 20.2

I 9 32.6
19 45-9

19 55-6
19 58.9

19 59-7
20 4.6

20 9.0
20 17.7
2O 38.0
2O 5I.O
21 2.4
21 II. 4
21 l6.2
21 24.5

21 55-7

22 1.9
22 16.0
22 52.1
22 59.4

23 8.5
23 II.9
23 44.0

23 57-0
23 59 5

26 13

+ 4 26
+39 7

-f- O II

- 8 9

- 4 54
26 27
26 24
-1-36 55
+34 53
+24 57
+32 36

+ 2 14

+55 15
-j-68 26

-- 2 31

--86 37
--38 41
--59 29
- 5 48
+ 11 44
+ 69 29
+ 8 36
-67 34
-66 26

+23 5

36 21
27 2O
21 4O

+44 55
44 29
+38 15
-39 15-

-|-62 10
12 56

-57 12
47 27
-72 44
-30 9
36 26

+56 37

14 22

+ I 52

+26 33
-37 5i

O.O2
0.40:

o.n:

0.05:

0.32
O.22

0.19
0.03:
O.I I
0.35:

O.O6
0.26:
0.23

0.00

o.39
0.06:

O.2O
0.02

0.13
0.28

0.15
0.05

M
1-3

7.6

3-7

6.8

8.8

7-9
4.6

6.7
3-3
5-9
3-2
5-4
8.0

4-9
7-9

4-1

4.4

O.I

8.9
9-3

5-3
4.8
0.9
6.6
3-6
7.2
5-4
5.8

8.2

i-3

7-5
4.8
6.8

2.6

9.1
4.8
1.9
5.8
i.3
7-4
5-6

8.2

8.7
5-8
8.5

9OO
0-3

4-7
25

O.I
O.O2

0.7

22
90
0.007

2.5

O.2
10

O.I

0.4
500

21
0.02

o.3

2.2

0.001

0.030
+0.003
0.049
0.063
0.062

0.037
0.038

O.OOI

+0.096

+0.002

+0.009

0.040
+0.018
+0.069
0.018
+0.019

+0.018
0.171
0.016
+0.050

+O.IOO

+0.036
+0.186
-j-o. 192

0.074

+0.037
+0.094
+0.037

0.000

0.050

+0.350
0.280

-J-O.O22

+0.070
+0.479

+0.01 1

4-0.280

+0.025

+0.573

+0.253
-0.035

+0.065

4-0.062
4-0.485

0.03

-0.39
0.09

-1.49

0.87

-1-15
1.17
1.14

o.oo

0.21

0.16

-1.05

1.22

+0.05
-1.25

1. 12

4-0.05
4-0.28
4-1.87

1.22

+0.63
-1.76

+0.38

0.67

-1.13

-0.94

-1.64
-0.24

1. 10

o.oo

-0.99

4-3.24

1.22

+0.05
0.28

-2.58

0.18

0.74
0.17

+I.I5

+0.30

1. 21

1. 00

-0.99

-2.58

Ll 30044

Ll ^0604.

Weisse 906

Ll ^iQt; 1 ;

Brad 21 79

it Herculis

Lac 7215 . .

co Herculis

Weisse 322 ....

y ' Draconis

OA 1 74m

70 Ophiuchi

8 Ursse Min ....

cc Lyrae

Anon

Anon . .

f>i Aquilss .

<5 Draconis

Lac. 8267

<5 Pavonis

Ll ^8-38-}

Lac 8362

Lac. 8381

O A 20452 ....

(x Cygni

Lac 8620

6 1 Cygni

Lac 8760

cc Cephei

Weisse 562

Indi

cc Gruis

y Indi ...

Fomalhaut

Lac 0^2

Brad 3077

Ll. 46650

ge Pesrasi

Cord. 32416

3 26 SPECTROSCOPTC BINARY SYSTEMS

III. List of spectroscopic binary systems.

Name of Star.

Position, 1900.

Mag.

Period
Days.

Orbital
Velocity
km. sec.

Authority or
Discoverer

R.A.

Dec.

rj Andromeda. .
Polaris

h m
o 52

I 22

I 4 8
2 8
2 36

2 47
3 2
3 55
5 9
5 27
5 52
6 58
7 28

7 55
8 42

9 36
ii 13
ii 43
13 20
13 20

13 49
14 6

14 52
15 19
15 53
16 o
1 6 26
16 45
16 55
16 56
17 38
18 23
18 37
18 42
18 46
18 50
19 16
19 47

20 10

20 15

21 II
21 40

22 2
22 25
22 38
23 5

23 33

+22 52

+88 46
+ 2 42
-- 8 23
--39 46

--52 22

--40 34

--I2 12

--45 54

+44 56
+20 43
+32 7
-48 50
+ 6 48

+ 10 21

+32 6
+20 46
+55 27
-io 38
46 48
+25 34
-42 44
- 9 57
-25 49
+58 50

+21 42

37 52
--65 17

--82 12

--68 48
--72 42
-99
4 5i
+33 15
+22 32
-16 8
+ o 45
+46 26
-15 5
+ 4 50
+25 ii
+24 5i
+57 54
+29 42
+74 5i
+45 56

4.6

2.1
4-7
4-4

4.9

4.0

2.5
Var.

O.2

2.4

2. I

Var.

2.0

5-o
3-6
3-8
3.8
4.6
2.4

1.2

2.7

4-8

2.8
5-2

3-1

4-2

2.8

3-6
4-7
4-5
4.9
3-7

4.4

Var.
4.6

4.7
Var.

3.8

3-4
4.0
4-2
4.0
Var.
3.1
4-5
4 o

3-97

2.8 7

IO4.O
I. 9
3.98
10.15
2.91
3-12

14.5

4.01

8.02

240+
1.57

9
412 +
1-45

282
12.91

7.18

IOOO +
IO.2

5-37
818.0

14
3

26
70
120

13
II

305
56

18
80

40
13

12
230

18
6
7
181

10
20.6

20
14

Campbell
Campbell
Campbell
Campbell
Campbell
Campbell and Miss Maury
Vogel
Belopolsky
Campbell and Newall
Deslandres
Miss Maury
Belopolsky and Campbell
Belopolsky
Pickering
Campbell
Campbell and Miss Maury
Wright
Campbell
Pickering
Vogel
Mrs. Fleming
Wright
Mrs. Fleming
Campbell
Miss Cannon
Campbell
Campbell
Bailey
Campbell
Campbell
Campbell
Campbell
Wright
Wright
Belopolsky
Wright
Campbell and Miss Maury
Belopolsky
Campbell and Miss Maury
Campbell and Miss Maury
Campbell and Miss Maury
Campbell
Campbell
Belopolsky
Campbell
Campbell
Campbell

Piscium

Ij Ceti

12 Persei

T Persei
ft Persei

A Tauri

oc. Aurigae

d Orionis
ft Aurigae

Geminor ....
a } Geminor. . .
A. G. C. 10534
Hydrae
I Leonis
o Ursae Maj . . .
93 Leonis
C Ursae Maj . . .
a Virginis ....
C Centauri ....
d Bootis

ft Lupi

8 Librae

Tt Scorpii

6 Draconis ....
ft Herculis. . . .
H Scorpii . .

h Draconis. . . .
Ursae Min. . .
GO Draconis. . .
X Draconis. . . .
2 Scuti

6 H. Scuti....
ft Lyrae. .

113 Herculis. .
v Sagittarii. . .
77 Aquilae. . . .
o 1 Cvgni .

ft Capricorni. .
a Equulei
H Pegasi .

i Pegasi

d Cephei

rj Pegasi
it Cephei
A Andromeda.

INDEX

Alcyone, central star of Pleiades, 79
Aldebaran, origin of name, 33
Algol, variable star, 101

type of, 102

Al-Sufi catalogues the stars, 43
Andersen discovers new stars, 132
Andromeda, great nebula of, 182
Andromedae, y, a triple system, 164
Annular nebulae, 183
Apex of" sun's motion, 88

its position in Lyra, 90, 91

Apical motions of the stars defined,

291

law of, 297

Aqueous vapour, lines of, 66
Aquilae, 77, variable star, 114
Arcturus, rapid motion of, 76
Arequipa Observatory, work of, 23
Argelander, his Durchmusterung,

46, 54

Argo, division of constellation, 32, 36
Argus, 77, variable star, 124

magnitude of, 127

Auriga, new star in, 132

Aurigae, a, spectroscopic binary, 168

Auwers, new star of 1860, 130

system of Sirivis, 160

proper motions of stars, 253

Bailey, variable stars in clusters, 173

stars in the Pleiades, 259

Barnard, diffused nebula of Orion,
187

Barnard, photographs of Milky Way,

268
Bayer, his Uranometria, 33, 44

system of star names, 33

Belopolsky, measures radial mo-
tions, 85

motion of 77 Aquilae, 86

Binary systems, defined, 157

of short period, 163

light and density of. 193, 199

law of period, 195

of gaseous density, 200

spectroscopic, 165

list of, 326

orbits of, 166

Bond photographs stars, 10
Boss, apex of solar motion, 88

proper motions of stars, 254

Brashear makes the Mills spectra,

graph, 12
Burnham observes double stars, 195

Campbell, work at Lick Observatory,

spectrogram of Polaris, 84

spectrographic work, 86

speed of solar motion, 93

spectrum of Nova Aurigae, 133

Canopus, great luminosity of, 192
Cape Observatory, activity of, 8
Cape Photographic Durchmusterung^

by Gill, 48
Capella, a binary system, 168

328

INDEX.

Carrigan, position of galaxy, 242
Castor, double star, 158
Catalogue of stars, defined, 45
made by Hipparchus and Ptol-
emy, 41

by Al-Sufi, 42

by Ulugh Beigh, 43

by Argelander and Schonfeld, 46

of nebulae and clusters, 179

Celoria, star-gauges of, 248
Centauri, a, the nearest star, 146

orbit of, 162

Centauri, GO, star-cluster, 173
Cephei, 5, variable star, 115
Ceti, o, variable star, early observa-
tions, 94

type and period of, 99

spectrum of, 119

Chandler catalogues variable stars,

96
Chase, search for stellar parallaxes,

151
Clark, Alvan, separates companion

of y Andromeda, 164
Clark, A. G., discovers companion of

Sirius, 161
Classification, of star-spectra, 67

of variable stars, 116

Clerke, list of new stars, 173
Cluster, Great, of Hercules, 171

of Perseus, 171

of co Centauri, 173, 175

Clusters^ stars, 169

variable stars in, 173

gravitation in, 177

Collision theory of new stars, 137
Colours of stars, supposed changes in,

121

Coma Berenices, cluster of, 260
Common, nebula of Orion, 180
Constellations, study of, 28

how named, 29

outlines of, not definite, 31, 35

Constitution of the stars, 191

Constitution of the stars, gaseous,

206
Cordoba, Observatory of, origin and

work, 6

Durchmuslerung, 47, 55

Coronae, T, new star of 1866, 130

spectrum of, 130

Cross motion of stars defined, 291
statistics of, 301

Crossley reflector of Lick Obs., 172

work of, 1 86

Cygni, Y, variable star, 109

6 1, a binary system, 159

parallax first determined,

144

Dawes measures double stars, 155
Declination defined, 39
Density of some stars, 202
Distance of double star defined, 156
Distribution, of the stars over the

sky, 238

of lucid stars, 240

of fainter stars, 247

of proper motion stars, 252

of fifth type stars, 256

of stars in space, 305

Double stars, defined, 153
particulars observed, 155

See also Binary systems
Draper photographs the moon, 10
Dreyer, catalogue of nebulae, 179
Durchmusterung, defined, 46

Argelander's, 46, 54

Schonfeld's, 46

Cordoba, 47

Cape Photographic, 48

counts of stars in, 248

Easton, stars in Milky Way, 273
Elkin, measures parallax of stars, 149

triangulates Pleiades, 170

Evolution of the stars, 217

INDEX.

329

Fifth type stars, number and distrib-
ution of, 256

Flamstead assigns numbers to
stars, 34

Flint measures stellar parallax, 149

Galaxy, crowding of stars toward,

240, 246

position of circle of, 242

belt of bright stars near, 243

course of, 264

See also Milky Way
Gill, his work at the Cape, 8
photographs and catalogues the

stars, 48

measures stellar parallaxes, 149

Gilliss, catalogues southern stars, 5
Gould, founds Cordoba Observatory,

6
his Uranometria Argentina, 7,

revises southern constellations, 31

photographs star-clusters, 47

distribution of stars, 243

Graham, zone of stars by, 260

Halley, voyage to St. Helena, 4

catalogues 77 Argus, 124

Hartwig, nature of Z Herculis, 113
Harvard Observatory, work of, 8
Heis, maps of lucid stars, 46
Herculis, Z, variable star, 113
Herschel, J., expedition to Cape of
Good Hope, 4

observes rj Argus 126

catalogues nebulae, 180

Herschel, W., observes double stars,

153

form of the universe, 233

Hevelius forms new constellations,

Hind, new star of 1848, 129
Hipparchus, supposed star-catalogue,

Huggins, observes radial motions, n

spectrum of T Coronae, 130

spectrum of nebulae, 188

life history of the stars, 219

Huyghens observes nebula of Orion,
178

Innes, star of greatest proper motion,

77
magnitude of rj Argus, 127

Jacoby measures photographs, 150
Johnson observes at St. Helena, 5

Kant, his antinomies, 228
Kapteyn, work on Cape Durchmus-
terung, 49

star of greatest prop, mot., 77

parallaxes of stars, 149

search for parallaxes, 150

mean parallaxes of stars, 291,

294, 313

law of proper motions, 291

Keeler, annular nebulae, 184

number of nebulae, 186

Kelvin, heat of the sun, 208
Kempf, Potsdam photometry, 24
Kepler, new star of 1604, 129
Kepler's laws in binary systems, 193
Kirchhoff s law, 58

Lacaille observes at the Cape, 4
Lambert, stellar system of, 232
Lane, law of solar heat, 210

limit of this law, 213

Lick Observatory, recent work of, 12
Light, wave-lengths of, 65, 82

colours of, 65

of stars, total, 229

possible extinction of, in space,

231

Line of sight, motions in, 81
Lockyer, the meteoritic hypothesis,

190

330

INDEX.

Lyra, annular nebula of, 184
Lyrae, /?, variable star, 106

type of, 108

constitution of, 107

Magellanic clouds, stars in, 256

Magnitudes of stars, 15

ancient system of designating,

16
modern system of designating,

18, 52

photographic, 21

photometric scale of, 25

relation to light of sun, 26

possible changes in, 121

Maury, Miss, classification of spectra,

Melbourne Observatory, 5
Mensurae Micrometricae, Struve's,

154

Michell, grouping of stars, 169
Milky Way, light of, 230

description of, 264

rifts in, 270

lucid stars in, 271

fainter stars in, 273, 275

possible distance of, 316

Mills spectrograph, presented Lick

Observatory, 12.

work with, 86

Miiller, Potsdam photometry, 24
Myers, constitution of ft Lyras, 106
constitution of U Pegasi, in

Names of the stars, early, 32

Bayer system of, 33

Flamstead system, 34

list of special, 322

Nebula, of Andromeda, 182

of Cygnus, 186

of Orion, 180

Omega, 183

Triphid, 182

Nebulae, 178

Nebulae, spiral, 181

annular, 183

planetary, 185

number of, 186

diffused, 187

distribution of, 188

spectrum of, 188

vast extent of, 188

constitution of, 189

energy of, 224

New star, of Tycho, 128

of Janson, 129

of Kepler, 129

in Corona, 130

in Auriga, 132

in Perseus, 138

New stars, 123
list of, 128

rapid rise of, 130, 139

theories of, 137

nebular constitution of, 138

Novae, see New stars

Number, of stars, possible total 3,

320
of lucid stars, 52

Omega nebula, 183
Orbit of a Centauri, 162
Orbits of binary systems, 160
Orion, great nebula of, 179

diffused nebula of, 187

Trapezium of, 164

proper motions in, 261

Orion type of star-spectra, 72
Oxford photometry, 24

Parallactic motion of the stars, de-
fined, 89

relation to parallax, 289

Parallax, of the stars, 140

relative and absolute, 146

early attempts to measure, 141

first measures of, 144

of a Centauri, 145, 324

INDEX.

Parallax, of 61 Cygni, 144, 325

of a Lyrse, 145, 325

Parallaxes, list of, 323

grouping of, 307

mean, of Vogel's stars, 290

mean, of stars of different mag-
nitudes, 313

statistics of, by Chase, 151

Pegasi, U, variable star, no
Periods of variable stars, lengths of,

97
Perseus, new star in, 138

cluster of, 170

Peter measures parallaxes of stars,

149
Photographic chart of the heavens,

its origin, 48

Photography of the stars, 10
Pickering, E. C., Harvard photo-
metry, 23

period of U Pegasi, in

classifies variable stars, 116

law of binary systems, 195

distribution of fifth type stars,

256
Pickering, W. H., diffused nebula of

Orion, 187
Pleiades, their proper motion, 79,

170

counts of stars in, 259

Poincare", revolving stars, forms of,

112

Polaris, spectrogram of, 84
Porter, apex of solar motion, 90
Position-angle of a double star, 156
Potsdam photometry of the stars, 24
Praesepe, star-cluster, 170

number of stars in, 261

Pritchard, photometry of the stars,

measures stellar parallaxes, 159

Procyon, orbit of companion, 161
mass of, 204

Proper motions of stars, defined, 75

measures of, 76

mean speed of, 299, 304

components of, 287

of Pleiades, 79

of types I and II compared, 292

apical and cross, 291. 301

lists of greatest, 78, 323

cases of common, 79, 81

greatest known, 77

: relation to parallax, 312
Ptolemy, describes constellations, 29

catalogue of stars, 41

Purkinje phenomenon, effect of, 20

Radial motions of the stars, 81
Rayet, fifth type of spectra, 70
Rees measures Rutherfurd's photo-
graphs, 150

Right ascension defined, 39
Ristenpart, law of proper motions,

297
Ritter writes on gaseous celestial

bodies, 210

Roberts, A. W., density of certain
stars, 201

catalogues variable stars, 96

Roberts, I., great nebula of An-
dromeda, 182
Rowland, map of solar spectrum,

Russell, density of stars, 202
Rutherfurd photographs stars, 10

Schiaparelli, colour of Sirius, 122

distribution of stars, 244

Schjellerup translates Al-Sufi, 42
Schonfeld catalogues the stars, 46
Schumann, ultra-violet rays, 62
Secchi, types of stellar spectra, 67
See, colour of Sirius, 121
binary systems of short period,

159
orbit of a Centauri, 162

332

INDEX.

Seeliger, distribution of stars, 247
progression in number of stars,

279

nature of Z Herculis, 113

Seven Stars (see Pleiades), 169

Sidereal time, use of, 40

Sirius, light compared with sun, 27

supposed change of colour of,

121

binary system of, 160

mass of, 204

Solar motion, speed of, 92, 303

apex of, 88

South measures double stars, 155
Spectra of the stars, 56

classification of, 67

Spectrograph of Lick Observatory,

86
Spectroscopic binary systems, list

of, 326

Spectroscopy, introduction of, 9
Spectrum, nature and definition of,

of gaseous bodies, 59

plan of, 65

designation of lines in, 63

description of, 61

colours of, 65, 67

lines in, changed by motion, 82

Spectrum analysis, method of, 58

canons of, 59

Kirchhoff's law of, 58

Spiral nebulae, 182

Star clustering, law of, 262

Star drift, 81

Stars, number of, 3, 52, 320

progression in number, 277

names of, 322

chemical elements of, 73

radial motions of, 8 1

double, 153

density of, 202

gaseous constitution of, 206

heat of, how maintained, 206

Stars, light of, possible total, 229, 283

temperature of, 215, 278

triple, 163

evolution of, 217

parallactic motion of, 89, 289

See also Double stars, Binary sys-
tems, Catalogues, Magnitude,
Distribution, Proper motion,
Constitution, Spectra, Radial
motions, New stars, Variable
stars

Struve, W., measures double stars,

155

extinction of light in space, 231

form of the universe, 234

Stumpe, apex of solar motion, 90

proper motion of the stars, 296 .

Swift discovers nebulae, 186
Sun, magnitude of, as a star, 26
motion of, in space (see Solar

motion), 87

Taurus, proper motions in, 81
Tebbut, magnitude of rj Argus, 126
Thal6n catalogues lines of iron, 63
Thome, Cordoba Durchmusterung,

Trapezium of Orion, 164
Triple stars, 163

Tycho Brahe catalogues the stars, 44
new star of 1572, 128

Ulugh Beigh catalogues the stars, 43
Universe, extent of, 228

in general structure of, 226

possible forms of, 235

general conclusions as to, 318

Uranometria Argentina, Gould's,

7, 3i

Ursa Major, motions of stars in, 80
Ursae Majoris, , a binary system, 167

Variable stars, first observations, 94
classification of, 95, 116

INDEX.

333

Variable stars, periods of v 97

periodic, defined, 96

light-curve of, 98, 102

spectra of, 118

Algol type of, 102, 104

ft Lyrae type of, 106

in clusters, 173

catalogued by Chandler, 96

Virginis, a, spectroscopic binary, 165
Vogel improves spectroscopic meth-
ods, 12

Vogel, classification of star spectra,

70
measures of radial motion, 85,

290

spectrum of Nova Aurigse, 134

orbit of a Virginis, 165

Wave-length of light, how changed

by motion, 82

Wendell, variation of U Pegasi, no
Wolf, fifth type of star spectra, 70

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EVOLUTION OF TO-DAY. A summary of the theory
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