GIFT OF
* Of A
LESSONS IN ASTRONOMY
INCLUDING URANOGRAPHY
A BRIEF INTRODUCTORY COURSE
WITHOUT MATHEMATICS
BY
CHARLES A. YOUNG, PH.D., LL.D.
LATE PROFESSOR OF ASTRONOMY IN PRINCETON UNIVERSITY, AUTHOR
OF A "GENERAL ASTRONOMY FOR COLLEGES AND SCIENTIFIC
SCHOOLS," OF A "MANUAL OF ASTRONOMY," AND
OF "ELEMENTS OF ASTRONOMY"
REVISED EDITION
WITH ADDITIONS AND CORRECTIONS
GINN AND COMPANY
BOSTON NEW YORK CHICAGO LONDON
ATLANTA DALLAS COLUMBUS SAN FRANCISCO
ENTERED AT STATIONERS 1 HALL
COPYRIGHT, 1891, 1903, BY
CHARLES A. YOUNG
COPYRIGHT, 1918, BY
G1NN AND COMPANY
ALL RIGHTS RESERVED
A622.ll
i -
ct
Cfte
G1NN AND COMPANY PRO-
PRIETORS BOSTON U.S.A.
PREFACE TO THE ORIGINAL EDITION
THIS volume has been prepare4 to meet the want of
certain classes of schools which find the author's " Elements
of Astronomy " rather too extended and mathematical to
suit their course and pupils. It is based upon the Ele-
ments, but with many condensations, simplifications, and
changes of arrangement: everything has been carefully
worked over and rewritten in order to adapt it to those
whose mathematical attainments are not sufficient to enable
them to use the larger work to advantage.
Of course, such pupils cannot gain the same insight into
the mechanism of the heavens as those who take up the
subject at a more advanced stage in their education. They
must often be contented with the bare statement of a fact
without any explanation of the manner in which its truth
is established, and thus will necessarily miss much that is
most valuable in the discipline to be derived from the study
of Astronomy.
But enough remains surely there is no other science
which, apart from all questions of How or Why, supplies
so much to widen the student's range of thought and to
make him comprehend his place in the infinite universe.
The most important change in the arrangement of the
book has been in bringing the Uranography, or " constella-
tion-tracing," into the body of the text and placing it near
iii
iv PREFACE
the beginning, a change in harmony with the accepted
principle that those whose minds are not mature succeed
best in the study of a new subject by beginning with what
is concrete and appeals to the senses, rather than with the
abstract principles. It has been thought well also to add
brief notes on the legendary mythology of the constellations
for the benefit of such pupils as are not likely to become
familiar with it in the study of classical literature.
In the preparation of the book great pains have been
taken not to sacrifice accuracy and truth to compactness,
and no less to bring everything thoroughly down to date.
The Appendix contains in its first chapter descrip-
tions of the most used astronomical instruments, and where
time permits, might profitably be brought into the course.
The second chapter of the Appendix is designed only
for the use of teachers and the more advanced pupils.
Sees. 431-434, however, explaining how the sun's dis-
tance may be found in the simplest way, might well be
read by all.
1891.
PREFACE TO THE REVISED EDITION
SINCE the original publication of this work twelve years
ago, a number of editions have been issued in which it was
attempted to keep up to date, as far as possible, by such
minor changes and corrections as typographical considera-
tions would permit. It has now, however, seemed best to
reprint the book from entirely new plates, and this has
given an opportunity for a thorough revision of the work
and the free introduction of all desirable improvements
and additions. The former rather unsatisfactory star-maps
have been replaced by new ones, and a considerable number
of beautiful half-tone illustrations have been added.
The publishers have spared no pains or expense in the
mechanical execution of the volume, and it is hoped that,
so far as its scope permits, the book will now be found
to offer a satisfactory summary of the present state of
Astronomy.
C. A. YOUNG.
PRINCETON, N.J.,
January, 1903.
PREFACE TO ISSUE OF 1918
WHILE the greater part of the text remains as it was
written by its author, such changes have been made in
this issue as are necessary to bring it down to date.
ANNE SEWELL YOUNG.
MOUNT HOLYOKB COLLEGE,
October, 1917.
CONTENTS
CHAPTER I. INTRODUCTION Fundamental Notions
and Definitions The Celestial Sphere and its Circles
Altitude and Azimuth Right Ascension and Dec-
imation Celestial Latitude and Longitude . . 1-19
CHAPTER II. URANOGRAPHY Globes and Star-Maps
Star Magnitudes Names and Designations of
Stars The Constellations in Detail . . . . 20-63
CHAPTER III. FUNDAMENTAL PROBLEMS Latitude
and the Aspect of the Celestial Sphere Time, Lon-
gitude, and the Place of a Heavenly Body . . . 64-77
CHAPTER IV. THE EARTH Its Form and Dimen-
sions; its Rotation, Mass, and Density Its Orbital
Motion and the Seasons Precession The Year and
the Calendar . . .... . . . 78-104
CHAPTER V. THE MOON Her Orbital Motion and
the Month Distance, Dimensions, Mass, Density, and
Force of Gravity Rotation and Librations Phases
Light and Heat Physical Condition Telescopic
Aspect and Surface . . . ...... 105-128
CHAPTER VI. THE SUN Its Distance, Dimensions,
Mass, and Density Its Rotation, Surface, and Spots
The Spectroscope and the Solar Spectrum The
Chemical Constitution of the Sun The Chromosphere
and Prominences The Corona The Sun's Light
Measurement and Intensity of the Sun's Heat
Theory of its Maintenance and Speculations regarding
the Age and Duration of the Sun .... 129-170
vii
viii CONTENTS
PAGES
CHAPTER VII. ECLIPSES AND THE TIDES Form and
Dimensions of Shadows Eclipses of the Moon
Solar Eclipses, Total, Annular, and Partial Number
of Eclipses in a Year Recurrence of Eclipses and
the Saros Occupations The Tides . ._ .171-187
CHAPTER VIII. THE PLANETARY SYSTEM The Plan-
ets in General Their Number, Classification, and
Arrangement Bode's Law Orbits of the Planets
Kepler's Laws and Gravitation The Apparent
Motions of the Planets and the Systems of Ptolemy
and Copernicus Determination of the Planets' Diam-
eters, Masses, etc. Herschel's Illustration of the
System Description of Individual Planets The
< Terrestrial ' Planets, Mercury, Venus, and Mars . 188-224
CHAPTER IX. PLANETS (Continued ) The Asteroids
Intramercurian Planets and the Zodiacal Light
The Major Planets, Jupiter, Saturn, Uranus, and
Neptune Ultra-Neptunian Planet . . 4 . .225-251
CHAPTER X. COMETS AND METEORS Comets, their
Number, Designation, and Orbits Their Constituent
Parts and Appearance Their Spectra, Physical Con-
stitution, and Probable Origin Remarkable Comets
Photography of Cornets Aerolites, their Fall and
Characteristics Shooting-Stars and Meteoric Showers
Connection between Meteors and Comets . . 252-293
CHAPTER XI. THE STARS Their Nature, Number,
and Designation Star-Catalogues and Charts Their
Proper Motions and the Motion of the Sun in Space
Stellar Parallax Star Magnitudes and Photometry
Variable Stars Stellar Spectra , : . . .294-325
CHAPTER XII. THE STARS (Continued) Double and
Multiple Stars Clusters and Nebulae The Milky
Way and Distribution of Stars in Space The Stellar
Universe Cosmogony and the Nebular Hypothesis , 326-357
CONTENTS ix
APPENDIX
PAGES
ASTRONOMICAL INSTRUMENTS. The Telescope,
Simple Refracting, Achromatic, and Reflecting The
Equatorial The Filar Micrometer The Transit-
Instrument The Clock and the Chronograph The
Meridian Circle The Sextant . . . . .. .359-378
MISCELLANEOUS (FOR THE MOST PART SUPPLEMEN-
TARY TO ARTICLES IN THE TEXT). Hour- Angle and
Time Twilight Determination of Latitude Place
of a Ship at Sea Finding the Form of the Earth's
Orbit The Ellipse Illustrations of Kepler's " Har-
monic " Law The Equation of Light and the Sun's
Distance determined by it Aberration of Light
De 1'Isle's Method of getting the Sun's Parallax from a
Transit of Venus The Parabola and the Conic Sec-
tions Determination of Stellar Parallax . . .378-397
QUESTIONS FOR REVIEW . . . . . .398-400
TABLES OF ASTRONOMICAL DATA
I. Astronomical Constants -_.: . V . 401
II. The Principal Elements of the Solar System . 402
III. The Satellites of the Solar System . . . 403
IV. The Principal Variable Stars . . . . 404
V. The Best Determined Stellar Parallaxes . . 405
The Greek Alphabet and Miscellaneous Symbols . 406
INDEX . . . . . . . . __.;.,,. . . 407-420
STAR-MAPS
LESSONS IN ASTRONOMY
CHAPTER I
INTRODUCTION
Fundamental Notions and Definitions The Celestial Sphere and its Circles
Altitude and Azimuth Right Ascension and Declination Celestial
Latitude and Longitude
1. Astronomy 1 is the science which deals with the
heavenly bodies.
As it is the oldest of the sciences, so also it is one of the
most perfect, and in certain aspects the noblest, as being
the most " unselfish " of them all. And yet, although not
bearing so directly upon the material interests of life as
the more modern sciences of Physics and Chemistry, it is
of high utility.
By means of Astronomy the latitudes and longitudes of
places upon the earth's suface are determined, and by such
determinations alone is navigation made secure. More-
over, all the operations of surveying upon a large scale,
such as the determination of national boundaries, depend
more or less upon astronomical observations. The same
is true of operations which, like the railway service, require
an accurate knowledge and observance of time ; for the
fundamental timekeeper is the diurnal revolution of the
heavens.
1 The term is derived from two Greek words : astron (a heavenly body)
and noinos (a law).
1
2 LESSONS IN ASTRONOMY
In ancient times the science was supposed to have a still higher
utility. It was believed that human affairs of every kind, the wel-
fare of nations, and the life history of individuals alike, were con-
trolled, or at least prefigured, by the motions of the stars and planets ;
so that from the study of the heavens it ought to be possible to pre-
dict futurity. Hence originated the pseudo-science of Astrology,
which, baseless and absurd as it has been proved to be, still retains
a remarkable hold on the popular mind.
2. The heavenly bodies include, first, the solar system,
that is, the sun and the planets which revolve around
it, with their attendant satellites; second, the comets and
the meteors, which also move around the sun, but are
bodies of a very different nature from the planets and
travel in different orbits ; and, third, the stars and nebulse.
The earth on which we live is one of the planets, and
the moon is the earth's satellite. The stars which we see
are bodies of the same kind as the sun, shining like him
with fiery heat, while the planets and the satellites are
dark and cool like the earth and visible only by the sun-
light they reflect. As for the comets and nebulae, they
appear to be mere clouds, composed of gas or swarms
of little particles, perhaps not very hot, but luminous.
It is likely, practically certain indeed, that besides the
visible stars there are also multitudes of others too cool
to shine, some of winch manifest their existence by
affecting the motion of certain of the visible stars. It is
hardly necessary to add that while with the naked eye
we see only a few thousand stars, the telescope reveals
millions.
3. As we look off from the earth at night, the stars
appear to be all around us, like glittering points fastened
to the inside of a huge hollow globe. Really they are at
INTRODUCTION 3
very different distances, all enormous as compared with
any distances with which geography makes us familiar.
Even the moon is eighty times as far away as New York
from Liverpool, and the sun is nearly four hundred times
as distant as the moon, and the nearest of the stars is
nearly three hundred thousand times as distant as the sun ;
as to the remoter stars, some of them are certainly thou-
sands of times as far away as the nearer ones, so far
that light itself is thousands of years in coming to us from
them. These are facts which are certain, not mere guesses
or beliefs.
Then, too, as to their motions. Although most of the
heavenly bodies seem to us to be at rest, except as the
earth's rotation makes them appear to rise and set, yet
really they are all moving, and with a swiftness of which
we can form no conception. A cannon-ball is a snail com-
pared with the slowest of them. The earth itself in its
revolution around the sun is flying eighteen and a half
miles in a second, which is more than fifty times as fast as
the swiftest rifle bullet. We fail to perceive the motion
simply because it is so smooth and so unresisted. The
space outside our air contains nothing that obviously
obstructs either sight or motion.
4. But this knowledge as to the real distance and
motions of the heavenly bodies was gained only after
long centuries of study. If we go out to look at the stars
some moonless night, we find them apparently sprinkled
over the dome of the sky in groups, or constellations, which
are still substantially the same as in the days of the earliest
astronomers. At first these constellations were figures of
animals and other objects, and many celestial globes and
4 LESSONS IN ASTRONOMY
maps still bear grotesque pictures 1 representing them. At
present, however, a constellation is only a certain region
of the sky, limited by imaginary lines which divide it
from the neighboring constellations, just as countries are
divided in geography. As to the exact boundaries of these
constellations, and even their number, there is no precise
agreement among astronomers. Forty-eight of them have
come down to us from the time of Ptolemy (the greatest
astronomer of antiquity, who flourished at Alexandria about
A.D. 130), and even in his day many of them were already
ancient.
About twenty others, proposed by later astronomers, are
now generally recognized, and at least as many more have
been suggested and abandoned.
5. Uranography, or Description of the Visible Heavens.
The study of the constellations, or the apparent arrange-
ment of the stars in the sky, is called Uranography. 2 It
is not an essential part of Astronomy, but it is an easy and
pleasant study; and in becoming familiar with the con-
stellations and their principal stars the pupil will learn
more readily and thoroughly than in any other way the
most important facts in relation to the apparent motions
of the heavenly bodies, and the principal points and
circles of the celestial sphere. For this reason the teacher
is urged to take the earliest opportunity to have his
pupils trace such of the constellations as happen to be
visible in the evening sky when they begin the study of
Astronomy, and to continue it from time to time as the
progress of the seasons gives opportunity.
1 Most of these figures follow the designs of Albert Diirer.
a From the Greek, ouranos (heavens) and grapM (description).
INTRODUCTION 5
6. The Celestial Sphere. 1 The sky appears like a hollow
vault, to which the stars seem to be attached like specks
of gilding upon the inner surface of a dome. We cannot
judge of the distance of this surface from the eye, further
than to perceive that it must be very far away. It is there-
fore natural and extremely convenient to regard the dis-
tance of the sky as everywhere the same and unlimited.
The celestial sphere, as it is called, is conceived of as so
enormous that the whole world of stars and planets lies
in its center like a few grains of sand in the middle of
the dome of the Capitol. Its diameter is assumed to be
immeasurably greater than any actual distance known,
and greater than any quantity assignable. In technical
language it is taken as infinite.
Since the celestial sphere is thus infinite, any two
parallel lines drawn from distant points on the surface of
the earth, or even from points as distant as the earth and
the sun, will seem to meet at one point on the surface of the
sphere. If the two lines were anywhere a million miles
apart, for instance, they will, of course, still be a million
miles apart when they reach the surface of the sphere;
but at an infinite distance even a million miles is a mere
nothing, so that, to our observation, the two lines are close
together and make apparently but a single point 2 where
they pierce the sphere.
7. The Apparent Place of a Heavenly Body. This is
simply the point where a line drawn from the observer
1 The study of the celestial sphere and its circles is greatly facilitated
by the use of a globe, or armillary sphere. Without some such apparatus
it is not easy for a young person to get clear ideas upon the subject.
2 This is the same as the "vanishing point " of perspective.
LESSONS IN ASTRONOMY
through the body in question, continued outward, pierces
the celestial sphere. It depends solely upon the direction
of the body, and is in no way affected by its distance from
us. Thus, in Fig. 1, A, B, C, etc., are the apparent places
of a, b, c, etc., the observer being at 0. Objects that are
nearly in line with each other, however great the real dis-
tances between them, as h, i, k, will appear close together
in the sky. The moon, for instance, often looks to us
u very near" a star, which
is really of course at an
enormous distance beyond
her.
8. Angular Measurement.
It is clear that we cannot
properly describe the appar-
ent distance of- two points
upon the celestial sphere from
each other by feet or inches.
To say that two stars are
about five feet apart, for in-
stance, and it is not very uncommon to hear such an
expression, means nothing unless we know how far from
the eye the five-foot measure is to be held. The proper
units for expressing apparent distance in the sky are those
of angle, viz. : degrees (), minutes ('), and seconds (") ; the
circumference of a circle being divided into 360 degrees,
each degree into 60 minutes, and each minute into 60
seconds. Thus, the Great Bear's tail, or " Dipper-handle,"
is about 16 long, and the long side of the " Dipper-bowl "
is about 10; the moon and the sun are each about half a
degree, or 30', in diameter.
FIG. 1
INTRODUCTION 7
It is very important that the student in Astronomy should become
accustomed as soon as possible to estimate celestial measures in this
way. A little practice soon makes it easy, though at first one is apt
to be embarrassed by the fact that the sky looks to the eye not like
a true hemisphere but like a flattened vault, so that the estimates of
distances for all objects near the horizon are apt to be too large.
The moon, when rising or setting, looks to most persons much larger
than when overhead ; x and the Dipper-bowl, when underneath the
pole, seems to cover a much larger area than when above it.
9. Circles and Principal Points of the Celestial Sphere.
Just as the surface of the earth in Geography is covered
with a network of imaginary lines, meridians and par-
allels of latitude, so the sky is supposed to be marked
off in a somewhat similar way. Two such sets of points
and reference circles are in common use to describe the
apparent places of the stars, and a third was used by the
ancients and is still employed for some purposes. The first
system depends upon the direction of the force of gravity
shown by a plumb-line at the point where the observer
stands ; the second upon the direction of the axis of the
earth, which points very near to the so-called Pole-star;
and the third depends upon the position of the orbit in
which the earth travels around the sun.
10. The Gravitational or Up-and-Down System. (a) The
Zenith and Nadir. The point in the sky directly above
the observer is called the zenith; the opposite point, under
the earth and of course invisible, the nadir?
1 This is a pure illusion due to physiological causes affecting judg-
ment of distance and size. The moon at the horizon is really about
4000 miles more distant from the observer than when nearly overhead,
and its apparent diameter, as measured by an astronomical instrument, is
actually less by about one-thirtieth.
2 These are Arabic terms. About A.D. 1100 the Arabs were the world's
g LESSONS IN ASTRONOMY
(b) The Horizon (pronounced ho-ri'-zon, not hor'-i-zon).
This is a "great circle '^around the sky, half-way between
the zenith and the nadir, and therefore everywhere 90
from the zenith. The word is derived from a Greek word
which means a "boundary"; i.e., the line where the earth
or sea limits the sky. The actual line of division, which
on the land is always more or less irregular, is called the
visible horizon, to distinguish it from the true, or astro-
nomical, horizon denned above.
We may also define the horizon as the great circle where
a plane which passes through the observer's eye perpen-
dicular to the plumb-line cuts the celestial sphere.
11. Vertical Circles and the Meridian ; Altitude and Azi-
muth. Circles drawn from the zenith to the nadir cut the
horizon at right angles, and are known as vertical circles.
Each star has at any moment its own vertical circle.
That particular vertical circle which passes north and
south is known as the Celestial Meridian ; while the ver-
tical circle at right angles to this is called the prime vertical.
Small circles drawn parallel to the horizon are known as
parallels of altitude, or almucantars. Fig. 2 illustrates these
definitions.
By their help we can easily define the apparent position
of a heavenly body.
Its Altitude is its apparent elevation above the horizon ;
that is, the number of degrees between it and the horizon,
measured on a vertical circle. Thus, in Fig. 2, the
chief astronomers, and have left their mark upon the science in numerous
names of stars and astronomical terms.
1 "Great Circles" are those which divide the sphere into two equal
parts.
INTRODUCTION
9
vertical circle ZMH passes through the point M. The arc
MH, measured in degrees, is the altitude of M, and the
arc ZM is called its zenith distance.
The Azimuth of a heavenly body is the same as its
" bearing " in Surveying, but measured from the true
meridian and not from the magnetic. 1 It is the arc of
the horizon, measured in degrees, intercepted between the
FIG. 2. The Horizon and Vertical Circles
O, the place of the observer.
OZ, the observer's vertical.
Z, the zenith ; P, the pole.
SWNE, the horizon.
SZPN, the meridian.
EZW, the prime vertical.
M, some star.
ZMH, arc of the star's vertical circle.
TMR, the star's almucantar.
Angle TZM, or arc SH, star's azimuth.
Arc HM, star's altitude.
Arc ZM, star's zenith-distance.
south point and the foot of the vertical circle which passes
through the object.
There are various ways of reckoning azimuth. Many
writers express it in the same way as the "bearing" in
Surveying, i.e., so many degrees east or west of north or
south. In the figure, the azimuth of M thus expressed
is about $, 50 E. The more usual way at present is,
1 The reader is reminded that the magnetic needle hardly anywhere
points exactly north. Its direction varies widely at different parts of the
earth, and, moreover, is continually changing to some extent.
10 LESSONS IX ASTRONOMY
however, to reckon clear around from the south, through
the west, to the point of beginning. Expressed in this
way, the azimuth of M would be about 310, i.e., the
arc SWNEH.
Altitude and azimuth, however, are inconvenient for
many purposes, because they continually change for a
celestial object as it apparently moves across the sky.
12. The Apparent Diurnal Rotation of the Heavens.
If we go out on some clear evening in the early autumn,
say about 8 P.M. on the 22d of September, and face the
north, we shall find the appearance of that part of the
heavens directly before us substantially as shown in Fig. 3.
In the north is the constellation of the Great Bear (Ursa
Major), characterized by the conspicuous group of seven
stars known as the " Great Dipper." It now lies with its
handle sloping upward to the west. The two eastern-
most stars of the four which form its bowl are called the
" Pointers," because they point to the Pole-star, which is
a solitary star not quite half-way from the horizon to the
zenith (in the latitude of New York), and about as bright
as the brighter of the two Pointers.
High up on the opposite side of the Pole-star from the
Great Dipper, and at nearly the same distance, is an
irregular zigzag of five stars, each about as bright as the
Pole-star itself. This is the constellation of Cassiopeia.
If now we watch these stars for only a few hours, we
shall find that while all the forms remain unaltered, their
places in the sky are slowly changing. The Great Dipper
slides downward towards the north, so that by eleven o'clock
(on September 22) the Pointers are directly un\der the
Pole-star. Cassiopeia still keeps opposite, however, rising
i
INTRODUCTION
11
towards the zenith ; and if we continue the watch through
the whole night, we shall find that all the stars appear to
be moving in circles around a point near the Pole-star,
revolving in the opposite direction to the hands of a watch
FIG. 3. The Northern Circumpolar Constellations
)
(as we look towards the north) with a steady motion which
takes them completely around once a day, or, to be more
exact, once in 23 h 56 m 4 8 .l of ordinary time. They behave
12 LESSONS IN ASTRONOMY
just as if they were attached to the inner surface of a huge
revolving sphere.
Instead of watching the stars by the eye we may advan-
tageously employ photography. A camera is pointed up
towards the Pole-star and kept firmly fixed while the stars
by their diurnal
motion impress
their "trails" upon
the plate. Fig. 4
was made in this
way with an ex-
posure of about
nine hours.
To indicate the
position of the stars
as it will be at mid-
night of September 22,
the figure must be
held so that XII in
FIG. 4. -Polar Star Trails the mar S in is at the
bottom ; at 4 A.M. the
stars will have come to the position indicated by bringing XVI
to the bottom, and so on. But at eight o'clock on the next night
we shall find things very nearly in their original position.
If instead of looking toward the north we now look
southward, we shall find that in that part of the sky also
the stars appear to move in the same kind of way. All
that are not too near the Pole-star rise somewhere in the
eastern horizon, ascend obliquely to the meridian, and
descend to their setting at points on the western horizon.
The next day they rise and set again at precisely the same
points, and the motion is always in an arc of a circle, called
INTRODUCTION 13
the star's diurnal circle, the size of which depends upon its
distance from the pole. Moreover, all of these arcs are
strictly concentric.
The ancients accounted for these fundamental and obvious
facts by supposing that the stars are really fastened to the
celestial sphere, and that this sphere really turns daily in
the manner indicated. According to this view there must
really be upon the sphere two opposite points which remain
at rest, and these are the poles.
13. Definition of the Poles. The Poles, therefore, may
be defined as those two points in the sky where a star would
have no diurnal motion. The exact position of either pole
may be determined with proper instruments by finding the
center .of the small diurnal circle described by some star
near it, as, for instance, by the Pole-star.
This definition of the pole is that which would be given
by one familiar with the sky but ignorant of the earth's
rotation, and it is still perfectly correct ; but knowing, as
we now do, that this apparent revolution of the celestial
sphere is due to the real spinning of the earth on its axis,
we may also define the poles as the two points where the
earth's axis of rotation, produced indefinitely, would pierce
the celestial sphere.
Since the two poles are diametrically opposite in the sky, only one
of them is usually visible from any given place. Observers north
of the earth's equator see only the north pole, and vice versa for
observers in the southern hemisphere.
The student must be careful not to confound the Pole
with the Pole-star. The pole is an imaginary point ; the
Pole-star is only that one of the conspicuous stars which
14
LESSONS IN ASTRONOMY
happens l now to be nearest to that point and at present is
about li distant from it. If we draw an imaginary line
from the Pole-star to the star Mizar (the one at the bend
of the Dipper-handle), it will pass almost exactly through
the pole itself ; the distance of the pole from the Pole-star
(often called Polaris) being
very nearly one quarter of
the distance between the two
"Pointers."
14. The Celestial Equator,
or Equinoctial ; Declination.
The Equator is a great circle
of the celestial sphere drawn
half-way between the poles,
everywhere 90 from each of
them, and is the great circle
in which the plane of the
earth's equator cuts the celes-
tial sphere. It is often
called the Equinoctial. Fig. 5 shows how the plane of the
earth's equator produced far enough would mark out such
a circle in the heavens.
Small circles drawn parallel to the equinoctial, like the
parallels of latitude on the earth, are known as Parallels
of Declination, the Declination of a star being its distance
in degrees north or south of the celestial equator ; + if north,
- if south. It corresponds precisely with the latitude of
a place on the earth's surface ; but it cannot be called
" celestial latitude," because that term has been preoccupied
by an entirely different quantity (Sec. 20).
i See Sec. 126.
FIG. 5. The Plane of the Earth's
Equator produced to cut the Celes-
tial Sphere
INTRODUCTION 15
A star's parallel of declination is identical with its
diurnal circle.
15. Hour-Circles. The great circles of the celestial
sphere which pass through the poles like the meridians on
the earth, and are therefore perpendicular to the celestial
equator, are called Hour-Circles. Some writers call them
" celestial meridians," but the term is objectionable since
it is sometimes used to indicate an entirely different set of
circles.
That particular hour-circle which at any moment passes
through the zenith of course coincides with the celestial
meridian already defined in Sec. 11.
16. The Celestial Meridian and the Cardinal Points. -
The best definition of the celestial meridian is, however,
the great circle which passes through the zenith and the poles.
The points where this meridian cuts the horizon (the circle
of level) are the north and south points, and the east and
west points of the horizon lie half-way between them, the
four being known as the " Cardinal Points." The student
is especially cautioned against confounding the north poinl
with the north pole. The north point is on4he horizon;
the north pole is high up in the sky.
In Fig. 6, P is the north celestial pole, Z is the zenith,
and SQZPN is the celestial meridian. P and P' are the
poles, PmP' is the hour-circle of m, and amRl V is its par-
allel of declination, or diurnal circle. N and S are the
north and south points respectively. In the figure, mY is
the declination of m, and mP is called its polar distance.
The angle made at the celestial pole between the merid-
ian and the hour-circle passing through a given star is
called the star's Hour-Angle for that moment. It is
16
LESSONS IN ASTRONOMY
usually reckoned westward from the meridian, and, for many
purposes, in time instead of in arc, i.e., in hours, minutes,
and seconds of time instead of degrees, etc. One hour
= 15, and one minute of time (l m ) =15 minutes of arc
(15'), etc. The hour-angle of a star is always equal to the
FIG. 6. Equator, Hour-Circles, etc.
0, place of the observer ; Z, his zenith.
S WNE, the horizon.
POP', line parallel to the axis of the
earth.
P and P', the two poles of the heavens.
EQWT, the celestial equator, or equi-
noctial.
X, the vernal equinox, or "first of
Aries."
PXP', the equinoctial colure, or zero
hour-circle.
TO, some star.
Ym, the star's declination; Pm, its
north-polar distance.
Angle mPH = a.TG QY, the star's (east-
ern) hour-angle ; = 24** minus star's
western hour-angle.
Angle XPm = arc XY, star's right
ascension.
Sidereal time at the moment = 24 11 minus
XPQ.
interval of sidereal time (see Sec. 91) elapsed since the
star last crossed the meridian.
17, The Vernal Equinox, or First of Aries. In order to
use this system of circles as a means of designating the
places of stars in the sky, it is necessary to fix upon some
one hour-circle, to be reckoned from in the same way that
INTRODUCTION 17
the meridian of Greenwich is used in reckoning longitude
on the earth's surface. The " Greenwich of the sky "
which has thus been fixed upon is the point where the
sun crosses the celestial equator in the spring. The sun
and moon and the planets do not behave as if they, like
the stars, were firmly fixed upon the celestial sphere, but
rather as if they were glow-worms crawling slowly about
upon its surface while it carries them in its diurnal rota-
tion. As every one knows, the sun in winter is far to
the south of the equator, and in the summer far to
the north, apparently completing a yearly circuit of the
heavens on a path known as the ecliptic. It crosses the
equator, therefore, twice a year, passing from the south
side of it to the north about March 21 (this is now
true, since leap year was skipped in 1900), and always
at the same point) neglecting for the present the effect
of what is known as "precession." This point, the
celestial Greenwich, is called the Vernal Equinox, and
is made the starting-point for many astronomical reckon-
ings. Unfortunately it is not marked by any conspicuous
star; but a line drawn from the Pole-star through Beta
Cassiopeise (the westernmost or " preceding " star in the
zigzag) (see Map I) and continued 90 from the pole,
strikes very near it. In Fig. 6, X represents this point.
It is also called the First of Aries, and designated by the
symbol f> .
18. Right Ascension. The right ascension of a star is
the arc of the celestial equator intercepted between the vernal
equinox and the point where the stars hour-circle cuts the
equator, and is reckoned always eastward from the equinox
and completely around the circle. It may be expressed
18 LESSONS IN ASTRONOMY
either in degrees or in hours. 1 A star one degree west of
the equinox has a right ascension of 359, or of 23 h 56 m .
Evidently the diurnal motion does not affect the right
ascension of a star, but this, like the declination, remains
practically unchanged for years. In Fig. 6, if X be the
vernal equinox, the right ascension of m is the arc XY
measured from X eastward.
19. Thus we can define the position of a star either by
its altitude and azimuth, which tell how high it is in the
sky, and how it " bears," as a sailor would say ; or we
may use its right ascension and declination, which do not
change from day to day (not perceptibly at least), and so
are better adapted to mapping purposes, corresponding as
they do precisely to latitude and longitude upon the surface
of the earth.
Perhaps the easiest way to think of these celestial circles
is the following: Imagine a tall pole standing straight up
from the observer, having attached to it at the top (the
zenith) two half circles coming down to the level of the
observer's eye, one of them running north and south
(the meridian), and the other east and west (the prime
vertical). The bottoms of these two semicircles are con-
nected by a complete circle (the horizon) at the level of
the eye. This framework, immense but fortunately only
imaginary and so not burdensome, the observer takes
with him wherever he goes, keeping always at its center,
while over it apparently turns the celestial sphere ; really,
of course, he and the earth and his framework turn
together under the celestial sphere.
1 Twenty-four hours of right ascension or hour-angle = 360 ; one
hour = 15.
INTRODUCTION 19
The other circles (the celestial equator and the hour-
circles) are drawn upon the celestial sphere itself and are
not affected at all by the observer's journeys, but are as
fixed as the poles and meridians upon the earth; the stars
also, to all ordinary observation, are fixed upon the sphere
just as cities are upon the earth. They really move, of
course, and swiftly, as has been said before, but they are
so far away that it takes centuries, as a rule, to produce
the slightest apparent change of place.
20. Celestial Latitude and Longitude. A different way of
designating the positions of the heavenly bodies in the sky has come
down to us from very ancient times. Instead of the equator it makes
use of another circle of reference in the sky, known as the Ecliptic.
This is simply the apparent path described by the sun in its annual
motion among the stars; for the sun appears to creep around the
celestial sphere in a circle once every year, and the Ecliptic may be
defined as the intersection of the plane of the earth's orbit with the
celestial sphere, just as the celestial equator is the intersection of the
earth's equator ; the vernal equinox is one of the points where the two
circles cross. Before the days of clocks, the Ecliptic was in many
respects a more convenient circle of reference than the equator and
was almost universally used as such by the old astronomers. Celestial
longitude and latitude are measured with reference to the Ecliptic,
in the same way that right ascension and declination are measured
with respect to the equator, except that celestial longitude cannot be
expressed in hours, minutes, and seconds of time like right ascen-
sion. Too much care can hardly be taken to avoid confusion between
terrestrial latitude and longitude and the celestial quantities that bear
the same name.
CHAPTER II
URANOGRAPHY
Globes and Star-Maps Star Magnitudes Designation of the Stars The
Constellations
NOTE. It is hardly necessary to say that this chapter is to be
treated by the teacher differently from the rest of the book. It is to
be dealt with, not as recitation matter, but as field-work : to be
taken up at different times during the course as the constellations
make their appearance in the evening sky.
For convenience of reference we add the following alphabetical
list of the constellations described or mentioned in the chapter :
ARTICLE
AndrdmSda 35
Anser, see Vulpe"cula ... 69
Antinoiis, see Aqulla . . . 71
Antlia 62
Aquarius 78
Aqulla (not Aquila) . . . 71
Argo Navis 51
Aries 38
Auriga 41
Bootes 59
Camelopdrdalis 31
Cancer 52
Canes Venatici .... 58
Canis Major 49
Canis Minor 48
Capricornus 73
Cassi6p<ia 28
ARTICLE
Centaurus 62
Cepheus 29
Cetus 39
Columba 45
Coma Ber8nices .... 57
Corona Borealis . . . ( . 60
Corvus 55
Crater 55
Cygnus 68
Delphmus 74
Draco 30
Equiileus 75
Erldanus 44
Gemini 47
Grus 79
Hercules 66
Hydra 55
20
URANOGRAPHY
21
ARTICLE
Lacerta 76
Leo 53
Leo Minor 54
Lepus .45
Libra . .. .. U , ... 61
Lupus . -i v . . . , 62
Lynx . ,- i v ';.'. . . 46
Lyra . ... . -. . . 67
Monoceros 50
Norma . " . '." .... 64
Ophiuchus . . . '. . . 65
Orion . . . .: i. .; . . 43
Pegasus . ...iVy, !,;. -. . . 77
Perseus . 40
Phoenix .."../. . . . 39
Pisces . 36
ARTICLE
Piscis Australis .'..-. 79
(Pleiades) ...... 42
Sagitta 70
Sagittarius 72
Scorpio 63
Sculptor . . . . . . .39
Serpens 65
Serpentarius, see Ophiuchus 65
Sextans . . . , . . . . 54
Taurus 42
Taurus Poniatovii ... 65
Triangulum ...... 37
Ursa Major 2&
Ursa Minor ...... 27
Virgo. 56
VulpSctila 69
21. Globes and Star-Maps. In order to study the con-
stellations conveniently, it is necessary to have either a
celestial globe or a star-map, by which to identify the
stars. The globe is better and more accurate, if of suffi-
cient size, but is costly and rather inconvenient. (For a
figure and description of the globe, see Appendix, Sec. 400.)
For most purposes a star-map will answer just as well as
the globe, but it can never represent any considerable por-
tion of the sky correctly without more or less distortion of
all the lines and figures near the margin of the map. Such
maps are made on various systems, each presenting its own
advantages. In all of them the heavens are represented
as seen from the inside, and not as on the globe, which
represents the sky as if seen from the outside.
22, Star-Maps of this Book. We present a series of
four small maps, which, though hardly on a large enough
22 LESSONS IN ASTRONOMY
scale to answer every purpose of a complete celestial atlas,
are quite sufficient to enable the student to trace out the
constellations, and to identify the principal stars. In the
map of the north circumpolar regions (Map I) the pole is
in the center, and at the circumference are numbered the
twenty-four hours of right ascension. The parallels of dec-
lination are represented by equidistant concentric circles.
On the three other rectangular maps, which show the equa-
torial belt of the heavens lying between 50 north and
50 south of the equator, the parallels of declination are
horizontal lines, while the hour-circles are represented by
vertical lines, also equidistant, but spaced at a distance
which is correct, not at the equator but for declination 35.
This keeps the distortion within reasonable bounds, even
near the margin of the map, and makes it very easy to lay
off the places of any object for which the right ascension
and declination are given. The ecliptic is the curved line
which extends across the middle of the map. The top of
the map is north; and the east is to the left, instead of
being at the right hand, as in a map of the earth's sur-
face ; so that if the observer faces the south, and holds the
map up before and above him, the constellations which are
near the meridian will be pretty truly represented.
The hours of right ascension are indicated on the central hori-
zontal line, which is the celestial equator, and at the top of the map
are given the names of the months. The word " September," for
instance, means that the stars which are directly under it on the map
will be near the meridian about 9 o'clock in the evening during that
month.
23. Star Magnitudes. To the eye the principal differ-
ence in the appearance of the different stars is in their
URANOGRAPHY 23
brightness, or their so-called " magnitude." Hipparchus
(125 B.C.) and Ptolemy divided the visible stars into six
classes, the brightest fifteen or twenty being called first-
magnitude stars, and the faintest which can be seen by
the naked eye being called sixth.
It has since been found that the light of the average first-magni-
tude star is just about one hundred times as great as that of the
sixth ; and at this rate the light of a first-magnitude star should be
a trifle more than equal to two and a half second-magnitude stars,
and a second-magnitude star, to two and a half third-magnitude
stars, etc.
Our maps show all the stars down to the fifth magnitude
about a thousand in number and all which can be
seen in a moonlight night. A few smaller stars are also
inserted where they mark some particular configuration
or point out some interesting telescopic object. A varia-
ble star is denoted by var. below the star symbol. A few
clusters and nebulae are also indicated. The letter M.
against one of these stands for " Messier," who made the
first catalogue of 103 such objects in 1784; e.g., M. 51
designates No. 51 on Messier's list.
For reference purposes and for study of the heavens in detail, the
more elaborate star-atlases of Proctor, Heis, Upton, or Schurig are
recommended, especially the last, which contains a great amount
of useful information in addition to the maps, and is very cheap
compared with the others. The student or teacher who possesses a
telescope will also find an invaluable accessory to it in Webb's
" Celestial Objects for Common Telescopes." (Published by Long-
mans, Green fy Co., New For/:.)
24, Designation of the Stars. A few of the brighter
stars are designated by names of their own, and upon the
24 LESSONS IN ASTRONOMY
map those names which are in most common use are indi-
cated. 1 Generally, however, the designation of visible stars
is by the letters of the Greek alphabet, on a plan proposed
in 1603 by Bayer, and ever since followed. The letters
are ordinarily applied nearly in the order of brightness,
Alpha being the brightest star in the constellation and
Beta the next brightest; but they are sometimes applied
to the stars in their order of position rather than in that
of brightness. When the stars of a constellation are so
numerous as to exhaust the letters of the Greek alphabet,
the Roman letters are next used, and then, if necessary,
we employ the numbers which Flamsteed assigned a cen-
tury later. At present every star visible to the naked eye
can be referred to and identified by v its number or letter in
the constellation to which it belongs. (For the Greek
alphabet, see Appendix, page 406.)
25. We begin our study of Uranography with the con-
stellations which are circumpolar (Le., within 40 of the
north pole), because these are always visible in the tJnited
States and so can be depended on to furnish land- (or
rather sky] marks to aid in tracing out the others. Since
in the latitude of New York the elevation of the pole is
about 41, it follows that there (and this is approximately
true of the rest of the United States) all the constella-
tions which are within 41 of the north pole will move
around it once in twenty-four hours without setting. For
this reason they are called circumpolar. Map I contains
them all.
a By far the best book upon the subject of stellar nomenclature is
Allen's ' ' Star-Names and their Meanings. " It is full of interesting matter
relating to the constellations and the myths and legends attached to them.
URANOGRAPHY 25
26. Ursa Major, the Great Bear (Map I). Of these
circumpolar constellations none is more easily recognized
than Ursa Major. Assuming the time of observation as
about 8 o'clock in the evening on September 22, it will be
found below the pole and to the west. Hold the map so
that VIII is at the bottom, and it will be rightly placed
for the time assumed.
The familiar Dipper is sloping downward in the north-
west, composed of seven stars, all of about the second mag-
nitude, excepting Delta (at the junction of the handle to the
bowl), which is of the third magnitude. The stars Alpha
(Dubhe) and Beta (Merak) are known as the "Pointers,"
because a line drawn from Beta through Alpha and pro-
duced about 30 passes very near the Pole-star. The
dimensions of the Dipper furnish a convenient scale of
angular measure. From Alpha to Beta is 5; from Alpha
to Delta is 10 ; and from Alpha to Eta, at the extremity
of the Dipper-handle (which is also the Bear's tail), is 26.
The Dipper (known also in England as the " Plough " and
as the " Wain," or wagon) comprises but a small part of
the whole constellation. The head of the Bear, indicated
by a small group of scattered stars, is nearly on the line
from Delta through Alpha, carried on about 15 ; at the
time assumed (September 22, 8 o'clock) it is almost exactly
under the pole.
Three of the four paws of the creature are marked each
by a pair of third- or fourth-magnitude stars li or 2
apart. The three pairs are nearly equidistant, about 20
apart, and almost on a straight line parallel to the diagonal
of the Dipper-bowl from Alpha to Gamma, but some 20
south of it. At the time assumed they are all three very
26 LESSONS IN ASTRONOMY
near the horizon for an observer in latitude 40, but during
the spring or summer, when the constellation is high in
the sky, they can be easily made out.
The star Zeta (Mizar), at the bend in the handle, is
easily recognized by the little star Alcor near it. Mizar
itself is a double star, easily seen as double with a small
telescope, and one of the most interesting recent astro-
nomical results is the discovery that it is really triple, the
larger of the two stars being itself a " spectroscopic double,"
invisibly so to the telescope, but revealing its double char-
acter by means of the lines in its spectrum. (See Sec. 373.)
The star Xi, the southern one of the pair, which marks the
left-hand paw, is also double and binary, i.e., the two stars
which compose it revolve about their common center of
gravity in .about sixty-one years. (For diagram of the
orbit, see Fig. 89, Sec. 369.) It was the first binary whose
orbit was computed.
According to the ancient legends, Ursa Major is Callisto, the
daughter of Lycaon, king of Arcadia. The jealousy of Juno 1
-changed her into a bear, and afterwards Jupiter placed her among
the constellations with Areas her son, who became Ursa Minor.
One of the quaint old authors explains the very un-bearlike length
of the creatures' tails by saying that they stretched as Jupiter lifted
them to the sky.
27. Ursa Minor, the Lesser Bear (Map I). The line
of the Pointers unmistakably marks out the Pole-star
1 We have followed throughout the Eoman nomenclature of the gods
and heroes, as used by Virgil and Ovid; but the reader should be reminded
that, in many important respects, these Koman personages differ from
the Greek divinities who were identified with them. It should be said,
also, that in many cases the old legends are greatly confused and often
contradictory ; as, for instance, in the case of Hercules.
URANOGRAPHY 27
(Polaris], a star of the second magnitude, standing quite
alone. It is at the end of the tail of Ursa Minor, or at
the extremity of the handle of the "Little Dipper"; for
in Ursa Minor, also, the seven principal stars form a dipper,
though with the handle bent in a different way from that
of the other Dipper. Beginning at Polaris, a curved line
(concave towards Ursa Major) drawn through Delta and
Epsilon brings us to Zeta, where the handle joins the
bowl. Two bright stars (second and third magnitude),
Beta and Gamma, correspond to the Pointers in the large
Dipper, and are known as the "Guardians of the Pole";
Beta is named Kochab. The pole now lies about li from
the Pole-star, on the line joining it to Mizar (at the bend
in the handle of the large Dipper).
It has not always been so. Some 4000 years ago the star Thuban
(Alpha Draconis) was the Pole-star, and 2000 years ago the present
Pole-star was very much farther from the pole than now. At present
the pole is coming nearer to the star, and towards the close of the next
century it will be within half a degree of it. Twelve thousand years
hence the bright star Alpha Lyrse will be the Pole-star, and this not
because the stars change their positions, but because the axis of the
earth slowly changes its direction, owing to precession. (See Sec. 125.)
The Greek name of the Pole-star was Cynosura, which
means the " tail of the Dog," indicating that at one time
the constellation was understood to represent a Dog instead
of a Bear.
As already said (Sec. 26), this constellation is by many writers
identified with Areas, Callisto's son. But more generally Areas is
identified with Bootes.
The Pole-star is double, having a small companion barely
visible with a telescope of two or three inches diameter.
28 LESSONS IN ASTRONOMY
28, Cassiopeia (Map I). This constellation lies on the
opposite side of the pole from the Dipper, and at about
the same distance from it as the Pointers. It is easily
recognized by the zigzag, "rail-fence "configuration of the
five or six bright stars that mark it. With the help of
the rather inconspicuous star Kappa, one can make out of
them a pretty good chair with the feet turned away from
the pole. But this is wrong. In the recognized figures
of the constellation the lady sits with feet towards the
pole, and the bright star Alpha is in her bosom, while
Zeta and the other faint stars south of Alpha are in her
head and uplifted arms ; Iota, on the line from Delta to
Epsilon produced, is in the foot. The order of the prin-
cipal stars is easily remembered by the word " Bagdei,"
i.e.. Beta, Alpha, Gamma, Delta, Epsilon, Iota.
Alpha, which is slightly variable in brightness, is known
as Schedir; Beta is called Caph. The little star Eta, which
is about half-way between Alpha and Gamma, a little off the
line, is a very pretty double star, the larger star orange,
the smaller one purple. It is binary (i.e., the two stars re-
volve around each other), with a period of about 206 years.
In the year 1572 a famous temporary star made its
appearance in this constellation, at a point on the line
drawn from Gamma through Kappa, and extended about
half its length. It was carefully observed and described
by Tycho Brahe, and at one time was bright enough to be
seen easily in broad daylight. There has been an entirely
unfounded notion that this was identical with the star of
Bethlehem, and there has been an equally unfounded
impression that its reappearance may be expected about
the present time.
URANOGRAPHY 29
Cassiopeia was the wife of Cepheus, king of Libya, and the mother
of Andromeda, who was rescued from the sea-monster, Cetus, by Per-
seus, who came flying through the air, and used the head of Medusa
(which he still holds in his hand) to turn his adversaries to stone.
Cassiopeia had indulged in too great boasting of her daughter's
beauty, and thus excited the jealousy of the Nereids, at whose insti-
gation the sea-monster was sent by Neptune to ravage the kingdom.
29. Cepheus (Map I). This constellation, though large,
contains very few bright stars. At the assumed time (8
o'clock, September 22) it is above Cassiopeia and to the
west, not having quite reached the meridian above the
pole. A line carried from Alpha Cassiopeia through Beta,
and produced 20, will pass very near to Alpha Cephei, a
star of the third magnitude in the king's right shoulder.
Beta Cephei is about 8 north of Alpha, and Gamma about
12 from Beta, both also of the third magnitude. Gamma
is so placed that it is at the obtuse angle of a rather flat
isosceles triangle of which Beta Cephei and the Pole-star
form the other two corners. Cepheus is represented as
sitting behind Cassiopeia (his wife) with his feet upon
the tail of the Little Bear, Gamma being in his left knee.
His head is marked by a little triangle of fourth- magnitude
stars, of which Delta is a remarkable variable with a period
of 5| days. It is worth noting that there are several other
small variable stars in the same neighborhood (none of them
bright enough to be shown upon the map). Beta is a very
pretty double star.
30. Draco, the Dragon (Map I). The constellation of
Draco is characterized by a long, winding line of stars,
mostly small, extending half-way around the pole and
separating the two Bears. A line from Delta Cassiopeia
drawn through Beta Cephei and extended about as far
30 LESSONS IN ASTRONOMY
again will fall upon the head of Draco, marked by an
irregular quadrilateral of stars, two of which are of the 2
and 3 magnitude. These two bright stars about 4 apart
are Beta and Gamma. The latter (named Etaniri), in its
daily revolution, passes almost exactly through the zenith
of Greenwich, and it was by observations upon it that the
"aberration of light" was discovered. (See Sec. 435.)
The nose of Draco is marked by a smaller star, Mu, some
6 beyond Beta, nearly on the line drawn through it from
Gamma. From Gamma we trace the neck of Draco, east-
ward and downward 1 toward the Pole-star, until we come
to Delta and Epsilon and some smaller stars near them.
There the direction of the line is reversed, as shown
upon the map, so that the body of the monster lies between
its own head and the bowl of the Little Dipper, and winds
around this bowl until the tip of the tail is reached, at the
middle of the line between the Pointers and the Pole-star.
The constellation covers more than twelve hours of right
ascension.
One star deserves special notice, the star Alpha, or
Thuban, a star of 3 magnitude, which lies half-way
between Zeta Ursae Majoris (Mizar) and Gamma Ursa
Minoris. Four thousand seven hundred years ago it was
the Pole-star, and then within a quarter of a degree of
the pole, much nearer than Polaris is at present or ever
will be. It is probable also that its brightness has con-
siderably fallen off within the last 200 years, since among
the ancient astronomers it was always reckoned as of the
second magnitude and is not now much above the fourth.
1 The description applies strictly only at the time assumed, 8 o'clock,
September 22.
URANOGRAPHY 31
The so-called " Pole of the Ecliptic " is in this constella-
tion, i.e., the point which is 90 distant from every point
in the Ecliptic, the circle annually described by the sun.
This point (see map) is the center around which precession
causes the pole to move nearly in a circle (see Sec. 126)
once in 25,800 years.
The mythology of this constellation is doubtful. According to
some it is the dragon which Cadmus slew, afterwards sowing its teeth,
from which sprung up the harvest of armed men who fought and slew
each other, leaving only the five survivors who were the founders of
Thebes. Others say that it was the dragon who watched the golden
apples of the Hesperides, and was killed by Hercules when he cap-
tured that prize. This accords best with the fact that in the heavens
Hercules has his foot on the dragon's head.
31. Camelopardalis. This is the only remaining one of the strictly
circumpolar constellations, a modern one containing no stars above
fourth magnitude, and established by Hevelius (1611-1687) simply to
cover the great empty space between Cassiopeia and Perseus on one
side, and Ursa Major and Draco on the other. The animal stands
on the head and shoulders of Auriga, and his head is between the
Pole-star and the tip of the tail of Draco.
The two constellations of Perseus (which at the time assumed is
some 20 below Cassiopeia) and of Auriga are partly circumpolar,
but on the whole can be more conveniently treated in connection
with the equatorial maps. Capella, the brightest star of Auriga,
and next to Vega and Arcturus the brightest star in the northern
hemisphere, is at the time assumed (8 o'clock, September 22) a few
degrees above the horizon in the northeast. Between it and the nose
of Ursa Major lies part of the constellation of the Lynx, a modern
one, made, like Camelopardalis, by Hevelius merely to fill a gap, and
without any large stars.
32. The Milky Way in the Circumpolar Region The
only circumpolar constellations traversed by the Milky
Way are Cassiopeia and Cepheus. It enters the circumpolar
32 LESSONS IN ASTRONOMY
region from the constellation of Cygnus, which at the
assumed time is near the zenith, sweeps down across
the head and shoulders of Cepheus, and on through
Cassiopeia and Perseus to the northeastern horizon in
Auriga. There is one very bright patch a few degrees
north of Beta Cassiopeia, and half-way between Delta
Cassiopeise and Gamma Persei there is another bright
cloud in which is the famous double cluster of the
" sword-handle of Perseus," a beautiful object for even
the smallest telescope.
33. For the most part the constellations shown upon
the circumpolar map (I) will be visible every night in the
northern part of the United States. At places farther
south the constellations near the rim of the map will
stay below the horizon for a short time every twenty-
four hours, since the height of the pole always equals the
latitude of the observer, and therefore only those stars
which have a polar distance less than the latitude will
remain constantly visible. In other words, if, with the
pole as a center, we draw a circle with a radius equal to
the height of the pole above the horizon, all the stars
within this circle will remain continually above the
horizon. This is called the circle of " Perpetual Appa-
rition" (Sec. 85). At New Orleans, in latitude 30, its
radius, therefore, is only 30, and only those stars which
are within 30 of the pole will make a complete circle
without setting. At stations in the northern part of the
United States, as Tacoma, it is nearly as large as the
whole map.
34. Before proceeding to consider the other constella-
tions, the student should be reminded that he will have
URANOGRAPHY 33
to select those that are conveniently visible at the time
of the year when he happens to be studying the subject,
and that, if he wishes to cover the whole sky, he must take
up the subject more than once, and at various seasons of the
year. The constellations near the southern limits of the
map can be seen only a few weeks in each year.
He will also be likely to be occasionally perplexed by
finding in the heavens certain conspicuous stars not on
the maps, stars much brighter than any that are given.
These are the planets Venus, Jupiter, Mars, and Saturn,
called planets i.e., " wandering stars " just because they
continually change their place, and so cannot be mapped.
The student will find it interesting and instructive, how-
ever, to dot down upon the star-map every clear night the
places of any planets he may notice, and thus to follow
their motion for a month or two.
Remember also that on these maps east always lies on
the left hand, so that the map should be held between
the eye and the sky in order to represent things cor-
rectly. We begin with Andromeda at the northwest
corner of Map II.
35. Andromeda (Maps II and IV) . November. Andromeda
will be found exactly overhead in our latitudes about
"9 o'clock in the middle of November. Its characteristic
configuration is the line of three second-magnitude stars,
Alpha, Beta, and Gamma, extending east and north from
Alpha (Alpheratz), which itself forms the northeast corner
of the so-called " Great Square of Pegasus," and is some-
times lettered as Delta Pegasi. This star may readily be
found by extending an imaginary line from Polaris through
Beta Cassiopeise and producing it about as far again ; Alpha
34 LESSONS IN ASTRONOM1
is in the head of Andromeda, Beta (Mirach) in her waist,
and Gamma (Almaach) in her left foot. A line drawn
northwesterly from Beta, nearly at right angles to the
line Beta Gamma, will pass through Mu at a distance of
about 5, and produced another 5 will strike the " great
nebula," which is visible to the naked eye like a little
cloud of light, and forms a small obtuse-angled triangle
with Nu and a little sixth-magnitude star. Andromeda
has her mother, Cassiopeia, close by on the north, with
her father, Cepheus, not far away, while at her feet is
Perseus, her deliverer. Her head rests upon the shoulder
of Pegasus. In the south, beyond the constellations of
Aries and Pisces, Cetus, the sea-monster, who was to have
devoured her, stretches his ungainly bulk.
We have 'already mentioned the nebula. Another very pretty
object is Gamma, which in a small instrument is a double star, the
larger one orange, the smaller a greenish blue. The small star is
itself double, making the system really triple, but as such is beyond
the reach of any but very large instruments.
When Neptune sent the leviathan, Cetus, to ravage Libya, the
oracle of Ammon announced that the kingdom could be delivered
only if Cepheue would give up his daughter. He assented and
chained the poor girl to a rock to await her destruction. But Per-
seus, returning through the air from the slaying of the Gorgon,
Medusa, saw her, rescued her, won her love, and made her his wife.
36, Pisces, the Fishes (Map II). November. Imme-
diately south of Andromeda lies Pisces, the first of the con-
stellations of the Zodiac, 1 which is a'belt 16 wide (8 on
1 The word is derived from the Greek word zoon ( a living creature)
and indicates that all the constellations in it (Libra alone excepted) are
animals. The zodiacal constellations are for the most part of remote
antiquity, antedating by many centuries even the Greek mythology.
URANOGRAPHY 35
each side of the ecliptic), encircling the heavens, and
including the space within the limits of which the sun, the
moon, and all the principal planets perform their apparent
motions. At present, in consequence of precession, it
occupies the sign of Aries. (See Sec. 126.) It has not a
single conspicuous star, and is notable only as now con-
taining the Vernal Equinox, or First of Aries, which lies
near the southern boundary of the constellation in a pecul-
iarly starless region. A line from Alpha Andromedae
through Gamma Pegasi, continued as far again, strikes
about 2 east of the point. The body of one of the two
fishes lies about 15 south of the middle of the southern
side of the " Great Square of Pegasus," and is marked by
an irregular polygon of small stars, 5 or 6 in diameter.
A long crooked " ribbon " of little stars runs eastward
for more than 30, terminating in Alpha Piscium (called
El Rischa, or " the knot "), a star of the fourth magni-
tude 20 south of the head of Aries. From there another
line of stars leads up northwest in the direction of Delta
Andromedse to the northern fish, which lies in the vacant
space south of Beta Andromedse.
Alpha is a very pretty double star, the two components being
about 2" apart.
The mythology of this constellation is not very well settled. One
story is that the fishes are Venus and her son Cupid, who were thus
transformed when endeavoring to escape from the giant Typhon.
The northern fish is Cupid, the southern his mother.
37. Triangulum, or Deltoton, the Triangle (Map II).
December. This little constellation, insignificant as it
is, is one of Ptolemy's ancient forty-eight. It lies half-way
between Gamma Andromeda and the head of Aries, and
36 LESSONS IN ASTRONOMY
is characterized by three stars of the third and fourth mag-
nitude, easily made out by the help of the map.
It may be regarded as a canonization of " Divine Geometry," but
has no special mythological legend connected with it.
38. Aries, the Ram (Map II). December. This is
the second of the zodiacal constellations, now occupying
the sign of Taurus. It lies just south of Triangulum and
Perseus. Its characteristic star-group is that composed of
Alpha (Hamal], Beta, and Gamma (see map), about 20 due
south of Gamma Andromedse. Alpha, a star of 2 mag-
nitude, is fairly conspicuous, forming a large isosceles tri-
angle with Beta and Gamma Andromedse.
Gamma Arietis is a very pretty double star with the components
about 9" apart. It is probably the first double star discovered,
having been noticed by Hooke in 1664.
The star 41 Arietis (3 magnitude), which forms a nearly equilat-
eral triangle with Alpha Arietis and Gamma Trianguli, constitutes,
with two or three other stars near it, the constellation of Musca
(Borealis), a constellation, however, not now generally recognized.
According to the Greeks, Aries is the ram which bore the Golden
Fleece and dropped Helle into the Hellespont, when she and her
brother, Phrixus, were fleeing on its back to Colchis. Long after-
wards the Argonautic Expedition, with Jason as its head and Her-
cules as one of its members, sailed from Greece to Colchis to recover
the fleece, and finally succeeded after long endeavors. .
39. Cetus, the Sea-Monster (Map II). November to
December. South of Aries and Pisces lies the huge con-
stellation of Cetus, the sea-monster, which backs up into
the sky from the southeastern horizon. The head lies
some 20 southeast of Alpha Arietis, and is marked by an
irregular five-sided figure of stars, each side being some
URANOGRAPHY 3T
5 or 6 long. The southern edge of this pentagon is-
formed by the stars Alpha, or Menkar (2i magnitude), and
Gamma (3i magnitude) ; Delta lies southwest of Gamma.
Beta (Deneb Ceti), 1 the brightest star of the constellation
(2 magnitude), stands by itself nearly 40 west and south
of Alpha. Gamma is a very pretty double star, but rather
close for a small telescope, the components being only
2".5 apart, yellow and blue.
Cetus is the leviathan that was sent by Neptune to ravage Libya
and devour Andromeda. Perseus turned him into stone by showing
him the head of the Gorgon, Medusa. On the globes he is usually
represented as a nondescript sort of beast, with a face like a puppy's,
and a tightly curled tail; as if the Gorgon's head had frightened
out all his savageness.
South of Cetus lies the modern constellation of Sculptoris Appa-
ratus (usually known simply as Sculptor), which, however, contains
nothing that requires notice here. South of Sculptor, and close to
the horizon, even when on the meridian, is Phoenix. It has some
bright stars, but none easily observable in the United States.
40. Perseus (Maps I and II) . January. Returning
now to the northern limit of the map, we come to the con-
stellation of Perseus. Its principal star is Alpha (Algenib),
rather brighter than the standard second magnitude, and
situated very nearly on the prolongation of the line of the
three chief stars of Andromeda. A very characteristic
configuration is the so-called " segment of Perseus "
(Map I), a curved line formed by Delta, Alpha, Gamma,
and Eta, with some smaller stars, concave towards the
northeast, and running along the line of the Milky Way
towards Cassiopeia. The remarkable variable star, Beta,
or Algol, is situated about 9 south. and a little west of
1 Deneb signifies "tail," and there are several stars of that name.
38 LESSONS IN ASTRONOMY
Alpha, at the right angle of a right-angled triangle which
it forms with Alpha Persei and Gamma Andromedse.
Algol and a few small stars near it form "Medusa's
Head," which Perseus carries in his hand. (For further
particulars and recent discoveries regarding this star, see
Sees. 358 and 360.)
In this constellation, nearly in the center of the triangle
formed by Algenib with Algol and Epsilon, appeared the
remarkable temporary star, or Nova^ of 1901, the most
brilliant of its kind for nearly 300 years. (See Sec. 355*.)
Epsilon is a very pretty double star with the components about
80" apart ; but the most beautiful telescopic object in the constel-
lation, perhaps the finest indeed in the whole heavens for a small
telescope, is the pair of clusters about half-way between Gamma
Persei and Delta Cassiopeise, visible to the naked eye as a bright
knot in the Milky Way, and already referred to in Sec. 32.
Perseus was the son of Danae by Jupiter, who won her in a
shower of gold. He was sent by his enemies on the desperate
venture of capturing the head of Medusa, the only mortal one of
the three Gorgons, which were frightful female monsters with wings,
tremendous claws, and brazen teeth, and serpents for hair j of such
aspect that the sight turned to stone all who looked at them. The
gods helped Perseus by various gifts, which enabled him to approach
his victim, invisible and unsuspected, and to deal the fatal blow
without looking at the sight himself. From the blood of Medusa,
where her body fell, sprang Pegasus, the winged horse, and where
the drops fell on the sands of Libya, as Perseus was flying across
the desert, thousands of venomous serpents swarmed. On his way,
returning home, he saw and rescued Andromeda, as already men-
tioned (Sees. 28 and 35). Hercules was one of their descendants.
41. Auriga, the Charioteer (Maps I and II). January.
Proceeding east from Perseus we come to Auriga, who is
represented as holding in his arms a goat and her kids.
URANOGRAPHY 39
The constellation is instantly recognized by the bright
yellow star Capella (the Goat) and her attendant " Hcedi "
(the Kids). Alpha Aurigse (Capella) is, according to
Pickering, precisely of the same brightness as Vega, both
of them being about of a magnitude fainter than Arc-
turus, but distinctly brighter than any other stars visible
in our latitudes except Sirius itself. The spectroscope
shows that Capella is very similar in character to our own
sun, though probably vastly larger. It has recently been
discovered to be a spectroscopic binary like Mizar (Sec. 26).
About 10 east of Capella is Beta Aurigse (Menkalinari)
of the second magnitude; Epsilon, Zeta, and Eta, which
form a long triangle 4 or 5 south of Alpha, are the Kids.
There seems to be no well-settled mythological history for this con-
stellation, though some say that he is the charioteer of (Enomaus,
king of Elis ; while others connect him with the story of Phaethon,
the son of Apollo, who borrowed the horses of his father and was
overthrown in mid-heaven. The goat is supposed to be Amalthea,
the goat which suckled Jupiter in his infancy. Capella and the
Kids were always regarded by astrologers as of kindly influence,
especially towards sailors.
42. Taurus, the Bull (Map II). January. This, the
third of the zodiacal constellations, lies directly south of
Perseus and Auriga, and north of Orion. It is unmistak-
ably characterized by the Pleiades, and by the Y-shaped
group of the Hyades which forms the face of the bull,
with the red Aldebaran (Alpha Tauri), a standard first-
magnitude star, blazing in the creature's eye, as he charges
down upon Orion. His long horns reach out towards
Gemini and Auriga, and are tipped with the second- and
third-magnitude stars, Beta and Zeta. As in the case of
40 LESSONS IN ASTRONOMY
Pegasus, only the head and shoulders appear in the con-
stellation. Six of the Pleiades are easily visible, and on
a dark night a fairly good eye will count nine of them.
With a three-inch telescope about one hundred stars are
visible in the cluster, which is more fully described with a
figure in Sec. 376. The brightest of the Pleiades is called
Alcyone, and was assigned to the dignity of the " Central
Sun " by Maedler (Sec. 386).
About 1 west and a little north of Zeta is a nebula (Messier 1),
which has many times been discovered by tyros with a small tele-
scope as a new comet ; it is an excellent imitation of the real thing.
According to the Greek legends, Taurus is the milk-white bull
into which Jupiter changed himself when he carried away Europa
from Phoenicia to the island of Crete, where she became the mother
of Minos and the grandmother of Deucalion, the Noah of Greek
mythology. But Taurus, like most of the other zodiacal constel-
lations, is really far older than the Greek mythology, and appears
in the most ancient zodiacs of Egypt, where it was probably con-
nected with the worship of the bull, Apis; so also in the ancient
Astronomy of Chaldea and India.
The Pleiades were daughters of the giant Atlas. Of .the seven
sisters, one, who married a mortal, lost her brightness, according to
the legend, so that only six remain visible. Some say that Merope
was the one who thus gave up her immortality for love, but her star
is still visible, while Celseno and Asterope are both faint. The now
recognized names of the stars in the group (see map, Sec. 376)
include Atlas and Pleione, the parents of the family, as well as the
seven sisters. As for the Hyades, who were half-sisters of the
Pleiades, there is less legendary interest in their case. They are
always called by the poets the " rainy Hyades."
43. Orion (not O'rion) (Map II). February. This is
the most splendid constellation in the heavens. As the
giant stands facing the bull, his shoulders are marked by
URANOGRAPHY 41
the two bright stars Alpha (Betelgeuze, pronounced BStel-
jeuze) and Gamma (JBellatrix), the former of which in color
closely matches Aldebaran, though its brightness is some-
what variable. In his hand he holds up the lion skin,
indicated by the curved line of little stars between Gamma
and the Hyades. The top of the club, which he brandishes,
lies between Zeta Tauri and Mu and Eta Geminorum. His
head is marked by a little triangle of stars of which Lambda
is the chief. His belt, through the northern end of which
passes the celestial equator, consists of three stars of the
second magnitude, pointing obliquely southeast toward
Sirius. It is very nearly 3 in length, and is known in Eng-
land as the " Ell and Yard." From the belt hangs the sword,
composed of three smaller stars lying more nearly north and
south; the middle one of them is the multiple, Theta, in the
great nebula, which even in a small telescope is a beautiful
object, the finest nebula in the sky. (See Fig. 94, Sec. 378.)
Beta Orionis, or Rigel, a magnificent white star, is in one of
his feet, and Kappa is in the knee of the other leg. (Orion
has only one foot, or if he has another it is hidden behind
Lepus.) The quadrilateral Alpha, Gamma, Beta, Kappa,
with the diagonal belt, Delta, Eta, Zeta, once learned can
never be mistaken for anything else in the heavens.
Rigel is a very pretty double star, the larger star having a very
small companion about 10" distant. The two stars at the extremities
of the belt are also double.
Orion was a giant and mighty hunter, son of Neptune, and beloved
by both Aurora and Diana. The legends of his life and exploits are
numerous, and often contradictory. He conquered every creature
except the Scorpion, which stung and killed him. As a winter con-
stellation his influence was counted stormy, and he was greatly
dreaded by sailors.
42 LESSONS IN ASTRONOMY
44. Eridanus, the River Po (Map II). January. This constel-
lation lies south of Taurus, in the space between Cetus and Orion,
and extends far below the southern horizon. The portion near the
south pole has a pair of bright stars, which, of course, are never visible
at the United States. Starting with Beta (Cursa, as it is called),
of the third magnitude, about 3 north and a little west of Rigel, one
can follow a sinuous line of stars westward to the paws of Cetus,
where the stream turns at right angles and runs southward and
southwest to the horizon. To trace it conveniently, however, requires
a map on a larger scale than the one we present.
45. Lepus and Columba (Map II). February. The con-
stellation of Lepus (the Hare), one of Orion's victims, is one
of the ancient forty-eight, and lies just south of the giant,
occupying a space of some 15 square. Its characteristic
configuration is a quadrilateral of third- and fourth-magni-
tude stars, with sides from 3 to 5 long, about 10 south
of Kappa Orionis, and 15 west of Sirius.
. Columba, the Dove, lies next south of Lepus, too far
south to be well seen in the Northern States. Its principal
star, Alpha (Phact), is of 2 magnitude, and is readily found
by drawing a line from Procyon to Sirius and prolonging
it about the same distance. In passing, we may note that
a similar line drawn from Alpha Orionis through Sirius,
and produced, will strike near Zeta Argus, or Naos, a star
about as bright as Phact, the two lines which intersect
at Sirius making the so-called " Egyptian X."
Columba is a modern constellation, commemorating Noah's dove
returning to the ark with the olive branch.
46. Lynx (Maps I, II, and III). February. Returning now
to the northern limit of the map, we find the modern constellation
of the Lynx lying just east of Auriga, and enveloping it on the north
and in the circumpolar region, as shown on the map. It contains
URANOGRAPHY 43
no stars above the fourth magnitude, and is of no importance except
as occupying an otherwise vacant space.
47. Gemini, the Twins (Map II). February and March.
This is the fourth of the zodiacal constellations, now
lying mostly in the sign of Cancer. It contains the sum-
mer solstitial point the point where the sun turns from
its northern motion to its southern in the summer. At
present it is about 2 west and a little north of the star
Eta. Gemini lies northeast of Orion and southeast of
Auriga, and is sufficiently characterized by the two stars
Alpha and Beta (about 4 apart), which mark the heads
of the twins. The southern one, Beta, or Pollux, is now
the brighter; but Alpha (Castor) is much more interesting,
as being double (easily seen with a small telescope). The
feet are marked by the third-magnitude stars Gamma and
Mu, some 10 east of Zeta Tauri.
Castor and Pollux were the sons of Jupiter by Leda, and ancient
mythology, especially that of Rome, is full of legends relating to
them. Many of our readers will remember Macaulay's ballad of " The
Battle of Lake Regillus," when they won the fight for Rome. They
were regarded as the special patrons of the sailor, who relied much on
their protection against the evil powers of Orion and the Hyades.
48. Canis Minor, the Little Dog (Map III). March.
This constellation, about 20 south of Castor and Pollux,
is marked by the bright star Procyon, which means " before
the dog," because it rises about half an hour before the
Dog Star (Sirius). Alpha, Beta, and Gamma form together
a configuration closely resembling that formed by Alpha,
Beta, and Gamma Arietis. Procyon, Alpha Orionis, and
Sirius form a nearly equilateral triangle, with sides of
about 25.
44 LESSONS IN ASTRONOMY
The animal is supposed to have been one of Orion's dogs, though
some say the dog of Icarus, whom they identify with Bootes.
49. Canis Major, the Great Dog (Map II). February.
This glorious constellation hardly needs description. Its
Alpha is the Dog Star (Sirius), beyond all comparison the
brightest star in the heavens, and one of our nearer neigh-
bors, so distant, however, that it requires more than
eight years for light to come to us from it. It is nearly
pointed at by a line drawn through the three stars at
Orion's belt. Beta, at the extremity of the uplifted paw,
is of the second magnitude, and so are several of the stars
farther south in the rump and tail of the animal, who sits
up watching his master Orion, but with an eye out for
Lepus.
50. Monoceros, the Unicorn (Map II). March. This is one of
the modern constellations organized by Hevelius to fill the gap
between Gemini and Canis Minor on the north, and Argo Navis and
Canis Major on the south. It lies just east of Orion and has no
conspicuous stars, but is traversed by a brilliant portion of the Milky
Way. The Alpha of the constellation (fourth magnitude) lies about
half-way between Alpha Orionis and Sirius, a little west of the line
that joins them. 11, or Alpha, Monocerotis, a fine triple star (see
Fig. 88, Sec. 366), fourth magnitude, is very nearly pointed at by a
line drawn from Zeta Canis Majoris northward through Beta, and
continued as far again.
51. Argo Navis, the Ship Argo (genitive Argus) (Maps II
and III). March. This is one of the largest, oldest, and
most important of the constellations, lying south and east
of Canis Major. Its brightest star, Alpha Argus (Canopus),
ranks next to Sirius and is visible in the Southern States,
but not in the Northern. The constellation, huge as it is,
is only a half one, like Pegasus and Taurus, only the
UBAISTOGRAPHY 45
stern of a vessel, with mast, sail, and oars ; the stem being
wanting. In the part of the constellation covered by our
maps there are no very conspicuous stars, though there are
some of third and fourth magnitude which lie east and
southeast of the rump and tail of Canis Major. We have
already mentioned Zeta, or Naos, at the southeast extremity
of the Egyptian X."
The constellation is so large that for convenience it has recently
been divided into four sub-constellations, Mains (the mast), Vela
(the sails), Puppis (the stern), and Carina (the keel or hull). This
new division sometimes leads to misunderstanding ; thus Eta Carinse
is not always at first recognized as the Eta Argus of older astronomers.
According to the Greek legends, this is the miraculous ship in
which Jason and his fifty companions sailed from Greece to Colchis
to recover the Golden Fleece. It had in its bow a piece of oak from
the sacred grove of Dodona, which enabled the ship to talk with its
commander and give him advice.
Some see in the constellation the ark of Noah.
52. Cancer, the Crab (Maps II and III). March. This
is the fifth of the zodiacal constellations, lying just east of
Canis Minor. It does not contain a single conspicuous
star, but is e-asily recognizable from its position, and in a
dark night by the nebulous cloud known as Prcesepe, or the
" Manger," with the two stars Gamma and Delta near it,
-the so-called Aselli, or "Donkeys." Prsesepe, some-
times also called the " Beehive," is really a coarse cluster of
seventh- and eighth-magnitude stars, resolvable by an opera-
glass. The line from Castor through Pollux, produced
about 12, passes near enough to it to serve as a pointer.
The star Zeta is a very pretty triple star, though with a small tel-
escope it can be seen only as double. It is easily found by a line
from Castor through Pollux, produced 2 times as far.
46 LESSONS IN ASTRONOMY
By the Greeks this was identified as the Crab who attacked
Hercules when he was fighting the Lernaean Hydra. In the old
Egyptian zodiacs the Crab is replaced by the Scarabaeus, or Beetle ;
and in some of the more recent zodiacs by a pair of asses, still
recognized in the name Aselli, given to the two stars Gamma
and Delta.
53. Leo, the Lion (Map III). April East of Cancer
lies the noble constellation of Leo, which adorns the even-
ing sky in March and April ; it is the sixth of the zodiacal
constellations, now occupying the sign of Virgo. Its lead-
ing star, Regulus, or " Cor Leonis," is of the first magni-
tude, and two others, Beta (Denebola) and Gamma, are of
the second magnitude. Alpha, Gamma, Delta, and Beta
form a conspicuous irregular quadrilateral (see map), the
line from Regulus to Denebola being about 26 long.
Another characteristic configuration is the " Sickle," of
which Regulus is the handle, and the curved line Eta,
Gamma, Zeta, Mu, and Epsilon is the blade, the cutting
edge being turned towards Cancer.
The " radiant " of the November meteors lies between Zeta and
Epsilon. Gamma, in the Sickle, and at the southeast corner of the
quadrilateral, is a very pretty double star binary with a period
of about 400 years.
According to classic writers, this is the Nemsean Lion which was
killed by Hercules, as the first of his Twelve Labors ; but, like Aries
and Taurus, the constellation is far older than the Greeks and stands
in its present form on all the ancient zodiacs.
54. Leo Minor and Sextans (Map III). April. Leo Minor
(the Smaller Lion) is an insignificant modern constellation com-
posed of a few small stars north of Leo, between it and the feet
of Ursa Major. It contains nothing deserving special notice. The
same remark holds good as to Sextans (the Sextant), and even more
emphatically.
URANOGRAPHY 47
55. Hydra (Map III). March to June. This constel-
lation, with its riders, Crater (the Cup) and Corvus (the
Raven), is a large and important one, though not very
brilliant. The head is marked by a group of five or six
fourth- and fifth-magnitude stars just 15 south of Prsesepe.
A curving line of small stars leads down southeast to
Alpha, Cor Hydrce, or Alphard (which means "the soli-
tary"), a 2-magnitude star standing very much alone.
From there, as the map shows, an irregular line of fourth-
magnitude stars running far south and then east, almost
to the boundary of Scorpio, marks the creature's body and
tail, the whole extending very nearly 90. About the
middle of the length of Hydra, and just below the hind
feet of Leo (30 due south from Denebola), we find the
little constellation of Crater; and just east of it the still
smaller but much more conspicuous one of Corvus, with
two second-magnitude stars in it, and four of the third
and fourth magnitudes. It is well marked by a character-
istic quadrilateral (see map), with Delta and Eta together
at its northeast corner. The order of the letters in Corvus
differs widely from that of brightness, suggesting that
changes may have occurred since the letters were applied.
Epsilon Hydrae and Delta Corvi are pretty double stars, the latter
easily seen with a small telescope ; colors, yellow and purple.
Hydra, according to the Greeks, is the immense hundred-headed
monster which inhabited the Lernsean Marsh, and was killed by Her-
cules as his second labor. But the Hydra of the heavens has only
one head, and is probably much older than the legends of Hercules.
An old legend says that Corvus is Coronis, a nymph who was
transformed into a raven to escape the pursuit of Neptune. Another
story is that she was changed into a crow for telling tales of some
imprudent actions of Jupiter which came under her notice.
48 LESSONS IN ASTRONOMY
56. Virgo (Map III). May. East and south of Leo
lies Virgo, the seventh zodiacal constellation, mostly in
the sign of Libra. Its Alpha (Spica Virginis) is of the
1J magnitude and, standing rather alone, 10 south of
the celestial equator, is easily recognized as the southern
apex of a nearly equilateral triangle which it forms with
Denebola (Beta Leonis) to the northwest, and Arcturus
northeast of it. Beta Virginis, of the third magnitude, is
14 south of Denebola. A line drawn eastward and a little
south from Beta (third magnitude) and then carried on,
curving northward, passes successively (see map) through
Eta, Gamma, Delta, and Epsilon, of the third magnitude.
(Notice the word " Begde," like " Bagdei " in Cassiopeia,
Sec. 28.)
Gamma is a remarkable binary star, at present easily visible as
double in a small telescope. Its period is 185 years, and it has
completed pretty nearly a full revolution since its first discovery.
(For a diagram of its orbit, see Fig. 89, Sec. 369.) A few degrees
north of Gamma lies the remarkable nebulous region of Virgo, con-
taining hundreds of these curious objects; but for the most part
they are very faint, and observable only with large telescopes.
The classic poets recognize Virgo as Astrsea, the goddess of jus-
tice, who, last of all the old divinities, left the earth at the close of
the Golden Age. She holds the Scales of Justice (Libra) in one hand,
and in the other a sheaf of wheat.
Some identify her with Erigone, the daughter of Icarus or Bootes.
Others recognize in her the Egyptian Isis.
57. Coma Berenices, Berenice's Hair (Map III). May. This
little constellation, composed of a great number of fifth- and sixth-
magnitude stars, lies 30 north of Gamma and Eta Virginis, and about
15 northeast of Denebola. It contains a number of interesting
double stars, but they are not easily found without the help of a
telescope equatorially mounted.
URANOGRAPHY 49
The constellation was established by the Alexandrian astronomer
Conon, in honor of the queen of Ptolemy Soter. She dedicated her
splendid hair to the gods, to secure her husband's safety in war.
58, Canes Venatici, the Hunting-Dogs (Map III). May.-
These are the dogs with which Bootes, the huntsman, is
pursuing the Great Bear around the pole ; the northern of
the two is Asterion, the southern Char a. Most of the stars
are small, but Alpha is of the 2^- magnitude, and is easily
found by drawing from Eta Ursse Majoris (the star in the
end of the Dipper-handle) a line to the southwest, perpen-
dicular to the line from Eta to Zeta (Mizar), and about
15 long; in England it is generally known as Cor Caroli
(the Heart of Charles), in allusion to Charles I. With
Arcturus and Denebola it forms a triangle much like that
which they form with Spica.
The remarkable whirlpool nebula of Lord Rosse is situated in this
constellation, about 3 west and somewhat south of the star Eta
Ursse Majoris. In a small telescope it is by no means conspicuous,
but in a large telescope is a wonderful object.
The constellation is modern, formed by Hevelius.
59. Bootes, the Huntsman (Maps I and III). June.
This fine constellation extends more than 60 in declina-
tion, from near the equator quite to Draco, where the
uplifted hand holding the leash of the hunting-dogs over-
laps the tail of the Bear. Its principal star, Alpha (Arctu-
rus, meaning "bear-driver"), is of a ruddy hue, and in
brightness is excelled only by Sirius among the stars visible
in our latitudes. It is at once recognizable by its forming
with Spica and Denebola the great triangle already men-
tioned (Sec. 56). Six degrees west and a little south of it
is Eta, of the third magnitude, which forms with it, in
50 LESSONS IN ASTRONOMY
connection with Upsilon, a configuration like that in the
head of Aries. Epsilon is about 10 northeast of Arcturus,
and in the same direction about 1 farther lies Delta. The
map shows the pentagon which is formed by these two stars
along with Beta, Gamma, and Rho.
Epsilon is a fine double star ; colors, orange and greenish blue ;
distance, about 3".
The legendary history of this constellation is very confused. One
legend makes it to be Icarus, the father of Erigone (Virgo), but the
one most usually accepted makes it to be Areas, son of Callisto. After
she was changed to a bear (Ursa Major), her son, not recognizing
her, hunted her with his dogs, "and was on the point of killing her,
when Jupiter interfered and took them both to the stars.
60. Corona Borealis, the Northern Crown (Map III).
June. This beautiful little constellation lies 20 north-
east of Arcturus, and is at once recognizable as an almost
perfect semicircle composed of half a dozen stars, among
which the brightest, Alpha (G-emma, or Alphaccci), is of the
second magnitude. The extreme northern one is Theta;
next comes Beta, and the rest follow on the Bagdei order,
just as in Cassiopeia. About a degree north of Delta, now
visible with an opera-glass, is a small star which in 1866
suddenly blazed out until it became brighter than Alphacca
itself. (See Sec. 355.)
The little star Eta is a rapid binary with a period of less than
forty-two years. At times it can be easily divided by a small
telescope.
The constellation is said to be the crown that Bacchus gave to
Ariadne, before he deserted her on the island of Naxos.
61. Libra, the Balance (Map III). June. This is the
eighth of the zodiacal constellations, lying east of Virgo,
URANOGRAPHY 51
bounded on the south by Centaurus and Lupus, on the
east by the upstretched claw of Scorpio, and on the north
by Serpens and Virgo. It is inconspicuous, the most
characteristic figure being the trapezoid formed by the
lines joining the stars Alpha, Iota, Gamma, and Beta.
Beta, which is the northern one, is about 30 due east
from Spica, while Alpha is about 10 southwest of Beta.
The remarkable variable, Delta Librae, is 4 west and a
little north from Beta. Most of the time it is of the 4 or
5 magnitude, but runs down nearly two magnitudes, to
invisibility, once in 2i days ("Algol" type, Sec. 358).
Libra is the Balance of Virgo, the goddess of justice, and was not
recognized by the classic writers as a separate constellation until the
time of Julius Caesar, the space now occupied by Libra being then
covered by the extended claws of Scorpio.
The cluster M. 5, situated on the extreme northern border of
the constellation, is remarkable for the number of variable stars it
contains (Sec. 361).
62. Antlia, Centaurus, and Lupus (Map III). April to
June. These constellations lie south of Hydra and Libra.
Antlia Pneumatica (the Air-Pump) is a modern constellation of no
importance and hardly recognizable by the eye, having only a single
star as bright as the 4| magnitude.
Centaurus, on the other hand, is an ancient and exten-
sive asterism, containing in its south (circumpolar) regions,
not visible in the United States, two stars of the first mag-
nitude, Alpha and Beta. Alpha Centauri stands next after
Sirius and Canopus in brightness and, as far as present
knowledge indicates, is our nearest neighbor among the stars.
The part of the constellation which becomes visible in our
52 LESSONS IN ASTRONOMY
latitudes is not especially brilliant, though it contains sev-
eral stars of the 2 and 3 magnitudes in the region lying
south of Corvus and Spica Virginis.
Lupus (the Wolf), also one of Ptolemy's constellations, lies due east
of Centaurus and just south of Libra. It contains a considerable
number of third- and fourth-magnitude stars ; but it is too low for
any satisfactory study in our latitudes. It is best seen late in June.
These constellations contain numerous objects interesting for a
southern observer, but not observable by us.
The Centaurs were a fabulous race, half man, half horse, who
lived in Thessaly and herded cattle. Chiron was the most distin-
guished of them, the teacher of almost all the Greek heroes in every
manly and noble art, and the friend of Hercules, by whom, however,
he was accidentally killed. Jupiter transferred him to the stars.
(See Sagittarius, Sec. 72.) The wolf is represented as transfixed by
the Centaur's spear.
63, Scorpio (or Scorpius; genitive Scorpii), the Scorpion
(Map IV). July. This, the ninth of the zodiacal con-
stellations and the most brilliant of them all, lies southeast
of Libra, which in ancient times used to form its claws
(Chelse). It is recognized at once by the peculiar configu-
ration of the stars, which resembles a boy's kite, with a
long streaming tail extending far down to the south and
east, and containing several pairs of stars. The principal
star of the constellation, Antares, is of the first magnitude,
and fiery red like the planet Mars. From this it gets its
name, which means "the rival of Ares" (Mars). Antares
is a very pretty double star, with a beautiful little green
companion just to the west of it, not very easy to be seen,
however, with a small telescope. Beta (second magnitude)
is in the arch of the kite bow, about 8 or 9 northwest of
Antares, while the star which Bayer lettered as Gamma
URANOGRAPHY 58
Scorpii is well within Libra, 20 west of Antares. (There
is considerable confusion among uranographers as to the
boundary between the two constellations.) The other
principal stars of the constellation are easily found on
the map.
Many of them are of the second magnitude. One of the finest
clusters known, and easily seen with a small telescope, is M. 80,
which lies about half-way between Alpha and Beta.
Mu 1 is one of the most remarkable of the spectroscopic binaries
(Sec. 374), the relative velocity of the two stems of the pair being
about 300 miles a second, and the period of revolution only a day
and ten hours.
According to the Greek mythology, this is the scorpion that killed
Orion. It was the sight of this monster of the heavens that fright-
ened the horses of the sun, when poor Phaethon tried to drive them
and was thrown out of his chariot. Among astrologers, the influence
of Scorpio has always been held as baleful to the last degree.
64. Norma Nilotica, the rule with which the height of the Nile
was measured, lies west of Scorpio, while Ara lies due south of Eta
and Theta. Both are modern constellations, small and of no impor-
tance in our latitudes.
65. Ophiuchus and Serpens (Map IV). July. Ophiu-
chus means the "serpent-holder," and probably refers to
the great physician ^Esculapius. The hero is represented
as standing with his feet on Scorpio and grasping the
serpent. The two constellations, therefore, are best treated
together. The head of Serpens is marked by a group
of small stars lying just south of Corona and 20 due
east of Arcturus. Beta and Gamma are the two brightest
stars in the group, their magnitudes 3 and 4. Delta
lies 6 southwest of Beta, and there the serpent's body
bends southeast through Alpha and Epsilon Serpentis
54 LESSONS IN ASTRONOMY
(see map) to Delta and Epsilon Ophiuchi in the giant's
hand. The line of these five stars carried upwards passes
nearly through Epsilon Bobtis, and downwards through
Zeta Ophiuchi. A line crossing this at right angles, nearly
midway between Epsilon Serpentis and Delta Ophiuchi,
passes through Mu Serpentis on the southwest and Lambda
Ophiuchi to the northeast. The lozenge-shaped figure
formed by the lines drawn from Alpha Serpentis and Zeta
Ophiuchi to the two stars last mentioned is one of the most
characteristic configurations of the summer sky. Alpha
Ophiuchi (2 magnitude) (Ras Alaghue) is easily recog-
nizable in connection with Alpha Herculis, since they
stand rather isolated, about 6 apart, on the line drawn
from Arcturus through the head of Serpens, and produced
as far again. Alpha Ophiuchi is the eastern and the
brighter of the two, and forms with Vega and Altair a
nearly equilateral triangle. Beta Ophiuchi lies about 9
southeast of Alpha.
Five degrees east and a little south of Beta are five small stars in
the Milky Way, forming a V with the point to the south, much like
the Hyades of Taurus. They form the head of the now discredited
constellation, " Poniatowski's Bull" (Taurus Poniatovii), proposed in
1777, and found in many maps. 70 Ophiuchi (the middle star in
the eastern leg of the V of Poniatowski's Bull) is a very pretty
double star binary with a period of ninety-three years. Just at
present the star is too close to be resolved by a small instrument.
Kepler's "new star" of 1604 was situated in the left leg of
Ophiuchus, between Eta and Theta.
Ophiuchus is identified with ^Esculapius, who was the first great
physician, the son of Apollo and the nymph Coronis, educated in the
art of medicine by Chiron, the Centaur. The serpent and the cock
were sacred to him in his character as a deity. But the constellation
is older than the classic legends.
URANOGRAPHY 55
66. Hercules (Maps I and IV). July This noble con-
stellation lies next north of Ophiuchus, between it and
Draco. The hero is represented as resting on one knee,
with his foot on the head of Draco, while his head is close
to that of Ophiuchus. The constellation contains no stars
of the first or even of the second magnitude, but there are
a number of the third. The most characteristic figure
is the keystone-shaped quadrilateral formed by the stars
Epsilon, Zeta, Eta, with Pi and Rho together at the north-
east corner. It lies about midway on the line from Vega
to Corona.
On its western boundary, a third of the way from Eta towards
Zeta, lies the remarkable cluster, Messier 13, on the whole the
finest of all star clusters in the northern hemisphere, barely
visible to the naked eye on a dark night. Alpha Herculis (Ras
Algethi), in the head of the giant, is a very beautiful double star;
colors, orange and blue ; distance, about 5". It is also notably
variable, and has a remarkable spectrum, characterized by numerous
dark bands.
Hercules, the son of Jupiter and Alcmena (a granddaughter of
Andromeda), was the Greek incarnation of gigantic strength. His
heroic actions and freaks occupy more space in their mythology than
those of any personage except Jupiter himself. He was the pupil of
Chiron, but by the will of Jupiter, his father, was subjected to the
power of Eurystheus, the king of Tiryns, for many years. At his
bidding he performed the great enterprises known as the Twelve
Labors of Hercules, for w T hich we must refer the reader to the Clas-
sical Dictionaries. Among them we have already mentioned the con-
quest of the Nemaean Lion and of the Lernsean Hydra. Another
was to bring from the garden of the Hesperides the golden apples
which were guarded by the dragon that he killed, and on which his
feet rest in the sky. His last and greatest achievement was to bring
to the earth the three-header' dog, Cerberus, the guardian of the
infernal regions.
56 LESSONS IN ASTRONOMY
67. Lyra (Map IV). August. This constellation is
sufficiently marked by the great white or blue star, Vega,
one of the finest stars in the whole sky, and certainly many
times larger than our own sun. It is attended on the east
by two fourth-magnitude stars, Epsilon and Zeta, which
form with it a little equilateral triangle having sides about
2 long. Epsilon is a double-double or quadruple star.
A sharp eye, even unaided by a telescope, divides the star
into two, and a large telescope splits each of the compo-
nents. It is a very pretty object even for a small telescope
(Fig. 88). Beta and Gamma, of the third magnitude (Beta
is variable), lie about 8 southeast from Vega, 2 apart.
(See Sec. 357.)
On the line between Beta and Gamma, one-third of the -way from
Beta, lies Messier 57, the Annular Nebula, which can be seen as a
small hazy ring even by a small telescope, though of course it is
much more interesting with a larger one.
According to the legends this constellation is the lyre of Orpheus,
with which he charmed the stern gods of the lower world, and per-
suaded them to restore to him his lost Eurydice.
68, Cygnus (Maps I and IV). September. This con-
stellation lies due east from Lyra, and is easily recognized
by the cross that marks it. The bright star Alpha (1
magnitude) is at the top, and Beta (third magnitude) at
the bottom, while Gamma is where the cross-bar from Delta
to Epsilon intersects the main piece, which lies along the
Milky Way from the northeast to the southwest. Beta
(Albireo) is a beautiful double star, orange and dark blue,
one of the finest of the colored pairs for a small telescope.
61 Cygni, which is memorable as the first star to have its
parallax determined (by Bessel in 1838), is easily found by
URANOGRAPHY 57
completing the parallelogram of which Alpha, Gamma, and
Epsilon are the other three corners. Sigma and Tau form
a little triangle with 61, which is the faintest of the three.
61 is a fine double star. Delta is also a fine double, but
too difficult for an instrument of less than six inches
aperture.
According to Ovid, Cygnus was a friend of Phaethon's, who
mourned his unhappy fate and was changed to a swan. Others see
in the constellation the swan in whose form Jupiter visited Leda,
the mother of Castor and Pollux and of Helen of Troy.
69. Vulpecula et Anser, the Fox and the Goose (Map IV).
September. This little constellation is one of those originated by
Hevelius and has obtained more general recognition among astrono-
mers than most of his creations. It lies just south of Cygnus and is
bounded to the south by Delphinus, Sagitta, and Aquila. It has no
conspicuous stars, but it contains one very interesting telescopic
object, the "Dumb-bell Nebula," Messier 27. It may be found
on a line from Gamma Lyrse through Beta Cygni, produced as far
again.
70. Sagitta (Map IV). August. This little constellation,
though very inconspicuous, is one of the old forty-eight. It lies
south of Vulpecula, and the two stars Alpha and Beta, which mark
the feather of the arrow, lie nearly midway between Beta Cygni and
Altair, while its point is marked by Gamma, 5 farther east and
north. Beta, the middle star of the shaft of the arrow, is a very
pretty double star ; distance, about 8" : the larger star is itself a close
double.
71. A'quila (not Aquila) (Map IV). August. This
constellation lies on the celestial equator, east of Ophiu-
chus and north of Sagittarius and Capricornus. Its charac-
teristic configuration is that formed by Alpha (Altair), with
Gamma to the north and Beta to the south. It lies about
20 south of Beta Cygni and forms a fine triangle with
58 LESSONS IN ASTRONOMY
Beta and Alpha Ophiuchi. Altair is taken as the standard
first-magnitude star. Of course several of those which
are ordinarily called first magnitude, like Sirius and Vega,
are very much brighter than this, while others fall consid-
erably below it.
Aquila was the bird of Jupiter, which he kept by the side of his
throne and sent to bring Ganymede to him.
The southern part of the region allotted to Aquila on our maps has
been assigned to Antinoiis, which is recognized on some celestial
globes. The constellation existed even in Ptolemy's time, but he
declined to adopt it. Hevelius appropriated the eastern part of
Antinotis for his constellation of Scutum Sobieski, which, however, is
now seldom recognized.
72. Sagittarius, the Archer (Map IV). August. This,
the tenth of the zodiacal constellations, contains no stars
of the first magnitude, but a number of the second and
third magnitude, which make it reasonably conspicuous.
The most characteristic configuration is the little inverted
" milk-dipper," formed by the five stars Lambda, Phi,
Sigma, Tau, and Zeta, of which the last four form the
bowl, while Lambda (in the Milky Way) is the handle.
(See map.) Delta, Gamma, and Epsilon, which form a
triangle, right-angled at Delta, lie south and a little west
of Lambda, the whole eight together forming a very strik-
ing group. There is a curious disregard of any apparent
principle in the lettering of the stars of this constellation ;
Alpha and Beta are stars not exceeding in brightness the
fourth magnitude, about 4 apart on a north and south
line, and lying some 15 south and 5 east of Zeta (see
map), while Sigma is now a bright second-magnitude star,
strongly suspected of being irregularly variable. The
URANOGRAPHY 59
constellation contains an unusual number of known vari-
ables. The Milky Way in Sagittarius is very bright and
complicated in structure, full of knots and streamers and
dark pockets, and containing many beautiful and inter-
esting objects.
This constellation is said by many writers to commemorate the
Centaur, Chiron, but the same constellation appears on the ancient
zodiacs of Egypt and India, and it seems probable, therefore, that,
like the Bull and the Lion, it was not representative of any particular
individual.
73. Capricornus (Map IV). September. This, the
eleventh of the zodiacal constellations, follows Sagittarius on
the east. It has no bright stars, but the configuration formed
by the two Alphas (a x and a 2 ) with each other and with Beta,
3 south, is characteristic, and not easily mistaken for any-
thing else. The two Alphas, a pretty double to the naked
eye, lie on the line drawn from Beta Cygni (at the foot
of the cross) through Altair, and produced about 25.
Some say that this constellation represents the god Pan, who was
represented by the Greeks as having the legs of a goat and the head
of a man. Others find in the goat Amalthea (the foster-mother of
the infant Jupiter), who is also, it will be remembered, represented
in the constellation of Auriga.
74. Delphinus, the Dolphin (Map IV). September.
This constellation, though small, is one of the ancient forty-
eight and is unmistakably characterized by the rhombus of
third-magnitude stars known as " Job's Coffin." It lies
about 15 east of Altair. There are a few stars visible
to the naked eye, in addition to the four that form the
rhombus. Epsilon, about 3 to the southwest, is the only
conspicuous one.
60 LESSONS IN ASTRONOMY
Gamma, at the northwest angle of the rhombus, is a very pretty
double star. Beta is also a very close and rapid binary, beyond the
reach of all but large telescopes.
This is the dolphin that preserved the life of the musician Arion,
who was thrown into the sea by sailors, but carried safely to land
upon the back of the compassionate fish, who loved his music.
75. Equuleus, the Little Horse (Map IV). This little constella-
tion, simply a horse's head, though still smaller than the Dolphin
and less conspicuous, is also one of Ptolemy's. It lies about 20 due
east of Altair, and 10 southeast of the Dolphin. (See map.)
76. Lacerta, the Lizard (Maps I and IV). This is one of Heve-
lius's modern constellations, lying between Cygnus and Andromeda,
with no stars above the 4 magnitude, and of no importance for our
purposes.
77. Pe'gasus (not Pegas'us) (Map IV). October. This
winged horse covers an immense space. Its most notable
configuration is the " great square," formed by the second-
magnitude stars Alpha (Markab), Beta, and Gamma
Pegasi, in connection with Alpha AndromedaB (sometimes
lettered Delta Pegasi) at its northeast corner. The stars
of the square lie in the body of the horse, which has no
hind quarters. A line drawn from Alpha Andrbmedse
through Alpha Pegasi, and produced about an equal dis-
tance, passes through Xi and Zeta in the animal's neck
and reaches Theta in his ear. Epsilon (Enif], the bright
star 8 northwest of Theta, marks his nose. The fore legs
are in the northwestern part of the constellation just east
of Cygnus and are marked, one of them by the stars Eta and
Pi, and the other by Iota and Kappa. 15 M. Pegasi is a fine
cluster but little inferior to that in Hercules.
Pegasus is the winged horse which sprang from the blood of
Medusa, after Perseus had cut off her head. He fixed his residence
on Mt. Helicon, where he was the favorite of the Muses, and after
UUANOGRAPHY 61
being tamed by Minerva he was given to Bellerophon to aid him in
conquering the Chimsera. After the destruction of the monster,
Bellerophon attempted to ascend to heaven upon Pegasus, but the
horse threw off his rider and continued his flight to the stars.
78. Aquarius, the Water-Bearer (Map IV). October. -
This, the twelfth and last of the zodiacal constellations,
extends more than 3 h in right ascension, covering a con-
siderable region which by rights ought to belong to Capri-
cornus. The most notable configuration is the little Y of
third- and fourth-magnitude stars which marks the " water-
jar" from which Aquarius pours the stream that meanders
down to the southeast and south for 30, till it reaches
the Southern Fish. The middle of the Y is about 18
south and west of Alpha Pegasi and lies almost exactly
on the celestial equator.
Zeta, the central star of the Y, is a pretty and interesting double
star ; distance, about 4". The " green nebula," nearly on the line
from Alpha through Beta, produced about its own length, 1 west
of Nu, is a planetary nebula and curious from the vividness of its
color.
There are various opinions respecting the origin of this constel-
lation. According to a Greek legend it represents Deucalion, the
hero of the Greek Deluge; but among the Egyptians it evidently
had reference to the rising and falling of the Nile.
79. Piscis Austrinus (or Australis), the Southern Fish
(Map IV). October. This small constellation, lying
south of Capricornus and Aquarius in the stream that
issues from the Water-Bearer's, urn, presents little of
interest. It has one bright star, Fomalhaut (pronounced
Fomal-hawt 1 ), of the 1| magnitude, which is easily recog-
nized from its being nearly on the same hour-circle with
the western edge of the Great Square of Pegasus, 45 to
62 LESSONS IN ASTRONOMY
the south of Alpha Pegasi, and solitary, having no star
exceeding the fourth magnitude within 15 or 20. An
incorrect pronunciation (Fomalo) is common; but "haut"
is Arabic, not French.
This constellation is by some said to represent the transformation
of Venus into a fish, when fleeing from Typhon (but see Pisces).
South of the Southern Fish, barely rising above the southern hori-
zon, lie the constellations of Microscopium and Grus. The former is
of no account. In the southern hemisphere Grus is a conspicuous
constellation, and its two brightest stars, Alpha and Beta, of the
second magnitude, rise high enough to be seen in latitudes south
of Washington. They lie about 20 south and west of Fomalhaut.
URANOGRAPHY
63
CHAPTER III
LATITUDE, TIME, AND LONGITUDE
Latitude, and the Aspect of the Celestial Sphere Time Longitude The
Place of a Heavenly Body
80, Latitude defined. In Geography the latitude of a
place is "usually denned simply as its distance north or
south of the equator, measured in degrees. This is not
explicit enough, unless it is stated how the degrees them-
selves are to be measured. There would be no difficulty
if the earth were a perfect sphere ; but since the earth
is a little flattened at the poles, the degrees (geographical)
are of somewhat different lengths at different parts of
the earth. The exact definition of the astronomical lati-
tude of a place istJie angle between the direction of Jjie
observer's plumb-line and the plane of the earth's equators-
-L _ -L _ * J. . *
ancT this is the same as the altitude, or angle of elevation,
of the pole, as will be clear from Fig. 7. Here the angle
ONQ is the latitude as denned. If now at we draw
HH 1 perpendicular to OZ, it will be a level line, and will
point to the horizon. From also draw OP", parallel to
CP\ the earth's axis. Since OP" and CP' are parallel,
they will be directed apparently to the same point in the
celestial sphere (Sec. 6), and this point is the celestial
pole. The angle H' OP" is therefore the altitude of the
pole, as seen at 0, and it obviously equals ONQ ; and this
is true whether the earth be a sphere, or whatever its
64
LATITUDE
65
form. This fundamental relation, that the Altitude <>f the
Pole is Identical with the Observer's Latitude, cannot be
too strongly impressed on the mind.
81. Method of measuring the Latitude. The most obvi-
ous method is to observe, with a suitable instrument, the
altitude of some star near the pole (a " circumpolar " star)
at the moment when
it is crossing the me- Z
ridian above the pole,
and again twelve hours
later, when it is once
more on the meridian
below the pole. In the
first position its eleva-
tion is the greatest pos-
sible ; in the second,
the least. The average
Of these two altitudes, Fl . 7. -Relation of Latitude to the Elevation
of the Pole
when corrected for re-
fraction, is the latitude of the observer. It is exceedingly
important that the student understand this simple method
of determining the latitude.
The instrument ordinarily used for making observations of this
kind at an observatory is called a meridian circle, and a brief descrip-
tion is given in the Appendix. (See Sec. 418.)
82. Refraction When we observe the altitude of a
heavenly body with any instrument we do not find it the
same that it would be if our atmosphere had no effect
upon the rays of light. As they enter the earth's atmos-
phere they are bent downward by " refraction," excepting
only such as come from exactly overhead. Since the
66 LESSONS IN ASTRONOMY
observer sees the object in the direction in which the rays
enter the eye, without any reference to its real position, this
bending down of the rays causes every object seen through
the air to look higher up in the sky than it would be if the
air were absent ; and we must therefore correct the observed
altitude by subtracting the proper amount. Under ordinary
conditions, refraction elevates a body at the horizon about
35', so that the sun and moon in rising appear clear of the
horizon while they are still wholly below it. The refraction
correction diminishes very rapidly as the body rises. At
an altitude of only 5 the refraction is but 10'; at 44,
it is about V ; and at the zenith, zero, of course.
Its amount at any given time is affected quite sensibly, however,
by the temperature and by the height of the barometer, increasing
as the thermometer falls or as the barometer rises ; so that whenever
great accuracy is required in measures of altitude we must have
observations of both the barometer and thermometer to go with the
reading of the circle. There are tables by which the refraction can
be computed for an object at any altitude and in any state of the
weather. But this indispensable correction is very troublesome, and
always involves more or less error.
(For other methods of determining the latitude, see
Appendix, Sec. 424.)
83, Effect of the Observer's Latitude upon the Aspect of
the Heavens ; the Right Sphere. If the observer is situ-
ated at the earth's equator, i.e., in latitude zero, the
celestial poles will evidently be on the horizon, and the
celestial equator will pass through the zenith and coincide
with the prime vertical (Sec. 11). At the earth's equator,
therefore, all heavenly bodies will rise and set vertically,
and their diurnal circles will be equally divided by the
ASPECT OF THE HEAVENS
67
horizon, so that they will be twelve hours above it and
twelve hours below it, and the length of the night (neglect-
ing refraction) will always equal that of the day. This
aspect of the heavens is called the right sphere.
84. Parallel Sphere. If the observer is at one of the
poles of the earth, where the latitude equals 90, then the
corresponding celestial pole will be exactly overhead, and
the celestial equator will coincide with the horizon. If he
is at the north pole, all
the stars north of the
celestial equator will re-
main permanently visible,
never rising or setting,
but sailing around the sky
on parallels of altitude,
while the stars south of
the equator will never rise
to view. Since the sun
and the moon move in
such a way that during
half the time they are
north of the equator and
FIG. 8. The Oblique Sphere
half the time south of it, they will therefore be half the
time above the horizon and half the time below it (that is,
approximately, since refraction has a noticeable effect).
The moon will be visible for about a fortnight at a time,
and the sun for about six months.
85. The Oblique Sphere At any station between the
pole and the equator the pole will be elevated above the
horizon, and the stars will rise and set in oblique circles,
as shown in Fig. 8. Those stars whose distance from the
68 LESSONS IN ASTRONOMY
elevated pole is less than PN, the latitude of the observer,
will never set, the radius of this circle of perpetual appa-
rition being just equal to the altitude of the pole, and
becoming larger as the latitude increases. On the other
hand, stars within the same distance of the depressed pole
will lie within the circle of perpetual occultation, and will
never rise above the observer's horizon. An object which
is exactly on the celestial equator will have its diurnal
circle, EQ WQ!, equally divided by the horizon, and will be
above the horizon just as long as below it.
For an observer in the United States a star north of the
equator will have more than half of its diurnal circle above
the horizon, and will be visible for more than twelve hours
of each day; as, for instance, the star at A. Whenever
the sun is north of the celestial equator the day will there-
fore be longer than the night for all stations in northern
latitude ; how much longer will depend both on the latitude
of the place and the sun's distance from the equator (the
sun's declination}.
86. Moreover, when the sun is north of the equator, it
will, in the northern latitudes, rise at a point north of east,
as at B in the figure, and will continue to shine, on the
north side of every wall that runs east and west until, as
it ascends, it crosses the prime vertical, EZW, at some
point, as V. In the latitude of New York the sun in June
is south of the prime vertical for only about eight hours
of the whole fifteen during which it is above the horizon.
During seven hours of the day, therefore, it shines into
north windows.
If the latitude of the observer is such that PN, in the
figure, is greater than the sun's polar distance at the time
TIME 69
when it is farthest north, the sun at midsummer will make
a complete circuit of the heavens without setting, thus
producing the phenomenon of the " midnight sun," visible
at the North Cape and at all stations within the Arctic
Circle.
87. A celestial globe will be of great use in studying
these diurnal phenomena. The north pole of the globe
must be elevated to an angle equal to the latitude of the
observer, which can be done by means of the degrees marked
on the metal meridian ring. It will then be seen at once
what stars never set, which ones never rise, and during
what part of the twenty-four hours any heavenly body at
a known distance from the equator is above or below the
horizon. (For description of the celestial globe, see Appen-
dix, Sec. 400.)
TIME
Time is usually denned as " measured duration," and
the standard unit of time has always been obtained in some
way from the length of the day.
88. Apparent Solar Time. The most natural way, since
we are obliged to regulate our lives by the sun, is to reckon
time by him ; i.e., to call it noon when the sun is on the
meridian and highest, and to divide the day from one noon
to another into its hours, minutes, and seconds. Time
thus reckoned is called apparent solar time (see Appendix,
Sec. 422), and is the time shown by a correctly adjusted
sundial. But because the sun's eastward motion in the
sky is not uniform (owing to the oval form of the earth's
orbit and its inclination to the equator), these apparent
solar days are not exactly of the same length. Thus, for
70 LESSOXS IN ASTRONOMY
instance, the interval from noon of December 22 to noon
of December 23 is. nearly a minute longer than the inter-
val between the noons of September 15 and 16. As a con-
sequence, it is only by very complicated and expensive
machinery that a watch or clock can be made to keep time
precisely with the sundial; nor is it worth while, since
it is much better to have the timekeeper uniform in its
motion. Apparent solar time is now used only in commu-
nities where clocks and watches are rare and sundials are
the usual timepieces, as in China and in much of the "East.
89. Mean Solar Time. At present, for civil ancf busi-
ness purposes, time is almost universally reckoned Jn days
ail~i)f~ which have precisely the same length, and are just
equal to the average apparent solar day; and
called mean solar time (Appendix, Sec. 422), is that whic
is kept by all good timepieces.
Sundial time agrees with mean time four times a year; viz., upon
April 15, June 14, September 1, and December 24. The greatest
differences occur on November 2 and February 11, when the sundial
is respectively 16 m 20 8 fast of the clock and 14 m 30 s slow. . During
the summer the difference never exceeds 6 m . Tills, variable differ-
ence is called the Equation of Time, and is given i
every day in the year.
90. The Civil Day and the Astronomical Day. The astronomical
day begins at noon ; the civil day at midnight, tw r elve hours earlier.
Astronomical mean time is reckoned around through the whole
twenty -four hours, instead 01 oeing counted in two series o
hours each. Thus, 8 A.M. of Tuesday, August 12, civil reckoning,
is Monday, August 11, 20 h , of astronomical reckoning. Beginners
need to bear this in mind in referring to the almanac.
91. Jidereal Time, or Time reckoned by the Stars. As
has been said (Sec. 17), the sun is not fixed on the celestial
DETERMINATION OF TIME 71
sphere, but appears to creep completely around it once
a year, moving : daily about one degree eastward among the
stars. The~interval from noon to noon does not therefore
correspond to the true diurnal revolution of the heavens.
If we reckoned by the interval between two successive
passages of any given star across the observer's meridian,
we should find that this true day, the sidereal day, as it
is (-idled, is nearly 4 m shorter (3 m 56 s .9) than the ordinary
solar day, from noon to noon, the relation being such that
in a year the number of sidereal days exceeds that of solar by
exactly one. For many purposes, astronomers find it much
more convenient to reckon by the stars than by the sun.
They count the time, however, not by any real star, but
from the Vernal Equinox, the sidereal clock being so set
and regulated that it always shows zero hours, minutes,
and seconds (sidereal noon) at the moment when the vernal
equinox is on the meridian. (See Appendix, Sec. 422.)
This kind of time, of course, would not answer for busi-
ness purposes, since its noon comes at all hours of the day
and night at different seasons of the year. The almanac
gives data by which sidereal time and mean solar time can
be easily converted into each other.
92, The Determination of Time. In practice, the
problem always takes the shape of finding the error of a
timepiece of some sort ; i.e., ascertaining how many seconds
it -is fast or slow. The instrument now ordinarily used
for the purpose is the transit instrument, which is a small
telescope mounted on an axis, placed exactly east and
west, and level, so that as the telescope is turned it will
follow the meridian ; at least, the middle cross-wire in the
field of view will do so. It is the same as the meridian
72 LESSONS IN ASTRONOMY
circle, except that it does not require the costly graduated
circle with its appendages. (For description, see Appendix,
Sec. 416.)
To determine with the transit the error of the sidereal
clock which is ordinarily used in connection with it, it is
only necessary to observe the exact time indicated by the
clock when some star whose right ascension is known
passes, or " transits," the middle wire of the instrument.
93. The right ascension of a star (Sec. 18) is the num-
ber of " hours " of arc (measured along the equator) by which
the star is east of the vernal equinox ; and therefore when the
star is on the meridian the right ascension also equals the
number of hours, minutes, and seconds since the transit
of the vernal equinox. In other words, we may say that"-
the right ascension of a star is the local sidereal time at the
moment of its meridian transit. (This is often called the
observatory definition of right ascension.) For instance,
the right ascension of Vega (Alpha Lyrse) is 18 h 33 m . If
we observe its transit to occur at 18 h 40 m by the clock, the
clock is obviously 7 m fast.
With a good instrument, a skilled observer by observing
a number of stars can thus determine the clock-error
within about one-thirtieth of a second of time.
To get solar time, we may observe the sun itself, the
moment of its transit being " apparent noon." But it is
better, and it is usual, to get the sidereal time first, and to
deduce from that the solar time by means of the necessary
data which are furnished in the almanac.
The method by the transit instrument is most used, and is, on the
whole, the most convenient ; but since the instrument requires to be
mounted upon a firm pier, it is not always available. When not, we
LONGITUDE 73
use some one of various other methods, for which reference must be
made to the General Astronomy. At sea, and by travelers on scientific
expeditions, the time is usually determined by observing the altitude
of the sun with a sextant some hours before or after noon. (See
Appendix, Sec. 427.)
LONGITUDE
94. The problem of finding the longitude is in many
respects the most important of what may be called the
" economic " problems of Astronomy; i.e., those of business
utility to mankind. The great observatories of Greenwich
and Paris were founded for the express purpose of fur-
nishing the necessary data to enable the sailor to determine
his longitude at sea; and the English government has
given great prizes for the construction of clocks and chro-
nometers fit to be used in such determinations.
The longitude of a place on the earth is defined as the
arc of the equator intercepted between the meridian which
passes through the place and some meridian which is taken
as the standard. 1
Now, since the earth turns on its axis at a uniform rate,
this arc is strictly proportional to, and may be measured by,
the interval of sidereal time between the transits of a given
star across the two meridians, or by the interval of mean
solar time between the transits of the sun. The longitude
of a place may therefore be defined as the amounT~try--w&ich
the time at G-reenwich is earlier or later than, the time at the
station of the observer, and this whether we reckon by solar
or by sidereal time. Accordingly, terrestrial longitude is
1 As to the standard meridian, there is a variation of usage among dif-
ferent nations. The French reckon from the meridian of Paris, but most
other nations use the meridian of Greenwich, at least at sea.
74 LESSONS IN ASTRONOMY
usually reckoned in hours, minutes, and seconds, rather
than hi degrees. Since the observer can easily find his
own local time by the transit instrument, or by some of
the many other methods, the knot of the problem is simply
this : to find the Greenwich time at any moment without
going to Greenwich; then we get the longitude at once
by simply comparing it with our own time.
95. Methods of determining Longitude. Incomparably
the best method, whenever it is available, is to make a
direct telegraphic comparison between the clock of the
observer and that of some station the longitude of which
is known. The difference between the two clocks, duly
corrected for their " errors " (Sec. 92), will be the true dif-
ference of longitude. The wireless telegraph is now being
used for this purpose, and is especially convenient at sea,
where ordinary telegraphic communication is impossible.
Time signals are sent out daily from Arlington, Va., and
any one within the radius of these signals can get accurate
eastern standard time, which is exactly five hours behind
Greenwich time.
96, A second method is to use a chronometer, which is
simply a very accurate watch. This is set to Greenwich
time at some place whose longitude is known, and after-
wards is supposed to keep that time wherever carried.
The observer has only to compare his own local time,
determined with the transit instrument or sextant, with
the time shown by such a chronometer, and the difference
is his longitude from Greenwich. This is the ordinary
method at sea.
Practically, of course, no chronometer goes absolutely without
gaining or losing ; hence, it is always necessary to know and to
LOCAL AND STANDARD TIME 75
allow for its gain or loss since the time it was last set. Moreover, it
is never safe to trust a single chronometer, because of the liability of
such instruments to change their rate in transportation. A number
(three or more) should be used, if possible.
Before the days of telegraphs and chronometers, astrono-
mers were generally obliged to get their Greenwich time
from the moon, which may be regarded as a clock-hand
with the stars for dial figures; but observations of this
kind are troublesome, and the results inaccurate as com-
pared with those obtained by the telegraph and chronom-
eter. (For further details, see General Astronomy,
Arts. 109-116.)
97. Local and Standard Time. Until recently it has
been always customary to use local time, each station
determining its own time by its own observations, and
having, therefore, a time differing from that of all other
stations not on the same meridian. Before the days of
the telegraph, and while traveling was comparatively
slow, this was best. At present there are many reasons
why it is better to give up the old system in favor of a
system of standard time. The change greatly facilitates
all railway and telegraphic business, and makes it practi-
cally easy for everybody to have accurate time, since the
standard time can be daily wired from some headquarters
to every telegraph office.
According to the system now established in North
America, there are five such standard times in use, the
colonial, the eastern, the central, the mountain, and the
Pacific, which differ from Greenwich time by exactly
four, five, six, seven, and eight hours respectively, the
minutes and seconds being everywhere identical, and the
76 LESSONS IN ASTRONOMY
same with those of the clock at Greenwich. In order to
determine the standard time by observation, it is neces-
sary only to find the local time by one of the methods
given and correct it according to the observer's longitude
from Greenwich.
98. Where the Day begins. It is clear that if a trav-
eler were to start from Greenwich on Monday noon, and
travel westward as fast as the earth turns to the east
beneath his feet, he would have the sun upon the meridian
all day long, and it would be continual noon. But what
noon? It was Monday when he started, and when he
gets back to London twenty-four hours later it will be
Tuesday noon there, and yet he has had no intervening
night. When did Monday noon become Tuesday noon?
It is agreed among mariners to make the change of
date at the 180h meridian from Greenwich. Ships cross-
ing this line from the east skip one day in so doing. If
it is Monday afternoon when a ship reaches the line, it
becomes Tuesday afternoon the moment she passes it, the
intervening twenty-four hours being dropped from the
reckoning on the log-book. Vice versa, when a vessel
crosses the line from the western side it counts the same
day twice, passing from Tuesday back to Monday.
This 180th meridian passes mainly over the ocean, hardly touch-
ing land anywhere. There is some irregularity as to the date actually
used on the different islands of the Pacific. Those which received
their earliest European inhabitants via the Cape of Good Hope have,
for the most part, adopted the Asiatic date, even if they really lie
east of the 180th meridian, while those which were first approached
via Cape Horn have the American date. When Alaska was trans-
ferred from Russia to the United States it was necessary to drop
one day of the week from the official dates.
PLACE OF A CELESTIAL OBJECT 77
DETERMINATION OF THE POSITION OF A
HEAVENLY BODY
As the basis of our investigations in regard to the
motions of the heavenly bodies, we require a knowledge
of their places in the sky at known times. By determin-
ing the " place " of a body, we mean finding its right
ascension and declination.
99. By the Meridian Circle (see Appendix, Sec. 418).
If a body is bright enough to be seen by the telescope of the
meridian circle, and comes to the meridian in the nighttime,
its right ascension and declination are best determined by
the Meridian Circle. If the instrument is in exact adjust-
ment, the right ascension of the body is simply the sidereal
time when it crosses the middle vertical wire of the reticle.
The " circle-reading," on the other hand, corrected for
refraction, gives the declination. A single complete obser-
vation with the meridian circle determines accurately both
the right ascension and the declination of the object.
100. By the Equatorial. If the body a comet, for
instance is too faint to be observed by the telescope of
the meridian circle, seldom very powerful, or comes to the
meridian only in the daytime, we usually accomplish our
object by using the equatorial (Appendix, Sec. 414), and
determine the position of the body by measuring with
some kind of " micrometer " the difference of right ascen-
sion and declination between it and a neighboring star
whose place is given in some star-catalogue.
CHAPTER IV
THE EARTH
Its Form and Dimensions; its Rotation, Mass, and Density; its Orbital
Motion and the Seasons Precession The Year and the Calendar
101. In a science which deals with the "heavenly
bodies," there might seem at first to be no place for the
Earth. But certain facts relating to the Earth, just such
as we have to investigate with respect to her sister planets,
are ascertained by astronomical methods, and a knowledge
of them is essential as a base of operations. In fact, Astron-
omy, like charity, " begins at home," and it is impossible to
go far in the study of the bodies which are strictly " heav-
enly " until we have first acquired some accurate knowledge
of the dimensions and motions of the earth itself.
102. The astronomical facts relating to the earth are
broadly these :
1. The earth is a great ball about 7920 miles in diameter.
2. It rotates on its axis once in twenty-four " sidereal "
hours.
3. It is not exactly spherical, but is slightly flattened at
the poles ; the polar diameter being nearly twenty-seven
miles, or about ^^ part less than the equatorial.
4. It has a mean density of about 5.5 times that of
water, and a mass represented in tons by 6 with twenty-
one ciphers following (six thousand millions of millions
millions of tons).
78
THE EARTH 79
5. It is flying through space in its orbital motion around
the sun, with a velocity of about eighteen and a half miles
a second; i.e., about seventy-five times as swiftly as an
ordinary cannon-ball.
103. The Earth's Approximate Form and Size It is
not necessary to dwell on the jmlinary proofs of the globu-
larity of the earth. We simply mention them.
1. It can be sailed around.
2. The appearance of vessels coming in from the sea
indicates that the surface is everywhere convex.
3. The fact that as one goes from the equator towards
the north the elevation of the pole increases in proportion
to the distance from the equator, proves the same thing.
^L__The outline of the earth's shadow, as seen upon the moon
during lunar eclipses, is such as only a sphere could cast.
We may add, as to the smoothness and roundness of the
earth, that if the earth be represented by an eighteen-inch
globe, the difference between its greatest and least diam-
eters would be only about one-sixteenth of an inch; the
highest mountains would project only about one-eightieth
of an inch, and the average elevation of continents and
depths of the ocean would be hardly greater than a film
of varnish. Relatively, the earth is really much smoother
and rounder than most of the balls in a bowling-alley.
104. One of the simplest methods of showing the curvature of
the earth is the following :
In an expanse of still, shallow water (a long reach of canal, for
instance) set a row of three poles about a mile apart, with their
tops projecting to exactly the same height above the surface. On
sighting across, it will then be found that the middle pole projects
above the line that joins the tops of the two end ones, and from the
amount of this projection, after due correction for refraction (which
80
LESSONS IN ASTRONOMY
reduces it from about eight inches to six under ordinary conditions
of temperature), a rough estimate of the size of the earth can be
made. (See General Astronomy, Art. 134.)
105. Measure of the Earth's Diameter. The only accu-
rate method of measuring the diameter of the earth is the
following, the principle of which is very simple, and should
be thoroughly mastered by the
student :
It consists infmding_the
length in miles of an arc of
the earth's surface containing a
known number of degrees. From
this we get the length of one
degree, and this gives the circum-
ference of the earth (since it
contains 360), and from this the
diameter is obtained by dividing
it by 3.14159.
To do this, we select two
stations, a and b (Fig. 9), some
hundreds of miles apart on the
same meridian, and determine
the latitude / Qr the a l t i tu de of
FIG. O.-Measuring the Earth's
Diameter
the pole) at each station by
astronomical observation. The difference of latitude (i.e.,
ECl EC a) is evidently the number of degrees in the arc
ab, and the determination of this difference of latitude
is the only astronomical operation necessary.
Next, the distance in miles between the two stations
must be measured. This is geodetic work, and it is
enough for our purpose here to say that it can be
THE EARTH'S ROTATION 81
done with great precision by a process which is called
" triangulation."
This measurement of arcs has been made on many parts
of the earth's surface, and the result is that the average
length of a degree is found to be a little more than sixty-
nine miles, and the mean diameter of the earth about
7918 miles. The reason why we say average length and
mean diameter is that the earth, as has been said, is not
quite spherical, but is slightly flattened at its poles, so
that the lengths of the degrees differ in different parts of
the earth, as we shall soon see (Sec. 110).
106. The Rotation of the Earth. Ptolemy understood
that the earth was round^ but he and all his successors
deliberately rejected the theory of its rotation. Though
the idea that the earth might turn upon an axis was not
unfamiliar, they considered that there were conclusive
reasons against it. At the time when Copernicus of Thorn,
in Poland (1473-1543), proposed his theory of the solar
system, the only argument he could urge in favor of the
earth's rotation l was that this hypothesis was much more
probable than the older one that the heavens themselves
revolve. All the phenomena then known would be sen-
sibly the same on either supposition. The apparent daily
motion of the heavenly bodies can be perfectly accounted
for (within the limits of such observations as were then
possible) either by supposing that they are actually attached
to the celestial sphere, which turns daily, or that the earth
1 The word ** rotation " denotes a spinning motion, like that of a wheel
on its axis. The word "revolve" is more general, and may be used to
describe such a spinning motion or (and this is the more common use in
Astronomy) to describe the motion of a body traveling around another,
as when we say the earth " revolves " around the sun.
82
LESSONS IN ASTRONOMY
itself spins upon an axis once in twenty-four hours ; and
for a long time the latter hypothesis did not seem to most
people so reasonable as the older and more obvious one.
A little later, after the telescope had been invented, analogy
could be appealed to ; for we can see with the telescope
that the sun and moon -and many of the planets really
rotate upon axes. At present we can go still further, and
can absolutely demon-
strate the earth's rota-
tion by experiments,
some of which even
make it visible.
107. Foucault's Pen-
dulum Experiment. -
Among these experi-
mental proofs the most
impressive is the "pen-
dulum experiment"
devised by Foucault in
1851. From the dome
of the Pantheon, in
Paris, he hung a heavy
iron ball by a slender
wire more than 200 feet
long (Fig. 10). A circular rail, with a little ridge of sand
built upon it, was placed in such a way that a pin attached
to the swinging ball would just scrape the sand and leave
a mark at each vibration. To put the ball in motion, it was
drawn aside by a cotton cord and left for some hours, until
it came absolutely to rest. Then the cord was burned off,
and the pendulum started to swing in a true plane.
FIG. 10. Foucault's Pendulum in the
Pantheon
THE EARTH'S ROTATION 83
But this plane at once began to deviate slowly towards
the right, so that the pin on the pendulum ball cut the
sand ridge in a new place at each swing, shifting at a rate
which would carry the line fully around in about thirty-
two hours, if the pendulum did not first come to rest. In
fact, the floor was actually and visibly turning under the
plane defined by the swinging of the pendulum.
The experiment created great enthusiasm at the time and has since
been frequently performed (in Paris, very recently). The pendulum
used in such experiments must, in order to secure success, have a
round ball, must be suspended by a round wire or on a point, and
must be very heavy, very long, and very carefully protected against
currents of wind. At the pole the plane of the pendulum will shift
completely around once in twenty-four hours ; at the equator it will
not turn at all; and in the intermediate regions it will shift more
or less rapidly according to the latitude of the place where the
experiment is performed. (For fuller description, see General
Astronomy, Arts. 140 and 141.)
There are a number of other experimental proofs of the earth's
rotation, which are really just as conclusive as the one above cited
(General Astronomy, Arts. 138-144).
108, Invariability of the Earth's Rotation. It is a
question of great importance whether the day ever changes
its length. Theoretically, it must almost necessarily do so.
The friction of the tides and the fall of meteors upon the
earth both tend to retard the rotation, while, on the other
hand, the earth's loss of heat by radiation and the conse-
quent shrinkage of the globe must tend to accelerate it,
and to shorten the day. Then geological changes, the
elevation and subsidence of continents, and the transporta-
tion of soil by rivers, act, some one way and some the
other. At present we can only say that the change, if any
84
LESSONS IN ASTRONOMY
change has occurred since Astronomy became accurate, has
been too small to be detected. The day is certainly not
longer or shorter by the ^ part of a second than it was
in the days of Ptolemy; probably it has not changed by
the TliW P art of a second, though of that we can hardly
be sure.
109. Shiftings of the Earth's Axis Theoretically, any changes
in the distribution of materials within or upon the globe of the earth
ought to produce corresponding displacements of the axis, and these
would principally show
themselves as variations in
the latitudes and longitudes
of observatories. The actual
variations are so minute,
however, that it is only as
recently as 1889 that they
were first clearly detected by
certain German observers,
whose results have since been
abundantly confirmed and
FIG. 11. - Effect of Earth's Rotation on its extended - Jt w now beyond
Form doubt that the earth really
"wobbles" in whirling; and
this causes each pole to describe an apparently irregular path around
its mean position, never departing from it, however, by more than
forty or fifty feet. Dr. Chandler has shown that this motion is com-
pounded of two : one oval, with a period of a year ; the other circular,
with a period of 428 days.
To explain certain geological phenomena it has been surmised that
great and permanent displacements of the poles have occurred in the
distant past. But of this we have, as yet, no satisfactory evidence.
110. Effect of the Earth's Rotation on its Form. The
whirling of the earth on its axis tends to make the globe
bulge at the equator and flatten at the poles, in the way
THE EARTH'S FORM 85
illustrated by the well-known little apparatus shown in
Fig. 11. That the equator does really bulge in this way
is shown by measuring the length of a degree of latitude
on the various parts of the earths surface between the equator
and the pole, in the manner indicated a few pages back
(Sec. 105). More than twenty such arcs have been meas-
ured, and it appears that the length of the degrees increases
regularly from the equator towards the poles, as shown in
the following table :
equator, one degree = 68.704 miles.
AUat. 20 =68.786
" " 40 " " = 68.993 "
" 60 " " = 69.230
80 " = 69.386 "
At the pole, " = 69.407
The difference between the equatorial and polar degree
of latitude is more than 0.7 of a mile, or over 3700 feet,
while the probable error of measurement cannot exceed a
foot or two to the degree.
From this .table it can be calculated, by methods which
cannot be explained without assuming too much mathe-
matical knowledge in our readers, that the earth is Qrange-
shaped, or "an oblate spheroid," the diameter from pole
to pole being 7899.74 miles, while the equatorial diameter
is 7926.61 miles. The difference, 26.87 miles, is about ^
of the equatorial diameter. This fraction, ^^, is called
the ollateness, or ellipticity, of the earth.
Students are often puzzled by the fact that although the pole is
nearer the center of the earth than the equator, yet the degrees of
latitude are longest at the pole. It is because the earth's surface
86
LESSONS IN ASTRONOMY
there is more nearly flat than anywhere else, so that a person has to
travel more miles to change the direction of his plumb-line one
degree. Fig. 12 illustrates this. The angles adb audfhy are equal,
but the arc ab is longer than fg.
111. Effect of the Earth's Rotation and Ellipticity upon
the Force of Gravity. For two reasons the force of gravity
is less at the equator than at the poles. (1) The surface
of the earth is there thirteen and one-half miles farther
from the center, and this fact diminishes the gravity at
the equator by about 5-^. ( (2) The centrifugal force of
the earth's rotation
/& reduces the gravity
at the equator by
about ^-Q ; the
whole reduction,
therefore (^^ -j-
2l*) is ver y nearl y
equal to I ^- a ; i.e.,
an object which
weighs 190 pounds
at the equator
would weigh 191 pounds near the pole, weighed by an
accurate spring-balance. (In an ordinary balance the loss
of weight would not show, simply because the weights
themselves would be affected as much as the body weighed,
so that the balance would not be disturbed.)
The effect of this variation of gravity from the pole to the
equator is especially evident in the going of a pendulum
clock. Such a clock, adjusted to keep accurate time at the
equator, would gain 3 m 37 8 a day near the pole. In fact,
one of the best ways of determining the form of the earth
FIG. 12. Length of Degrees in Different
Latitudes
THE EARTH'S MASS AND DENSITY 87
is by experiments with a pendulum at stations which differ
considerably in latitude.
112. Surface and Volume of the Earth. The earth is
so nearly spherical that we can compute its surface and
volume with sufficient accuracy by the formula for a per-
fect sphere, provided we put the earth's mean semi-diameter
for the radius of the sphere. This mean semi-diameter is
not the average of the polar and equatorial diameters, but
is found by adding the polar diameter to twice the equa-
torial, and dividing by three. It comes out 7917.66 miles.
From this we find the earth's surface to be, in round num-
bers, 197,000000 square miles, and its volume, or bulk,
260000,000000 cubic miles.
113. TfceJSarth's Mass and Density. The volume (or
bulk) of a globe is simply the number of cubic miles of
space which it contains. If the earth were all made of
feathers or of lead, its volume would remain the same, as
long as the diameter was not altered. The earth's mass,
on the other hand, is the quantity of matter in it, the
number of tons of rock and water which compose it, and
of course it makes a great difference with this whether the
material be heavy or light. The density of the earth is the
number of times its mass exceeds that of a sphere of pure
water having the same dimensions.
The methods by which the mass of the earth can be measured
depend upon a comparison between the attraction which the earth
exerts upon a body at its surface and the attraction which is exerted
upon the same body by another body of known mass and at a known
distance. The necessary experiments are delicate and difficult,
because the attraction exerted by a body of any manageable size
is extremely minute. We must refer for details to our larger
book, General Astronomy, Arts. 164-170.
88 LESSONS IN ASTRONOMY
According to the best data at present available the earth's
density is about 5.53, and its mass about 6000 millions of
millions of millions of tons.
Among the recent determinations the most trustworthy
perhaps are those made by Boys in England in 1894, and
by Braun in Bohemia about the same time.
114. Constitution of the Earth's Interior. Since the
average density of the earth's crust does not exceed three
times that of water, while the mean density of the whole
earth is about ^5.5^ it is clear that at the earth's center the
density must be very much greater than at the surface.
Very likely it is as high as eight or ten times the density
of water, and equal to that of the heavier metals.
There is nothing surprising in this. If the earth were once fluid,
it is natural to suppose that the densest materials, in the process of
solidification, would settle towards the center.
Whether the center of the earth is now solid or fluid, it is difficult
to say with certainty. Certain tidal phenomena, to be mentioned
hereafter, have led Sir William Thomson to conclude that the earth
as a whole is solid throughout, and " more rigid than glass," vol-
canic centers being mere " pustules," so to speak, in the general
mass. His conclusions were confirmed by Michelson and Gale in
1913.
EARTH'S ORBITAL MOTION 89
THE APPARENT MOTION OF THE SUN AND THE
ORBITAL MOTION OF THE EARTH, AND THEIR
IMMEDIATE CONSEQUENCES
115. ThejBun's Apparent Motion among the Stars. The
sun's apparent motion among the stars, 1 which makes it
describe the circuit of the heavens once a year, must have
been among the earliest recognized astronomical phenomena,
as it is one of the most important. The sun, starting in
the spring, mounts northward in the sky each day at noon
for three months, appears to stand still a few days at the
summer solstice, and then descends towards the south, reach-
ing in autumn the same noonday elevation which it had in
the spring. It keeps on its southward course to the winter
solstice (in December), and then returns to its original
height at the end of a year, by its course causing and
marking the seasons.
Nor is this all. The sun's motion is not merely north
and south, but it also advances continually eastward among
the stars, completing the circuit in a year. It is true that
we cannot see the stars near the sun in the same -way that
we can those about the moon, so as to be able directly to
perceive this motion; but in the spring the stars which are
rising in the east at sunset are different from those which
are found there in the summer or in the winter. In March
the most conspicuous of the eastern constellations at
sunset are Leo and Bootes. A little later Virgo appears ;
in the summer Ophiuchus and Libra; still later Scorpio;
student must carefully discriminate between "motion among
the stars" and the diurnal motion, in which sun, moon, planets, and
comets all partake along with the stars.
90 LESSONS IN ASTRONOMY
while in midwinter Orion and Taurus are ascending as the
sun goes down. The combination of these two motions in
declination and right ascension annually carries the sun
around the heavens in the ecliptic (Sec. 20).
So far as the obvious appearances are concerned, it is
quite indifferent whether we suppose the earth to revolve
around the sun, or vice versa. That the earth really moves,
however, is absolutely demonstrated by two phenomena too
minute and delicate for observation without the telescope,
but accessible to modern methods. One of them is the
aberration of light, the other the annual parallax of the
Jixed stars. These can be explained only by the actual
motion of the earth, but we postpone their discussion for
the present. (See Sec. 343, and Appendix, Sec. 435.)
116, The Ecliptic; its Related Points and Circles. By
observing daily with the meridian circle the sun's declina-
tion and the difference between its right ascension and
that of some standard star, we obtain a series of positions
of the sun's center which can be plotted on the globe, and
we can thus mark out the path of the sun among the stars.
It turns out to be a great circle, as is shown by'its cutting
the celestial equator at two points just 180 apart (the
so-called "equinoctial points," or "equinoxes"), where it
makes an angle with the equator of approximately 23
(23 27' 08" in 1900).
This great circle, already several times referred to, is
called the Ecliptic, because, as was early discovered, eclipses
happen only when the moon is crossing it. Its position
among the constellations is shown upon the equatorial star-
maps. It may be defined as the circle in which the plane
of the earth's orbit cuts the celestial sphere.
THE ECLIPTIC AND THE ZODIAC 91
The angle which the ecliptic makes with the equator at the equi-
noctial points is called the Obliquity of the Ecliptic. This obliquity is-
evidently equal to the sun's greatest distance from the equator, i.e.,
its maximum declination (23 27'), which is reached in December
and June.
117. The two points in the ecliptic midway between the
equinoxes are called the Solstices, because at these points
the sun "stands," that is, ceases to move north or south.
Two circles drawn through the solstices parallel to the
equator are called the Tropics, or " turning-lines," because
there the sun turns from its northward motion to the
southward, or vice versa. The two points in the heavens
90 distant from the ecliptic are called the Poles of the
Ecliptic. The northern one is in the constellation of Draco,
about midway between the stars Delta and Zeta Draconis,
at a distance from the pole of the heavens equal to the
obliquity of the ecliptic, and on the Solstitial Colure, the
hour-circle which runs through the two solstices ; the hour-
circle which passes through the equinoxes being called the
Equinoctial Colure. Great circles drawn through the poles
of the ecliptic, and therefore perpendicular, or "second-
aries," to the ecliptic, are known as "circles of latitude."
It will be remembered (Sec. 20) that celestial longitude and
latitude are measured with reference to the ecliptic, and
not to the equator.
118. The Zodiac and its Signs. A belt 16 wide (8
on each side of the ecliptic) is called the Zodiac, or zone
of animals, the constellations in it, excepting Libra, being
all figures of animals. It is taken of that particular
width simply because the moon and all the principal
planets always keep within it. It is divided into the
LESSONS IN ASTRONOMY
so-called signs, each 30 in length, having the following
names and symbols :
Spring
f Aries
<j Taurus
L Gemini
f Cancer
Summer < Leo
[Virgo
fLibra ==
Au tuning Scorpio TT^
^Sagittarius f
TCapricornus V?
Winter < Aquarius sxx
[ Pisces x
The symbols are for the most part conventionalized pictures of
the objects. The symbol for Aquarius is the Egyptian character for
water. The origin of the signs for Leo, Capricornus, and Virgo is
not quite clear.
The zodiac is of extreme antiquity. In the zodiacs of
the earliest history the Fishes, Ram, Bull, Lion, and
Scorpion appear precisely as now.
119. The Earth's Orbit. The ecliptic must not be con-
founded with the earth's orbit. It is simply a great circle
of the infinite celestial sphere, the trace made upon that
sphere by the plane of the earth's orbit, which is its path
in space. The fact that the ecliptic is a great circle gives
us no information about the earth's orbit itself, except
that it lies in a plane passing through the sun. It tells us
nothing as to the orbit's real form and size.
By reducing the observations of the sun's right ascension
and declination through the year to longitude and latitude
(the latitude would always be exactly zero except for some
slight perturbations due chiefly to the moon's revolution
around the earth), and combining these data with observa-
tions of the sun's apparent diameter, we can, however,
ascertain the form of the earth's orbit and the law of its
THE EARTH'S ORBIT
93
motion. (The size of the earth's orbit, i.e., its scale of
miles, cannot be fixed until we find the sun's distance.)
The result is that the orbit is found to be very nearly a
circle, but not exactly so. It is an oval or ellipse, with
the sun at one of its foci (as illustrated in Fig. 13), but is
much more nearly circular than the oval there represented.
Its eccentricity is only about ^ ; that is to say, the dis-
tance from the center of the sun to the middle of
ellipse is only about g 1 ^ of
the average distance of the
sun from the earth.
The method by which
we proceed to ascertain the
form of the orbit may be
found in the Appendix,
the
FIG. 13. The Ellipse
Sec. 428. (For a description
of the ellipse, see Sec. 429.)
120. Definition of Terms.
The points where the earth is nearest to and most
remote from the sun are called respectively the Perihelion
and the Aphelion (December 31 and June 30), the line
joining them being the major axis of the orbit. This line,
indefinitely produced in both directions, is called the
Line of Apsides (pronounced Ap'si-deez), the major axis
being a limited piece of it. A line drawn from the sun to
the earth, or to any other planet at any point in its orbit,
as SP in Fig. 13, is called the planet's Radius Vector.
The variations in the sun's apparent diameter due to our
changing distance are too small to be detected without a
telescope, so that the ancients failed to perceive them.
Hipparchus, however, about 120 B.C. discovered that the
94 LESSONS IN ASTRONOMY
earth is not in the center 1 of the circular orbit which he sup-
posed the sun to describe around it with uniform velocity.
Obviously the sun's apparent motion is not uniform,
because it takes 186 days for the sun to pass from the
vernal equinox, March 20, to the autumnal, September 22,
and only 179 days to return. Hipparchus explained this
on the hypothesis that the earth is out of the center of the
circle.
121. The Law of the Earth's Motion. By combining
the measured apparent diameter of the sun with the differ-
ences of longitude from day
to day we can deduce mathe-
matically not only the form
of the earth's orbit, but the
law of her motion in it. It
can be shown from the com-
parison that the earth moves
in such a way that its radius
FIG. 14. Equable Description of vector describes areas propor-
tional to the time, a law which
Kepler first brought to light in 1609 ; that is to say, if ab,
cd, and ef (Fig. 14) be portions of the orbit described by the
earth in different weeks, the areas of the elliptical sectors
aSb, cSd, and eSf are all equal. A planet near perihelion
moves faster than at aphelion in just such proportion as
to preserve this relation.
As Kepler left the matter, this is a mere fact of obser-
vation. Newton afterwards proved that it is the necessary
1 Hipparchus (and every one else until the time of Kepler, 1607)
assumed on metaphysical grounds that the sun's orbit must necessarily
be a circle, and described with a uniform motion.
CHANGES IN THE EARTH'S ORBIT 95
mechanical consequence of the fact that the earth moves
under the action of a force always directed towards the sun.
It is true in every case of the elliptical motion of a heavenly
body, and enables us to find the position of the earth or of any planet,
when we once know the time of its orbital revolution (technically
the "period") and the time when it was last at perihelion. The
solution of the problem, first worked out by Kepler, lies, however,
quite beyond the scope of the present work.
122. Changes in the Earth's Orbit. The orbit of the
earth changes slowly in form and position, though in the
long run it is unchangeable as regards the length of its
major axis and the duration of the year.
These so-called "secular changes" are due to "pertur-
bations " caused by the action of the other planets upon
the earth. Were it not for their attraction the earth would
keep her orbit with reference to the sun and stars abso-
lutely unaltered from age to age.
Besides these secular perturbations of the earth's orbit,
the earth itself is also continually being slightly disturbed
in its orbit. On account of its connection with the moon
it oscillates each month a few hundred miles above and
below the true plane of the ecliptic, and by the action of
the other planets is sometimes set backwards or forwards
in its orbit to the extent of some thousands of miles. Of
course every such displacement of the earth produces a
corresponding slight change in the apparent position of
the sun and of the nearer planets.
123, The Seasons. The earth in its motion around the
sun always keeps its axis nearly parallel to itself during
the whole year, for the mechanical reason that a spinning
globe maintains the direction of its axis invariable, unless
96
LESSONS IN ASTRONOMY
disturbed by some outside force (very prettily illustrated
by the gyroscope). Fig. 15 shows the way in which the
north pole of the earth is tipped with reference to the sun
at different seasons of the year. At the vernal equinox
(March 20) the earth is situated so that the plane of its
equator passes through the sun. At that time, therefore,
the circle which bounds the illuminated portion of the
earth passes through the two poles, as shown in Fig. 16, B,
Autumnal Equinox
Vernal Equinox
FIG. 15. The Seasons
and day and night are therefore equal, as implied by the
term " equinox." The same is again true on the 22d of
September. About the 21st of June the earth is so situ-
ated that its north pole is inclined towards the sun by
about 23|, as shown in Fig. 16, A. The south pole is
then in the unlighted half of the earth's globe, while the
north pole receives sunlight all day long, and in all por-
tions of the northern hemisphere the day is longer than
THE SEASONS 97
the night. In the southern hemisphere, on the other hand,
the reverse is true.
At the time of the winter solstice the southern pole has
continual sunshine, and the north pole is in the night.
At the equator of the earth day and night are equal at
all times of the year, and at that part of the earth there
are no seasons in the proper sense of the word, though
there are usually alternations of rain and drought due to
changes in the direction of the winds. Everywhere else
the day and night are unequal,
except when the sun is at one
of the equinoxes.
In high latitudes the inequal-
ity between the lengths of the
day in summer and in winter
is Very great; and at places FIG. 16,- Position of Pole at
Solstice and Equinox
within the polar circle there
are always days in winter when the sun does not rise at
all, and others in the summer when it does not set, but
exhibits the phenomenon of the "midnight sun," as
already explained in Sec. 86. At the pole itself the
summer is one perpetual day, six months in length, while
the winter is a six-months night.
Perhaps the student will get a better idea by thinking of the earth
as a globe floating, just half immersed, on a sheet of still water, and
so weighted that its poles dip at an angle of 23^, while it swims in
a circle around the sun, a much larger globe, also floating on the
same surface. The sheet of water corresponds to the ecliptic, while
the plane of the equator is a circle on the globe itself, drawn square
to the axis. If now the axis is kept pointing always the same way
(always north, for instance), while the globe swims around, things
will correspond to the motion of the earth around the sun.
98 LESSONS IN ASTRONOMY
124, Effects on Temperature. The changes in the dura-
tion of insolation (exposure to sunshine) at any place involve
changes of temperature, thus producing the seasons. It is
clear that the surface of the soil at any place in the north-
ern hemisphere will receive daily from the sun more than
the average amount of heat whenever he is north of the
celestial equator, and for two reasons :
1. Sunshine lasts more than half the day.
2. The mean altitude of the sun during the day is greater
than the daily average for the year, since he is higher at
noon than at the time of the
equinox, and in any case
reaches the horizon at rising
and setting.
Now the more obliquely
the rays strike, the less heat
they bring to each square
FIG. 17. -Effect of Sun's Elevation inch of surface, as is obvious
on Amount of Heat imparted to from Fig. 17. A beam of SU11-
shine which would cover the
surface AC, if received squarely, will be spread over a
much larger surface, Ac, if it falls at the angle h. The
difference in favor of vertical rays is further exaggerated
by the absorption of heat in our atmosphere, because the
rays that are nearly horizontal have to traverse a much
greater thickness of air before reaching the ground.
For these two reasons, therefore, the temperature rises
rapidly for a place in the northern hemisphere as the sun
comes north of the equator. We, of course, receive the
most heat in twenty-four hours at the time of the summer
solstice ; but this is not the hottest time of the summer.
PRECESSION 99
The weather is then getting hotter, and the maximum
will not be reached until the increase ceases, i.e., not
until the amount of heat lost in twenty-four hours equals
that received in the same time. This maximum is reached
in our latitude about the 1st of August. For similar
reasons the minimum temperature in winter occurs about
February 1.
125, Precession of the Equinoxes.
ward motion of the equinoxes along the ecliptic. In explain-
ing the seasons we have said (Sec. 123) that the earth keeps
its axis nearly parallel to itself during its annual revolu-
tion. It does not maintain strict parallelism, however ; but
owing to the attraction of the sun and moon on that portion
of the mass of the earth which projects, like an equatorial
ring, beyond the true spherical surface, the earth's axis
continually but slowly shifts its place, keeping always
nearly the same inclination to the plane of the ecliptic, so
that its pole revolves in a small circle of 23 radius around
the pole of the ecliptic once in 25,800 years. Of course
the celestial equator must move also, since it has to keep
everywhere just 90 from the celestial pole ; and, as a
consequence, the equinoxes move westward on the ecliptic
about 50". 2 each year, as if to meet the sun. This motion
of the equinox was called " precession" by Hipparchus, who
discovered 1 it about 125 B.C., but could not explain it.
The explanation was not reached until the time of Newton,
about 200 years ago, who showed it to be a necessary result
of gravitation operating under the actual conditions.
1 He discovered it by finding that in his time the place of the equinox
among the stars was no longer the same that it used to be in the days of
Homer and Hesiod, several hundred years before.
100 LESSONS IN ASTRONOMY
126. Effect of Precession upon the Pole and the Zodiac.
At present the Pole-star, Alpha Ursse Minoris, is about
li from the pole, while in the time of Hipparchus the
distance was fully 12. During the next two centuries
the distance will diminish to about 30', and then begin to
increase.
If upon the celestial globe we trace a circle of 23
radius around the pole of the ecliptic as a center, it will
mark very nearly the track of the celestial pole among
the stars.
Other causes slightly shift the position of the ecliptic and its pole,
so that the actual path of the pole among the stars deviates sensibly
from an exact circle.
It passes not very far from Alpha Lyrse (Vega), on the opposite
side of the circle from the present Pole-star ; about 12,000 years hence
Vega will, therefore, be the Pole-star. Reckoning backwards, we
find that some 4000 years ago Alpha Draconis (Thuban) was the
Pole-star, and about 3 from the pole.
Another effect of precession is that the signs of the
zodiac do not now agree with the constellations, which
bear the same name. The sign of Aries is now in the
constellation of Pisces, and so on, each sign having
"backed" bodily, so to speak, into the constellation west
of it.
The forces which cause precession do not act quite uni-
formly, and as a result the rapidity of the precession varies
somewhat, and there is also a slight tipping or nodding of
the earth's axis, which is called nutation. (For a fuller
account of the whole matter, see General Astronomy,
Arts. 209-215.)
EARTH'S ORBITAL '^MOTION 101
THE YEAR AND THE CALENDAR
127. Three different kinds of "year" are now recog-
nized, the Sidereal, the Tropical (or Equinoctial), and
the Anomalistic.
The sidereal year, as its name implies, is the time
occupied by the sun in apparently completing the circuit
from a given star to the same star again. Its length is
365 d 6 h 9 m 9 8 . From the mechanical point of view this is
the true year, i.e., it is the time occupied by the earth in
completing its revolution around the sun from a given
direction in space to the same direction again.
The tropical year is the time included between two suc-
cessive passages of the vernal equinox by the sun. Since
the equinox moves yearly 50". 2 towards the west, the trop-
ical year is shorter than the sidereal by about twenty minutes,
its length being 365 d 5 h 48 m 46 8 . Since the seasons depend
on the surfs place with respect to the equinox, the tropical
year is the year of chronology and civil reckoning.
The third kind of year is the anomalistic year, the time between
two successive passages of the perihelion by the earth. Since the
line of apsides of the earth's orbit makes an eastward revolution once
in about 108,000 years, this kind of year is nearly five minutes longer
than the sidereal, its length being 365 d 6 h 13 m 48 8 . It is but little used
except in calculations relating to perturbations of the planets.
128. The Calendar. The natural units of time are the
day, the month, and the year. The day is too short for
convenience in dealing with considerable periods, such as
the life of a man, for instance ; and the same is true even
of the month; so that for all chronological purposes the
tropical year (the year of the seasons) has always been
102 LESSONS IN ASTRONOMY
employed. At the same time, so many religious ideas and
observations have been connected with the changes of the
moon that there has been a constant struggle to reconcile
the month with the year. Since the two are incommen-
surable, no really satisfactory solution is possible, and the
modern calendar of civilized nations entirely disregards the
lunar phases. In early times the calendar was in the hands
of the priesthood and was mainly lunar, the seasons being
either disregarded or kept roughly in place by the occa-
sional putting in or dropping of a month. The Moham-
medans still use a purely lunar calendar, having a " year "
of twelve months, which contains alternately 354 and 365
days. In their reckoning the seasons fall continually in
different months, and their calendar gains on ours about
one year in thirty-three.
129. The Julian Calendar. When Julius Caesar came
into power he found the Roman calendar in a state of
hopeless confusion. He, therefore, with the advice of
Sosigenes, the astronomer, established (45 B.C.) what is
known as the Julian calendar, which still, either untouched
or with a trifling modification, continues in use among civil-
ized nations. Sosigenes discarded all reference to the
moon's phases, and adopting 365i days as the true
length of the year, he ordained that every fourth year
should contain 366 days, the extra day being inserted
by repeating the sixth day before the Calends of March
(whence such a year is called " Bissextile "). He also
transferred the beginning of the year, which before Caesar's
time had been in March (as is indicated by the names of
several of the months, December, the tenth month, for
instance), to January 1.
THE CALENDAR 103
Caesar also took possession of the month Quintilis, naming it
July after himself. His successor, Augustus, in a similar manner
appropriated the next month, Sextilis, calling it August, and to vin-
dicate his dignity and make his month as long as his predecessor's
he added to it a day stolen from February.
The Julian calendar is still used unmodified in the
Greek Church, and also in many astronomical reckonings.
130. The Gregorian Calendar. The true length of the
tropical year is not 365i days, but 365 d 5 h 48 m 46 s , leaving
a difference of Il m 14 s by which the Julian year is too
long. This difference amounts to a little more than three
days in 400 years. As a consequence the date of the
vernal equinox comes continually earlier and earlier in
the Julian calendar, and in 1582 it had fallen back to
the llth of March instead of occurring on the 21st as it,
did at the time of the Council of Nice (A.D. 325).
3 Pope Gregory, therefore, under the astronomical advice
of Clavius, ordered that the calendar should be restored by
adding ten days, so that the day following Oct. 4, 1582,
should be called the 15th instead of the 5th; further, to
prevent any future displacement of the equinox, he decreed
that thereafter only such century years should be leap years
as are divisible by 400. Thus, 1700, 1800, 1900, and 2100
are not leap years, but 1600 and 2000 are.
The change was immediately adopted by all Catholic
countries, but the Greek Church and most Protestant
nations refused to recognize the pope's authority. The new
calendar was, however, at last adopted in England in 1752,
so that now the " old style " is used only in Russia and
Greece, and a few other minor nations of eastern Europe.
At present (since the years 1800 and 1900 were leap years-
104 LESSONS IN ASTRONOMY
in the Julian calendar and not in the Gregorian) the differ-
ence between the two calendars is thirteen days.
In 1900 there was a good deal of discussion about
the beginning of the twentieth century. According to the
accepted chronological method of reckoning, the begin-
ning of the Christian era is reckoned from the beginning
of the year A.D. 1, the year preceding being 1 B.C., with
no intervening year "zero." It follows that the first
century was not completed until the end of the year
A.D. 100, and that the second century began with A.D. 101,
as the twentieth did with the year 1901.
Certain chronologers about two hundred years ago tried
to reform the method of reckoning by inserting a year
A.D. as the beginning of the Christian era, and the plan
would offer some slight advantages. It did not, however,
meet with any general acceptance, though it was for a time
adopted in a few astronomical books and tables.
CHAPTER V
THE MOON
Her Orbital Motion and the Month Distance, Dimensions, Mass, Density,
and Force of Gravity Rotation and Librations Phases Light and
Heat Physical Condition Telescopic Aspect and Peculiarities of the
Lunar Surface
131. Next to the sun, the moon is the most conspicuous
and to us the most important, of the heavenly bodies ; in
fact, she is the only one except the sun which exerts the
slightest perceptible influence upon the interests of human
life. She owes her conspicuousness and her importance,
however, solely to her nearness; for she is really a very
insignificant body as compared with stars and planets.
132. The Moon's Apparent Motion ; Definition of Terms,
etc. One of the earliest observed of astronomical phe-
nomena must have been the eastward motion of the moon
with reference to the sun and stars, and the accompany-
ing change of phase. If, for instance, we note the moon
to-night as very near some conspicuous star, we shall find
her to-morrow night at a point considerably farther east,
and the next night farther yet; she changes her place
about 13 daily, and makes the complete circuit of the
heavens, from star to star again, in about 2Yi days. In
other words, she revolves around the earth in that time,
while she accompanies us in our .annual journey around
the sun. Since the moon moves eastward among the stars
so much faster than the sun (which takes a year in going
105
106 LESSONS IN ASTRONOMY
once around), she overtakes and passes him at regular
intervals; and as her phases depend upon her apparent
position with reference to the sun, this interval from new
moon to new moon is specially noticeable, and is what we
ordinarily understand as the " month."
The angular distance of the moon east or west of the sun
at any time is called her Elongation. At new moon it is zero,
and the moon is said to be in Conjunction. At full moon
the elongation is 180, and she is said to be in Opposition.
In either case the moon is in Syzygy. (Syzygy means " yoked
together," the sun, moon, and earth being then nearly inline.)
When the elongation is 90 she is said to be in Quadrature.
133. Sidereal and Synodic Months. The sidereal month
is the time it takes the moon to make her revolution from
a given star to the same star again; its length is 271 days
(27 d 7 h 43 m ll 8 .524). The mean daily motion, therefore, is
360 divided by this, or 13 11' (nearly). The sidereal
month is the true month from the mechanical point of
view. On account of " perturbations," it varies in length
by as much as three hours from time to time.
The synodic month is the time between two successive
conjunctions or oppositions; i.e., between two successive
new or full moons. Its average length is about 29 days
<29 d 12 h 44 m 2 8 .841), but it varies nearly thirteen hours,
mainly on account of the eccentricity of the moon's orbit.
If M be the mean length of the moon's sidereal period in days,
E the length of the sidereal year, and S the mean length of the
synodic month, the three quantities are connected by a simple relation
easily demonstrated. is the fraction of a circumference moved
M
over by the moon in a day. Similarly, is the apparent daily motion
E
THE MOON'S PATH 107
of the sun. The difference is the amount which the moon gains on
the sun daily. Now it gains a whole revolution in one synodic
month of S days, and therefore must gain daily of a circum-
o
ference. Hence we have the important equation
JL_I-I
M~E~~S'
which is known as the equation of synodic motion. In a sidereal
year the number of sidereal months is exactly one greater than the
number of synodic months, the numbers being respectively 13.309 +
and 12.369 +.
134. The Moon's Path among the Stars. By observing
the moon's right ascension and declination daily with
suitable instruments we can map out its apparent path,
just as in the case of the sun (Sec. 116). This path turns
out to be (very nearly) a great circle, inclined to the eclip-
tic at a slightly variable angle of about 5 8'. The two
points where it cuts the ecliptic are called the "nodes,"
the ascending node being where the moon passes from the
south side to the north side of the ecliptic, while the
opposite node is called the descending node.
The moon at the end of the month never comes back exactly to
the point of beginning among the stars, on account of 'the so-called
" perturbations " of her orbit, due mostly to the attraction of the
sun. One of the most important of these perturbations is the
" regression of the nodes." These slide westward on the ecliptic just
as the vernal equinox does (precession), but much faster, completing
their circuit in about nineteen years instead of 26,000.
135. Interval between the Moon's Successive Transits ;
Daily Retardation. Owing to the eastward motion of
the moon among the stars it comes to the meridian about
51 minutes later each day, on the average ; but the
108 LESSONS IN ASTRONOMY
retardation ranges all the way from 38 minutes to 66
minutes, on account of the variation in the rate of the
moon's motion.
The average retardation of the moon's rising and setting
is also the same 51 minutes ; but the actual retardation
is still more variable than that of the meridian transits,
depending to some extent on the latitude of the observer
as well as on the variations in the moon's motion.
At New York the range is from 23 minutes to I h 17 m ;
that is to say, on some nights the rising of the moon is
only 23 minutes later than on the preceding night, while
at other times it is more than an hour and a quarter behind-
hand. In high latitudes the differences are still greater.
In very high latitudes the moon, when it has its greatest
possible declination, becomes circumpolar for a certain time
each month, and remains visible without setting at all
(like the midnight sun) for a greater or less number of
days, according to the latitude of the observer.
There is always one day in the month on which the moon does
not rise, and another on which it does not set. Why ?
136. Harvest and Hunter's Moon. The full moon that
occurs nearest the autumnal equinox is called the " harvest
moon " ; the one next following, the " hunter's moon." At
that time of the year the moon, while nearly full, rises for
several consecutive nights almost at the same hour, so that
the moonlight evenings last for an unusually long time.
The phenomenon, however, is much more striking in north-
ern Europe and in Canada than in the United States.
137. Form of the Moon's Orbit. By observation of the
moon's apparent diameter in connection with observations
FORM OF MOON'S ORBIT 109
of her place in the sky, we can determine the form of her
orbit around the earth in the same way that the form of
the earth's orbit around the sun was worked out. (See
Appendix, Sec. 428.) The moon's apparent diameter ranges
from 33' 33", when as near the earth as possible, to 29' 24",
when most remote ; and her orbit turns out to be an ellipse
like that of the earth around the sun, but of much greater
eccentricity, averaging about ^ (as against g 1 ^). We say
" averaging " because the actual eccentricity is variable on
account of perturbations.
The point of the moon's orbit nearest the earth is called
the Perigee, that most remote the Apogee, and the indefi-
nite line passing through these points the Line of Apsides,
while the major axis is that portion of this line which lies
between the perigee and apogee. This line of apsides is
in continual motion on account of perturbations (just as
the line of nodes is, Sec. 134), but it moves eastward instead
of westward, completing its revolution in about nine years.
In her revolution about the earth the moon observes the
same law of equal areas that the earth does in her orbit
around the sun (Sec. 121).
THE MOON'S DISTANCE
138. In the case of any heavenly body, one of the first
and most fundamental inquiries relates to its distance from
us ; until the distance has been measured we can get no
knowledge of the real dimensions of its orbit, nor of the
size, mass, etc., of the body itself. The problem is usually
solved by measuring the apparent " parallactic " displace-
ment of the moon as seen by observers at widely separated
110 LESSONS IN ASTRONOMY
stations. Before proceeding -farther we must, therefore,
say a few words upon the subject of parallax.
139. Parallax. In general, the word " parallax " means
the difference between the directions of a heavenly body
as seen by the observer and as seen from some standard
point of reference. The annual or heliocentric parallax of
a star is the difference of the star's direction as seen from
the earth and from the sun. The diurnal or geocentric
parallax of the sun, the moon, or a planet is the difference
between its direction as seen from the center of the earth
and from the observer's station on the earth's surface ; or,
what comes to the same thing, the geocentric parallax is the
angle at the body made by two lines drawn from it, one to
the observer, the other to the center of the earth. (Stars have
no sensible geocentric parallax; the earth as seen from
them is a mere point.)
In Fig. 18 the parallax of the body P, for an observer
at 0, is the angle OP C. Obviously this diurnal parallax
is zero for a body directly overhead at Z, and is the greatest
possible for a body on the horizon, as at P h .
Moreover, and this is to be specially noted, this parallax
of a body at the horizon the " horizontal parallax " is
simply the angular semi-diameter of the earth as seen from
the body. When, for instance, we say that the moon's hori-
zontal parallax is 57', it is equivalent to saying that seen
from the moon the earth appears to have a diameter of 114'.
In the same way, since the sun's parallax is 8". 8, the
diameter of the earth as seen from the sun is 17 ".6.
140. Relation between Parallax and Distance When
the horizontal parallax of any heavenly body is ascertained
its distance follows at once through our knowledge of the
PARALLAX
111
earth's dimensions. If we know how large a ball of given
size appears, we can tell how far away it is ; if we know
how large the earth looks from the moon, we can find the
distance between them. Thus, when in the triangle CP h O
(Fig. 18) we know the angle at P A , and the side CO, the
radius of the earth, we can compute CP h by a very easy
trigonometrical calculation. Evidently the more remote
the body, the smaller its
parallax.
Since the radius of the
earth varies slightly in dif-
ferent latitudes, we take the
equatorial radius as a stand-
ard, and the equatorial hori-
zontal parallax is the earth's
equatorial semi-diameter as
seen from the body. It is
this which is usually meant
when we speak simply of
" the parallax " of the moon, of the sun, or of a planet
without adding any qualification, but never when we speak
of the parallax of a star; then we always mean the annual
parallax.
141. Parallax, Distance, and Velocity of the Moon. -
The moon's equatorial horizontal parallax found by corre-
sponding observations made at different parts of the earth is
3422" (57' 2") according to Neison, but varies considerably
on account of the eccentricity of the orbit. From this paral-
lax we find that the moon's average distance from the earth
is about 60.3 times the earth's equatorial radius, or 238,840
miles, with an uncertainty of perhaps twenty miles.
FIG. 18. Diurnal Parallax
112 LESSONS IN ASTRONOMY
The maximum and minimum values of the moon's distance are
given.by Nelson as 252,972 and 221,617 miles. It will be noted that
the average distance is not the mean of the two extremes.
Knowing the size and form of the moon's orbit, the
velocity of her motion is easily computed. It averages a
little less than 2300 miles an hour, or about 3350 feet per
second. Her mean apparent angular velocity among the
stars is about 33', which is just a little greater than the
apparent diameter of the moon itself.
142. Diameter, Area, and Bulk of the Moon. The mean
apparent diameter of the moon is 31' 7". Knowing its
distance, its real diameter comes out 2163 miles. This
is 0.273 of the earth's diameter.
Since the surfaces of globes vary as the squares of their
diameters, and their volumes as the cubes, this makes
the surface area of the moon equal to about -fa of the
earth's, and the volume (or bulk) almost exactly ^ of
the earth's.
No other satellite is nearly as large as the moon in comparison
with its primary planet. The earth and moon together, as seen from
a distance, are really in many respects more like a double planet than
like a planet and satellite of ordinary proportions. At a time, for
instance, when Venus happens to be nearest the earth (at a distance
of about 25,000000 miles) her inhabitants (if she has any) would
see the earth just about as brilliant as Venus herself at her best
appears to us, and the moon would be about as bright as Sirius,
oscillating backwards and forwards about each side of the earth,
once a month.
143. Mass, Density, and Superficial Gravity of the Moon.
Her mass is about ^ of the earth's mass (0.0125). The
actual measurement of the moon's mass is an extremely
THE MOON'S ROTATION 113
difficult problem, and the methods pursued are quite beyond
JY/T o co
the scope of this book. Since the density is equal to ^, ,
the density of the moon as compared to that of the earth
is found 'to be 0.613, or about 3.4 the density of water
(the earth's density being 5.58). This is a little above
the average density of the rocks which compose the crust
of the earth.
The " superficial gravity," or the attraction of the moon
for bodies at its surface, is only about one-sixth that at the
surface of the earth. This is a fact that
must be borne in mind in connection JL
with the enormous scale of the craters on I ! . :
the moon. Volcanic forces there would
throw materials to a vastly greater dis-
tance than on the earth.
144, Rotation of the Moon. The
moon turns on its axis once a month, in
exactly the time occupied by its revo-
lution around the earth; its day and
night are, therefore, each about a fortnight in length, and
in the long run it keeps the same side always toward the
earth. We see to-day precisely the same face of the moon
which Galileo did when he first looked at it with his tele-
scope. The opposite face has never been seen from the
earth, and probably never will be.
It is difficult for some to see why a motion of this sort should
be considered a rotation of the moon, since it closely resembles the
motion of a ball carried on a revolving crank (Fig. 19). Such a
ball, they say, " revolves around the shaft, but does not rotate on its
own axis." It does rotate, however ; for if we mark one side of the
114 LESSONS IN ASTRONOMY
ball, we shall find the marked side presented successively to every
point of the compass as the crank turns around, so that the ball
turns on its own axis as really as if it were whirling upon a pin
fastened to the table. By virtue of its connection with the crank,
the ball has two distinct motions: (1) the motion of translation,
which carries its center in a circle around the shaft; (2) an addi-
tional motion of rotation around a line drawn through its center of
gravity parallel to the shaft.
Rotation consists essentially in this : A line connecting any two
points in the rotating body, and produced to the celestial sphere, will
sweep out a circle upon it. In every rotating body one line, however,
can be drawn through the center of the body, so that the circle
described by it in the sky will be infinitely small. This is the axis
of the body.
145. Librations. The behavior of the moon, however, differs
essentially from that of the ball on the crank, showing that her rota-
tion and orbital revolution are really independent, though identical
in period. While in the long run the moon keeps the same face
towards the earth, it is not so from day to day. With reference to
the center of the earth, -it is continually oscillating a little, and
these oscillations constitute what are called Librations, of which \ve
distinguish three : (1) -the libration in latitude, by which the north
and south poles are alternately presented to the earth ; (2) the
libration in longitude, by" which the east and west sides of the moon
are alternately tipped a little towards us ; and (3) the diurnal libra-
tion, which enables us to look over whatever edge of the moon is
uppermost when it is near the horizon. Owing to these librations,
we see considerably more than half of the moon's surface at one time
and another. About 4V per cent of it is always visible ; 41 per cent
never visible ; and a belt at the edge of the moon, covering about
18 per cent, is rendered alternately visible and invisible by libration.
The explanation of the peculiarity of the moon's rotation is to be
found in the theory of " tidal evolution." (See Manual of Astronomy,
Sec. 346.)
146. Phases of the Moon. Since the moon is an opaque
globe shining merely by reflected light, we can see only
THE MOON'S PHASES
115
that hemisphere of her surface on which the sun is shining,
and of the illuminated hemisphere only that portion which
happens to be turned towards the earth.
When the moon is between the earth and the sun (new
moon) the side presented to us is dark, and the moon is
FIG. 20. The Moon's Phases
then invisible. A week later, at the end of the first quarter,
half of the illuminated hemisphere is visible, and we have
the half-moon, as we also do a week after the full. Between
the new moon and the half-moon, during the first and last
116 LESSONS IN ASTRONOMY
quarters of the lunation, we see less than half of the
illuminated portion, and then have the " crescent " phase.
Between half-moon and the full moon, during the second
and third quarters of the lunation, we see more than half
of the moon's illuminated side, and we have then what is
called the " gibbous " phase.
Fig. 20 (in which the light is supposed to come from a point far
above the circle which represents the moon's orbit) shows the way in
which the phases are distributed through the month.
The line which separates the dark portion of the disk
from the bright is called the Terminator, and is always a
semi-ellipse, since it is a semicircle viewed obliquely, as
shown by Fig. 21, A. Draftsmen sometimes incorrectly
represent the crescent form by a construction like Fig. 21, B,
in which a smaller circle has a por-
tion cut out of it by an arc of a
larger one. It is to be noticed also
that ab, the line which joins the
"cusps," or points, of the crescent,
is always perpendicular to a line
drawn from the moon to the sun, so
that tlip %r w - g "<rp "^"nys titrnfl j-!ra*fiy ninny f^^ fflf <?*/
The precise position in which they will stand at any time
is, therefore, perfectly predictable and has nothing whatever
to do with the weather. (Pupils have probably heard of
the " wet moon " and " dry moon " superstition.)
147. Earth-Shine on the Moon Near the time of new
moon the portion of the moon's disk which does not get
the sunlight is easily visible, illuminated by a pale reddish
light. This light is earth-shine, the earth as seen from
the moon being then nearly " full." The red color is due to
THE MOON'S PHYSICAL CHARACTERISTICS 117
the fact that the light sent to the moon from the earth has
passed twice through our atmosphere, and so has acquired
the sunset tinge. Seen from the moon, the earth would
be itself a magnificent moon about 2 in diameter, showing
the same phases as the moon does to us.
Taking everything into account, the earth-shine is probably fifteen
to twenty times as strong as the light of the moon at similar phases.
Since the moon keeps always the same face towards the earth, the
earth is visible only from that part of the moon which faces us, and
remains nearly stationary in the lunar sky, neither rising nor setting.
It is easy to see that she would be a very beautiful object, on account
of the changes which would be continually going on upon her surface
due to snow, storms, clouds, growth of vegetation, etc.
PHYSICAL CHARACTERISTICS OF THE MOON
148. Absence of Air and Water. The moon's atmos-
phere, if there is any, is extremely rare, its density at the
moon's surface being probably not more than y^ part of
that of our own atmosphere.
The evidence on the point is twofold : First, the telescopic appear-
ance. There is no haze, shadows are perfectly black; there is no
sensible twilight at the points of the crescent, and all outlines are
visible sharply and without the least blurring such as would be due
to the intervention of an atmosphere. Second, the absence of refrac-
tion when the moon intervenes between us and any distant body.
When the moon " occults " a star, for instance, there is no distortion
or discoloration of the star -disk, but both the disappearance and the
reappearance are practically instantaneous.
Of course if there is no air, there can be no liquid water,
since the water would immediately evaporate and form an
atmosphere of vapor if air were not present. It is not impos-
sible, however, nor perhaps improbable, that solid water (ice
118 LESSONS IN ASTRONOMY
and snow) may exist on the moon's surface. Although ice
and snow liberate a certain amount of vapor, yet at a low
temperature the quantity would be insufficient to make an
atmosphere dense enough to be observed from the earth.
If the moon once formed a portion of the earth, as is likely, the
absence of air and water requires explanation, and there have been
many interesting speculations on the subject into which we cannot
enter. (The student is referred to the Manual of Astronomy,
Sec. 209.)
149. The Moon's Light. In its quality moonlight is
simply sunlight, showing a spectrum identical in every
detail with that of the light coming from the sun itself,
except as the intensity of different portions of the spectrum
is slightly altered by its reflection from the lunar surface.
The brightness of full moonlight as compared with sun-
light is about one six-hundred-thousandth. According to
this, if the whole visible hemisphere were packed with full
moons, we should receive from it only about one-eighth of
the light of the sun.
The half-moon does not give nearly half as much light
as the full moon. Near the full the brightness is suddenly
and greatly increased, probably because at any time except
the full the moon's visible surface is more or less darkened
by shadows which disappear at the moment of full.
The average " albedo," or reflecting power, of the moons
surface is given by Zollner as 0.174 ; i.e., the moon's sur-
face reflects a little more than one-sixth of the light that
falls upon it. There are, however, great differences in the
brightness of the different portions of the moon's surface.
Some spots are nearly as white as snow or salt, and others
as dark as slate.
THE MOON'S HEAT 119
150. Heat of the Moon. For a long time it was impos-
sible to detect the moon's heat by observation. Even when
concentrated by a large lens, it is too feeble to be shown
by the most delicate thermometer. With modern appa-
ratus, however, it is easy enough to perceive the heat of
lunar radiation, though the measurement is extremely diffi-
cult. The total amount of heat sent by the full moon to
the earth appears to be about yy-oVFo ^ * na ^ sen ^ ^7 the
sun ; i.e., the full moon in two days sends us about as much
heat as the sun does in one second. But the results of
different observers differ rather widely.
A considerable portion of the lunar heat seems to be
simply reflected from the surface like light, while the rest,
perhaps three-fourths of the whole, is " obscure heat," i.e.^
heat which has first been absorbed by the moon's surface
and then radiated, like the heat from a brick that has been
warmed by the sunshine.
As to the temperature of the moon's surface, it is impos-
sible to be very certain. During the long lunar night of
fourteen days the temperature must inevitably fall appall-
ingly low, perhaps 200 or 300 below zero. On the
other hand, the lunar rocks are exposed to the sun's rays
in a cloudless sky for fourteen days at a time, so that if
they were protected by air, like the rocks upon the earth,
they would certainly become intensely heated. The recent
observations of Very, which are apparently conclusive,
seem to show that on all the dark portion of the moon,
and near its boundary on the illuminated portion even, the
temperature is far below zero, and may fall as low as that
of liquid air ; but that in the equatorial regions the temper-
ature a few hours after "noon" rises very high, probably
120 LESSONS IN ASTRONOMY
above that of boiling water, thus confirming Lord Rosse's
conclusion of more than thirty years ago. But the mean
temperature of even the equatorial regions is probably
everywhere below the freezing point of water.
151. Lunar Influences on the Earth. The most impor-
tant effect produced upon the earth by the moon is the
generation of the tides in cooperation with the sun. There
are also certain well-ascertained disturbances of the terres-
trial magnetism connected with the approach and recession
of the moon in its oval orbit ; and this ends the chapter of
proved lunar influences.
The multitude of current beliefs as to the controlling
influence of the moon's phases and changes upon the weather
and the various conditions of life are mostly unfounded.
It is quite certain that if the moon has any influence at all
of the sort imagined, it is extremely slight, so slight that
it has not yet been demonstrated, though numerous inves-
tigations have been made expressly for the purpose of
detecting it. Different workers continually come to con-
tradictory results.
152. The Moon's Telescopic Appearance. Even to the
naked eye the moon is a beautiful object, diversified with
curious markings connected with numerous popular legends.
In a powerful telescope these naked-eye markings vanish,
and are replaced by a multitude of smaller details which
make the moon, on the whole, the most interesting of all
telescopic objects especially to instruments of moderate
size, say from six to ten inches in diameter, which gener-
ally give a more pleasing view than instruments either
much larger or much smaller. An instrument of this size,
with magnifying powers between 250 and 500, virtually
THE MOON'S SURFACE STRUCTURE
121
brings the moon within a distance ranging from 1000 to
500 miles. Any object half a mile in diameter on the
moon is distinctly visible. A long line or streak even less
than a quarter of a mile across can easily be seen.
For most purposes the best time to look at the moon is when it is
between six and ten days old ; at the time of full moon few parts of the
surface are well seen. It is evident that while with the telescope we
should be able to see such objects as lakes, rivers, forests, and great cit-
ies, if they existed on the moon, it would be hopeless to expect to distin-
guish any of the minor indications of life, such as buildings or roads.
153. The Moon's Surface Structure. The moon's sur-
face for the most part is extremely broken. The earth's
mountains are
mainly in long
ranges, like the
Andes and Hima-
layas. On the
moon the ranges
are few in num-
ber; but, on the
other hand, the
surface is pitted
all over with great
craters, which
resemble very
closely the volcanic craters on the earth's surface, though
on an immensely greater scale. The largest terrestrial
craters do not exceed six or seven miles in diameter; many
of those on the moon are fifty or sixty miles across, and
some more than a hundred, while scores are from five to
twenty miles in diameter.
FIG. 22. Normal Lunar Crater
122
LESSONS IN ASTROXOMY
The normal lunar crater (Fig. 22) is nearly circular, sur-
rounded by a mountain ring, which rises anywhere from
1000 to 20,000 feet above the neighboring country. The
floor within the ring may be either above or below the out-
side level ; some craters are deep, and some are filled
nearly to the brim. Frequently in the center of the
crater there rises a group of peaks which attain the same
elevation as the
encircling ring, and
these central peaks
often show holes or
minute craters in
their summits.
On some portions
of the moon these
craters stand very
thickly. This is es-
pecially the case near
the moon's south
pole. It is noticeable,
also, that as on the
earth the youngest
mountains are gen-
erally the highest, so
on the moon the most
recent craters are generally deepest and most precipitous.
The height of a lunar mountain can be measured with
notable accuracy by means of its shadow.
The striking resemblance of these lunar craters to terrestrial
"volcanoes makes it natural to assume that they have a similar
origin. This, however, is not quite certain, for there are notable
FIG. 23. Gassendi
LUNAR FORMATIONS
128
difficulties in the way of the volcanic theory, especially in the case of
what are called the great "Bulwark Plains," so extensive that a,
person standing in the center could not even see the summit of the
surrounding ring at any point ; and yet there is no line of distinction
between them and the smaller craters, the series is continuous.
Moreover, on the earth volcanoes necessarily require the action of
air and water, which do not now exist on the moon ; so that if these
lunar craters are really
the result of volcanic
eruptions, they must be
ancient formations, for
there is no satisfactory
evidence of any present
volcanic activity. Fig. 23
represents one of the
finest lunar craters, Gas-
sendi, about fifty-six
miles in diameter, which
is best seen about three
days after the half-
moon.
154. Other Lunar
Formations. The
craters and mount-
ains are not the only
interesting features
on the moon's sur-
face. There are many
which go by the name of " rills," and may once have been
watercourses. (See Fig. 24.) Then there are many straight
" clefts " half a mile or so wide, and of unknown depth,,
running in some cases several hundred miles straight
through mountain and valley, without any apparent regard
to the accidents of the surface.
FIG. 24. Copernicus
deep, narrow, crooked valleys-
124 LESSONS IN ASTRONOMY
Most curious of all are the light-colored streaks, or
" rays," which radiate from certain of the craters, extend-
ing in some cases a distance of many hundred miles.
They are usually from five to ten miles wide, and neither
elevated nor depressed to any considerable extent with
reference to the general surface. Like the clefts, they
pass across valley and mountain, and sometimes straight
through craters, without any change in width or color.
No satisfactory explanation of them has yet been given.
The most remarkable of these " ray-systems " is the one
connected with the great crater Tycho, not very far from
the moon's south pole. The rays are not very conspicuous
until within a few days of full moon, but at that time they,
and the crater from which they diverge, constitute by far
the most striking feature of the telescopic view.
155. Changes on the Moon. It is certain that there
are no conspicuous changes on the moon's surface ; no such
transformations as would be presented by the earth viewed
with a telescope from the moon, no clouds, no storms,
no snow of winter, and no spread of verdure in the spring.
At the same time it is confidently maintained by some
observers that here and there perceptible alterations do
take place in the details of the lunar surface. Professor
W. H. Pickering, the younger brother of the Director of
the Harvard Observatory, is at present the most prominent
supporter of this view.
The difficulty in settling the question arises from the
great changes which take place in the appearance of a
lunar object, according to the angle at which the sunlight
strikes it. Other conditions also, such as the height of the
moon above the horizon and the clearness and steadiness
LUNAR MAPS AND NOMENCLATURE 125
of the air, affect the appearance ; and it is very difficult to
secure a sufficient identity of conditions at different times
of observation to be sure that apparent changes are real.
It is probable that the question will finally be settled by
photography. (For further discussion of this subject, see
General Astronomy, Art. 272.)
156. Lunar Maps and Nomenclature. A number of
maps of the moon have been constructed by different
observers. The most recent and extensive is that by
Schmidt of Athens, on a scale of seven feet in diameter ;
it was published by the Prussian government in 1878.
Perhaps the best for ordinary observers is that given in
Webb's " Celestial Objects for Common Telescopes." We
present here (Fig. 25) a skeleton map, which indicates the
position of about fifty of the leading objects.
As for the names of the lunar objects, the great plains
upon the surface were called by Galileo " oceans," or " seas"
(Maria), because he supposed that these grayish surfaces,
which are visible to the naked eye and conspicuous in a
small telescope, though not with a large one, were covered
with water. Thus we have the " Oceanus Procellarum "
(Sea of Storms) and " Mare Imbrium " (Sea of Showers).
The ten mountain ranges on the moon are mostly named
for terrestrial mountains, as Caucasus, Alps, Apennines,
though two or three bear the names of astronomers, like
Leibnitz, Doerfel, etc. The conspicuous craters bear the
names of ancient and medieval astronomers and philoso-
phers, as Plato, Archimedes, Tycho, Copernicus, Kepler,
and Gassendi. This system of nomenclature seems to
have originated with Riccioli, who made one of the first
maps of the moon in 1650.
126
LESSONS IN ASTRONOMY
156*. Lunar Photography. The earliest success in lunar
photography was that of W. C. Bond at Cambridge (U.S.)
in 1850, using the old daguerreotype process. This was
FIG. 25. Map of the Moon, reduced from Nelson
soon followed by the work of De la Rue in England, and a
little later by Dr. Henry Draper and Lewis M. Rutherfurd
in New York. Until very lately Mr. Rutherfurd's pictures
remained unrivaled ; but since 1890 there has been a great
LUNAR PHOTOGRAPHY
127
advance. At various places, especially at Cambridge and
the Lick and Yerkes observatories in this country, and at
Paris, most admirable photographs have been made which
bear enlargement well, and show details almost (not quite)
as perfectly as they can be seen with the telescope.
Already maps of the lunar surface have been made from
them exceeding in accuracy even the great map of Schmidt
mentioned in the preceding article.
KEY TO THE PRINCIPAL OBJECTS INDICATED IN FIG. 25
A. Mare Humorum.
B. Mare Nectaris.
C. Oceanus Procellarum.
D. Mare Fecunditatis.
E. Mare Tranquillitatis.
F. Mare Crisium.
G. Mare Serenitatis.
K . Mare Nubium.
L. Mare Frigoris.
T. Leibnitz Mountains.
U. Doerfel Mountains.
V. Rook Mountains.
W. D'Alembert Mountains.
X. Apennines.
H. Mare Imbrium.
Y. Caucasus.
7. Sinus Iridum.
Z. Alps.
1.
Clavius.
14.
Alphonsus.
27.
Eratosthenes.
2.
Schiller.
15.
Theophilus.
28.
'Proclus.
3.
Maginus.
16.
Ptolemy.
28'.
Pliny.
4.
Schickard.
17.
Langrenus.
29.
Aristarchus.
5.
Tycho.
18.
Hipparchus.
30.
Herodotus.
6.
Walther.
19.
Grimaldi.
31.
Archimedes.
7.
Purbach.
20.
Flarnsteed.
32.
Cleomedes.
8.
Petavius.
21.
Messier.
33.
Aristillus.
9.
" The Railway."
22.
Maskelyne.
34.
Eudoxus.
10.
Arzachel.
23.
Triesnecker.
35.
Plato.
11.
Gassendi.
24.
Kepler.
36.
Aristotle.
12.
Catherina.
25.
Copernicus.
37.
Endymion.
13.
Cyrillus.
26.
Stadius.
128 LESSONS IN ASTRONOMY
The half-tone engraving which forms the frontispiece is from two
photographs, the first of which, of the moon a little past the full,
was made by Professor Hale in 1892 at his Kenwood Observatory in
Chicago ; the other is enlarged from a magnificent photograph made
by Ritchey with the non-photographic forty-inch telescope of the
Yerkes Observatory, a yellowish color-screen being interposed in
front of the sensitive plate to cut off the red, violet, and ultra-violet
rays in accordance with a suggestion by Professor Hale. The
original negative, about six inches in diameter, is certainly unsur-
passed by any hitherto made with photographic lenses or reflectors.
The portion shown includes the great crater Theophilus, 60 miles
in diameter and 17,000 feet deep, with its neighbors Cyrillus and
Catherina.
The reader will notice the relative ages of the craters. On
the moon the deepest craters and the highest mountains are the
youngest, as is the case with the mountains on the earth. The
Himalayas, the Alps, and the Andes are infants compared with
the Laurentian range, now low because worn down by time.
CHAPTER VI
THE SUN AND SPECTROSCOPE
Its Distance, Dimensions, Mass, and Density Its Rotation, Surface, and
Spots The Spectroscope and the Chemical Constitution of the Sun
The Chromosphere and Prominences The Corona The Sun's Light
Measurement and Intensity of the Sun's Heat Theory of its Maintenance
and Speculations regarding the Age of the Sun
157. The sun is a star, the nearest of them a hot,
self-luminous globe, enormous as compared with the earth
and moon, though probably only of medium size as a star ;
but to the earth and the other planets which circle around
it, it is the grandest and most important of all the heav-
enly bodies. Its attraction controls their motions, and its
rays supply the energy which maintains every form of
activity upon their surfaces.
158. The Sun's Distance. The mean distance of the
sun from the earth (the astronomical unit of distance) is a
little less than 93,000,000 miles. There are many methods
of determining it, some of which depend on a knowledge of
the Velocity of Light (Appendix, Sees. 434 and 436), while
others depend on finding the sun's horizontal parallax.
(For a resumS of the subject, see General Astronomy,
Chap. XIV, or Chap. XV of the Manual of Astronomy.)
The mean value of this parallax is very nearly 8". 8. In
other words, as seen from the sun, the earth has an
apparent diameter of about 17".6 (Sec. 139). The dis-
tance is variable, to the extent of about 1,500000 miles,
129
130 LESSONS IN ASTRONOMY
on account of the eccentricity of the earth's orbit, the
earth being almost 3,000000 miles nearer to the sun on
December 31 than on July 1.
Knowing the distance of the earth from the sun, the
earth's orbital velocity follows at once by dividing the cir-
cumference of the orbit by the number of seconds in a
year. It comes out 18.5 miles per second. (Compare this
with the velocity of a cannon-ball, which seldom exceeds
2500 feet per second.) In traveling this 18? miles, the
deflection of the earth's motion from a perfectly straight line
amounts to less than one-ninth of an inch.
159. The distance of the sun is of course enormous compared
with any distance upon the earth's surface. Perhaps the simplest
illustration which will give us any conception of it is that drawn
from the motion of a railway train, which, going a thousand miles
a day (nearly forty-two miles an hour without stops) would take
254^ years to make the journey. If sound were transmitted through
interplanetary space, and at the same rate as in our own air. it would
make the passage in about fourteen years ; i.e., an explosion on the
sun would be heard by us fourteen years after it actually occurred.
Light traverses the distance in 499 seconds.
160. Dimensions of the Sun. The sun's mean apparent
diameter is 33' 4". Since at its mean distance 1" equals
450.36 miles, its diameter is 866,500 miles, or 109 times
that of the earth. If we suppose the sun to be hollowed
out, and the earth placed at the center of it, the sun's
surface would be 433,000 miles away. Now, since the
distance of the moon from the earth is about 239,000 miles,
she would be only a little more than half-way out from
the earth to the inner surface of the hollow globe, which
would thus form a very good background for the study of
the lunar motions.
THE SUN'S DIMENSIONS, MASS, AND DENSITY 131
If we represent the sun by a globe two feet in diameter, the earth
on the same scale would be 0.22 of an inch in diameter, the size of
a very small pea. Its distance from the sun would be just about
220 feet, and the nearest star, still on the same scale, would be 8000
miles away, on the other side of the earth.
Since the surfaces of globes are proportional to the
squares of their radii, the surface of the sun exceeds
that of the earth in the ratio of (109. 5) 2 : 1; i.e., the
area of its surface is about 12,000 times the surface of
the earth.
The volumes of spheres are proportional to the cubes of
their radii ; hence the sun's volume, or bulk, is (109.5) 3 , or
1,300000 times that of the earth.
161. The Sun's Mass, Density, and Superficial Gravity.
The mass of the sun is about 332,000 times that of the
earth. There are various ways of getting at this result, but
they lie rather beyond the mathematical scope of this work.
Its density, as compared with that of the earth, is found
by simply dividing its mass by its bulk (both as compared
with the earth) ; i.e., the sun's density equals y/FoVA"
= 0.255, a little more than a quarter of the earth's density.
To get its specific gravity (i.e., its density compared
with water), we must multiply this by the earth's mean
specific gravity, 5.53. This gives 1.41. In other words,
the sun's mean density is only about 1.4 times that of
water, a very significant result as bearing on its physical
condition, especially when we know that a considerable
portion of its mass is composed of metals.
Of course this low density depends upon the fact that the tem-
perature is enormously high and the materials are mainly in a state
of cloud, vapor, or gas.
132
LESSONS IN ASTRONOMY
The superficial gravity is about 27.6 as great as gravity
on the earth ; that is to say, a body which weighs one pound
on the surface of the earth would there weigh 27.6 pounds,
and a person who weighs 150 pounds here would there
weigh nearly two tons. A body would fall 444 feet in the
first second, and a pendulum which vibrates seconds on the
earth would vibrate in less than a fifth of a second there.
162. The Sun's Rotation. Dark spots are often visible
upon the sun's surface, passing across the disk from east
to west and indicating an
axial rotation. The aver-
age time occupied by a
spot in passing around
the sun and returning to
the same apparent posi-
tion, as sejm__Jj-om the
earth, is about 27.25 days;
different observers, how-
ever, get slightly different
results, because, as we
shall see, the spots are
not firmly attached to the
sun's surface, but drift
about to some extent. This interval,- however, is not
the true time of the sun's rotation, but the synodic, as is
evident from Fig. 26. Suppose an observer on the earth
at E sees a spot on the center of the sun's disk at S ; while
the sun rotates E will also move forward in its orbit, and
the observer, the next time he sees the spot on the center
of the disk, will be at E', the spot having gone around
the whole circumference plus the arc SS 1 .
FIG. 26. Synodic and Sidereal Revolu-
tions of the Sun
THE SUN'S ROTATION
133
The equation by which the true, or sidereal, period is deduced from
the synodic is the same as in the case of the moon, viz. :
1 = 1 -A,
S~ T E
T being the true period of the sun's rotation, E the length of the
year, and S the observed synodic rotation. This gives' T= 25.35.
The paths of the spots across the sun's disk are usually
more or less oval, showing that the sun's axis is inclined
to the ecliptic, and so inclined that the north pole is tipped
about 7i towards the position which the earth occupies
December 6 1* March 6 June 5*
FIG. 27. Spot Belts and Paths
September 5 th
near the 1st of September. Twice a year the paths
become straight, when the earth is in the plane of the
sun's equator, June 3 and December 5 (Fig. 27).
163. Peculiar Law of the Sun's Rotation It was
noticed quite early that different spots give different
results for the period of rotation, but the researches of
Carrington, half a century ago, first brought out the
fact that the differences are largely systematic, so that at
the solar equator the time of solar rotation is less than on
either side of it. For spots near the sun's equator it is
about 25 days; for solar latitude 30, 26.5 days ; and in
solar latitude 40, 27 days. The time of rotation of the sun's
surface in latitude 45 is fully two days longer than at the
134 LESSONS IN ASTRONOMY
equator; but we are unable to follow the law further towards
the poles of the sun, because spots are almost never found
beyond the parallel of 45, though faculse which have been
observed in higher latitudes give substantially the same
result, as do certain spectroscopic observations.
Possibly this equatorial acceleration may be due in some way to
the tremendous outpour of heat from the solar surface, as Emdcn
has attempted to show in a recent paper. The more general impres-
sion is, however, that it is due not
to any causes now operating, but is a
lingering survival from the sun's past
history, and destined ultimately to
disappear.
164. Study of the Sun's Suis
face. The heat and light of
the sun are so intense that we
FIG. 28. Telescope and Screen . , , , . J , J . . . J ,
cannot look directly at it with
a telescope, as we do at the moon, and it is necessary,
therefore, to provide either a special eyepiece with suit
able shade-glass, or arrange the telescope, as in Fig. 28,
so as to throw an image of the sun upon a screen.
In the study of the sun's surface, photography is for
some purposes very advantageous and much used. Tele-
scopes are often made with lenses specially construct rd
for' photographic operations, since an object-glass which
would give admirable results for visual purposes would
be worthless photographically. Visual telescopes may,
however, be used with the spectroheliograph (see Sec. 182*)
for photographing the sun in light of a single wave-length.
The exposure required for a photograph is practically
instantaneous. The negatives are usually from two inches
STUDY OF THE SUN'S SURFACE: 135
to eight or ten in diameter, and some of the best of them
bear enlarging to forty inches.
Photographs have the great advantage of freedom from prepos-
session on the part of the observer, and in an instant of time they
secure a picture of the whole surface of the sun such as would require
FIG. 29. Greenwich Photograph of Sun, Sept. 10, 1898
a skillful draftsman hours to copy. But, on the other hand, they
take no advantage of the instants' of fine seeing, but represent the
solar surface as it happened to appear at the moment when the
plate was uncovered, aifected by all the momentary distortions due
to atmospheric disturbances.
136
LESSONS IN ASTRONOMY
165. The Photosphere. The sun's surface seen with a
telescope, under a medium magnifying power, appears to be
of nearly uniform texture, though distinctly darker at the
edges, and usually marked here and there with certain dark
FIG. 30. Nodules and Granules on the Sun's Surface
After Langley
spots. With a higher power it is evident that the visible
surface (called the photosphere) is by no means uniform,
but is made up, as shown in Fig. 30, of a comparatively
darkish background sprinkled over with grains, or "nod-
ules," as Herschel calls them, of something more brilliant,
THE PHOTOSPHERE AND
137
"like snowflakes on a gray cloth," according to Langley.
These nodules, or " rice grains," are from 400 to 600 miles
across, and, when the seeing is best, themselves break up
into more minute "granules." For the most part, the
nodules are about as broad as they are long, though of
irregular form; but here and there, especially in the
neighborhood of the spots, they are drawn out into long
streaks, known as " filaments," " willow leaves," or " thatch
straws."
Certain bright streaks called " faculse " are also usually
visible here and there upon the sun's surface, and though
not very obvious
near the center
of the disk, they
become con-
spicuous near
the " limb," or
edge, of the disk,
especially in the
neighborhood
of the spots,
as shown in
Fig. 31. These
faculse are masses of the same material as the rest of
the photosphere, but elevated above the general level
and intensified in brightness. When one of them passes
off the edge of the disk, it is sometimes seen as a little
projection. The fact, however, that their spectrum shows
bright lines of calcium vapor makes it uncertain whether
they may not be clouds of that substance floating high
above the photosphere.
FIG. 31. Spots and Faculae
After De la Rue
138
LESSONS IN ASTRONOMY
sV*V
In their nature, the photospheric nodules and faculse
are generally believed to be luminous clouds, floating in a
less luminous atmosphere, just as a snow or rain cloud,
which has been formed by the condensation of water-
vapor, floats in the earth's atmosphere. Such a cloud,
while at a temperature even lower than that of the sur-
rounding gases, has a vastly greater power of emitting
light, and therefore,
like the " mantle "
of a Welsbach gas-
burner, appears very
brilliant in compari-
son with the gas in
which it floats.
There is consider-
able probability that
the principal ele-
ment in the photo-
sphere is carbon.
There are, however,
some serious diffi-
culties with this
cloud theory,
which may or may
not be removed by further investigation.
166. Sun-Spots, Sun-spots, whenever visible, are the
most interesting and conspicuous objects upon the solar
surface. The appearance of a normal sun-spot (Fig. 32),
fully formed and not yet beginning to break up, is that
of a dark central " umbra," more or less circular, with a
fringing "penumbra" composed of converging filaments.
FIG. 32. Normal Sun-Spot
After Secchi
SUN-SPOTS 139
The umbra itself is not uniformly dark throughout, but is
overlaid with filmy clouds, which usually are rather hard
to see, but sometimes are conspicuous, as in the figure.
Usually, also, within the umbra there are a number of
round and very black spots, sometimes called " vortices,"
but often referred to as "Dawes's holes," after the name
of their first discoverer.
Even the darkest portions of the umbra, however, are
dark only by contrast. Photometric observations show
FIG. 33. Group of Spots from a Greenwich Photograph, Sept. 11, 1898
(hat the nucleus of a spot gives about one per cent as
much light as a corresponding area of the photosphere ;
the blackest portion of a sun-spot is really more brilliant
than a calcium light.
Very few spots are strictly normal. Frequently the
umbra is out of the center of the penumbra, or has a
140 LESSONS IN ASTRONOMY
penumbra on one side only, and the penumbral filaments,
instead of converging regularly towards the nucleus, are
often distorted in every conceivable way. Spots are often
gathered in groups within a common penumbra, separated
from each other by brilliant " bridges," which extend across
from the outside photosphere. Occasionally a spot has no
penumbra at all, and sometimes we have what are called
" veiled " spots, in which there seems to be a penumbra
without any central nucleus.
167. Nature of Sun-Spots. Until very recently sun-
spots have been believed to be cavities in the photosphere
filled with gases and vapors, cooler, and therefore darker,
than the surrounding region. This theory is founded on
the fact that many spots as they cross the sun's disk
behave as if they were saucer-shaped hollows, with sloping
sides colored gray and the bottom black.
This theory has, however, of late been seriously called
in question ; many spots, possibly a majority, as shown by
photographs and drawings, fail to present the appearances
described. Spectroheliograph pictures (Sec. 182*). show
that there is a whirling motion of the hydrogen and calcium
vapors that lie above and around the spots, and it has
been suggested that sun-spots are really something like
water-spouts at sea, the penumbra of the spot correspond-
ing to the spreading top, the darker umbra to the stem.
Fig. 34, copied from such a photograph made at the
Mt. Wilson Solar Observatory, January 5, 1917, shows
the curvature of the hydrogen filaments in the region
surrounding a group of spots.
In the neighborhood of the spot the surrounding photo-
sphere is usually much disturbed and elevated into faculse,
NATURE AND DIMENSIONS OF SUN-SPOTS 141
which ordinarily appear before the spot is formed and
continue after it disappears.
168. Dimensions of Sun-Spots, etc. The diameter of
the umbra of a sun-spot varies all the way from 500 miles,
in the case of a very small one, to 50,000 miles, in the case
of a very large one. The penumbra surrounding a group
FIG. 34. Hydrogen Flocculi around a Sun-Spot
of spots is sometimes 150,000 miles across, though that is
an exceptional size. Quite frequently sun-spots are large
enough to be visible with the naked eye, and can actually
be thus seen at sunset or through a fog, or by the help
of a colored shade-glass.
The Chinese have many records of such objects, but
their real discovery dates from 1610, as an immediate
consequence of the invention of the telescope.
142 LESSONS IK ASTRONOMY
The duration of sun-spots varies greatly, but they are
always short-lived phenomena, from the astronomical point
of view, sometimes lasting only for a few days, though
more frequently for a month or two. In one instance a
spot group attained the age of eighteen months.
As to their cause, positive knowledge is still wanting.
Numerous theories, more or less satisfactory, have been
proposed. Professor Young, the author of our text, be-
lieved them to be the effect of eruptions breaking through
the photosphere. He did not, however, consider them to be
the holes, or craters, through which the eruptions break
out, as Secchi at one time thought, and as Mr. Proctor
maintained to the very last, but rather thought, in accord-
ance with Secchi's later views, that when an eruption
takes place, a hollow, or sink, results in the neighboring
cloud-surface, and in this hollow the cooler gases and
vapors collect. It has been generally supposed that in
some way they are due to matter descending from above
upon the photosphere, although recent investigations make
it seem possible that they are due to ascending currents
material flowing outward from the sun's interior, becom-
ing cooler at the higher level, and therefore appearing dark
against the brighter photosphere.
169. Distribution of Spots, and their Periodicity. It is
a significant fact that the spots are confined mostly to two
zones of the sun's surface between 5 and 40 of north
and south solar latitude. Practically none are ever found
beyond the latitude of 45, but at the time when spots are
most numerous a few appear near the equator.
In 1843 Schwabe of Dessau, by the comparison of an
extensive series of observations covering nearly twenty
PERIODICITY OF SUN-SPOTS 143
years, showed that the sun-spots are probably periodic,
being at some times much more numerous than at others,
with a roughly regular recurrence every ten or eleven
years. A few years later he fully established this remark-
able result. Wolf of Zurich has collected all the observa-
tions discoverable, and has obtained a pretty complete
record back to 1610, when Galileo first discovered these
objects. The average period is 11.1 years, but the maxima
are somewhat irregular, both in time and as to the extent
of the surface covered by spots. The last maximum
occurred in 1917.
During the maximum the sun is never without spots,
from twenty-five to fifty being visible at once. During
the minimum, on the contrary, weeks and even months
pass without the appearance of a single one. The cause
of this periodicity is not yet known.
Another curious and important fact has recently been brought
out by Spoerer, though not yet explained. Speaking broadly, the
disturbance which produces the spots of a given period first mani-
fests itself in two belts, about 30 north and south of the sun's
equator. These belts then draw in towards the equator, and the
spot-maximum occurs when their latitude is about 16; while the
disturbance finally dies out at a latitude of from 5 to 10, about
twelve or fourteen years after its first outbreak. Two or three years
before this disappearance, however, two new zones of disturbance
show themselves. Thus, at the spot-minimum there are usually four
well-marked spot-belts : two near the sun's equator, due to the expir-
ing disturbance, and two in high latitudes, due to the newly begin-
ning outbreak.
170. Terrestrial Influence of Sun-Spots One influence
of sun-spots on the earth is perfectly demonstrated.
When the spots are numerous, magnetic disturbances
144 LESSONS IX ASTRONOMY
(magnetic storms) are most numerous and most violent upon
the earth, a fact not to be wondered at, since notable
disturbances upon the sun's surface have been immediately
followed by magnetic storms with brilliant exhibitions of
the Aurora Borealis, as in 1859 and 1883. It seems
now that magnetic disturbances originate in the sun and
travel outward in certain definite directions. When such
a stream strikes the earth, we have a magnetic storm.
But it may pass above or below, and this explains why
a spot is not always accompanied by a disturbance on
the earth.
It has been attempted, also, to show that the periodical disturbance
of the sun's surface is accompanied by effects upon the earth's mete-
orology, upon its temperature, barometric pressure, storminess,
and the amount of rainfall. On the whole, it can only be said that
while it is possible and even probable that real effects are produced,
they must be very slight, and are almost entirely covered up by the
eif ect of purely terrestrial causes. The results obtained thus far
in attempting to coordinate sun-spot phenomena with meteorological
phenomena are unsatisfactory and often contradictory. We may add
that the spots cannot produce any sensible effect by their direct action
in diminishing the light and heat of the sun. They do not directly
alter the amount of solar radiation at any time by so much as one
part in a thousand.
THE SOLAR SPECTRUM AND ITS REVELATIONS
About 1860 the spectroscope appeared in the field as a
new and powerful instrument for astronomical research,
resolving at a glance many problems which before did not
seem even open to investigation. It is not extravagant
to say that its invention has done almost as much for
astronomy as that of the telescope itself.
PRINCIPLE OF THE SPECTROSCOPE 145
It enables us to study the light of distant objects and
read therein a record more or less complete of their
chemical composition and physical conditions; also to
measure the speed with which they are approaching or
receding, and sometimes, as in the case of the solar promi-
nences, to observe at any time objects otherwise visible
only on rare occasions. The spectroscope and its close
ally, the photographic plate, have together given us " the
New Astronomy."
171. Principle of the Spectroscope. The essential part
of the apparatus is either a prism or a train of prisms, or
else a diffraction " grating," * which is capable of perform-
ing the same office of " dispersing " (i.e., of spreading and
sending in different directions) the rays of different colors
and wave-lengths.
If with such a "dispersion piece," as we may call it
(either prism or grating), one looks at a distant point of
light, he will see instead of a point a long, bright streak,
red at one end and violet at the other. If the object
looked at is a line of light, parallel to the edge of the
prism or to the lines of the grating, then instead of a
colored streak without width, he gets a colored band or
ribbon of light, the spectrum, which may show markings
that will give him much valuable informaticn. It is
usual to form this line of light by admitting the rays
through a narrow "slit" placed at one end of a tube,
which carries at the other end an achromatic object-glass
having the slit in the principal focus. This tube, with
!The "grating" is merely a piece of glass or speculum metal, ruled
with many thousand straight, equidistant lines, from 5000 to 20,000 in
the inch.
146
LESSONS IN ASTRONOMY
slit and lens, constitutes the " collimator." Instead of
looking at the spectrum with the naked eye, it is better
also in most cases to use a small " view telescope," so
called to distinguish it from the large telescope to which
the spectroscope is often attached.
172. Construction of the Spectroscope. The instrument,
therefore, as usually constructed, and shown in Fig. 35,
Prism Spectroscope
Direct-Vision Spectroscope
FIG. 35. Different Forms of Spectroscope
consists of three parts, collimator, dispersion piece, and
view telescope, although in the " direct-vision " spectro-
scope, shown in the figure, the view telescope is omitted.
If the slit S be illuminated by strictly homogeneous light
(i.e., light all of one color), say yellow, the "real image"
of the slit will be found at Y. If, at the same time, light
of a different color red, for instance be also admitted,
THE SOLAR SPECTRUM
147
i second image will be formed at 7, and the observer will
then see a spectrum consisting of two bright lines, one
yellow, the other red, which are really nothing more than
images of the slit.
If violet light be admitted, a. third image will be formed
at F, and there will be three bright lines. If light from
a candle be admitted, there will be an infinite number of
these slit-images close together, like the pickets in a fence,
without interval or break, and we then get what is called
a " continuous " spectrum.
If, however, we look at sunlight or moonlight or the light
of a star, we shall find a spectrum continuous in the main,
FIG. 36. Small Portion of Solar Spectrum (green)
Photographed by Higgs
but crossed by thousands of dark lines, or missing slit-images
(as if some of the fence pickets had been destroyed, leav-
ing gaps in the series). The cause of these dark lines,
first noticed by Wollaston in 1800, but later and inde-
pendently discovered and carefully observed by Fraunhofer
in 1814, was a mystery for nearly fifty years, until the
epoch-making work of Kirchhoff.
173. Principles upon which Spectrum Analysis depends.
These, substantially, as announced by Kirchhoff in 1858,
are the three following:
1 . A continuous spectrum is given by bodies which are so
dense that the molecules interfere with each other in such a
148 LESSONS IN ASTRONOMY
way as to prevent their free vibration ; i.e., by bodies which
are either solid or liquid, or, if gaseous, are under pressure.
2. The spectrum of a luminous gas under low pressure
is discontinuous, that is, it is made up of bright lines or
bands, and these lines are -characteristic. The same sub-
stance under similar conditions always gives the same set
of lines, and usually it does so even under conditions which
differ rather widely; but when the circumstances differ
too much, it may give two or more different spectra.
3 (and most important for our purpose just now). A
gas or vapor absorbs from a beam of white light passing
through it precisely those rays of which its own spectrum con-
sists ; so that the spectrum of white light which has been
transmitted through such a vapor, if the vapor is cooler
than the original source of light, exhibits a "reversed"
spectrum of the gas ; i.e., we get a spectrum which shows
dark lines in place of the characteristic bright lines, as in
the spectrum of sunlight.
We therefore infer that the sun is covered by an
envelope of gases, not so hot as the luminous clouds
which form the photosphere, and that these gases by their
absorption produce the dark lines in its spectrum.
174. Experiment illustrating Reversal of Spectrum.
The principle of reversal is illustrated by Fig. 37. Sup-
pose that in front of the spectroscope we place a spirit lamp
with a little carbonate of soda and some salt of thallium
upon the wick. We shall then get a spectrum showing the
two yellow lines of sodium and the green line of thallium, all
bright, as in the upper of the two spectra. If now the lime-
light be started behind the flame, we shall at once get the
effect shown in the lower figure, a continuous spectrum
REVERSAL OF SPECTRUM LINES
149
Screen
crossed by three black lines which exactly replace the
brighter ones. Thrust a screen between the lamp flame and
the lime, and the dark lines instantly turn bright again.
The dark lines which appear when the screen is removed are dark
only relatively to the background: when the screen is taken away they
really brighten a
little (say two or
three per cent);
but the brightness
of the background
increases hundreds
of times, and so far
exceeds that of the
lines themselves
that they look
black. The dark
lines of the solar
spectrum are really
bright, and can be
photographed as
such by arranging
matters so that
one of them shall
fall upon a nar-
FIG. 37. Reversal of the Spectrum
row slit in a diaphragm which excludes all the brighter background.
175. Chemical Constituents of the Solar Atmosphere. -
By taking advantage of these principles we can detect
a large number of well-known terrestrial elements in
the sun by means of the dark lines 1 in its spectrum,
1 They are generally referred to as Fraunhofer's lines, because Fraun-
hofer was the first to map them. To some of the principal ones he
assigned letters of the alphabet, which are still retained ; thus, A is a
strong red line at the extreme end of the spectrum ; (7, one in the scarlet ;
D, one in the yellow ; and H, one in the violet.
150
LESSONS IN ASTRONOMY
which, in an instrument of high power, number several
thousand.
By proper arrangements it is possible to identify among
these lines many which are due to the presence in the sun's
atmosphere of known terrestrial elements in the state of
vapor. To effect the comparison necessary for this purpose,
the spectroscope must be so arranged that the observer can
confront the spectrum of sunlight with that of the sub-
stance to be tested. In order to do this, half of the slit is
covered by a little reflector, or " comparison prism," which
reflects into the tube the light of the sun, while the other
FIG. 38. Photographic Comparison of the Solar Spectrum with that of Iron
Trowbridge
half of the slit receives directly the light of some flame
or electric spark. On looking into the spectroscope the
observer will then see a spectrum, the lower half of which,
for instance, is made by sunlight, while the upper half is
made by light coming from an electric spark between two
metal points, say of iron. This latter spectrum will show
the bright lines of iron vapor, and the observer can then
easily see whether they do or do not correspond exactly
with the dark lines of the solar spectrum.
In such comparisons photography may be most effectively used
instead of the eye. Fig. 38 is an excellent reproduction, on a reduced
scale, of a negative made by Professor Trowbridge of Cambridge.
ELEMENTS DISCOVERED IN THE SUN 151
The lower half is the violet portion of the sun's spectrum, and the
upper half the corresponding portion of that of an electric arc charged
with the vapor of iron. (In the negative the dark lines, of course, are
bright, and vice versa.} The reader can see for himself with what
absolute certainty such a photograph indicates the presence of iron
in the solar atmosphere. A few of the lines in the photograph which
do not show corresponding lines in the solar spectrum are due to
other substances than iron.
176. Elements known to exist in the Sun. As the result
of such comparisons we have the following list of thirty-
six elements which are now known to exist in the sun.
* Calcium, 11. * Strontium, 23. Copper, 30.
* Iron. 1. Vanadium, 8. Zinc, 29.
* Hydrogen, 22. * Barium, 24. Cadmium, 26.
* Sodium, 20. , Carbon, 7. * Cerium, 10.
* Nickel, 2. Scandium, 12. Glucinum, 33.
* Magnesium, 19. Yttrium, 15. Germanium, 32.
* Cobalt, 6. Zirconium, 9. Rhodium, 27.
Silicon, 21. Molybdenum, 17. Silver, 31.
Aluminium, 25. Lanthanum, 14. Tin, 34.
* Titanium, 3. Niobium, 16. Lead, 35.
* Chromium, 5. Palladium, 18. Erbium, 28.
* Manganese, 4. Neodymium, 13. Potassium, 36.
The substances are arranged according to the intensity of the dark
lines by which they are represented in the solar spectrum, while the
numbers appended indicate the rank which each would hold if the
arrangement had been based upon the number of lines. An asterisk
denotes that the lines of the element often or always appear as bright
lines in the spectrum of the chromosphere (Sec. 180). To these
elements must be added Helium (Sec. 181), which gives no dark
lines in the spectrum of the photosphere, but does give several
conspicuous bright lines in that of the chromosphere.
In the atmosphere of the sun these bodies must be, of
course, in the condition of vapor, which is somewhat cooler
152 LESSONS IN ASTRONOMY
than the clouds which form the photosphere. It will be
noticed that all of them, carbon and hydrogen alone
excepted, are metals, and that a number of the elements
which are among the most important in the constitution
of the earth fail to present themselves. Thus far chlorine,
bromine, iodine, sulphur, and phosphorus all appear to be
missing, and the indications of oxygen (which forms fully
half the mass of the earth's crust) are very feeble. Nitrogen
probably exists in combination with carbon.
We must be cautious, however, in drawing negative
conclusions. It is quite possible that the spectra of these
bodies under solar conditions may be so different from their
spectra as presented in our laboratories, that we cannot
easily recognize them: many substances, under different
conditions, give two or more widely different spectra.
177. The Reversing Layer. According to Kirchhoff's
theory, the dark lines are most of them 1 formed by the
passing of light emitted by the minute solid or liquid
particles of the photospheric clouds through the somewhat
cooler vapors which compose the substances that we recog-
nize by the dark lines in the spectrum. If this is so, the
spectrum of the gaseous envelope, which by its absorption
forms the dark lines, ought to show a spectrum of corre-
sponding bright lines when seen by itself. The opportu-
nities are rare when it is possible to obtain a spectrum of
1 Among the thousands of lines in the solar spectrum a considerable
number originate in the atmosphere of the earth. They are mostly due
to oxygen and water-vapor, and are especially abundant in the red and
yellow portions of the spectrum. These " telluric " lines are easily distin-
guished by the fact that they become extremely conspicuous when the
sun is near the horizon, but are feeble when he is near the zenith ; and
they also vary with the dryness of the air.
THE REVERSING LAYER 153
this gaseous envelope separate from that of the photo-
sphere ; but at the time of a total eclipse, at the moment
when the sun's disk has just been obscured by the moon,
and the sun's atmosphere is still visible beyond the moon's
limb, the observer ought to see this bright-line spectrum,
if the slit of the spectroscope be carefully directed to the
proper point ; and the observation has actually been made.
The lines of the solar spectrum, which up to the time of the
total obscuration of the sun remain dark as usual, are
suddenly reversed, and the whole field of the spectroscope
is filled with brilliant colored lines, which flash out quickly,
and then gradually fade away, disappearing in about two
seconds.
The natural interpretation of this phenomenon is that
the formation of the dark lines in the solar spectrum is,
mainly at least, produced by a very thin stratum closely
covering the photosphere, since the moon's motion in
two seconds would correspond to a thickness of only
500 miles.
This observation, first made by the author in 1870, remained
long uncorroborated, but received a beautiful photographic confirm-
ation in 1896. Mr. Shackleton, the photographer of an English
party which observed the eclipse of that year in Nova Zembla,
obtained a photograph of the spectrum at the critical moment with
an exposure of less than half a second, and found it just as described,
showing several hundreds of bright lines which correspond to the
dark Fraunhofer lines. A second photograph, made only five or
six seconds later, shows only some twenty lines, well known as
belonging to the spectrum of the chromosphere and prominences.
Similar results for the " flash spectrum," as it is called, were also
obtained by various observers during the eclipses of January, 1898,
May, 1900, and May, 1901, with instruments of still higher power
than that of Mr. Shackleton.
154
LESSONS IN ASTRONOMY
There are reasons, however, to doubt whether the lines are all
produced in such a thin layer. According to Sir Norman Lockyer,
the solar atmosphere is very extensive, and certain lines of the spec-
trum appear to be formed only in the regions of lower temperature
high above the surface of the photosphere. It is probable also that
many lines originate within the photosphere and not above it, being
caused by the vapors which lie between the cloud masses that give
the brilliant light.
178. Sun-Spot Spectrum. The spectrum of a sun-spot
differs from the general solar spectrum not only in
its diminished brilliancy, but in the great widening of
certain lines, the thinning of others, and the change
of some (especially the lines of hydrogen) to bright
lines on some occasions.
i The majority of the Fraun-
hofer lines, however, are
not much affected either
way.
In the green and blue
portions of the spectrum
the darkest part of a sun-
spot spectrum is found to be composed of fine dark
lines close packed. This shows that the darkening is
due to the- absorption of light by gases and vapors, not
by mist or smoke, for then the spectrum would be
continuous.
Sometimes, in connection with sun-spots, certain lines
of the spectrum are bent and broken, as shown in
Fig. 39. These distortions are explained by the swift
motion towards or from the observer of the gaseous mat-
ter, which by its absorption produces the line in question.
In the case illustrated in the figure hydrogen was the
FIG. 39. The C line in the Spectrum
of a Sun-Spot
DOPPLER-FIZEAU PBINCIPLE 155
substance, and its motion was from the observer, nearly
300 miles a second at one point.
179. Doppler's Principle The principle upon which
the explanation of this displacement and distortion of
lines depends was first enunciated by Doppler in 1842.
It is this : When the distance between us and a body which
is emitting regular vibrations, either of sound or of light, is
decreasing, then the number of pulsations received by us
in each second is increased, and the length of the waves is
correspondingly diminished. Thus, the pitch of a musical
tone rises in the case
supposed; and in the
same way the refrangi-
bility of a light- wave,
which depends upon
its wave-length, is in-
FIG. 40. The Doppler-Fizeau Principle
creased, so that it will
fall nearer the violet end of the spectrum. This principle
finds numerous applications in modern astronomical spec-
troscopy, and it is of extreme importance that the student
should clearly understand it. In its astronomical applica-
tions it is often called the JDoppler-Fizeau principle because
Fizeau first called attention to the shift that would be
produced in the lines of a spectrum.
Fig. 40 illustrates the principle. The lower strip is a small por-
tion of the yellow part of the spectrum of an imaginary star, and
the upper the corresponding part of the spectrum of sodium with
which it is compared. The shift of the lines of the star spectrum
indicates that it is coming nearer at the rate of nearly fifty miles
a second ; some stars move faster.
It was discovered in 1895, by Humphreys and Mohler at Baltimore,
that increase of pressure causes the lines in the spectrum of a luminous
156 LESSONS IN ASTRONOMY
gas to shift slightly towards the red, very much as if the gas were
receding, though not according to the same simple law. The shift is
very slight, however, for pressures not exceeding 200 or 300 pounds to
the inch ; but it is quite possible that in cases of explosion the pres-
sures would be sufficient to cause large displacements. (See Sec. 355.)
180. The Chromosphere. Outside the photosphere, or
shining surface of the sun, lies the so-called chromosphere,
of which the stratum of gases that produce the dark lines
in the solar spectrum is the hottest and densest portion.
The word is derived from the Greek, chroma (color), and
means " color sphere." It is so called because it is bril-
liantly scarlet, owing this color to the hydrogen gas which
is its most conspicuous component. In structure it is like
a sea of flame covering the photosphere to a depth of from
5000 to 10,000 miles, and seen through a telescope at the
time of a total eclipse has been well described as looking
like a "prairie on fire." There is, however, no real
burning in the case, i.e., no heat-producing combination
of hydrogen with oxygen or with any other element.
Under ordinary circumstances the chromosphere is invisi-
ble, drowned in the light of the photosphere. It can be
seen with the telescope for only a few seconds at a time,
during the fleeting moments of a total eclipse ; but with
the spectroscope it can be studied at other times, as we
shall see.
181. Prominences and their Spectrum. The promi-
nences, or protuberances, are scarlet clouds which are seen
during a total eclipse, projecting from behind the edge of
the moon. They are simply extensions of the chromo-
sphere, or isolated clouds of the same gaseous substances,
chiefly hydrogen, their true nature having been established
T11E PROMINENCES 157
at an eclipse in 1868, when their spectrum was first satis-
factorily observed. It is composed of numerous bright
lines, conspicuous among which are the lines of hydrogen,
together with a brilliant yellow line (sometimes called D 3
because near the two so-called D lines) and the so-called H
and K lines of calcium, with a number of others that are
always present though more difficult to observe. At times
also when the solar forces are peculiarly energetic hundreds
of other lines appear, especially those of iron, titanium,
magnesium, and sodium.
For a long time the D 3 line remained entirely unidenti-
fied, and the name of helium, or " sun-metal," was proposed
and accepted for the hypothetical element to which it was
supposed to be due. In 1895, however, Dr. Ramsay, one
of the discoverers of argon, found the D 3 line in the
spectrum of a gas disengaged by heating and pumping
from a rare mineral known as uraninite, and very soon
the new gas was found by him and other observers in
various other minerals and in meteoric iron. Along with
the D 3 line were also found in the spectrum of the gas a
number of other unidentified lines of the chromosphere
spectrum, and these also appear with D 3 and the hydrogen
lines in the spectra of certain nebulse and stars.
It was a great triumph thus to " run helium to earth,"
though as yet very little is known as to its nature and
properties except that, next to hydrogen, it is the lightest
of all known gases, in chemical inertness appears to
resemble argon itself, and thus far is the only gas which
resists liquefaction.
182. Spectroscopic Observations of the Prominences and
Chromosphere. Since the spectrum of these objects is
158
LESSONS IN ASTRONOMY
composed of a small number of brilliant lines, it is possible
to observe them with a spectroscope in full daylight. The
explanation of the way in which the spectroscope effects
this lies rather beyond our limitations ; but it is sufficient
for our purpose to say that by attaching a spectroscope
FIG. 41. Prominences
1. Quiescent Prominences 2. Quiescent Prominences
3. Eruptive Prominences Flames
4. Eruptive Prominences Jets and Spikes near Sun's Limb, Oct. 5, 1871
to a good telescope the prominences can now be studied
at leisure any clear day. They are wonderfully interest-
ing and beautiful objects. Some of them, the so-called
" quiescent " prominences, are of enormous size, 50,000 or
even 100,000 miles in height, faint and diffuse, remaining
PHOTOGRAPHY OF PROMINENCES 159
almost unchanged for days. Others are much more
brilliant and active, especially those that are associated
with sun-spots, as many of them are. These " eruptive "
prominences often alter their appearance very rapidly,
so fast that one can sometimes actually see the motion :
velocities from 50 to 200 miles a second are frequently
met with. As a rule the eruptive prominences are not so
large as the quiescent ones, but occasionally they surpass
10.34 10.40 10.58
FIG. 42. Photographs of Prominences, March 25, 1895
After Hale
them, and a few have been observed to attain elevations
of more than 200,000 miles. Fig. 41 gives specimens of
both kinds.
182*. Photography of Prominences. Quite recently it
has become possible to photograph these objects at any
time by utilizing the H and K lines in their spectrum.
An explanation of the method lies quite beyond our
scope, but Professor Hale, the director of the new Yerkes
Observatory, and Deslandres in Paris, have been spe-
cially successful in this line, and both have constructed
160 LESSONS IN ASTRONOMY
spectroscopic apparatus with which, at a single operation,
they obtain a picture of the entire chromosphere arid its
prominences surrounding an image of the sun itself with its
spots and faculous regions. The solar image is really only
a picture of those parts of the disk where the calcium lines
are bright, and reveals the presence of clouds, or " flocculi,"
of glowing calcium, at a somewhat higher level than the
photosphere. Similar photographs are obtained in " hydro-
gen light," so that we may now learn something of the
distribution of these elements in the sun. The new method
is a great step in the study of solar physics. Fig. 42 is from
one of Hale's photographs and illustrates well the rapidity
with which the prominences rise and change their forms.
183. The Corona. Probably the most beautiful and
impressive of all natural phenomena is the corona, the
"glory" of light which surrounds the sun at a total
eclipse. The portion of it near the sun is dazzlingly bright
and of a pearly luster, contrasting beautifully with the
scarlet prominences, which stud it like rubies. It seems
to be mainly composed of projecting filaments of light,
which near the sun are pretty well defined, but at a little
distance fade out and melt into the general radiance.
Near the poles of the sun the corona does not usually
extend very far and has a pretty definite outline, but in
the spot regions and near the sun's equator faint streams
sometimes extend to a distance of several degrees ; and at
the distance of the sun every degree means more than a
million and a half of miles.
A very striking and perplexing feature is the existence
of dark rays or rifts, which reach clear down to the very
edge of the sun.
THE CORONA 161
The corona varies greatly in brightness at different
eclipses, according to the apparent diameter of the moon
at the time. The portion of the corona nearest the sun
is so much brighter than the outer regions that a little
increase of the moon's diameter cuts off a very large pro-
portion of the light. The total light of the corona is
usually at least two or three times as great as that of the
full moon. Fig. 43 is from a photograph of the eclipse
FIG. 43. Corona of Eclipse of 1900, Wadesboro, N.C.
of May, 1900, made at Wadesboro, N.C. At that time
the sun-spots were at their minimum, and, as is then
usual, the equatorial "wings" were very long and the
polar streamers especially numerous and well defined.
184. Spectrum of the Corona. A characteristic feature
of its spectrum is a bright green line. This line was at
first, and for a long time, supposed to coincide with the
" 1474 " line of Kirchhoff's map of the spectrum a very
puzzling circumstance, as that line is due to iron, and iron
162 LESSONS IN ASTRONOMY
vapor seemed to be a veiy improbable substance to be
found at such an elevation above the hydrogen of the
chromosphere. Photographs of the corona spectrum made
in 1896 and at the later eclipses have, however, shown
that the supposed coincidence with 1474 was a mistake,
the corona line being slightly more refrangible and nearer
the blue end of the spectrum. The photographs have
also detected several other lines in the violet and ultra-
violet, and it is now clear that the green line and the
others are due to some still unknown gaseous element
(probably lighter than hydrogen), which has been provi-
sionally called coronium, after the analogy of helium. It is
to be hoped that before very long this substance also may
be " run to earth " as helium has been.
185, The corona is proved to be a true appendage of
the sun, and not, as has been at times supposed, a mere
optical phenomenon, nor one due to the atmosphere of the
earth or moon, by two established facts :
1st. That its spectrum is not that of reflected sunlight,
but of a self-luminous gas ; and
2d. Because photographs of the corona, made at widely
different stations along the track of an eclipse, agree closely
in details.
Its real nature and relation to the sun are very difficult
to explain. It is a gaseous envelope, at least largely gas-
eous, for it may, and probably does, contain much " dust "
and " fog." It does not, however, stand in any such rela-
tio'n to the globe below as does our atmosphere, since its
streamers strongly indicate that it is not in equilibrium
under the sun's attraction, but is largely maintained and
shaped by powerful repulsive forces.
THE SUN'S LIGHT 163
Its phenomena are not yet satisfactorily explained, and
remind us far more of auroral streamers and of comets'
tails than of anything that occurs in the lower regions of
the earth's atmosphere. (See, however, Sec. 306.)
Its material is of excessive rarity, as is shown by the
fact that in a number of cases comets have passed directly
through it (as, for instance, in 1882) without the slightest
perceptible disturbance. Its density, therefore, must be
almost inconceivably less than that of the best air-pump
vacuum which we are able to produce.
THE SUN'S LIGHT AND HEAT
186. The Sun's Light. By photometric measures, which
we cannot explain here, it is found that the sun gives us
about 1575 billions of billions (1575 followed by 24 ciphers)
times as much light as a standard candle 1 would do at
that distance.
The amount of light received from the sun is about
600,000 times that given by the full moon, about
7000,000000 times that of Sirius, the brightest of the
fixed stars, and fully 200000,000000 times that of the
Pole-star.
As to the intensity of sunlight, or the intrinsic brightness
of the sun's surface, we find that it is about 190,000
times as bright as that of the candle flame, and fully
150 times as bright as the lime of a calcium light; so
that even the darkest part of a sun-spot outshines the
1 The standard candle is a sperm candle weighing one-sixth of a pound
and burning 120 grains an hour. An ordinary gas-burner usually gives a
light equivalent to from ten to fifteen candles.
164 LESSONS IN ASTRONOMY
lime light. The brightest part of an electric arc-light
comes nearer sunlight in intensity than anything else we
know of, being from one-half to one-quarter as bright as
the solar surface itself.
The sun's disk is brightest near the center, but the
variation is slight until we get pretty near the edge, where
the light falls off rapidly. Just at the sun's limb, the
brightness is not much more than a third as great as at the
center. The color there is modified also, becoming a sort
of orange red. This darkening and change of color are
due to the general absorption of light by the lower por-
tions of the sun's atmosphere. According to Langley, if
this atmosphere were suddenly removed the surface would
shine out somewhere from two to five times as brightly as
now, arid its tint would become strongly blue, like the
color of an electric arc.
187. The Quantity of Solar Heat ; the Solar Constant.
The " solar constant " is the number of heat-units which a
square unit of the earth's surface, unprotected by any
atmosphere and squarely exposed to the sun's rays, would
receive from the sun in a unit of time. The heat-unit
most used at present is the Calory, which is the quantity
of heat required to raise the temperature of one kilogram
of water 1 C. ; and as the result of the best observations
thus far made (Langley's) it appears that the Solar Constant
is approximately 21 1 of these calories to a square meter in
one minute. At the earth's surface a square meter,
owing to the absorption of a large percentage of heat by
1 The results of the Smithsonian observations, 1902-1910, give the
probable value of the solar constant as 19.5. This would change a little
the numbers given in Sees. 188 and 189.
THE SOLAR CONSTANT 165
the air, would, however, seldom actually receive more than
from ten to fifteen calories in a minute.
The true value of the solar constant is still uncertain by
a very large percentage, different observers giving values
all the way from 20 to 40.
The method of determining the solar constant is simple,
so far as the principle goes, but the practical difficulties
are serious, and thus far have prevented our obtaining the
accuracy desirable. The determination is made by allowing
a beam of sunlight of known diameter to fall upon a known
quantity of water for a known time, and measuring how
much the water rises in temperature. The principal diffi-
culty lies in determining the proper allowance to be made
for absorption of the sun's heat in passing through the
air, since this absorption varies continually and to a great
extent with changing conditions. Besides this it is neces-
sary to measure and allow for the heat which is received
by the water during the experiment from other sources
than the sun.
188. Solar Heat at the Earth's Surface. Since it
requires about 80 calories of heat to melt one kilogram of
ice, it follows that, taking the solar constant at 21, the
heat received from the sun when overhead would melt in
an hour a sheet of ice about T 7 ^ of an inch thick, From
this it is easily computed that the amount of heat received
by the earth from the sun in a year would melt a shell of
ice 124 feet thick all over the earth's surface.
." Solar engines " have been constructed within the last
few years, in which the heat received upon a large reflector
is made to evaporate water in a suitable boiler, and to drive
a steam engine. It is found that the heat received upon a
166 LESSONS IN ASTRONOMY
reflector ten feet square can be made to give practically
about one horse-power.
189. Radiation from the Sun's Surface. If we attempt
to estimate the intensity of the radiation from the surface of
the sun itself, we reach results which are simply amazing.
We must multiply the solar constant observed at the earth
by the square of the ratio between the earth's distance
from the sun and the distance of the sun's surface from
its own center, i.e., by the square of ( a |ff f f -|p-)i or about
46,000 : in other words, the amount of heat emitted in a
minute by a square foot of the sun's surface is about
46,000 times as great as tha.t received by a square foot of
surface at the distance of the earth. Carrying out the
figures, we find that if the sun were frozen over com-
pletely to a depth of about 45 feet, the heat it emits would
be sufficient to melt the ice in one minute ; that if a
bridge of ice could be formed from the earth to the sun
by an ice column 2.1 miles square, and if in some way the
entire solar radiation could be concentrated upon it, it
would be melted in one second, and in seven more would
be dissipated in vapor.
Expressing it in terms of energy, we find that the solar
radiation is nearly 100,000 horse-power continuously
for each square meter of the sun's surface.
So far as we can now see, only a very small fraction of this whole
radiation ever reaches a resting place. The earth intercepts about
**inrtWTTre and the other planets of the solar system receive in
all perhaps from ten to twenty- times as much. Something like
seems to be utilized within the limits of the solar system.
190. The Sun's Temperature. We can determine with
some accuracy the amount of heat which the sun gives :
THE SUN'S TEMPERATURE 167
to find its temperature is a very different thing, and we
really have very little knowledge about it, except that it
must be extremely high, far higher than that of any
terrestrial source of heat now known. The difficulty is
that our laboratory experiments do not give the necessary
data from which we can determine what temperature sub-
stances like those of which the sun is composed must have,
in order to enable them to send out heat at the rate which
we observe. Of two bodies at precisely the same tempera-
ture, one may send out heat a hundred times more rapidly
than the other.
The estimates as to the temperature of the photosphere
run all the way from the very low ones of some of the
French physicists (who set it at about 2500 C.) to the
absurd values of Secchi and Ericsson, who put the figure
among the millions. The latest and most authoritative
determinations by Wilson and Gray in Ireland make it
about 7000 C., or 12,500 F. The highest terrestrial
temperature (attained in the electric arc) is about 4000 C.
A very impressive demonstration of the intensity of the
sun's heat is found in the fact that in the focus of a
powerful burning lens all known substances melt and
vaporize ; and yet it can be shown that at the focus of the
lens the temperature can never even nearly equal that of
the source from which the heat is derived.
191. Constancy of the Sun's Heat. - - It seems now
very probable that the amount of the sun's radiation
varies from time to time. 'Recent results obtained by
the Smithsonian observers indicate that the solar "con-
stant" is subject to fluctuations of from three to five
per cent.
168 LESSONS IN ASTRONOMY
As to any steady progressive increase or decrease in the
amount of heat received from the sun, it is quite certain
that no considerable change has occurred for the past two
thousand years, because the distribution of plants and
animals on the earth's surface is practically the same as in
the earliest days of history. It is, however, rather prob-
able than otherwise that the great changes of climate, which
Geology indicates as having formerly taken place on the
earth, may ultimately be traced to changes in the condition
of the sun.
192. Maintenance of the Solar Heat. We cannot here
discuss the subject fully, but must content ourselves with
saying, -
First, negatively, that this maintenance cannot be
accounted for on the supposition that the sun is a hot
body, solid or liquid, simply cooling , nor by combustion,
nor (adequately) by the fall of meteors on the sun's sur-
face, though this cause undoubtedly operates to a limited
extent.
Second, we can say positively, that the solar radiation can
be accounted for on the hypothesis first proposed by Helm-
holtz, that the sun is mainly gaseous, and shrinking slowly
but continuously. While we cannot see any such shrink-
age, because it is too slow, it is a matter of demonstration
that if the sun's diameter should contract about 200 feet
a year, heat enough would be generated to keep up its radi-
ation without any lowering of its temperature. If the
shrinkage were more than this, the sun would be hotter at
the end of the year than it was at the beginning.
We can only say that while no other theory meets the
conditions of the problem, this appears to do so perfectly,
AGE AND DURATION OF SUN 169
and therefore has probability in its favor. It seems to be
only a continuation of the process of condensation by
which the sun itself and the solar system have been
formed from the original cloud or nebula.
193. Age and Duration of the Sun. Of course if this
theory is correct, the sun's heat must ultimately come to
an end ; and looking backward, it must have had a begin-
ning. If the sun keeps up its present rate of radiation,
it must, on this hypothesis, shrink to about half its diam-
eter in some 5,000000 years at the longest. It will then be
eight times as dense as now, and can hardly continue to be
mainly gaseous, so that the temperature must begin to fall
quite sensibly. It is not, therefore, likely, in the opinion
of Professor Newcomb, that the sun will continue to give
heat sufficient to support the present conditions upon the
earth for much more than 10,000000 years, if so long.
On the other hand, it is certain that the shrinkage of the
sun to its present dimensions from a diameter larger than
that of the orbit of Neptune, the remotest of the planets,
would produce about 18,000000 times as much heat as
the sun now throws out in a year. Hence, if the sun's heat
has been, and still is, wholly due to the contraction of its
mass, it cannot have been emitting heat at the present rate,
on this shrinkage hypothesis, for more than 18,000000
years. But notice the " (" It is quite possible that a
part of the solar radiation may be due to radium and
other radioactive substances. If so, the solar system may
be much older.
194. Constitution of the Sun. To sum up : the received
opinion is that the sun is mainly composed of the same
chemical elements as the earth, but that in the body, or
170 LESSONS IN ASTRONOMY
nucleus, of the sun the heat is so tremendous that they are
all in the state of vapor or gas in spite of the great pressure
to which they are subjected.
The photosphere is probably a sheet of luminous clouds,
constituted mechanically like terrestrial clouds, i.e., of
small, solid, or liquid particles, very likely of carbon,
floating in gas.
These photospheric clouds float in an atmosphere com-
posed of those gases which do not condense into solid or
liquid particles at the temperature of the solar surface.
This atmosphere is laden, of course, with the vapors out
of which the clouds have been condensed, and constitutes
the reversing layer which produces the dark lines of the
solar spectrum.
The chromosphere and prominences appear to be com-
posed of permanent gases, mainly hydrogen and helium,
which are mingled with the vapors in the region of the
photosphere, but rise to far greater elevations. For the
most part the prominences appear to be formed by jets of
hydrogen and helium, ascending through the interstices
between the photospheric clouds, like flames playing over
a coal fire.
As to the corona, it is as yet impossible to give any
satisfactory explanation of all the phenomena that it pre-
sents, and since thus far it has been possible to observe it
only during the brief moments of total eclipses, progress
in its study has been necessarily slow.
CHAPTER VII
ECLIPSES AND THE TIDES
Form and Dimensions of Shadows Eclipses of the Moon Solar Eclipses
Total, Annular, and Partial Number of Eclipses in a Year Recurrence
of Eclipses and the Saros Occupations The Tides
195. Occasionally the sun or moon is for a short time
obscured by an Eclipse (literally, a "swoon"). Solar
eclipses, when total, are among the most impressive phe-
nomena in the range of human experience, and find place
all along the records of authentic history. To the super-
stitious and ignorant they have always been terrifying and
portentous; but to the astronomer wonderfully beautiful
golden opportunities for observations important and
otherwise impossible.
An eclipse of the moon is caused by its passing through
the shadow of the earth; an eclipse of the sun by the
moon's passing between the sun and the observer, or, what
comes to the same thing, by the passage of the moon's
shadow over the observer.
The "shadow," in Astronomy, is the space from which
sunlight is excluded by an intervening body ; speaking
geometrically, it is a solid, not a surface. Since the sun
and the other heavenly bodies are very nearly spherical, these
shadows are cones with their axes in the line which joins the
centers of the sun and the shadow-casting body, the point
being always directed away from the sun.
171
172
LESSONS IN ASTRONOMY
ECLIPSES OF THE MOON
196. Dimensions of the Earth's Shadow. The length
of the shadow is easily found. In Fig. 44,0 is the center
of the sun and E the center of the earth, and aCb is the
shadow of the earth cast by the sun. It is readily shown
by Geometry that if we call EC, the length of the shadow,
L, and OE, the distance of the earth from the sun, Z>, then
L = D x ( _ J R being OA, the radius of the sun, and r
being Ea, the radius of the earth. Putting in the values of
FIG. 44. The Earth's Shadow
R and r from Sees. 160 and 112 (where, however, the earth's
mean diameter is given instead of radius) the fraction,
/ r \ 1
( _ J i comes out nearly T77o~r > and multiplying this
by D (93,000000), we get 857,000 miles for the average
length of the earth's shadow.
The length varies about 14,000 miles on each side of
the mean, in consequence of the variation of the earth's
distance from the sun at different times of the year.
From the cone aCb all sunlight is excluded, or would be were it
not for the fact that the atmosphere of the earth bends some of the
LUNAE ECLIPSES 173
rays which pass near the earth's surface into its shadow. The effect
of this atmospheric refraction is to increase the apparent diameter
of the shadow about two per cent, but to make it less perfectly dark.
If we draw the lines Be and Ad, crossing at P, between
the earth and the sun, they will bound the penumbra,
within which a part, but not the whole, of the sunlight is
cut off ; an observer outside of the shadow, but within this
partly shaded space, would see the earth as a black body
encroaching on the sun's disk, though not covering it.
197. Lunar Eclipses. The axis, or central line, of the
earth's shadow is always directed to a point directly oppo-
site the sun. If, then, at the time of full moon, the moon
happens to be near the ecliptic, i.e., not far from one of
the nodes (the points where her orbit cuts the ecliptic),
she will pass through the shadow and be eclipsed. Since,
however, the moon's orbit is inclined 5 8' to the ecliptic,
lunar eclipses do not happen very frequently, seldom more
than twice a year, because the moon at the full usually
passes north or south of the shadow, without touching it.
Lunar eclipses are of two kinds, partial and total : total
when she passes completely into the shadow ; partial when
she only partly enters it, going so far to the north or south
of the center that only a portion of the disk is obscured.
An eclipse of the moon when central (i.e., when the moon
crosses the center of the shadow) may continue total for
about two hours, the interval from the first to the last
contact being about two hours more. This depends upon
the facts that the moon's hourly motion is nearly equal to
its own diameter, and that the diameter of the earth's
shadow where the moon crosses it is between two and
three times the diameter of the moon itself. The duration
174 LESSONS IN ASTKONOMY
of an eclipse that is not central varies of course with the
part of the shadow traversed by the moon.
198. Phenomena of Total Eclipses of the Moon. Half
an hour or so before the moon reaches the shadow, its edge
begins to be sensibly darkened by the penumbra, and the
edge of the shadow itself, when it first touches the moon,
appears nearly black by contrast with the bright parts of
the moon's surface. To the naked eye the outline of the
shadow looks fairly sharp ; but even with a small telescope
it appears indefinite, and with a large telescope of high
magnifying power the edge of the shadow becomes entirely
A'
FIG. 45. Light bent into Earth's Shadow by Refraction
indistinguishable, so that it is impossible to determine
within half a minute or so the time when it reaches any
particular point.
After the moon has wholly entered the shadow, her disk
is usually distinctly visible, illuminated with a dull, copper-
colored light, which is sunlight, deflected around the earth
into the shadow by the refraction of our atmosphere, as
illustrated by Fig. 45. The brightness of the moon's disk
during a total eclipse of the moon differs greatly at dif-
ferent times, according to the condition of the weather on
the parts of the earth which happen to lie at the edges of
the earth's disk as seen from the moon. If it is cloudy
and stormy there, little light will reach the moon ; if it
happens to be clear, the quantity of light deflected into
DIMENSIONS OF MOON'S SHADOW 175
the shadow may be very considerable. In the lunar eclipse
of 1884, the moon was for a time absolutely invisible to
the naked eye, a very unusual circumstance.
During the eclipse of Jan. 28, 1888, although the moon was
pretty bright to the eye, Pickering found that its photographic power,
when centrally eclipsed, was only about T CT$irro f what it had been
before the shadow covered it.
199. Computation of a Lunar Eclipse. The computation of a
lunar eclipse is not at all complicated, though we do not propose to
enter into it. Since all its phases are seen everywhere at the same
absolute instant wherever the moon is above the horizon, it follows
that a single calculation giving the Greenwich times of the different
phenomena is all that is needed. Such computations are made and
published in the Nautical Almanac. The observer needs only to cor-
rect the predicted time by simply adding or subtracting his longitude
from Greenwich, in order to get the true local time. With an eclipse
of the sun the case is very different.
ECLIPSES OF THE SUN
200. The Length of the Moon's Shadow is very nearly
? 1_ of its distance from the sun, and averages 232,150
miles. It varies not quite 7800 miles, ranging from
228,300 to 236,050.
Since the mean length of the shadow is less than the
mean distance from the earth (238,800 miles), it is evident
that on the average the shadow will fall short of the earth.
The eccentricity of the moon's orbit, however, is so great
that she is sometimes more than 31,000 miles nearer than
at others. If when the moon is nearest the earth, the
shadow happens to have at the same time its greatest pos-
sible length, its point may reach nearly 18,400 miles beyond
176 LESSORS IX ASTRONOMY
the earth's surface. In this case the cross-section of the
shadow where the earth's surface cuts it (at o in Fig. 46)
will be about 168 miles in diameter,* which is the largest
value possible. On the other hand, when the moon is
farthest from the earth, we may have the state of things
indicated by placing the earth at B in Fig. 44. The ver-
tex of the shadow, V, will then fall about 21,000 miles short
of the earth's surface, and the cross-section of the shadow
produced will have a diameter of 196 miles at 0', where
the earth's surface cuts it.
201, Total and Annular Eclipses. To an observer within
the shadow cone (i.e., between V and the moon, Fig. 46)
the sun will be totally eclipsed. An observer in the
fe
To Sun
FIG. 46. The Moon's Shadow on the Earth
"produced" cone beyond Twill see the moon apparently
smaller than the sun, leaving a ring of the sun uneclipsed ;
this is what is called an annular eclipse. These annular
eclipses are considerably more frequent than the total, and
now and then an eclipse is annular in part of its course
across the earth and total in part. This is when the point
of the moon's shadow extends beyond the surface of the
earth, but does not reach as far as its center.
The track of the eclipse across the earth will, of course, be
a narrow stripe having its width equal to the cross-section
of the shadow, and extending across the hemisphere which
is turned towards the moon at the time, though not
PENUMBRA AND PARTIAL ECLIPSES 177
necessarily passing the center of that hemisphere. Its
course is always from the west towards the east, but
usually considerably inclined towards the north or south.
202. The Penumbra and Partial Eclipses. The penumbra
can easily be shown to have a diameter on the line CI>
(Fig. 46) a little more than twice the diameter of the moon,
or over 4000 miles. An observer situated within this
penumbra has a partial eclipse. If he is near to the cone
of the shadow, the sun will be mostly covered by the moon ;
if near the outer edge of the penumbra, the moon will but
slightly encroach on the sun's disk. While, therefore, a
total or annular eclipse is visible as such only by observers
within the narrow path traversed by the shadow-spot, the
same eclipse will be visible as a partial one anywhere within
2000 miles on each side of the path; and the 2000 miles
must be reckoned square to the axis of the shadow, and
may correspond to a much greater distance upon the
spherical surface of the earth.
203. Velocity of the Shadow and Duration of an Eclipse.
Were it not for the earth's rotation, the moon's shadow
would pass the observer at the rate of about 2100 miles an
hour. The earth, however, is rotating towards the east in
the same general direction as that in which the shadow
moves, so that the relative velocity is usually much less.
A total eclipse of the sun observed at a station near the
equator, under the most favorable conditions possible, may
continue total for about 7 m 58 s . In latitude 40 the duration
can barely equal 6 m 15 8 .
An annular eclipse may last at the equator for 12 m 24 8 ,
the maximum width of the ring of the sun visible around
the moon being V 37".
178 LESSONS IN ASTRONOMY
In the observation of an eclipse, four contacts are recognized: the
first when the edge of the moon first touches the edge of the sun,
the second when the eclipse becomes total or annular, the third at
the cessation of the total or annular phase, and the fourth when the
moon finally leaves the solar disk. ^From the first contact to the
fourth the time may be a little over four hours. In a partial eclipse,
only the first and fourth are observable, and the interval between them
may be very small when the moon just grazes the edge of the sun.
The magnitude of an eclipse is usually reckoned in digits, the
digit being T V of the sun's diameter. An eclipse of nine digits is
one in which the disk of the moon covers three-fourths of the sun's
diameter at the middle of the eclipse.
204. Phenomena of a Solar Eclipse. There is nothing
of special interest until the sun is mostly covered, though
before that time the shadows cast by the foliage begin to be
peculiar.
The light shining through every small interstice among the leaves,
instead of forming as usual a circle on the ground, makes a little
crescent, an image of the partly covered sun.
About ten minutes before totality the darkness begins to
be felt, and the remaining light, coming, as it does, from the
edge of the sun, is not only faint but yellowish, more like
that of a calcium light than sunshine. Animals are per-
plexed, and birds go to roost. The temperature falls, and
dew appears. In a few moments, if the observer is so situ-
ated that his view commands the distant western horizon,
the moon's shadow is seen coming, much like a heavy
thunder-shower, and advancing with almost terrifying
swiftness. As soon as the shadow arrives, and sometimes
a little before, the corona and prominences become visible,
while the brighter planets and stars of the first three
magnitudes make their appearance.
FREQUENCY OF ECLIPSES 179
The suddenness with which the darkness pounces upon
the observer is startling. The sun is so brilliant that even
the small portion which remains visible up to the moment
of total obscuration so dazzles the eye that it is unprepared
for the sudden transition. In a few moments, however, the
eye adjusts itself, and it is found that the darkness is really
not very intense. If the totality is of short duration, say
not more than two minutes, there is not much difficulty in
reading an ordinary watch face. In an eclipse of long
duration (four or five minutes) it is much darker, and
lanterns become necessary.
205. Calculation of a Solar Eclipse. A solar eclipse cannot be
dealt with in any such summary way as a lunar eclipse, because the
absolute times of contact are different at every different station. The
path which the shadow of a total eclipse will describe upon the earth
is roughly mapped out in the Nautical Almanacs several years before-
hand, and with the chart are published the data necessary to enable
one to calculate with accuracy the phenomena for any given place ;
but the computation is rather long and somewhat complicated.
Th. Oppolzer, a Viennese astronomer, published some years ago a
remarkable book entitled " The Canon of Eclipses," containing the
elements of all eclipses (8000 solar and 5200 lunar) occurring between
the year 1207 B.C. and A.D. 2162, with maps showing the approximate
tracks of all the solar eclipses.
206. Frequency of Eclipses and Number in a Year. The
least possible number in a year is two, both of the sun ; the
largest seven, five solar and two lunar or fpur solar and
three lunar; the most usual number is four.
The eclipses of a given year always take place at two
opposite seasons, which may be called the eclipse months
of the year, near the times when the sun crosses the nodes of
the moon's orbit. Since the nodes move westward around
180 LESSONS IN ASTRONOMY
the ecliptic once in about nineteen years (Sec. 134), the
time occupied by the sun in passing from a node to the
same node again is only 346.62 days, which is sometimes
called the eclipse year.
Taking the whole earth into account, the solar eclipses
are the more numerous, nearly in the ratio of 3 : 2. It is
not so, however, with those which are visible at a given place.
A solar eclipse can be seen only by persons who happen
to be on the narrow track described by the moon's shadow
in its passage across the globe, while a lunar eclipse is
visible over considerably more than half the earth, either
at its beginning or end, if not throughout its whole duration.
This more than reverses the proportion, i.e., at any given
place lunar eclipses are considerably more frequent than
solar. Solar eclipses that are total somewhere or other on
the earth's surface are not very rare, averaging about one for
every year and a half. But at any given place a total eclipse
happens only once in about 360 years in the long run.
During the 19th century seven shadow tracks crossed the United
States, the last in May, 1900. During the 20th the same number
are predicted, the next in 1918, the track of which runs from
Oregon to Florida. (Our insular possessions are not included in
this reckoning.)
207. Recurrence of Eclipses ; the Saros. It was known
to the Egyptians, even in prehistoric times, that eclipses
occur at regular intervals of 18 years and 11 J days (10^
days, if there happen to be five leap years in the interval).
They named this period the Saros. It consists of 223 syn-
odic months, containing 6585.32 days, while 19 eclipse years
contain 6585.78. The difference is only about 11 hours, in
which time the sun moves on the ecliptic about 28'.
CAUSE OF THE TIDES 181
If, therefore, a solar eclipse should occur to-day with
the sun exactly at one of the moon's nodes, at the end of
223 months the new moon will find the sun again close to
the node (only 28' west of it), and a very similar eclipse
will occur again ; but the track of this new eclipse will lie
about 8 hours of longitude farther west on the earth, on
account of the odd -^ of a day in the Saros. The usual
number of eclipses in a Saros is a little over 70, varying
two or three one way or the other.
In the Saros closing Dec. 22, 1889, the total number was 72,
29 lunar and 43 solar. Of the latter, 29 were central (13 total, 16
annular), and 14 were only partial.
THE TIDES
208. Cause of the Tides. Since the tides depend upon
the action of the sun and of the moon upon the waters of
the earth, they may properly
be considered here before we
deal with the planetary sys-
tem. We do not propose to B-
go into the mathematical
theory of the phenomena at
all, as it lies far beyond our E
v ., ,. , FIG. 47. The Tides
limitations ; but any person
can see that a liquid globe falling freely towards an attract-
ing body, which attracts the nearer portions more powerfully
than the more remote, will be drawn out into an elongated
lemon-shaped form, as illustrated in Fig. 47, and if the
globe, instead of being liquid, be mainly solid, but has
large quantities of liquid on its surface, substantially the
182 LESSONS IN ASTRONOMY
same result will follow. Now the earth is free in space, and
though it has other motions, it is also falling towards the
moon and towards the sun, and is affected precisely as it
would be if its other motions did not exist. The conse-
quence is that at any time there is a tendency to elongate
those diameters of the earth which are pointed towards the
moon and towards the sun. The sun is so much farther
away than the moon that its effect in thus deforming the
surface of the earth is only about five-elevenths as great
as that of the moon.
209. The tides consist in a regular rise and fall of the ocean
surface, the average interval between corresponding high
waters on successive days at any given place being 24 h 51 m ,
which is precisely the same as the average interval between
two successive passages of the moon across the meridian ;
and since this coincidence is maintained indefinitely, it of
itself makes it certain that there must be some causal con-
nection between the moon and the tides. Some one has said
that the odd fifty-one minutes is the moon's " earmark."
That the moon is largely responsible for the tides is also
shown by the fact that when the moon is in perigee, at the
nearest point to the earth, the tides are nearly twenty per
cent higher than when she is in apogee.
210. Definitions. While the water is rising, it is flood-
tide ; while falling, it is ebb-tide. It is high water at the
moment when the water-level is highest, and low water
when it is lowest. The spring-tides are the largest tides
of the month, which occur near the times of new and full
moon, while the neap tides are the smallest, and occur at
half-moon, the relative heights of spring and neap tides
being about as 8 : 3 (11 + 5 : 11 - 5).
MOTION OF THE TIDES 183
At the time of the spring-tides, the interval between
the corresponding tides of successive days is less than the
average, being only about 24 h 38 m (instead of 24 h 51 m ), and
then the tides are said to prime. At the neap tides the
interval is greater than the mean, about 25 h 6 m , and
the tide lags.
The establishment of a port is the mean interval between
the time of high water at that port and the next preceding
passage of the moon across the meridian. The " establish-
ment" of New York, for instance, is 8 h 13 m . The actual
interval between the moon's transit and high water varies,
however, nearly half an hour on each side of this mean
value at different times of the month, and under varying
conditions of the weather.
211. Motion of the Tides. If the earth were wholly
composed of water, and if it kept always the same face
towards the moon, as the moon does towards the earth,
then (leaving out of account the sun's action for the
present) a permanent tide would be raised upon the earth,
as indicated in Fig. 47. The difference between the water-
level at A and D would be a little less than two feet.
Suppose, now, the earth put in rotation. It is evident
that the two tidal waves A and B would move over the
earth's surface, following the moon at a certain angle
dependent on the inertia of the water, and tending to
move with a westward velocity equal to the earth's east-
ward rotation, about 1000 miles an hour at the equator.
The sun's action would produce similar tides superposed
upon the moon's tide, and about five-elevenths as large ; and
at different times of the month these two pairs of tides
would sometimes conspire and sometimes be opposed.
184 LESSONS IN ASTRONOMY
If the earth were entirely covered with deep water, then,
according to Professor Darwin, and considering only the
lunar tide, the tide-waves would run around the globe
regularly, and if the depth of the water were not less than
14 miles, the two tide crests would keep on the line joining
the centers of the moon and earth.
If the depth were somewhat less, the tide crests on the
equator would follow the moon at an angle of 90, but in
the high latitudes they would still move as in the deeper
ocean, while in some intermediate latitude there would
be a belt of eddying currents without either rise or fall.
But the varying depth of the ocean in different regions
and the irregular contour of its shore-line greatly compli-
cate the problem. Moreover, the continents of North and
South America, with the southern Antarctic continent,
make a barrier almost from pole to pole, leaving only a
narrow passage at Cape Horn.
As a consequence it is quite impossible to determine by
theory what the course and character of tide-waves must
be. We have to depend upon observations, and observa-
tions are more or less inadequate, because, with the excep-
tion of a few islands, our only possible tide stations are
on the shores of continents where local circumstances
largely control the phenomena.
212. Free and Forced Oscillations. If the water of the
ocean is suddenly disturbed, as, for instance, by an earth-
quake, and then left to itself, a " free wave " is formed,
which, if the horizontal dimensions of the wave are large
as compared with the depth of the water (i.e., if it is many
hundred miles in length), will travel at a rate which depends
simply on the depth of the water.
COURSE OF THE TIDE-WAVE 185
Its velocity is equal, as can be proved, to the velocity acquired by
a body in falling through half the depth of the ocean. Observations
upon waves caused by certain earthquakes in South America and
.Japan have thus informed us that between the coasts of those
countries the Pacific averages between 2| and 3 miles in depth.
Now, as the moon in its apparent diurnal motion passes
across the American continent each day and comes over
the Pacific Ocean, it starts such a " parent " wave in the
Pacific, and a second one is produced twelve hours later.
And in the same manner the sun, of course, also starts its
own independent smaller tide-waves.
These waves, once started, move on nearly (but not
exactly) like a free earthquake wave not exactly, because
the velocity of the earth's rotation being about 1040 miles
at the equator, the moon moves (relatively) westward
faster than the wave can naturally follow it, and so for
a while the moon slightly accelerates the wave. The tidal
wave is thus, in its origin, a "forced oscillation"; in its
subsequent travel it is very nearly, but not entirely, " free."
Of course as the moon passes on over the Indian and
Atlantic oceans, it starts waves in them also, which com-
bine with the parent wave coming in from the Pacific.
213, Course of Travel of the Tide- Wave. The parent wave
appears to start twice a day in the Pacific Ocean, off Callao, on the
coast of South America. From this point the wave travels northwest
through the deep water of the Pacific at the rate of about 850 miles
an hour, reaching Kamchatka in ten hours. Through the shallow
water to the west and southwest the velocity is only from 400 to 600
miles an hour, so that the wave is six hours old when it reaches New
Zealand. Passing on by Australia and combining with the small
wave which the moon starts in the Indian Ocean, the resultant tide
crest reaches the Cape of Good Hope in about twenty-nine hours and
186 LESSONS IN ASTRONOMY
enters the Atlantic. Here it combines with a smaller tide-wave,
twelve hours younger, which has " backed " into the Atlantic around
Cape Horn, and it is also modified by the direct tide produced by the
moon and sun in the Atlantic. The tide resulting from the com-
bination of these waves then travels northward through the Atlantic
at the rate of about 700 miles an hour. It is about forty hours old
when it first reaches the coast of the United States in Florida ; and
our coast lies in such a direction that it arrives at all the principal
ports within two or three hours of the same time. It is forty-one or
forty-two hours old when it reaches New York and Boston.
To reach London it has to travel around the northern end of
Scotland and through the North Sea, and is nearly sixty hours old
when it arrives at that port.
In the great oceans there are three or four such tide crests, follow-
ing nearly in the same track, but with continual minor changes.
214. Height of the Tides. In mid ocean the difference
between high and low water is usually between two and
^ ^ ^ ^-^ ^^* A r
B ^w F y y
FIG. 48. Increase in Height of Tide on approaching the Shore
three feet, as observed on isolated islands in the deep water.
On the continental shores the height is ordinarily much
greater. As soon as the tide-wave "touches bottom," so
to speak, the velocity is diminished, the tide crests are
crowded more closely together, and the height of the tide
is very much increased, as indicated in Fig. 48.
Theoretically, it varies inversely as the fourth root of the depth ;
i.e., where the water is 100 feet deep the tide-wave should be twice
as high as at the depth of 1600 feet.
TIDES IN RIVERS 187
Where the configuration of the shore forces the tide into
a corner it sometimes rises very high. At Minas Basin, on
the Bay of Fundy, tides of 70 feet are reported as not
uncommon, and an altitude of 100 feet is said to occur
sometimes. At Bristol, in the English Channel, tides of
40 or 50 feet are reached ; at the same time, on the coast
of Ireland, just opposite, the tide is very small.
215. Tides in Rivers. The tide-wave ascends a river at a rate
which depends upon the depth of the water, the amount of friction,
and the swiftness of the stream. It may, and generally does, ascend
until it comes to a rapid where the velocity of the current is greater
than that of the wave. In shallow streams, however, it dies out
earlier. Contrary to what is usually supposed, it often ascends to an
elevation far above that of the highest crest of the tide-wave at the
river's mouth. In the La Plata and Amazon, the tide goes up to an
elevation of at least 100 feet above the sea-level. The velocity of a
tide-wave in a river seldom exceeds 10 or 20 miles an hour ; and is
ordinarily much less.
CHAPTER VIII
THE PLANETARY SYSTEM
The Planets in General Their Number, Classification, and Arrangement
Bode's Law Their Orbits Keplers Lawc and Gravitation Apparent
Motions and the Systems of Ptolemy and Copernicus Determination of
Data relating to the Planets, their Diameter, Mass, etc. Herschel's Illus-
tration of the Solar System Description of the Terrestrial Planets
Mercury, Venus, and Mars
216. The earth is one of a number of bodies called
Planets, i.e., " wanderers," which revolve around the sun
in oval orbits that are nearly circular and lie nearly in one
plane or level. There are eight which are of considerable
size, besides a group of several hundred minute bodies
called the "asteroids," which seem to represent in some
way a ninth planet, either broken to pieces, or somehow
ruined in the making.
217. Classification of the Planets. The four inner
ones have been called by Humboldt the terrestrial planets,
because the earth is one of them, and the others resemble it
in size and density. In the order of distance ,from the sun
they are Mercury, Venus, the Earth, and Mars. The four
outer ones Humboldt calls the major planets, because they
are much larger and move in larger orbits. They seem
to be bodies of a different sort from the earth, very much
less dense and probably of higher temperature. They are
Jupiter, Saturn, Uranus, and Neptune.
188
THE PLANETS IN GENERAL
189
The asteroids (from the Greek cutereido*, i.e., starlike
planets), called by some minor planets, lie in the vacant
space between Mars and Jupiter, and appear to contain in
the aggregate about as much material as would make a
planet not so large as Mars.
All of the planets except Mercury and Venus have
satellites. The Earth has one, Mars two, Jupiter nine,
Saturn nine, Uranus four, Neptune one, twenty-six
in all.
218. The following little table contains in round num-
bers the principal numerical facts as to the planets.
NAME
DISTANCE IN
ASTRONOMICAL
UNITS
PERIOD
DlAMETEll
Mercury
5t 0.4
3 months
3000 miles
Venus
^ 07
74- months
7700 "
Earth
^ 10
1 year
7918 "
if) 1.5
1 yr 10 mos
4200 "
Asteroids
3
3 years to 9 years
500 to 10 miles
aO 5.2
11.9 years
88 000 miles
Saturn
*,ijk> 95
29 5 "
74 000 "
Uranus
}ioo!9.2
84.0 "
30,000 "
Neptune
3-$ <> d 30.1
164.8 "
35 000 "
This table should be learned by heart. More accurate
data will be given hereafter, but the round numbers are
quite sufficient for all ordinary purposes and are much
more easily remembered.
219. Bode's Law. If we set down a row of 4's, to the
second 4 add 3, to the third 6, to the fourth 12, etc., a
series of numbers will result which, divided by 10, will
represent the planetary distances very nearly, except in the
190 LESSONS IN ASTRONOMY
case of Neptune, whose distance is only 30 instead of 39,
as the rule would make it. Thus :
4
3
7
9
4
6
10
4
12
16
$
4
24
[28]
4
48
4
96
4
192
4
384
52
It
100
196
388
(The characters below the numbers are the symbols of the
planets, used in almanacs instead of their names.)
This law seems to have been first noticed by Titius of Wittenberg,
but bears the name of Bode, Director of the Observatory of Berlin,
who first secured general attention to it.
No logical reason can yet be given for it. It may be a mere con-
venient coincidence, or it may be the result of the process of develop-
ment, which brought the solar system into its present state.
220. Kepler's Laws. Three famous laws discovered by
Kepler (1607-1620) govern the motions of the planets.
I. The orbit of each planet is an ellipse with the sun in
one of its foci. (For a description of the ellipse, see Appen-
dix, Sec. 429.)
II. In the motion of each planet around the sun, the
radius vector describes equal areas in equal times. (For
illustration, see Sec. 121, Fig. 14.) *
III. The squares of the periods of the planets are propor-
tional to the cubes of their mean distances from the sun. This
is known as the " Harmonic Law." Stated as a propor-
tion it reads : P x 2 : P 2 2 : : A^ : A, or in words :
The square of the period of planet No. 1 is to the square
of the period of planet No. 2 as the cube of the mean dis-
tance of planet No. 1 is to the cube of the mean distance of
planet No. 2. Planets No. 1 and No. 2 are any pair of
THE PLANETS IN GENERAL 191
planets selected at pleasure. (For fuller illustration, see
Appendix, Sec. 430.)
It was the discovery of this law which so filled Kepler
with enthusiasm that he wrote, "If God has waited 6000
years for a discoverer, I can wait as long for a reader."
221, Gravitation. When Kepler discovered these three
laws he could give no reason for them no more than we
can now for Bode's law; but some sixty years later
Newton showed that they all follow necessarily as conse-
quences of the law of gravitation, which he had discovered ;
namely, that " every particle of matter in the universe
attracts every other particle with a force that varies directly
as the masses of the particles, and inversely as the square of
the distance between them" It would take us far beyond
our limits to attempt to show how Kepler's laws follow
from this, but they do. The only mystery in the case is
the mystery of the "attraction" itself; for this word
" attraction " is to be taken as simply describing an effect
without in the least explaining it.
Things take place as if the atoms had in themselves intelligence
to recognize each other's positions, and power to join hands in some
way, and pull upon each other through the intervening space, whether
it be great or small. But neither Newton nor any one else supposes
that atoms are really endowed with any such power, and the^expla-
nation of gravity remains to be found. Very probably it is somehow
involved in that constitution of the material universe which makes
possible the transmission of light and heat and electric and mag-
netic forces through space apparently empty, but probably filled with
that mysterious substance " the ether " of the physicists.
222. Sufficiency of Gravitation to explain the Planetary
Motions. We wish to impress as distinctly as possible
upon the student one idea, this namely, that given a
192
LESSONS IN ASTRONOMY
planet once in motion, nothing further than gravitation is
required to explain perfectly all its motions forever after.
Many half-educated people have an idea that some other
force or mechanism must act to keep the planets going.
FIG. 49. The Smaller Planetary Orbits
v This is not so : not a single motion in the whole planetary
system has ever yet been detected for which gravitation
fails to -account.
223. Map of the Orbits. Fig. 49 shows the smaller
orbits of the system (including the orbit of Jupiter), drawn
THE PLANETS IN GENERAL 193
to scale, the radius of the earth's orbit being taken as
four-tenths of an inch.
On this scale, the diameter of Saturn's orbit would be 7.4 inches,
that of Uranus would be 13.4 inches, and that of Neptune about
2 feet. The nearest fixed star, on the same scale, would be a mile
and a quarter away.
It will be seen that the orbits of Mercury, Mars, Jupiter,
and several of the asteroids are quite distinctly "out of
center " with respect to the sun. The orbits are so nearly
circular that there is no noticeable difference between their
length and their breadth, but the eccentricity shows plainly
in the position of the sun.
224. Inclination of the Orbits. The orbits are drawn
as if they all lay on the plane of the ecliptic, i.e., on the
surface of the paper.
This is not quite cor-
rect. The orbit of the
asteroid Pallas should
be really tipped up at
an angle of nearly 30,
and that of Mercury, FIG. 50. Inclination and Line of Nodes
which is more inclined
to the ecliptic than the orbit of any other of the principal
planets, is sloped at an angle of 7. The inclinations, how-
ever, are so small (excepting the asteroids) that they may be
neglected for ordinary purposes. On the scale of the dia-
gram, Neptune, which rises and falls the most of all with ref-
erence to the plane of the ecliptic, would never be more than
a third of an inch above or below the level of the paper.
The line in which the plane of . a planet's orbit cuts the
plane of the earth's orbit at the ecliptic is called the Line
194
LESSONS IN ASTRONOMY
of Nodes. Fig. 50 shows how the line of nodes and, z,
the inclination of the two orbits, are related.
225. Geocentric Motions of the Planets, i.e., their Motions
with Respect to the Earth regarded as the Center of Obser-
vation. While the planets revolve regularly in nearly cir-
cular orbits around the sun, with velocities 1 which depend
upon their distance from it, the motions relative to the earth
are very different, being made up of the planet's real motion
combined with the appar-
ent motion due to that
of the earth in her own
orbit.
If, for instance, we
keep up observations, for
a long time, of the direc-
tion of Jupiter as seen
from the earth, at the
same time watching the
changes of its distance
by measuring the alter-
ations of the planet's
apparent size as seen in
the telescope, and then plot the results to get the form of
the orbit of Jupiter with reference to the earth, we get a
path like that shown in Fig. 51, which represents his
motion relative to the earth during a term of about
twelve years. The appearances are all the same as if the
earth were really at rest while the planet moved in this
odd way.
1 Q
1 A planet's velocity in miles per second equals very nearly
the distance being expressed as in Sec. 218.
FIG. 51. Apparent Geocentric Motion of
Jupiter
THE PLANETS IN GENERAL
195
The procedure for finding this relative, or geocentric, orbit of
Jupiter is the same as that indicated in Appendix, Sec. 428, for find-
ing the form of the earth's orbit around the sun.
226. Direct and Retrograde Motion. With the eye alone
the changes in a planet's diameter would not be visible,
and we should notice only the alternating direct (eastward)
and retrograde (westward) motion of the planet among the
stars. If we watch one of the planets (say Mars) for a
few weeks, beginning at the time when it rises at sunset,
FIG. 52. Apparent Motions of Saturn and Uranus in 1897
we shall find that each night it has traveled some little
distance to the west; and it will keep up this westward
or retrograde motion for some weeks, when it will stop or
become " stationary," and will then reverse its motion
and begin to move eastward. If we watch long enough
(1.0., for several years), we shall find that it keeps up this
oscillating motion all the time, the length of its eastward
swing being always greater than that of the corresponding
westward one. Fig. 52 shows the alternate progression
and retrogression of Saturn and Uranus during 1897. All
196
LESSONS IN ASTRONOMY
the planets, without exception, behave alike in this respect,
as to their alternate direct and retrograde motion among
the stars.
227. Elongation and Conjunction. The visibility of a
planet does not, however, depend upon its position among
the stars, but upon its position in the sky with reference
Conjunction
Greatest E.
ion
Opposition
FIG. 53. Planetary Configurations
to the sun's place. If it is very near the sun, it will be
above the horizon only by day, and generally we cannot
see it. The Elongation of a planet is the apparent distance
from the sun in degrees, as seen from the earth, of course.
In Fig. 53, for the planet P, it is the angle PES. When
the planet is in line with the sun as seen from the earth,
at B, C, or I in the figure, the elongation is zero, and the
THE PLANETS IN GENERAL 197
planet is said to be in conjunction; inferior conjunction,
if the planet is between the earth and the sun, as at J;
superior, if beyond the sun, as at B or C. When the
elongation is 180, as at A, the planet is said to be in
opposition. When the planet is at an elongation of 90,
as at F or G, it is in quadrature. Evidently only those
planets which lie within the earth's orbit, and are called
" inferior " planets, can have an inferior conjunction ; and
only those which are outside the earth's orbit (the " supe-
rior" planets) can come to quadrature or opposition.
228. Synodic Period. The synodic period of a planet is
the time occupied by it in passing from conjunction to con-
junction again, or from opposition to opposition ; so called
because the word "synod" is derived from two Greek
words which mean "a coming together." The relation
of the synodic period to the sidereal is the same for planets
as in the case of the moon. If E is the length of the
true (sidereal) year, and P the planet's sidereal period, S
being the length of the synodic period, then
(The difference between and is to be taken without
Mi JT
regard to which of the two is the larger.)
229. The Synodic Motion, or Apparent Motion of a Planet
with Respect to " Elongation " or to the Sun's Place in the
Sky. In this respect there is a marked difference between
the superior and inferior planets.
(a) The inferior planets are never seen very far from
the sun, but appear to oscillate back and forth in front of
and behind him. Venus, for instance, starting at superior
198 LESSONS IN ASTRONOMY
conjunction at C (Fig. 53), seems to come out eastward
from the sun as an evening star, until, at the point V, she
reaches her greatest eastern elongation, about 47 from the
sun. Then she begins to diminish her elongation, and
approaches the sun, until she comes to inferior conjunc-
tion, at /. From there she continues to move westward as
morning star, until she comes to V 1 , her greatest western
elongation, and there she begins to diminish her western
elongation until, at the end of the synodic period, she is
back at superior conjunction. The time taken to move
from V' to V through C is, in her case, more than three
times that required to slide back from V to V through /.
(b) The superior planets may be found at all elonga-
tions, and do not oscillate back and forth with reference to
the apparent place of the sun, but continually increase their
western elongation or decrease their eastern. They always
come to the meridian earlier on each successive night, though
the difference is not uniform. A superior planet is known
as morning star from the time it passes conjunction until
it reaches opposition, when it rises at sunset ; it is evening
star while passing from opposition back to conjunction.
230. Ptolemaic and Copernican Systems. Until the
time of Copernicus (about 1540) the Ptolemaic system
prevailed unchallenged. It rejected the idea of the earth's
rotation (though Ptolemy accepted the rotundity of the
earth), placing her at the center of things and teaching
that the apparent motions of the stars and planets were
real ones. It taught that the celestial sphere revolves daily
around the earth, carrying the stars and planets with it,
and that besides this diurnal motion, the moon, the sun,
and all the planets revolve around the earth within the
THE PLANETS IN GENERAL 199
sphere, the two former steadily, but the planets with the
peculiar looped motion shown in Fig. 51.
Copernicus put the sun at the center, making the earth
revolve on its axis and travel around the sun, and showed
that it was possible in this simple way to account for all
the otherwise hopelessly complicated phenomena of the
planetary and diurnal motions, so far as then known. It
was not until after the invention of the telescope and the
introduction of new methods of observation that the facts
which absolutely demonstrated the orbital motion of the
earth were brought to light, viz., Aberration of Light
(Appendix, Sec. 435) and Stellar Parallax (Sec. 343).
THE PLANETS THEMSELVES
231. In studying the planetary system we meet a num-
ber of inquiries which refer to the planet itself and not to
its orbit, relating, for instance, to its magnitude ; its mass,
density, and surface gravity ; its diurnal rotation and oblate-
ness; its brightness, phases, and reflecting power, or "albedo";
the peculiarities of its spectrum ; its atmosphere ; its surface
markings and topography ; and, finally, its satellite system.
232. Magnitude. The size of a planet is found by
measuring its apparent diameter (in seconds of arc) with
some form of "micrometer." (See Appendix, Sec. 415.)
Since we can find the distance of a planet from the earth
at any moment when we know its orbit, this micrometric
measure will give us the means of finding at once the
planet's diameter in miles.
If we take r to represent the number of times by which
the planet's semi-diameter exceeds that of the earth, then
200 LESSONS IN ASTRONOMY
the area of the planet's surface compared with that of the
earth equals r 2 , and its volume or bulk equals r 3 . The
nearer the planet, other things being equal, the more
accurately r and the quantities to be derived from it can
be determined. An error of 0".l in measuring the appar-
ent diameter of Venus when nearest us counts for less
than thirteen miles, while in Neptune's case, the same
error would correspond to more than 1800 miles.
233. Mass, Density, and Gravity. If the planet has a
satellite, its mass is very easily and accurately found from
the following proportion, which we simply state without
demonstration (see General Astronomy, Arts. 536, 539), viz. :
A 3 a 3
Mass of Sun : Mass of Planet : : - : ;
J- t
in which A is the mean distance of the planet from the
sun and T its sidereal period of revolution, while a is
the distance of the satellite from the planet and t its
sidereal period; whence
/a 3 T 2 \
Mass of Planet = Sun X I ^ x -p J.
The calculations indicated are very easy with the help of loga-
rithms, and if the student has learned to use them it will be well for
him to verify some of the planet masses from the data for the satel-
lites given in Table III, p. 403.
Substantially the same proportion may be used to compare the
planet with the earth, viz. :
(Earth + Moon) : (Planet + Satellite) : : ^ : ^;
*i 'a
! and ^ being here the period and distance of the moon, and a 2
and t 2 those of the planet's satellite.
If the planet has no satellite, the determination of its
mass is a difficult matter, depending upon perturbations
produced by it in the motions of the other planets.
THE PLANETS IN GENERAL 201
Having the planet's mass compared with the earth, we
get its density by dividing the mass by the volume, and
the superficial gravity is found by dividing by r 2 the mass
of the planet compared with that of the earth.
234, The Rotation Period and Data connected with it.
The length of the planet's day, when it can be determined
at all, is ascertained by observing with the telescope some
spot on the planet's disk, and noting the interval between
its returns to the same apparent position. -The inclination
of the planet's equator to the plane of its orbit, and the
position of its equinoxes, are deduced from the same
observations that give the planet's diurnal rotation ; we
have to observe the path pursued by a spot in its motion
across the disk. Only Mars, Jupiter, and Saturn permit
us to find these elements with any considerable accuracy.
The ellipticity or oblateness of the planet, due to its
rotation, is found by taking measures of its polar and
equatorial diameters.
235. Data relating to the Planet's Light. A planet's
brightness and its reflecting power, or " albedo," are deter-
mined by photometric observations, and the spectrum of the
planet's light is of course studied with the spectroscope.
The question of the planet's atmosphere is investigated by
means of various effects upon the planet's appearance and
light, and by the phenomena that occur when the planet
comes very near to a star or to some other heavenly body
which lies beyond. The planet's surface markings and
topography are studied directly with the telescope, by mak-
ing careful drawings of the appearances noted at different
times. Photography, also, is beginning to be used for
the purpose. If the planet has any well-marked and
LESSONS IN ASTRONOMY
characteristic spots upon its surface by which the time of
rotation can be found, then it soon becomes easy to identify
such as are really permanent, and after a time we can
chart them more or less perfectly ; but we add at once that
Mars is the only planet of which, so far, we have been able
to make anything which can be fairly called a map.
236. Satellite System. The principal data to be ascer-
tained are the distances and periods of the satellites. These
are obtained by micrometric measures of the .apparent
distance and direction of each satellite from the planet, fol-
lowed up for a considerable time. In a few cases it is pos-
sible to make observations by which we can determine the
diameters of the satellites, and when there are a number
of satellites together their masses may sometimes be ascer-
tained from their mutual perturbations. With the excep-
tion of our moon and the outer satellites of Jupiter and
Saturn, all the satellites of the solar system move very
nearly in the plane of the equator of the planet to which
they belong, at least so far as known, for we do not
know with certainty the position of the equators of Uranus
and Neptune. Moreover, all the satellites, except the moon,
Hyperion, and those recently discovered, move in orbits
that are very nearly circular.
237. Tables of Planetary Data. In the Appendix we
present tables of the different numerical data of the solar
system, derived from the best authorities and calculated
for a solar parallax of 8".80, the sun's mean distance being
therefore taken as 92,897000 miles. These tabulated
numbers, however, differ widely in accuracy. The periods
of the planets and their distances in " astronomical units "
are very accurately known ; probably the last decimal in
the table may be trusted. Next in certainty come the
THE PLANETS IN GENERAL
203
masses of such planets as have satellites, expressed in terms
of the sun's mass. The masses of Venus and Mercury are
much more uncertain.
The distances of the planets in miles, their masses in
terms of the earth's mass, and their diameters in miles, all
involve the solar parallax and are affected by the slight
uncertainty in its amount. For the remoter planets,
FIG. 54. Kelative Size of the Planets
diameters, volumes, and densities are all subject to a very
considerable percentage of error. The student need not
be surprised, therefore, at finding serious discrepancies
between the values given in these tables and those given
in others, amounting in some cases to ten or twenty per
cent, or even more. Such differences merely indicate the
actual uncertainty of our knowledge. Fig. 54 gives an
idea of the relative sizes of the planets.
204 LESSONS IN ASTRONOMY
The sun, on the scale of the figure, would be about a
foot in diameter.
238. Sir John Herschel's Illustration of the Dimensions of the
Solar System. In his "Outlines of Astronomy," Herschel gives
the following illustration of the relative magnitudes and distances
of the members of our system :
Choose any well-levelled field. On it place a globe two feet in
diameter. This will represent the sun. Mercury will be represented by
a grain of mustard seed on the circumference of a circle 164 feet in
diameter for its orbit ; Venus, a pea, on a circle of 284 feet in diameter ;
the Earth, also a pea, on a circle of 430 feet ; Mars, a rather large pin's
head, on a circle of 654 feet ; the asteroids, grains of sand, on orbits hav-
ing a diameter of 1000 to 1200 feet ; Jupiter, a moderate-sized orange, on
a circle nearly half a mile across ; Saturn, a small orange, on a circle of
four-fifths of a mile ; Uranus, a full-sized cherry or small plum, upon a
circumference of a circle more than a mile in diameter ; and, finally,
Neptune, a good-sized plum, on a circle about 2-J- miles in diameter.
We may add that on this scale the nearest star would be on the
opposite side of the earth, 8000 miles away.
THE TERRESTRIAL PLANETS MERCURY, VENUS,
AND MARS
MERCURY
239. Mercury has been known from the remotest antiq-
uity, and among the Greeks it had for a time two names,
Apollo when it was morning star, and Mercury when it
was evening star. It is so near the sun that it is com-
paratively seldom seen with the naked eye, but when near
its greatest elongation it is easily enough visible as a bril-
liant reddish star of the first magnitude, low down in the
twilight. It is best seen in the evening at such eastern
MERCURY 205
elongations as occur in the spring. When it is morning
star it is best seen in the autumn.
It is exceptional in the solar system in various ways. It
is the nearest planet to the sun, receives the most light and
heat, is the swiftest in its movement, and (excepting some
of the asteroids) has the most eccentric orbit, with the
greatest inclination to the ecliptic. It is also the smallest in
diameter (again excepting the asteroids), and has the least
mass of all the planets.
240. Its Orbit. The planet's mean distance from the
sun is 36,000000 miles, but the eccentricity of its orbit is
so great (0.205) that the sun is 7,500000 miles out of the
center, and the distance ranges all the way from 28 ^
to 43J millions, while the planet's velocity in the differ-
ent parts of its orbit varies from 36 miles a second to
only 23.
A given area upon its surface receives on the average
nearly seven times as much light and heat as the same area
would on the earth ; but the heat received when the planet
is at perihelion is 2| times greater than at aphelion. For
this reason there must be at least two seasons in its year,
due to the changing distance of the planet from the sun,
whatever may be the position of its equator or the length
of its day. The sidereal period is 88 days, and the syn-
odic period (or time from conjunction to conjunction) is
116 days. The greatest elongation ranges from 18 to 28,
and occurs about 22 days before and after the inferior
conjunction. The inclination of the orbit to the ecliptic
is about 7.
241. Planet's Magnitude, Mass, etc. The apparent
diameter of Mercury varies from 5" to about 13", according
206
LESSONS IN ASTRONOMY
to its distance from us, and its real diameter is very
near 3000 miles. This makes its surface about ^ that of
the earth, and its bulk, or volume, y 1 ^. The planet's mass
is very difficult to determine, since it has no satellite, and
consequently it is not accurately known. Probably it is
about 2\ of the earth's mass ; it is certainly smaller than
that of any other planet (asteroids excepted).
Our uncertainty as to the mass prevents us from assign-
ing certain values to its density or superficial gravity ; but
if its mass as given above is correct, it is probably not
FIG. 55. Phases of Mercury and Venus
quite so dense as the earth, and the force of gravity upon
it is about one-third what it is upon the earth.
242. Telescopic Appearances , Phases , etc . Seen through
the telescope the planet looks like a little moon, showing
phases precisely similar to those of our satellite. At infe-
rior conjunction the dark side is towards us, at superior con-
junction the illuminated surface. At greatest elongation
the planet appears as a half-moon. It is gibbous between
superior conjunction and greatest elongation, while between
inferior conjunction and greatest elongation it is crescent.
Fig. 55 illustrates these phases.
MERCURY 20T
The atmosphere of the planet cannot be as dense as that
of the earth or Venus, because at a transit it shows no
encircling ring of light, as Venus does (Sec. 248). Both
Huggins and Vogel, however, report that the spectrum of
the planet, in addition to the ordinary dark lines belonging
to the spectrum of reflected sunlight, shows certain bands
known to be due to water-vapor, thus indicating that water
exists in the planet's atmosphere.
Generally Mercury is so near the sun that it can be
observed only by day, but when proper precautions are
taken to screen the object-glass of the telescope from direct
sunlight, the observation is not especially difficult. The
surface presents very little of interest. The disk is brighter
at the edge than at the center, but the markings are not
well enough denned to give us any really satisfactory
information as to its topography.
The albedo, or reflecting power, of the planet is very
low, only 0.13, somewhat inferior to that of the moon
and very much below that of any other of the planets.
No satellite is known, and there is no reason to suppose
that it has any.
243. Diurnal Rotation of the Planet. In 1889 Schia-
parelli, the Italian astronomer, announced that he had dis-
covered certain markings upon the planet, and that they
showed that the planet rotates on its axis only once during
its orbital period of eighty-eight days, thus keeping the
same face always turned towards the sun, in the same way
that the moon behaves with respect to the earth. Owing
to the eccentricity of the planet's orbit, however, it must
have a large libration (Sec. 145), amounting to about 23
on each side of the mean ; i.e., seen from a favorable station
208 LESSONS IN ASTRONOMY
on the planet's surface, the sun, instead of rising and set-
ting as with us, would seem to oscillate back and forth
through an arc of 47 once in 88 days.
This asserted discovery is very important and has excited
great interest. Schiaparelli is probably correct, and Lowell
at the Flagstaff Observatory corroborates him; but some
are still skeptical, and it may be well to wait for confir-
mation of his observations by others before absolutely
accepting the conclusion.
244. Transits of Mercury. At the time of inferior
conjunction the planet usually passes north or south of
the sun, the inclination of its orbit being 7; but if the
conjunction occurs when the planet is very near its node
(Sec. 224), it crosses the sun's disk and becomes visible
upon it as a small black spot, not, however, large enough
to be seen without a telescope, as Venus can under similar
circumstances. Since the earth passes the planet's line of
nodes on May 7 and November 9, transits can occur only
near those days, and certain peculiarities in the planet's
orbit make the November transits about twice as numerous
as those that come in May.
Transits took place on May 9, 1891, Nov. 10, 1894, Nov. 14,
1907, and Nov. 7, 1914 ; the next will occur in May, 1924, and- in
November, 1927.
Transits of Mercury are of no particular astronomical importance,
except as furnishing accurate determinations of the planet's place in
the sky at a given time.
VENUS 209
VENUS
245. The second planet in order from the sun is Venus,
the brightest and most conspicuous of all. It is so brilliant
that at times it casts a shadow, and is often easily seen by
the naked eye in the daytime. Like Mercury, it had two
names among the Greeks, Phosphorus as morning star,
and Hesperus as evening star.
Its mean distance from the sun is 67,200000 miles, and
its distance from the earth ranges from 26,000000 miles
(93-67)tol60,000000 (93 + 67). No other body ever comes
so near the earth except the moon, and occasionally a comet.
The eccentricity of the orbit of Venus is the smallest in the
planetary system, only 0.007, so that the greatest and least
distances of the planet from the sun differ from the mean less
than 500,000 miles. Its sidereal period is 225 days, or
seven months and a half, and its synodic period 584 days,
a year and seven months. From inferior conjunction
to greatest elongation is only 71 days. The inclination of
its orbit is not quite 3, less than half that of Mercury.
246. Magnitude, Mass, Density, etc. The apparent
diameter of the planet varies from 67" at the time of
inferior conjunction to only 11" at superior, the great dif-
ference arising from the enormous variation in the distance
of thj planet from the earth. The real diameter of the
planet in miles is about 7700. Its surface compared with
that of the earth is T 9 ^-; its volume, -ffo. By means of
the perturbations she produces upon the earth, the mass of
Venus is found to be not quite four-fifths of the earth's
mass, so that her mean density is a little less than the
earth's. In magnitude she is the earth's twin sister.
210 LESSONS IN ASTRONOMY
247. General Telescopic Appearance, Phases, etc. The
general telescopic appearance of Venus is striking on
account of her great brilliancy, but exceedingly unsatisfac-
tory, because nothing is distinctly outlined upon the disk.
When about midway between greatest elongation and
inferior conjunction the planet has an apparent diameter
of 40", so that, with a magnifying power of only 45, she
looks exactly like the moon four days old, and of the same
apparent size. (Very few persons, however, would think
so on the first view through the telescope; the novice
always underrates the apparent size of a telescopic object.)
The phases of Venus were first discovered by Galileo in 1610, and
afforded important evidence as to the truth of the Copernican system
as against the Ptolemaic.
Fig. 56 represents the planet's disk as seen at five points in its orbit.
1, 3, and 5 are taken at superior conjunction, greatest elongation, and
near inferior conjunction, respectively, while 2 and 4 are at intermedi-
ate points. (No. 2 is badly engraved, however ; the sharp corners are
impossible since a " terminator " is always a semi-ellipse (Sec. 146)).
The planet attains its maximum brightness when its
apparent area is at a maximum, about thirty-six days before
and after inferior conjunction. According to Zollner, the
" albedo " of the planet is 0.50; i.e., it reflects about half the
light which falls upon it, the reflecting power being about
three times that of the moon and almost four times that of
Mercury. It is, however, slightly exceeded by the reflect-
ing power of Uranus and Jupiter, while that of Saturn is
about the same. The high albedo is, by most astronomers,
considered to indicate a surface mostly covered with clouds,
since few rocks or soils could match its brightness. (But
see Sec. 249.) Like Mercury, Mars, and the moon, the disk
VENUS
211
of Venus is brightest at the edge, in contrast with the
appearance of Jupiter and Saturn.
248. Atmosphere of the Planet. There is no question
that it has an atmosphere of some density. When the
planet is half-way upon the sun's disk at the time of a
"transit," the dark part of the planet outside the sun is
encircled by a thin line of light due to the refraction,
FIG. 56. Telescopic Appearances of Venus
reflection, and scattering of sunlight by the planet's atmos-
phere. And when the planet is near the sun, at the time
of inferior conjunction, the horns of its crescent extend far
beyond the diameter. When very near, as in 1898, the
horns coalesce, and the brightest part of the complete ring
is then on the side next the sun, showing that the illumina-
tion is then due mainly to reflection and not to refraction
212
LESSONS IN ASTRONOMY
as,. formerly supposed. The height and density of its
atmosphere appear to be about two-thirds as great as that
of the earth. Fig. 57 represents the appearance noted by
Vogel during the transit of 1882.
The presence of water-vapor was announced by some of
the earlier spectroscopists, but later observations fail to
confirm it, leaving
the fact somewhat
doubtful. Many
observers have also
reported faint lights
as visible at times
on the dark por-
tions of the planet's
disk. These cannot
be accounted for by
any mere reflection
or refraction of sun-
light, but must orig-
inate on the planet
itself. They recall
the Aurora Borealis
and other electrical
manifestations on
the earth, though it is impossible to give a certain expla-
nation of them as yet.
249. Surface Markings, Rotation, etc. As has been said,
Venus is a very unsatisfactory telescopic object. She pre-
sents no obvious surface markings, nothing but occasional
indefinite shadings. Sometimes, however, when in the cres-
cent phase, intensely bright spots have been reported near
FIQ. 57. Atmosphere of Venus as seen during
a Transit
Vogel, 1882
VENUS
213
the points of the crescent, which may perhaps be " ice-caps"
like those which are seen on Mars. The darkish shadings
may possibly be continents and oceans, dimly visible, but
the prevailing impression is that they are cloudlike and
purely atmospheric, the real surface of the planet being
always hidden.
Fig. 58 is from drawings made by Mascari at the observa-
tory on Mt. Etna, and is an excellent representation of the
appearance of the planet in a good telescope.
FIG. 58. Venus
After Mascari
As to the rotation period of the planet, nothing is yet
certainly known. The length of its day has been set, on
very insufficient grounds, at about 23 h 21 m ; but the recent
work of Schiaparelli makes it almost certain that this result
cannot be trusted, and renders it rather probable that Venus
behaves like Mercury in its diurnal rotation, the length of
its sidereal day being equal to the time of its orbital revo-
lution. Lowell indeed asserts this positively, but certain
other observers still maintain the correctness of the old
period. The spectroscope will probably settle the question
on Doppler's principle (Sec. 179), by showing how rapidly
214 LESSONS IN ASTRONOMY
the edge of the planet's disk moves towards or from the
earth. Thus far the observations rather favor the longer
period, but are hardly decisive.
The planet's disk shows no sensible oblateness.
No satellite has ever been discovered ; not, however, for
want of earnest searching.
250. Transits. Occasionally Venus passes between the
earth and the sun at inferior conjunction, giving us a
so-called " transit." She is then visible, even to the naked
eye, as a black spot on the sun's disk, crossing it from east
to west. When the transit is central it occupies about
eight hours, but when the track lies near
the edge of the disk the duration is cor-
respondingly shortened. Since the earth
passes the nodes of the orbit on June 5
and December 7, all the transits occur
near these days, but they are extremely
rare phenomena. Their special interest
FIG. 59. Transit of consists in their availability for the pur-
Venus Tracks ,. , , .,
pose of finding the sun s parallax. (See
Appendix, Sec. 437, and General Astronomy, Chap. XVI.)
The first observed transit in 1639 was seen by only two persons,
Horrox and Crabtree, in England, but the four which have occurred
since then have been observed in all parts of the world by scientific
expeditions sent out for the purpose by the different governments.
The transits of 1769 and 1882 were visible in the United States.
Transits of Venus have occurred or will occur at the following dates :
Dec. 7, 1631, Dec. 4, 1639, Dec. 9, 1874, Dec. 6, 1882,
June 5, 1761, June 3, 1769, June 8, 2004, June 6, 2012.
Fig. 58 shows the tracks of Venus across the sun's disk during the
transits of 1874 and 1882.
MARS 215
MARS
251, This planet, also, has always been known. It is so
conspicuous on account of its fiery red color and brightness,
as well as the rapidity and apparent capriciousness of its
movement among the stars, that it could not have escaped
the notice of the very earliest observers.
Its mean distance from the sun is a little more than one
and a half times that of the earth (141,500000 miles), and
the eccentricity of its orbit is so considerable (0.093) that
its radius vector varies more than 26,000000 miles. At
opposition the planet's average distance from the earth is
48,600000 miles; but when opposition occurs near the
planet's perihelion this distance is reduced to less than
36,000000 miles, while near aphelion it is over 61,000000.
At conjunction the average distance from the earth
is 234,000000.
The apparent diameter and brightness of the planet, of
course, vary enormously with these great changes of dis-
tance. At a favorable opposition (when the planet's
distance from us is the least possible) it is more than fifty
times as bright as at conjunction and fairly rivals Jupiter ;
when most remote, it is hardly as bright as the Pole-star.
The favorable oppositions occur always in the latter part of
August and at intervals of fifteen or seventeen years. The last such
opposition was in 1909.
The inclination of the orbit is small, 1 51'. The
planet's sidereal period is 687 days (one year, ten and a
half months) ; its synodic period is much the longest in
the planetary system, being 780 days, or nearly two years
216
LESSONS IN ASTRONOMY
and two months. During 710 of these 780 days it moves
towards the east, and retrogrades during 70.
252. Magnitude, Mass, etc. The apparent diameter of
the planet ranges from 3 ".6 at conjunction to 25" at a
favorable opposition. Its real diameter is approximately
4200 miles, with an error of perhaps 50 miles one way or
the other. This makes its surface about two-sevenths, and
its volume one-seventh of the earth's. Its mass is a little
less than one-ninth of the
earth's mass, its density
0.73, and its superficial grav-
ity 0.38 ; i.e., a body which
here weighs 100 pounds
would have a weight of only
38 pounds on the surface
of Mars.
253. General Telescopic
Aspect, Phases, etc. When
the planet is nearest it is
more favorably situated for
telescopic observation than
any other heavenly body,
the moon alone excepted.
It then shows a ruddy disk which, with a magnifying
power of 75, is as large as the moon. Since its orbit
is outside the earth's, it never exhibits the crescent
phases like Mercury and Venus ; but at quadrature it
appears distinctly gibbous, as in Fig. 60, about like the
moon three days from full. Like Mercury, Venus, and the
moon, its disk is brightest at the limb (i.e., at its circular
edge) ; but at the " terminator," or boundary between day
FIG. 60. Mars near Quadrature
Lowell, 1894
MARS 217
and night upon the planet's surface, there is a slight
shading which, taken in connection with certain other
phenomena, indicates the presence of an atmosphere.
This atmosphere, however, is probably much less dense
than that at the earth, as indicated by the infrequency of
clouds and of other atmospheric phenomena familiar to us
on the earth. Huggins and Vogel have reported that the
planet's spectrum shows the lines of water-vapor ; but the
later observations of Campbell, at the Lick Observatory,
do not confirm this and go to show that whatever atmos-
phere exists must be very rare indeed, not more than
one-fourth as dense as our own, and probably less.
Zollner gives the albedo of Mars as 0.26, just double
that of Mercury, and much higher than that of the moon,
but only about half that of Venus and the major planets.
Near opposition the brightness of the planet suddenly
increases in the same way as that of the moon near the
full (Sec. 149).
254. Rotation, etc. The spots upon the planet's disk
enable us to determine its period of rotation with great
precision. Its sidereal day is found to be 24 h 37 m 22 8 .67,
with a probable error not to exceed one-fiftieth of a second.
It is the only one of the planets which has the length of its
day determined with any such accuracy. The exactness is
obtained by comparing the drawings of the planet made
two hundred years ago with others made recently.
The inclination of the planet's equator to the plane of
its orbit is very nearly 24 50' (26 21' to the ecliptic}. So
far, therefore, as depends upon that circumstance, Mars
should have seasons substantially the same as our own, and
certain phenomena make it evident that such is the case.
218 LESSONS IN ASTRONOMY
The planet's rotation causes a slight flattening of the
poles, hardly sensible to observation, but probably about
2^. (Larger values, now known to be erroneous, are given
in many text-books.)
255. Surface and Topography. With even a small tele-
scope, not more than four or five inches in diameter, the
planet is a very beautiful object, showing a surface diver-
sified with markings light and dark, which, for the most
part, are found to be permanent. Occasionally, however,
we see others of a temporary character, supposed to be
clouds ; but these are surprisingly rare as compared with
clouds upon the earth. The permanent markings are
broadly divisible into three classes.
First, the white patches, two of which are specially con-
spicuous near the planet's poles and are generally supposed
to be masses of snow or ice, since they behave just as would
be expected if such were the case. The northern one
dwindles away during the northern summer, when the north
pole is turned towards the sun, while the southern one grows
rapidly larger ; and vice versa during the southern summer.
Second, patches of bluish gray or greenish shade, covering
about three-eighths of the planet's surface and generally
supposed to be bodies of water, though this is very far
from certain.
Third, extensive regions of various shades of orange and
yellow, covering nearly five-eighths of the surface, and
interpreted as land.
These markings are, of course, best seen when near
the center of the planet's disk; near the limb they are
lost in the brilliant light which there prevails, and at the
terminator they fade out in the shade.
MARS
219
Fig. 61, from drawings by the late Maxwell Green of Madeira,
gives an excellent idea of the usual appearance of the planet under
favorable conditions.
256. Recent Discoveries ; the Canals and their Gemi-
nation. In addition to these three classes of markings
the Italian astronomer Schiaparelli, in 1877 and 1879,
announced the discovery of a great number of fine straight
lines, or "canals," as he called them,
crossing the ruddy portions of the
planet's surface in various directions,
and in 1881 he announced that many
of them become double at times. For
several years some doubt remained,
because other observers, with tele-
scopes more powerful than his, were
and still are unable to make out any-
thing of the sort. More recently, how-
ever, his results have been confirmed
by several independent observers. It
appears that the power of the telescope
is not so important in the observation
of these objects as steadiness of the
air and keenness of the observer's eye.
Nor are they usually best seen when
Mars is nearest, but their visibility depends upon the sea-
son on the planet ; and this is especially the case with their
" gemination." There is, however, considerable reason to
suspect that this peculiar doubling is merely an illusion, 1
due to imperfect focusing of the telescope or a slight
astigmatism of the observer's eye.
1 See note on page 224.
FIG. 61. Telescopic
Views of Mars
Green, 1878
220 LESSONS IN ASTRONOMY
As to the real nature of these markings and their behav-
ior there is wide difference of opinion, and it is doubtful if
the true explanation has yet been proposed. According to
Mr. Lowell, the polar caps are really snow masses, which
melt in the (Martian) spring, and the water makes its
way towards the equator over the planet's mountainless
plains, obscuring for several weeks the well-known mark-
ings which are visible at other times. For him the dark por-
tions of the planet's surface are not seas, but land covered
with vegetation of some sort, while the ruddy portions are
rocky deserts, intersected by the "canals," which, in his
view, are really irrigating water courses ; and on account of
their straightness he is disposed to accept them as artificial.
When the waters reach these canals vegetation springs up
along their banks on either side, and these streaks of vegeta-
tion are what we see. Where the water courses cross each
other there are dark round "lakes," as they have been
called, which he interprets as oases.
Of course the difficulties of the theory are obvious : for
instance, the almost absolute levelness of the planet's sur-
face which it assumes, and especially the fact that at Mars
the solar radiation is only half as intense as upon the earth.
This, recalling the low density of his atmosphere, would
naturally lead to the supposition that the temperature
even at his equator must be lower than that at the sum-
mits of our highest mountains, and far below the freez-
ing point of water. It was this consideration that has led
some astronomers to suggest that the polar caps are not ice-
sheets at all, but formed of congealed carbon dioxide (CO 2 ),
or some substance which remains liquid and vaporous at
much lower temperatures than water.
MARS 221
But whatever the explanation may be, there is no longer
any doubt that at the poles and elsewhere the planet's
surface really undergoes noticeable changes of appearance
with the progress of the planet's seasons, as shown by
Fig. 62, from drawings made by Barnard at the Lick
Observatory in 1894. At the same time Professor Holden
of the Lick Observatory says that during the years 1888-
1895 nothing has been observed there, so far as he knows,
which goes to confirm Mr. Lowell's "very positive and
striking conclusions."
The day may perhaps come when photography will
lend further aid to the solution of the problem, or some
FIG. 62. Seasonal Changes on Mara
Barnard
heat measurer may be contrived sensitive enough to give
us positive information as to the planet's temperature. If
the polar caps are really caps of frozen water, Mars must
obtain surface heat from some still unexplained supply.
257. Maps of the Planet. A number of maps of Mars have
been constructed by different observers since the first one was made
by Maedler in 1830. Fig. 63 is reduced from one which was pub-
lished in 1888 by Schiaparelli and shows most of his "canals" and
their "geminations." While there may be some doubt as to the
reality of the canal system, there can be no doubt that the main
features of the planet's surface are substantially correct. The nomen-
clature, however, is in a very unsettled state. Schiaparelli has taken
222 LESSONS IN ASTRONOMY
his names mostly from ancient geography, while the English areog-
raphers, 1 following the analogy of the lunar maps, have mainly used
the names of astronomers who have contributed to our knowledge
of the planet's surface.
258. Satellites. The planet has two satellites, discov-
ered by Professor Hall, at Washington, in 1877. They
are extremely small and observable only with very large
telescopes. The outer one, Deimos, is at a distance of
14,600 miles from the planet's center and has a sidereal
period of 30 h 18 m ; while the inner one, Phobos, is at a dis-
tance of only 5800 miles and its period is only 7 h 39 m ,
less than one-third of the planet's day. (This is the only
case of a satellite with a period shorter than the day of its
primary.) Owing to this circumstance, it rises in the west,
as seen from the planet's surface, and sets in the east, com-
pleting its strange backward diurnal revolution in about
eleven hours. Deimos, on the other hand, rises in the
east, but takes nearly 132 hours in its diurnal circuit,
which is more than four of its months. Both the orbits
are sensibly circular and lie very closely in the plane of
the planet's equator.
Micrometric measures of the diameters of such small objects are
impossible ; but, from photometric observations, Professor E. C. Pick-
ering, assuming that they have the same reflecting power as that of
Mars itself, estimates the diameter of Phobos as about 7 miles, and
that of Deimos as 5 or 6. Lowell, however, from his observations
of 1894, deduces considerably larger values, viz., 10 miles for Deimos
and 36 for Phobos. If this is correct, Phobos, when in the zenith of
an observer on the planet's surface, would be about as large as the
moon, but not so bright. Deimos would be about as bright as Venus.
1 The Greek name of Mars is Ares; hence "Areography " is the
description of the surface of Mars.
224 LESSONS IN ASTRONOMY
259. Habitability of Mars. As to this question we can only
say that, while the conditions on Mars are certainly very different
from those prevailing on the earth, the difference is less than in the
case of any other heavenly body which we can see with our present
means of observation; and if life, such as we know life upon the
earth, can exist upon any of them, Mars is the place. It is much
more probable, however, that the conditions as to temperature and
atmosphere differ from our own quite enough to preclude all terres-
trial forms of life.
There is at present no scientific ground for belief one way or the
other as to the habitability of " other worlds than ours," passionately
as the doctrine has been affirmed and denied by men of opposite
opinions.
NOTE TO SECTION 256
Experiments recently made by various observers upon maps and
models viewed from different distances by sketchers ignorant as to what
they ought to see and draw, strongly confirm the suspicion that illusions
probably enter to some extent into the now generally accepted repre-
sentations of the surface of Mars, illusions due to a perfectly
honest misinterpretation of actual markings seen imperfectly. The
experiments show in many persons a strong tendency to see as defi-
nite lines what are really only the boundaries of faint shadings, or
more or less irregular rows of separate spots. The so-called "canals"
doubtless represent really existing features, but are probably less
definite and regular than shown on our maps.
In 1904-1905 Mr. Lampland, the photographer of the Flagstaff
Observatory, obtained photographs of Mars far superior to any pre-
viously made. They are about a quarter of an inch in diameter and
under a magnifier show nearly all the features of the planet visible
in ordinary telescopes. Mr. Lowell considers that they fully confirm
his own peculiar observations. An expedition sent by him in 1907
to northern Chile, in charge of Professor Todd, is reported to have
obtained photographs of the planet showing many of the canals, and
some of them double. Similar photographs were also obtained in
1909.
CHAPTER IX
THE PLANETS (Continued)
The Asteroids Intramercurian Planets and the Zodiacal Light The Major
Planets, Jupiter, Saturn, Uranus, and Neptune
THE ASTEROIDS OR MINOR PLANETS
260, The asteroids 1 are a multitude of small planets
circling around the sun in the space between Mars and
Jupiter. It was early noticed that between Mars and
Jupiter there is a gap in the series of planetary distances,
and when Bode's law (Sec. 219) was published in 1772
the impression became very strong that there must be
a missing planet in the space, an impression greatly
strengthened when Uranus was discovered in 1781, at a
distance precisely corresponding to that law.
The first member of the group was found by the Sicilian
astronomer, Piazzi, on the very first night of the nine-
teenth century (Jan. 1, 1801). He named it Ceres, after
the tutelary divinity of Sicily. The next year Pallas was
discovered by Olbers. Juno was found in 1 804 by Harding,
and in 1807 Olbers, who had broached the theory of an
exploded planet, discovered the fourth, Vesta, the only
one which is ever bright enough to be easily seen by the
1 They were first called asteroids (i.e., "starlike" bodies) by Sir
William Herschel early in the century, because, though really planets,
the telescope shows them only as stars, without a sensible disk.
225
226 LESSONS IN ASTRONOMY
naked eye. The search was kept up for some years longer,
but without success, because the searchers did not look for
small enough objects. The fifth asteroid (Astrsea) was
found in 1845 by Hencke, an amateur, who had resumed
the subject by studying the fainter stars. In 1847 three
more were discovered, and every year since then has added
from one to a hundred. They are usually designated by
their " numbers," but all the older ones also have names :
thus, Ceres is <D, Thule is (279), Eros is (433), etc. At pres-
ent more than eight hundred are known, and since
1891 the catalogue has been growing with rather incon-
venient rapidity on account of the substitution of pho-
tography for the old-fashioned method of planet-hunting.
A large camera is strapped on the back of a telescope
driven by clockwork, and a negative, covering from 5 to
10 square of the heavens, is taken with an exposure of
several hours. The thousands of stars that appear upon
the plate all show neat round disks, if the observer has
kept his telescope steadily pointed; but if there is a
planet anywhere in the field it will move quite percep-
tibly during the long exposure, and its image upon the
plate will be, not a dot, but a streak, which can be
recognized at a glance. Sometimes as many as seven
planets thus "show up" upon a single plate, old ones
as well as new of course; but a few nights' observation
will usually furnish data from which the orbits can be
computed with sufficient accuracy to decide all doubtful
questions. Max Wolf of Heidelberg, who first introduced
the method, and Charlois of Nice have been especially
successful in this kind of asteroid-hunting. Rev. J. H.
Metcalf of Taunton, Mass., has recently introduced an
THE ASTEROIDS 227
effective modification of this method, letting the stars trail,
while asteroid images are nearly round.
261. Their Orbits. The mean distances of the different
asteroids from the sun differ pretty widely, and the periods,
of course, correspond. Eros, (433), has by far the smallest
orbit, its mean distance from the sun being only 1.46
(135,500000 miles), and its period 643, even less than that
of Mars. The next in proximity to the sun is Hungaria, (434),
with a mean distance of 180,000000 miles, and a period of
three years and three days. The most remote are Achilles,
Patroclus, and Hector, whose orbits do not differ greatly
from that of Jupiter in size and period.
The inclinations of the orbits to the ecliptic average
nearly 8. The orbit of Pallas, , is inclined at an angle
of 35, and several others exceed 25. The eccentricity of
the orbits is very large in many cases. Albert, one of the
minor planets discovered in 1911, has the largest eccen-
tricity (0.54), and several others have an eccentricity ex-
ceeding 0.30. 1 It should be noted that the orbits of these
planets are subject to very great disturbances from the
attraction of Jupiter, and this makes the calculation of
their motions much more laborious than that of the larger
planets. Very few of them, therefore, are followed up
closely ; only those that for some reason or other possess
a special interest at some given time.
262. The Bodies themselves. The four first discovered,
and one or two others, when examined with a powerful
telescope, show disks that are perceptible, but too small
for satisfactory measurement with ordinary telescopes.
By photometric observations, assuming what is by no
i Ocllo has an eccentricity of 0.38.
228 LESSONS IN ASTRONOMY
means certain that their albedo is about the same as that
of Mars, it has been estimated that Vesta, the brightest,
has a diameter of about 320 miles, and that the other three
of the first four may be two-thirds as large. In 1895,
however, Mr. Barnard of the Lick Observatory measurecl
the diameters of Ceres, Pallas, and Vesta, micrometrically,
and obtained results that differ from these very widely,
and should probably be preferred. He finds Ceres to be
the largest, with a diameter of 488 miles. For Pallas,
Vesta, and Juno he gets diameters of 304, 248, and
118 miles, respectively. None of the rest can well exceed
100 miles; and the more newly discovered ones, which
are just fairly visible in a telescope with an aperture of
10 or 12 inches, cannot be many times larger than the
moons of Mars, say from 10 to 20 miles in diameter.
As to the individual masses and densities, we have no
certain knowledge.
Assuming the correctness of Barnard's measures, and that the
density of Ceres is about the same as that of the rocks which com-
pose the earth's crust, her mass may be as great as ^y 1 ^ that of the
earth. If so, gravity on her surface would be about -fa of gravity
here, so that a body would fall about seven inches in the first second.
Of course, on the smaller asteroids it would be much less.
From the perturbations of Mars, Leverrier has estimated
that the aggregate mass of the whole swarm cannot exceed
one-fourth the mass of the earth, something more than
double that of Mars ; a more recent calculation by Ravene
puts the limit as low as one per cent.
The united mass of those at present known would make only a
small fraction of such a body, hardly a thousandth of it ; probably,
however, those still undiscovered are very numerous.
THE ASTEROIDS 229
262*. Eros. The most interesting of these little bodies
from the astronomical point of view is Eros, (433), dis-
covered by Witt at Berlin in 1898.
Its mean distance and period, as already stated, are less
than those of Mars, but the eccentricity of its orbit (0.22)
is such that it goes far outside the Martial orbit at aphe-
lion, while at perihelion it comes within 13,500000 miles
of the orbit of the earth. This is only a little more than
half the nearest approach of Venus, and gives the planet
immense importance as a means of determining the solar
parallax by the method explained in Sec. 468 of the
Manual. But it is only when the perihelion passage
occurs about January 20 that the earth is rightly situated
to utilize the conditions, and unfortunately these close
approaches are very rare.
One occurred in 1894, before the discovery of the
planet; the next will be in 1931. But in the winter of
19001901 the conditions were better than they will be
again for thirty years, the nearest approach being within
about 30,000000 miles. An enormous number of obser-
vations were made, both visual and photographic, the
results of which will require some years for their complete
discussion.
The planet's inclination is about 11, so that at the
time of a close opposition it moves among the stars nearly
from north to south, instead of retrograding from east to
west like other planets.
It is very small, probably less than twenty miles in
diameter, and seldom visible except in great telescopes ; at
its close approaches, however, it may become nearly bright
enough to be visible by the naked eye.
230 LESSORS IK ASTRONOMY
In certain positions relative to the earth there is a
marked periodic variation of its light, and from this
Director Pickering of Harvard has deduced by photomet-
ric observations a rotation period of about 5i hours. One
or two other asteroids are suspected of similar behavior,
and are also under observation.
263. Origin. As to this we can only speculate. It is
hardly possible to doubt, however, that this swarm of little
rocks in some way represents a single planet of the " ter-
restrial " group. A commonly accepted view is that the
material, which, according to the nebular hypothesis, once
formed a ring (like one of the rings of Saturn), and ought
to have collected to make a single planet, has failed to
be so united ; and the failure is ascribed to the perturba-
tions produced by the next neighbor, the giant Jupiter,
whose powerful attraction is supposed to have torn the
ring to pieces, and thus prevented its normal development
into a planet.
Another view is that the asteroids may be fragments of
an exploded planet. If so, there must have been not one
but many explosions, first of the original body, and then
of the separate pieces ; for it is demonstrable that no single
explosion could account for the present tangle of orbits.
INTRAMERCURIAN PLANETS AND THE ZODIACAL
LIGHT
264. Intramercurian Planets. It is very possible, indeed not
improbable, that there is a considerable quantity of matter circu-
lating around the sun inside the orbit of Mercury. It has been
somewhat persistently supposed that this intramercurian matter is
concentrated into one, or possibly two, planets of considerable size,
THE ZODIACAL LIGHT 231
and such a planet has several times been reported as discovered, and
has even been named Vulcan. The supposed discoveries have never
been confirmed, however, and the careful observations of total solar
eclipses during the past ten years make it practically certain that
there is no " Vulcan." Possibly, however, there is a family of intra-
mercurian asteroids ; but they must be very minute or some of them
would certainly have been found either during eclipses or crossing
the sun's disk; a planet as much as 200 miles in diameter could
hardly have escaped discovery. Recently attempts have been made
to detect any existing body of this kind by photographing the region
of the sky in the neighborhood of the sun during a total solar eclipse.
None has yet been found.
265. The Zodiacal Light. This is a faint, ill-defined
pyramidal beam of light extending from the sun both ways
along the ecliptic. In the evening it is best seen in the
early spring, and in our latitude then extends about 90
eastward from the sun ; in the tropics it is said that it can
be followed quite across the sky. The region near the sun
is fairly bright and even conspicuous, but the more distant
portions are extremely faint and can be observed only in
places where there is no illumination of the air by artificial
lights. At the point opposite the sun in the heavens there
is also a faint patch of light, ten degrees or so in diameter,
known as the G-egenschein, or " counter glow."
The spectrum of the zodiacal light is a simple, con-
tinuous spectrum without markings of any kind, so far
as can be observed. We emphasize this because of late it
is often mistakenly stated that the bright line which char-
acterizes the spectrum of the Aurora Borealis appears in
the spectrum of the zodiacal light.
The cause of the phenomenon is not certainly known.
Some imagine that the zodiacal light is only an extension
232 LESSONS IN ASTRONOMY
of the solar corona (whatever that may be), which is not
perhaps unlikely; but on the whole the more prevalent
opinion seems to be that it is due to sunlight reflected from
myriads of small meteoric bodies circling around the sun,
nearly in the plane of the ecliptic, thus forming a thin flat
sheet (something like one of Saturn's rings), which extends
far beyond the orbit of the earth. As to the Gegenschein,
it is generally ascribed to a brightening up of the little
bodies when they come opposite to the sun, similar to the
moon's great increase of brightness at the full (Sec. 149).
THE MAJOR PLANETS JUPITER, URANUS, AND
NEPTUNE
JUPITER
266. Jupiter, the nearest of the major planets, stands
next to Venus in the order of brilliance among the heavenly
bodies, being fully five or six times as bright as Sirius, and
decidedly superior to Mars, even when Mars is nearest. It
is not, like Venus, confined to the twilight sky, but at the
time of opposition dominates the heavens all night long.
Its orbit presents no marked peculiarities. The mean
distance of the planet from the sun is a little more than
five astronomical units (483,000000 miles), and the eccen-
tricity of the orbit is not quite ^, so that the actual dis-
tance ranges about 21,000000 miles each side of the mean.
At an average opposition the planet's distance from the
earth is about 390,000000 miles, while at conjunction it is
distant about 580,000000.
The inclination of its orbit to the ecliptic is only 1 19'.
Its sidereal period is 11.86 years, and the synodic is 399
JUPITER 233
days (a figure easily remembered), a little more than a year
and a month ; i.e., each year Jupiter comes to opposition a
month and four days later than in the preceding year.
267. Dimensions, Mass, Density, etc. The planet's
apparent diameter varies from 50" to 32", according to its
distance from the earth. The disk, however, is distinctly
oval, so that while the equatorial diameter is nearly 90,000
miles, the polar diameter is only 84,200. The mean diameter
(see Sec. 112) is 88,000 miles, a little more than eleven
times that of the earth.
These values are from recent measures by Barnard and See, and
quite possibly need correction for irradiation. They are notably
larger than those determined by earlier observers with a different
kind of micrometer and given in Table II of the Appendix. Very
likely the truth is intermediate.
Its surface, therefore, is 122, and its volume or bulk 1355,
times that of the earth. It is by far the largest of all the
planets, larger, in fact, than all the rest united.
Its mass is very accurately known, both by means of
its satellites and from the perturbations it produces upon
certain asteroids. It is y-Q\^ of the sun's mass, or about
316 times that of the earth.
Comparing this with its volume, we find its mean density
to be 0.24, i.e., less than one-fourth the density of the
earth and almost precisely the same as that of the sun.
Its surface gravity is about two and two-thirds times that
of the earth, but varies nearly twenty per cent between the
equator and poles of the planet on account of the rapid
rotation.
268. General Telescopic Aspect, Albedo, etc. In a small
telescope the planet is a fine object; for a magnifying
234 LESSONS IN ASTRONOMY
power of only 60 makes its apparent diameter, even when
remotest, equal to that of the moon. With a large instru-
ment and a magnifying power of 200 or 300 it is magnifi-
cent, the disk being covered with an infinite variety of
detail, interesting in outline and rich in color, changing
continually as the planet turns on its axis. For the most
part, the markings are arranged in " belts " parallel to the
planet's equator, as shown in Fig. 64.
This is from an admirable drawing made in 1889 by the late
lamented Keeler, and still continues to be an excellent represen-
tation of the planet, wanting only the varied colors to make it
perfect.
Near the limb the light is less brilliant than in the center
of the disk, and the belts there fade out. The planet shows
no perceptible phases, but the edge which is turned away
from the sun is usually sensibly darker than the other.
According to Zdllner, the mean albedo of the planet is 0.62,
which is extremely high, that of white paper being only
0.78. The question has been raised whether Jupiter is
not to some extent self-luminous, but there is no proof, and
little probability, that such is the case.
269. Atmosphere and Spectrum. The planet's atmos-
phere must be very extensive. The forms which we see
with the telescope are all evidently atmospheric. In fact,
the low mean density of the planet makes it very doubtful
whether there is anything solid about it anywhere,
whether it is anything more than a ball of fluid, overlaid
by cloud and vapor.
The spectrum of the planet differs less from that of mere
reflected sunlight than might have been expected, showing
that the light is not obliged to penetrate the atmosphere
1889,JULYlO d 8 h 45 n PST.
FIG. 64. Jupiter
After drawings by Keeler, at Lick Observatory
235
236 LESSONS IN ASTRONOMY
to any great depth before it encounters the reflecting
envelope of cloud. There are, however, certain unex-
plained dark shadings in the red and orange parts of the
spectrum that are probably due to the planet's atmosphere,
and seem to be identical in position with certain bands
which, in the spectra of Uranus and Neptune, are much
more intense.
270. Rotation. Jupiter rotates on its axis more swiftly
than any other of the planets. Its sidereal day has a length
of about 9 h 55 m ; but the time can be given only approxi-
mately, because different results are obtained from differ-
ent spots, according to their nature and their distance
from the equator, the differences amounting to six or
seven minutes as determined by spots of different char-
acter and in different latitudes. White spots generally make
the circuit quicker than dark spots near them.
In consequence of the swift rotation, the planet's oblate-
ness, or " polar compression," is quite noticeable, about -fa.
The inclination of the planet's equator to its orbit is only
3, so that there can be no well-marked seasons on the
planet due to such causes as produce our own seasons.
271. Physical Condition. This is obviously very dif-
ferent from that of the earth or Mars. No permanent
markings are found upon the disk, though occasionally
there are some which may be called " sub-permanent," as,
for instance, the great red spot, shown in Fig. 64. This
was first noticed in 1878, became extremely conspicuous
for several years, and is still visible, though only a
faded ghost of itself. Were it not that during the first
eight years of its visibility it changed the length of its
apparent rotation by about six seconds (from 9 h 55 m 34 8 .9 to
JUPITER 237
9 h 55 m 40 8 .2), we might suppose it permanently attached
to the planet's surface, and evidence of a coherent mass
underneath. As it is, opinion is divided on this point;
the phenomenon is as puzzling as the canals of Mars.
Many things in the planet's appearance indicate a high
temperature, as, for instance, the abundance of clouds and
the swiftness of their transformations ; and since on Jupi-
ter the solar light and heat are only J y as intense as here,
we are forced to conclude that it gets very little of its
heat from the sun, but is probably hot on its own account,
and for the same reason that the sun is hot, viz., as the
result of a process of condensation. In short, it appears
very probable that the planet is a sort of semi-sun, hot,
though not so hot as to be sensibly self-luminous.
272. Satellites. Jupiter has nine satellites, four of
them large and easily seen with a very small telescope. The
fifth, found by Barnard in 1892, and the sixth and seventh
by Perrine, on photographs, in 1905 (all at Mt. Hamilton),
are extremely small, and visible only in great telescopes.
The four large satellites were the first heavenly bodies
ever discovered. Galileo found them in January, 1610,
within a few weeks after the invention of his telescope.
These are now usually known as the first, second, etc.,
in the order of their distance from the planet. The dis-
tances range from 262,000 to 1,169000 miles, being
respectively 6, 9, 15, and 26 radii of the planet (nearly).
Their sidereal periods range from 42 hours to 16 f days.
Their orbits are sensibly circular and lie very nearly in
the plane of the equator. The third satellite is much the
largest, having a diameter of about 3600 miles, while the
others are between 2000 and 3000.
238 LESSONS IN ASTRONOMY
For some reason, the fourth satellite is a very dark-complexioned
body, so that when it crosses the planet's disk it is hardly distin-
guishable from its own shadow; the others under similar circum-
stances appear bright, dark, or invisible, according to the brightness
of the background. In the case of the fourth satellite a certain reg-
ular change of brightness suggests that it probably follows the exam-
ple of our moon in always keeping the same face towards the planet,
and Douglass from the Flagstaff Observatory, in 1897, announced a
similar behavior of the third. The other satellites are very faint.
The fifth is nearest of all to the planet, being only 112,500 miles
from its center. The sixth and seventh seem to be tiny twin satel-
lites, moving in orbits that are nearly equal and "interlocked,"
7,500,000 miles from the planet. The eighth was discovered by
Melotte in 1908 on photographs made at Greenwich for the sixth
and seventh, and a ninth was found by Nicholson at the Lick Observ-
atory in 1914. These two are another pair of twins, twice as far
from Jupiter as the sixth and seventh, and revolving in the opposite
direction.
273, Eclipses and Transits. The orbits of the satellites
are so nearly in the plane of the planet's orbit that with
the exception of the fourth, which escapes about half the
time, they are eclipsed at every revolution. Ordinarily
we see only the beginning or the end of an eclipse ; but
when the planet is very near quadrature the shadow pro-
jects so far to one side that the whole eclipse of every
satellite, except the first, takes place clear of the disk,
and both the disappearance and reappearance can be
observed. At opposition neither is visible.
Two important uses have been made of these eclipses :
they have been employed for the determination of longi-
tude, and they furnish the means of ascertaining the time
required by light to traverse the space between the earth and
the sun. (See Appendix, Sees. 431-434.)
SATURN 239
SATURN
274. This is the most remote of the planets known to
the ancients. It appears as a star of the first magnitude
(outshining all of them, indeed, except Sirius) with a
steady, yellowish light, not varying much in appearance
from month to month, though in the course of fifteen
years it alternately gains and loses nearly fifty per cent
of its brightness with the changing phases of its rings;
for it is unique among the heavenly bodies, a great globe
attended by nine 1 satellites and surrounded by a system of
rings which has no counterpart elsewhere in the universe,
so far as known.
Its mean distance from the sun is about 9J astronomical
units, or 886,000000 miles; but the distance varies over
100,000000 miles on account of the considerable eccen-
tricity of the orbit (0.056). Its least distance from the
earth is about 774,000000 miles, the greatest about
1028,000000. The inclination of the orbit to the ecliptic
is 2J. The sidereal period is about 29 years, the synodic
period being 378 days, or nearly a year and a fortnight.
275, Dimensions, Mass, etc. The apparent mean
diameter of the planet varies according to the distance,
from 14" to 20". The planet is more flattened at the
poles than any other (nearly -Jj), so that while the equa-
torial diameter is about 76,000 miles, the polar is only
70,000 ; the mean diameter (Sec. 112) being not quite
74,000, a little more than nine times that of the earth.
Its surface is about 84 times that of the earth, and its
volume 770 times. Its mass is found (by means of its
1 The presence of a tenth has been suspected, but not fully confirmed.
240 LESSONS IN ASTRONOMY
satellites) to be 95 times that of the earth, so that its
mean density comes out only one-eighth that of the earth,
actually less than that of water ! It is by far the least
dense of all the planetary family.
Its mean superficial gravity is about 1.2 times as great
as gravity upon the earth, varying, however, nearly twenty-
five per cent between the equator and the pole, so that at
the planet's equator it is practically the same as upon the
earth. It rotates on its axis in about 10 h 14 m , but different
spots give various results, as in the case of Jupiter.
The equator of the planet is inclined about 27 to the
plane of its orbit about 28 to the ecliptic.
276. Surface, Albedo, Spectrum. The disk of the
planet, like that of Jupiter, is shaded at the edge, and, like
Jupiter, it shows a number of belts arranged parallel to
the equator. The equatorial belt is very bright, and is
often of a delicate pinkish tinge. The belts in higher
latitudes are comparatively faint and narrow, while just at
the pole there is usually a cap of olive green (see Fig. 65).
Zollner makes the mean albedo of the planet 0.52, about
the same as that of Venus.
The planet's spectrum is substantially like that of
Jupiter, but the dark bands are more pronounced. These
bands, however, do not appear in the spectrum of the ring,
which probably has very little atmosphere. As to its phys-
ical condition and constitution, the planet is probably much
like Jupiter, though it does not seem to be "boiling"
quite so vigorously.
277. The Rings. The most remarkable peculiarity of
the planet is its ring system. The globe is surrounded by
three thin, flat, concentric rings, like circular disks of
FIG. 65. Saturn
After Proctor
241
242 LESSONS IN ASTRONOMY
paper pierced through the center. They are generally
referred to as A, B, and (7, A being the exterior one.
Galileo half discovered them in 1610 ; i.e., he saw with his little
telescope two appendages, one on each side of the planet ; but he
could make nothing of them, and after a while he lost them. The
problem remained unsolved for nearly fifty years, until Huyghens
explained the mystery in 1655. Twenty years later D. Cassini dis-
covered that the ring is double, i.e., composed of two concentric
rings, with a dark line of separation between them, and in 1850,
Bond of Cambridge (U.S.) discovered the third " dusky " or " gauze "
ring between the principal ring and the planet. (It was discovered
a fortnight later, independently, by Dawes in England.)
The outer ring, J, has a diameter of about 173,000
miles and a width of about 11,000. Cassini's division is
about 2000 miles wide ; the ring J5, which is much the
broadest of the three, is about 18,000. The semi-transpar-
ent ring, (7, has a width of about 11,000 miles, leaving a
clear space of very nearly 6000 miles in width between
the planet's equator and its inner edge. The thickness of
the rings is extremely small, probably not over 50 miles,
as proved by the appearance presented when once in 15
years we view them edgewise.
The recent researches of H. Struve show that the
mass of the rings and their mean density are also sur-
prisingly small, so small that the rings exert hardly
more influence on the motion of the satellites than if they
were composed of " immaterial light," to use his own expres-
sion. A very recent discussion by Professor Hall indi-
cates, however, that the mass, though certainly extremely
small, is by no means insensible, being about yyVo f the
planet's mass, and about two thirds that of Titan, the
largest satellite.
SATURN 243
278. Phases of the Rings. The plane of the rings
coincides with the plane of the planet's equator, and is
inclined about 28 to the ecliptic. It, of course, remains
parallel to itself at all times. Twice in a revolution of
the planet, therefore, this plane sweeps across the orbit
of the earth (too small to be shown in Fig. 66), occu-
pying nearly a year in so doing ; and whenever the plane
passes between the earth and the sun the dark side of
the ring is towards us and the edge alone is visible,
FIG. 66. The Phases of Saturn's Rings
as when the planet is at 1 or 2 ; when it is at the inter-
mediate points, 3 and 4, the rings present their widest
opening.
When the ring is exactly edgewise towards us, only the largest
telescopes can see it, like a fine needle of light piercing the planet's
ball, as in the uppermost engraving of Fig. 65. It becomes obvious
at such times that the thickness of the rings is not uniform, since
considerable irregularities appear upon the line of light at different
points. The last period of disappearance was in 1907.
244 LESSONS IN ASTRONOMY
279. Structure of the Rings. It is now universally
admitted that they are not continuous sheets, either solid
or liquid, but mere swarms of separate particles, each par-
ticle pursuing its own independent orbit around the planet,
though all moving nearly in a common plane.
The idea was first suggested by J. Cassini in 1715, but was lost
sight of until again brought into notice by Bond in 1850. A little
later Peirce proved from mechanical considerations that the rings
could not be solid; and not long after, Maxwell showed that they
could not be " continuous sheets " of any kind, either solid or liquid,
but might be composed of separate particles moving independently.
More recently Miiller and Seeliger have shown from photometric
observations that the variations in the brightness of the ring corre-
spond to this "meteoric theory" ; and still more recently (in 1895)
Keeler demonstrated, by a most beautiful and delicate spectroscopic
observation, that the outer edge of the ring in its rotation really
moves more slowly than the inner, just as the theory requires.
It remains uncertain whether the rings constitute a system that
is permanently stable, or whether they are liable ultimately to be
broken up and disappear.
280. Satellites. Saturn has nine 1 of these attendants.
Titan, the largest, was discovered by Huyghens in 1655.
It looks like a star of the ninth magnitude, and is easily
seen with a three-inch telescope. Tethys, Dione, and Rhea
are fainter and closer to the bright planet. They can be
seen with a five-inch telescope, as can the more distant
lapetus. All the others are very faint.
Since the order of discovery does not agree with that of distance,
it has been found convenient to designate them by the names
assigned by Sir John Herschel, as follows, beginning with the most
remote, viz. : lapfitus, (Hyperion), Titan, Rhea, Dione, Tethys ;
Enoeladus, Mimas. (The name Hyperion was not given by Herschel,
but interpolated after its discovery by Bond.)
1 See footnote on page 239.
URANUS 245
The range of the system is enormous. lapetus has a distance of
2,225000 miles, with a period of 79 days, nearly as long as that of
Mercury. On the western side of the planet this satellite is always
much brighter than upon the eastern, showing that, like our own
moon, it keeps the same face towards its primary.
Titan, as its name suggests, is by far the largest. Its distance is
about 770,000 miles and its period a little less than 16 days. It is
probably 3000 or 4000 miles in diameter, and, according to Stone,
its mass is %$-$$ of Saturn's, or about double that of our moon.
The orbit of lapetus is inclined nearly 10 to the plane of the
rings, but all of the other satellites move almost exactly in their
plane, and all the five inner ones in orbits nearly circular. In 1899
W. H. Pickering announced the discovery of an extremely small
ninth satellite on photographs made at Arequipa the preceding year.
The data were then insufficient to determine its orbit : but the dis-
covery has since been fully confirmed, and the distance of the satel-
lite (Phoebe) from Saturn is found to be 8,000000 miles, its period 18
months, its motion apparently retrograde, and its diameter about 200
miles.
URANUS
281. Uranus (not U-ra/nus) was the first planet ever
" discovered," and the discovery created great excitement
and brought the highest honors to the astronomer. It was
found accidentally by the elder Herschel on March 13,
1781, while "sweeping" for interesting objects with a
seven-inch reflector of his own construction. He recog-
nized it at once by its disk as something different from a
star, but supposed it to be a peculiar sort of comet, and
its planetary character was not demonstrated until nearly
a year had passed. It is easily visible to a good eye as
a star of the sixth magnitude.
Its mean distance from the sun is about 19 times that of
the earth, or about 1800,000000 miles, and the eccentricity
246 LESSONS IN ASTRONOMY
of its orbit is about the same as that of Jupiter's. The
inclination of the orbit to the ecliptic is very slight,
only 46'. The sidereal period is 84 years, and the synodic
3691 days.
In the telescope it shows a greenish disk about 4" in
diameter, which corresponds to a real diameter of about
30,000 miles. This makes its bulk about 54 times that
of the earth. The planet's mass is found from its satel-
lites to be about 14.6 times that of the earth ; its density,
therefore, is 0.27, about the same as that of Jupiter and
the sun.
The albedo of the planet, according to Zollner, is very
high, 0.64, even a little above that of Jupiter. The
spectrum exhibits intense dark bands in the red, due to
some unidentified substance in the planet's atmosphere.
These bands explain the marked greenish tint of the
planet's light. The atmosphere is probably dense.
The disk is obviously oval, with an ellipticity of about
j* ? . There are no clear markings upon it, but there seem
to be faint traces of something like belts. No spots are
visible from which to determine the planet's diurnal
rotation. Probably, however, it is rapid. 1
282. Satellites. The planet has four satellites,
Ariel, Umbriel, Titania, and Oberon, Ariel being the
nearest to the planet.
The two brightest, Oberon and Titania, were discovered by Sir
William Herschel a few years after his discovery of the planet ; Ariel
and Umbriel, by Lassell in 1851.
1 A period of 10 h 50 m was found with the spectroscope at the Lowell
Observatory in 1912, the direction of rotation corresponding to that of
the revolution of the satellites.
NEPTUNE 247
They are among the smallest bodies in the solar system,
visible only in the largest telescopes.
Their orbits are sensibly circular, and all lie in one
plane, which ought to be, and probably is, coincident with
the plane of the planet's equator.
They are very close packed also, Oberon having a distance of only
375,000 miles and a period of 13 d ll h , while Ariel has a period of
2 d 12 h at a distance of 120,000 miles. Titania, the largest and
brightest of them, has a distance of 280,000 miles, somewhat
greater than that of the moon from the earth, with a period of
The most remarkable thing about this system remains to
be mentioned. The plane of their orbits is inclined 82.2,
or almost perpendicularly, to the plane of the ecliptic, and
in that plane they revolve backwards.
NEPTUNE
283. Discovery. The discovery of this planet is con-
sidered the greatest triumph of mathematical astronomy.
Uranus failed to move precisely in the path computed for
it, and was misguided by some unknown influence to an
extent which could almost be seen with the naked eye.
The difference between the actual and computed places in
1845 was the " intolerable quantity " of nearly two minutes
of arc.
This is a little more than half the distance between the two prin-
cipal components of the double-double star, Epsilon Lyrse, the north-
ern one of the two little stars which form the small equilateral
triangle with Vega (Sees. 67 and 375). A very sharp eye detects
the duplicity of Epsilon without the aid of a telescope.
248 LESSONS IN ASTRONOMY
One might think that such a minute discrepancy between
observation and theory was hardly worth minding, and that
to consider it "intolerable" was putting the case very
strongly. But just these minute discrepancies supplied
the data which were found sufficient for calculating the
position of a great unknown world, and bringing it to
light. As the result of a most skillful and laborious inves-
tigation, Leverrier (born 1811, died 1877) wrote to Galle 1
in substance :
" Direct your telescope to a point on the ecliptic in the constella-
tion of Aquarius, in longitude 326, and you will find within a degree
of that place a new planet, looking like a star of about the ninth
magnitude, and having a perceptible disk."
The planet was found at Berlin on the night of Sept. 23,
1846, in exact accordance with this prediction, within
half an hour after the astronomers began looking for it
and within 52' of the precise point that Leverrier had
indicated.
We cannot here take the space for an historical statement, further
than to say that the English Adams fairly divides with Leverrier the
credit for the mathematical discovery of the planet, having solved
the problem and deduced the planet's approximate place even earlier
than his competitor. The planet 'was being searched for in England
at the time it was found in Germany. In fact, it had already been
observed, and the discovery would necessarily have followed in a few
weeks, upon the reduction of the observations.
284. Error of the Computed Orbit. Both Adams and Leverrier,
besides calculating the planet's position in the sky, had deduced ele-
ments of its orbit and a value for its mass, which turned out to be
1 Galle, long director of the observatory at Breslau, died in 1910, at
the advanced age of ninety-eight years.
NEPTUNE 249
seriously wrong, and certain high authorities have therefore charac-
terized the discovery as a "happy accident." This is not so, how-
ever. While the data and methods employed were not sufficient
to determine the planet's orbit with accuracy, they were adequate
to ascertain the planet's direction from the earth. The computers
informed the observers where to point their telescopes, and this was all
that was necessary for finding the planet.
285. JThe Planet and its Orbit The planet's mean dis-
tance from the sun is a little less than 2800,000000 miles
(800,000000 miles nearer the sun than it should be accord-
ing to B ode's law). The orbit is very nearly circular, its
eccentricity being only 0.009. The inclination of the orbit
is about 1|. The period of the planet is about 164 years
(instead of 217, as it should have been according to Lever-
rier's computed orbit) and the orbital velocity is about
3 miles per second.
Neptune appears in the telescope as a small star of
between the eighth and ninth magnitudes, absolutely
invisible to the naked eye, though easily seen with a
good opera-glass. Like Uranus, it shows a greenish disk,
having an apparent diameter of about 2".6. The real
diameter of the planet is about 35,000 miles, according to
the "American Ephemeris," which makes its volume about
86 times that of the earth.
Its mass, as determined by means of its satellite, is about
18 times that of the earth, and its density about 0.20.
The planet's albedo, according to Zollner, is 0.46,
a trifle less than that of Saturn and Venus.
There are no visible markings upon its surface, and
nothing certain is known as to its rotation.
250 LESSONS IN ASTRONOMY
The spectrum of the planet appears to be like that of
Uranus, but of course is rather faint.
It will be noticed that Uranus and Neptune form a "pair of
twins," very much as the earth and Venus do, being almost alike in
magnitude, density, and many other characteristics.
286. Satellite. Neptune has one satellite, discovered
by Lassell within a month after the discovery of the planet
itself. Its distance is about 222,000 miles, and its period
5 d 21 h . Its orbit is inclined to the ecliptic at an angle of
34 48', and it moves backward in it from east to west r
like the satellites of Uranus. From its brightness, as com-
pared with that of Neptune itself, its diameter is estimated
as about the same as that of our own moon.
287. The Solar System as seen from Neptune. At
Neptune's distance the sun itself has an apparent diam-
eter of only a little more than one minute of arc, about
the diameter of Venus when nearest us, and top small to
be seen as a disk by the naked eye, if there are eyes on
Neptune. The solar light and heat there are only -g^ of
what we get at the earth.
Still, we must not imagine that the Neptunian sunlight
is feeble as compared with starlight, or even moonlight.
Even at the distance of Neptune the sun gives a light
nearly equal to 700 full moons. This is about 80 times
the light of a standard candle at one meter's distance, and
is abundant for all visual purposes. In fact, as seen from
Neptune, the sun would look very like a large electric arc
lamp at a distance of a few yards.
288. Ultra-Neptunian Planets. Perhaps the breaking down of
Bode's law at Neptune may be regarded as an indication that the
STABILITY OF SOLAR SYSTEM 251
solar system terminates there, and that there is no remoter planet;
but of course it does not make it certain. If such a planet exists, it
is sure to be found sooner or later, either by means of the disturb-
ances it produces in the motion of Uranus and Neptune, or else by
the methods of the asteroid hunters, although its slow motion will
render its discovery in that way difficult. Quite possibly such a dis-
covery may come within a few years as a result of the photographic
star -charting operations now in progress.
288*. Stability of the Solar System. It is an interesting and
important question, once long and warmly discussed, whether the
so-called "perturbations," which result from the mutual attractions
of the planets, can ever seriously derange the system. It is now
nearly a century since Laplace and Lagrange were supposed to have
demonstrated that they cannot ; that the system is stable in itself,
all the disturbances due to gravitation being either of such a charac-
ter, or so limited in extent, that they can never produce any seriously
harmful effects upon the earth or any of the larger planets. But the
recent work of mathematicians has proved that this sweeping conclu-
sion is unwarranted. The system is secure for thousands, perhaps
for millions, of years ; perhaps forever ; but it is not yet demonstrated
that in some remote future the accumulated perturbations may not
result in disaster.
Moreover, besides gravitational disturbances, there are other causes
which may work destructively. Many such are conceivable, such,
for instance, as the retardation of the speed of the planets, which
would be caused by the presence of a resisting medium in space, or
by the encounter of the system with a sufficiently dense and extended
cloud of meteors.
But so far as we can now judge, the ultimate cooling of the sun
(Sec. 193) is likely to extinguish life upon the planets long before
the mechanical destruction of the system can occur.
NOTE. The values given in Table II of the Appendix are allowed to
stand as in former editions, in order that their comparison with those
given in the text may illustrate to the student the measure of uncertainty
that still remains in such astronomical data.
CHAPTER X
COMETS AND METEORS
The Number, Designation, and Orbits of Comets Their Constituent Parts
and Appearance Their Spectra and Physical Constitution Their Prob-
able Origin Remarkable Comets Photography of Comets Aerolites,
their Fall and Characteristics Shooting-Stars, Meteoric Showers Con-
nection between Comets and Meteors
COMETS
289. Comets, their Appearance and Number. The
word " comet " (derived from the Greek kome) means a
" hairy star." The appearance is that of a rounded cloud
of luminous fog with a star shining through it, often
accompanied by a long fan-shaped train, or " tail," of hazy
light. They present themselves from time to time in the
heavens, mostly when unexpected, move across the con-
stellations in a path longer or shorter according to circum-
stances, and remain visible for some weeks or months
until they fade out and vanish in the distance. The large
ones are magnificent objects, sometimes as bright as Venus
and visible by day, with a head as large as the moon, and
having a train which extends from the horizon to the
zenith, and is really long enough to reach from the earth
to the sun. Such comets are rare, however ; the majority
are faint wisps of light, visible only with the telescope.
Fig. 67 is a representation of Donati's comet of 1858,
which was one of the finest ever seen.
252
FIG. 67. Naked-Eye View of Donati's Comet, Oct. 4, 1858
Bond
253
254 LESSONS IN ASTRONOMY
In ancient times comets were always regarded with terror, as at
least presaging evil, if not actively malignant, and the notion still
survives in certain quarters, though the most careful research goes
to prove that they exert upon the earth not the slightest perceptible
influence of any kind.
Thus far, up to the beginning of the new century, our
lists contain 800 recorded appearances, not all, however,
of different comets, for some (periodic) have been counted
several times. About 400 were observed before .the inven-
tion of the telescope in 1609, and therefore must have
been fairly bright. Of those observed since then, only a
small proportion have been conspicuous to the naked eye,
perhaps one in five. The total number that visit the solar
system must be enormous ; for there is seldom a time
when one at least is not in sight, and even with the tele-
scope we see only the few which come near the earth and
are favorably situated for observation.
290. Designation of Comets. A remarkable comet gen-
erally bears the name of its discoverer or of some one who
has " acquired its ownership," so to speak, by some impor-
tant research concerning it. Thus we have Halley's,
Encke's, and Donati's comets. The ordinary telescopic
comets are designated only by the year of discovery, with
a letter indicating the order of discovery in that year, as
comet " a, 1890 " (the letter preceding the year) ; or, still
again, with the year and a Roman numeral following and
denoting the order of perihelion passage, as 1890-1, the
latter method being the most used. In some cases a comet
bears a double name, as the Lexell-Brooks comet (1889-V),
which was investigated by Lexell in 1770, and discovered
by Brooks on its recent return in 1889,
COMETS 255
291. Duration of Visibility and Brightness. The great
comet of 1811 was observed for seventeen months, and
the little comet, known as 1889-1, for more than two
years, the longest period of visibility on record. On
the other hand, the whole* appearance sometimes lasts only
a week or two. The average is probably not far from
three months.
As to brightness, comets differ widely. About one in
five reaches the naked-eye limit, and a very few, say four
or five in a century, are bright enough to be seen in the
daytime. The great comet of 1882 and comet a, 1910,
were the last ones so visible.
292. Their Orbits. A large majority of the comets move
in orbits that are sensibly parabolas. (See Appendix, Sees.
439-440.) A comet moving in such an orbit approaches
'the sun from an enormous distance, far beyond the limits
of the solar system, sweeps once around the sun, and goes
off, never to come back. The parabola does not return
into itself and form a closed curve, like the circle and
ellipse, but recedes to infinity. Of the nearly 400 orbits
that have been computed, more than 300 appear to be of
this kind. About 85 orbits are more or less distinctly
elliptical, and about half a dozen are perhaps hyperbolas
(see Appendix, Sec. 440); but the hyperbolas differ so
slightly from parabolas that the hyperbolic character is not
really certain in a single case.
Comets which have elliptical orbits of course return at
regular intervals. Of the apparently elliptical orbits,
there are about a dozen to which computation assigns
periods near to or exceeding 1000 years. These orbits
approach parabolas so closely that their real character is
256
LESSONS IN ASTRONOMY
still rather doubtful. About 75 comets, however, have
orbits which are distinctly and certainly elliptical, and
60 have periods of less than one hundred years. About
20 of these have been actually observed at two or more
returns to perihelion. As to the rest of them, some are
now due within a few years, and some have probably been
lost to observation, either like Biela's comet (Sec. 312), or
by having their
orbits transformed
by perturbations.
293. The first
comet ascertained to
move in an elliptical
orbit was that known
as Halley's, with a
period of about sev-"
enty-six years, its peri-
odicity having been
announced by Halley
in 1705. It. has since
been observed in 1759
and 1835 and at its
last return in 1909 and
1910. The second of
the periodic comets
(in the order of dis-
covery) is Encke's, with the shortest period known, only three and
one-half years. Its periodicity was discovered in 1819, though the
comet itself had been observed several times before. Fig. 68 shows
the orbits of a number of short-period comets (it would cause confu-
sion to insert more of them) and also a part of the orbit of Halley's
comet. These comets all have periods ranging from three and one-
half to eight years, and it will be noticed that they all pass very near
to the orbit of Jupiter. Moreover, each comet's orbit crosses that of
FIG. 68. Orbits of Short-Period Comets
ORBITS OF COMETS 257
Jupiter near one of its nodes, the node being marked by a short cross
line on the comet's orbit. The fact is very significant, showing that
these comets at times come very near to Jupiter, and it points to an
almost certain connection between that planet and these bodies.
294. Comet-Groups. There are several instances in which a
number of comets, certainly distinct, chase each other along almost
exactly the same path, at an interval usually of a few months or
years, though they sometimes appear simultaneously. The most
remarkable of these " comet-groups " is that composed of the great
comets of 1668, 1843, 1880, 1882, and 1887. It is, of course, nearly
certain that the comets of such a " group " have a common origin.
295. Perihelion Distance, etc. Eight of the 300 come-
tary orbits, thus far determined, approach the sun within
less than 6,000000 miles, and four have a perihelion
distance exceeding 200,000000. A single comet (that of
1729) had a perihelion distance of more than four "astro-
nomical units," or 375,000000 miles. It must have been
an enormous one to be visible at all under the circum-
stances. There may, of course, be any number of comets
with still greater perihelion distances, because, as a rule,
we are able to see only such as come reasonably near the
earth, and this is probably only a small percentage of the
total number that visit the sun.
The inclinations of cometary orbits range all the way
from zero to 90. As regards the direction of motion, all
the elliptical comets having periods of less than one
hundred years move direct, i.e., from west to east, except
Halley's comet and Tempel's comet of 1866. Other
comets show no decided preponderance either way.
296. Parabolic Comets are Visitors. The fact that the
orbits of most comets are sensibly parabolic, and that their
planes have no evident relation to the ecliptic, indicates
258 LESSONS IN ASTRONOMY
(though it does not absolutely prove) that these bodies do
not in any proper sense belong to the solar system, but
are only visitors. Such comets come to us precisely as if
they simply dropped towards the sun from an enormous
distance among the stars ; and they leave the system with
a velocity which, if no force but the sun's attraction acts
upon them, will carry them away to an infinite distance,
or until they encounter the attraction of some other
sun. Their motions are just what might be expected of
ponderable masses moving among the stars under the
law of gravitation.
A slightly different view is advocated by some high authorities,
and is perhaps more probable, that these comets come from a great
distance indeed, but not from among the stars. It may be that our
solar system, in its journey through space (Sec. 342), is accompanied
by outlying clouds of nebulous matter, and that these are the source
of the comets. It is argued that if this were not the case the number
of hyperbolic orbits would be much greater, because we should meet
so many more comets than could overtake us.
297. Origin of Periodic Comets But while the para-
bolic comets are thus probably strangers and visitors,
there is a question as to the periodic comets which move
in elliptical orbits. Are we to regard them as native
citizens, or only as naturalized foreigners, so to speak?
It is evident that, somehow or other, many of them stand
in peculiar relations to Jupiter, Saturn, and other planets,
as already indicated in Sec. 293.
All short>period comets (those which have periods ran-
ging from three to eight years) pass very close to the orbit
of Jupiter, and are now recognized and spoken of as Jupi-
ter's " family of comets " ; more than twenty are known at
THE CAPTURE THEORY 259
present. Similarly, Saturn is credited with two comets,
and Uranus with two, one of them being Tempel's comet,
which is closely connected with the November meteors and
should have returned in 1900, but was not seen. Finally,
Neptune has a family of six ; among them Halley's comet,
and two others which have returned a second time to
perihelion since 1880.
298. The Capture Theory The generally accepted
theory as to the origin of these " comet-families " is one
first suggested by Laplace nearly one hundred years ago,
that the comets which compose them have been captured by
the planet to which they stand related. A comet entering
the system in a parabolic orbit and passing near a planet
will be disturbed, either accelerated or retarded. If it
is accelerated, it is easy to prove that the original para-
bolic orbit will be changed to an hyperbola, and the
comet will never be seen again, but will pass out of the
system forever; but if it is retarded, the orbit becomes
elliptical, and the comet will revolve around the sun (not
around the capturing planet), returning at each successive
revolution to the place where it was first disturbed.
But this is not the end. After a certain number of
revolutions, the planet and the comet will come together
a second time at or near the place where they met before.
The result may then be an acceleration which will send
the comet out of the system finally ; but it is an even
chance at least that it may be a second retardation and
that the orbit and period may thus be further diminished ;
and this may happen over and over again, until the comet's
orbit falls so far inside that of the planet that there is no
further disturbance to speak of.
260 LESSONS IN ASTRONOMY
Given time enough and comets enough, and the result
would inevitably be such a comet-family as really exists.
Its membership can hardly be permanent, however ; sooner
or later, if not first disintegrated, each captured comet will
almost certainly again encounter its captor under such
circumstances as to be thrown out of the system, never
to return.
299. The Lexell-Brooks Comet The " capture theory "
has recently received an interesting illustration in the case
of a little comet, 1889-V, discovered by Mr. Brooks of
Geneva, N.Y., in July, 1889. It was soon found to be
moving with a period of about seven years, in an elliptical
orbit which passes very near to that of Jupiter. (We
remark in passing that this comet, in August, divided into
four fragments ; see Sec. 314.) On investigating the orbit
more carefully, Dr. S. C. Chandler of Cambridge (U.S.)
discovered that, in 1886, the comet and the planet had
been close together for some months, and that as a conse-
quence the comet's orbit must have been greatly changed,
the previous orbit having been a much larger one with a
probable period of nearly twenty-seven years.
Now, in 1770, a famous comet appeared, which was
bright, came very near the earth, and, according to Lexell's
calculations, was then moving in an orbit with a period of
only five and a half years, the first instance of a short-
period comet on record ; but it was never seen again. The
calculations of Laplace, and later of Leverrier, showed that,
in 1779, it must have passed very near to Jupiter and
been thrown into an orbit too large to allow it to be seen
from the earth ; also that the period might probably be
about twenty-seven years. This would bring it very near
CONSTITUTION OF COMETS 261
to Jupiter again in 1886, and it was natural, therefore, for
Dr. Chandler to infer the probable identity of the two
comets, a conclusion for a time generally accepted.
Subsequent calculations by Dr. Charles L. Poor of Balti-
more threw doubt upon it, however, and the observations
made during the return of the comet in 1896 make it on
the whole more likely that Brooks's comet is not identical
with Lexell's, but very probably a member of the same
comet-group (Sec. 294). Dr. Poor found that the comet,
in 1886, passed between Jupiter and the orbit of its first
satellite within about 200,000 miles of the planet's surface,
which accounts for its separation into four parts.
PHYSICAL CONSTITUTION OF COMETS
300. Constituent Parts of a Comet. (a) The essential
part of a comet that which is always present and gives
the comet its name is the coma, or nebulosity, a hazy
cloud of faintly luminous transparent matter.
(b) Next, we have the nucleus, which, however, is want-
ing in many comets, and makes its appearance only as the
comet comes near the sun. It is a bright, more or less
starlike point near the center of the comet. In some
cases it is double, or even multiple.
(c) The tail, or train, is a stream of light which com-
monly accompanies a bright comet and is sometimes pres-
ent even with a telescopic one. As the comet approaches
the sun the tail follows it, but as the comet moves away
from the sun it precedes. It is always, speaking broadly,
directed away from the sun, though its precise form and
position are determined partly by the comet's motion.
262 LESSONS IN ASTRONOMY
It is practically certain that it consists of extremely rarefied
matter, which is thrown off by the comet and powerfully
repelled by the sun.
It certainly is not like the smoke of a locomotive or train of a
meteor simply left behind by the comet, because as the comet is
receding from the sun the tail goes before it, as has been said.
(d) Jets and Envelopes. The head of a comet is often
veined by short jets of light, which appear to be spurted
out from the nucleus ; and sometimes the nucleus throws
off a series of concentric envelopes like hollow shells, one
within the other. These phenomena, however, are seldom
observed in telescopic comets.
301. Dimensions of Comets. The volume, or bulk, of a
comet is often enormous, almost inconceivably so, if the
tail is included in the estimate. The head, as a rule, is
from 40,000 to 50,000 miles in diameter (comets less than
10,000 miles in diameter would stand little chance of dis-
covery). Comets exceeding 150,000 miles are rather rare,
though there are several on record.
The comet of 1811 at one time had a diameter of fully 1,200000
miles, forty per cent larger than that of the sun. The head of the
comet of 1680 was 600,000 miles in diameter, and that of Donati's
comet of 1858 about 250,000. Holmes's comet (1892) exceeded
800,000.
The diameter of the head changes continually and
capriciously ; on the whole, while the comet is approach-
ing the sun, the head usually contracts, expanding again
as it recedes.
No entirely satisfactory explanation is known for this behavior,
but Sir John Herschel has suggested that the change is merely optical,
that near the sun a part of the nebulous matter is evaporated
MASS OF COMETS 263
by the solar heat and so becomes invisible, condensing and reappear-
ing again when the comet gets to cooler regions.
The nucleus ordinarily has a diameter ranging from
100 miles up to 5000 or 6000, or even more. Like the
comet's head, it also varies greatly in diameter, even from
day to day, so that it is probably not a solid body. Its
changes, however, do not seem to depend in any regular
way upon the comet's distance from the sun, but rather
upon its activity in throwing off jets and envelopes.
The tail of a comet, as regards simple magnitude, is
by far the most imposing feature. Its length is sel-
dom less than from 5,000000 to 10,000000 miles. It
frequently attains 50,000000, and there are several cases
where it has exceeded 100,000000; while its diameter, at
the end remote from the comet, varies from 1,000000
to 15,000000.
302. Mass of Comets. While the bulk of comets is
thus enormous, their masses are apparently insignificant,
in no case at all comparable with that of our little earth
even. The evidence on this point, however, is purely neg-
ative ; it does not enable us in any case to say just what
the mass really is, but only to say how great it is not:
i.e., it only proves that a comet's mass is not greater than
TTFTo o"o ^ the earth's, 1 how much less we cannot yet
find out. . The evidence is derived from the fact that no
sensible perturbations are produced in the motions of a
planet when a comet comes even very near it, although
in such a case the comet itself is fairly "sent kiting,"
1 One one-hundred-thousandth of the earth's mass is about ten times
the mass of the earth's whole atmosphere and is equivalent to the mass
of an iron ball about 150 miles in diameter.
264 LESSONS IN ASTRONOMY
thus showing that gravitation has its full effect between
the two bodies.
Lexell's comet in 1770, and Biela's comet on several occasions,
have come so near the earth that the computed length of the comet's
period was changed by several weeks, while the year was not altered
by so much as a single second. It would have been changed by
many seconds if the comet's mass had been as much as -nnforo f
that of the earth.
303. Density of Comets. This is, of course, almost
inconceivably small, the mass of comets being so minute
and their volume so enormous. If the head of a comet
50,000 miles in diameter x has a mass jo"oVo"o that ^ the
earth, its mean density must be about Q-^Q-Q that of the air
at the sea-level, far below that of the best air-pump
vacuum. As for the tail, the density must be almost
infinitely lower yet. It is nearer to an "airy nothing"
than anything else we know of.
The extremely low density of comets is shown also by
their transparency. Small stars can be seen through the
head of a comet 100,000 miles in diameter, even very near
its nucleus, and with hardly a perceptible diminution of
their luster.
We must bear in mind, however, that the low mean density of a
comet does not necessarily imply a low density of its constituent
particles. A comet may be to a considerable extent composed of
small heavy bodies and still have a low mean density, provided they
are far enough apart. There is much reason, as we shall see, for
supposing that such is really the case, that the comet is largely
composed of small meteoric stones, carrying with them a certain
quantity of enveloping gas.
Another point should be referred to. Students often
find it impossible to conceive how such impalpable "dust
THE LIGHT OF COMETS 265
clouds" can move in orbits like solid masses, and Avith
such enormous velocities. They forget that in a vacuum
a feather falls as swiftly as a stone. Interplanetary space
is a vacuum far more perfect than anything we can pro-
duce by air-pumps, and in it the lightest bodies move as
freely and swiftly as the densest, since there is nothing to
resist their motion. If all the earth were suddenly anni-
hilated except a single feather, the feather would keep right
on and continue the same orbit with unchanged speed.
304. The Light of Comets. To some extent their light
may be mere reflected sunlight, \p*k in the main it is light
emitted by the comet itself under the stimulus of solar
action. That the light depends in some way on the sun
is shown by the fact that its brightness usually varies with
its distance from the sun, according to the same law as
that of a planet.
But the brightness frequently varies rapidly and capri-
ciously without any apparent reason ; and that the comet
is self-luminous when near the sun is proved by its spectrum,
which is not at all like the spectrum of reflected sunlight,
but is a spectrum of bright bands, three of which are usually
seen and have been identified repeatedly and certainly with
the spectrum of gaseous hydrocarbons. (All the different
hydrocarbon gases give the same spectrum at the tempera-
ture of a Bunsen burner.) This spectrum is absolutely iden-
tical with that given by the blue base of a candle flame, or,
better, by a Bunsen burner consuming ordinary coal gas.
Occasionally a fourth band is seen in the violet, and when the comet
approaches unusually near the sun, the bright lines of sodium and
other metals (probably iron), sometimes appear. There are also a few
comets with anomalous spectra in which different bands replace the
266
LESSONS IN ASTRONOMY
ordinary ones, as in the case of Borrelly's comet of 1877. Holmes's
comet in 1892 showed a purely continuous spectrum. The spectrum
makes it almost certain that hydrocarbon gases are present in con-
siderable quantity, and that these gases are somehow rendered lumi-
nous ; not probably by any general heating, however, for there is no
FIG. 69. Head of Donati's Comet
Bond
reason to think that the general temperature of a comet is very high.
Nor must we infer that the hydrocarbon gas, because it is so con-
spicuous in the spectrum, necessarily constitutes most of the comet's
mass ; more likely it is only a very small fraction of the whole.
COMETARY PHENOMENA
267
To Sun
305. Phenomena that accompany a Comet's Approach to
the Sun. When the comet is first discovered it is usually
a mere round, hazy cloud of faint nebulosity, a little brighter
near the middle. As it approaches the sun it brightens
rapidly, and the nucleus appears. Then on the sunward
side the nucleus begins to emit luminous jets, or else to
throw off more or less symmetrical envelopes, which follow
each other at intervals of
some hours, expanding or
growing fainter, until they
are lost in the nebulosity of
the head.
Fig. 69 shows the envel-
opes as they appeared in
the head of Donati's comet
of 1858. At one time
seven of them were visible
together ; very few comets,
however, exhibit this phe-
nomenon with such sym-
metry. More frequently
the emissions from the nucleus take the form of jets
and streamers.
306. Formation of Tail. The tail appears to be formed
of material which is first projected from the nucleus of
the comet towards the sun and then afterwards repelled
by the sun, as illustrated by Fig. 70. At least, this theory-
has the great advantage over all others which have been
proposed that it not only accounts for the phenomenon
in a general way, but admits of being worked out in detail
and verified mathematically, by comparing the actual size
FIG. 70. Formation of a Comet's Tail
by Matter expelled from the Head
268 LESSONS IN ASTRONOMT
and form of the comet's tail at different points in the orbit
with that indicated by the theory ; and the accordance is
usually satisfactory.
As to the nature of this repulsive force there has been much specu-
lation. For some time it has generally been believed to be electrical,
and it is still probable that such forces play an important part. But
the recent experimental demonstrations (1901-1902) of the repul-
sive force of light-waves, long ago pointed out by Clerk Maxwell
as a necessary consequence of his electro-magnetic theory of light
(now regarded as established . by the experiments of Herz), make it
almost certain that this is the principal agent in driving off the come-
tary particles. The two theories are, however, supplementary rather
than contradictory.
The repelled particles are still subject to the sun's gravi-
tational attraction, and the effective force acting upon them
is, therefore, the difference between the gravitational attrac-
tion and the repulsion. This difference may or may not
be in favor of the attraction, but in any case the sun's
attracting force is, at least, lessened. The consequence is
that those repelled particles, as soon as they get a little
away from the comet, begin to move around the sun in
hyperbolic orbits (see Sec. 439), which lie in the plane of
the comet's orbit, or nearly so, and are perfectly amenable
to calculation.
In the case of a great comet the tail is usually a sort of
curved, hollow cone, including the head of the comet at
its smaller extremity ; in smaller comets the tail is gener-
ally a comparatively narrow streamer where it issues from
the head of the comet, brushing out as it recedes, and often
showing in photographs peculiar knots and condensations,
which are not visible with the telescope.
FORMATION OF COMETS' TAILS 269
The tail is curved, because the repelled particles, after
leaving the comet's head, retain their original motion, so
that they are arranged, not along a straight line drawn
from the sun to the comet, but on a curve convex to the
comet's motion, as shown in Fig. 71 ; but the stronger
the repulsion, the less the curvature and the straighter the
tail. There is no reason to suppose that the matter driven
off from the comet is ever recovered by it.
FIG. 71. A Comet's Tail at Different Points in its Orbit near Perihelion
307. Types of Comets' Tails. Bredichin of Moscow
has found that the trains of comets may be classified under
three different types, as indicated by Fig. 72.
First. The long, straight rays, composed of matter upon which the
solar repulsion is from ten to fifteen times as great as the attraction
of gravity, so that the particles leave the comet with a velocity of
four or five miles a second, which is afterwards increased until it
becomes enormous. The nearly straight rays, shown in Fig. 67,
belong to this type. For plausible reasons, Bredichin supposes these
straight rays to be composed of hydrogen.
270
LESSONS IN ASTRONOMY
The second type is the ordinary curved plumelike train, like
the principal tail of Donati's comet. In trains of this type, supposed
to be due to hydrocarbon
vapors, the repulsive force
varies from 2.2 times the
attraction of gravity for
particles on the convex
edge of the train to half
that amount for those on
the inner edge. The spec-
trum is the same as that
of the comet's head.
Third. A few comets
show tails of still a third
type, short, stubby
brushes, violently curved,
and due to matter on
which the repulsive force
is feeble as compared
with gravity. These are
assigned by Bredichin to
metallic vapors of consid-
erable density, with an ad-
mixture of sodium, etc.
308. Unexplained
and Anomalous Phe-
nomena. A curious
phenomenon, not yet
explained, is the dark
stripe which in a large
FIG. 72. Bredichin 's Three Types of comet approaching the
Cometary Tails , ,
sun runs down the
center of the tail, looking very much as if it were a
shadow of the comet's head. It is certainly not a shadow,
NATURE OF COMETS 271
however, because it usually makes more or less of an angle
with the sun's direction. It is well shown in Fig. 69.
When the comet is at a greater distance from the sun
this central stripe is usually bright, as in Fig. 73 ; and
in the case of small comets, generally all the tail they
show is such a narrow streamer.
Not unfrequently, moreover, comets possess anomalous tails,
tails directed sometimes straight towards the sun and sometimes
at right angles to that direction.
Then sometimes there are luminous
sheaths, which seem to envelop the
head of the comet and project
towards the sun (Fig. 74), or little
clouds of cometary matter, which
leave the main comet, like puffs of
smoke from a bursting bomb, and ^73. - Bright-Centered Tail of
Coggia's Comet, June, 1874
travel off at an angle until they
fade away (see Fig. 74). None of these appearances are contradic-
tory to the theory above stated though they are not yet clearly
included in it.
309. The Nature of Comets. All things considered,
the most probable hypothesis as to the constitution of a
comet, so far as we can judge at present, is that its head
is a swarm of small meteoric particles, widely separated
(say pinheads, many yards apart), each carrying with it
an envelope of rarefied gas and vapor, in which light
is produced either by electric discharges between the
solid particles, or by some action due to the rays of the
sun. As to the size of the constituent particles opinions
differ widely. Some maintain that they are large rocks ;
Professor Newton calls a comet a " gravel bank " ; others
say that it is a mere " dust cloud." The unquestionable
272 LESSONS IN ASTRONOMY
close connection between meteors and comets (Sec. 327)
almost compels some " meteoric hypothesis."
310. Danger from Comets. In all probability there is very
little. It has been supposed that comets might do us harm in three
ways, either by actually striking the earth or by falling into the
sun, and thus producing such an increase of solar heat as to burn us
up, or, finally, by filling our atmosphere with irrespirable if not
poisonous gases.
As regards the possibility of a collision between a comet and the
earth, the event is certainly possible. In fact, if the earth lasts long
enough, it is practically sure to happen, for there are several cometary
orbits which pass nearer to the earth's orbit than the semi-diameter
of the comet's head.
As to the consequence of such a collision, it is impossible to speak
with absolute confidence for want of certain knowledge as to the
constitution of a comet. If the solid " particles " of which the main
portion of the comet is probably composed are no larger than pin-
heads, the result would be only a fine meteoric shower ; if, on the
other hand, they weigh tons, the bombardment would be a very
serious matter. It is possible too that the mixture of the comet's
gases with our atmosphere might be a source of danger by rendering
the air irrespirable or explosive.
The encounters, however, will be very rare. If we accept the
estimate of Babinet, they will occur on the average once in about
15,000000 years.
If a comet actually strikes the sun, which would necessarily be a
very rare phenomenon, it is not likely that the least injury will fol-
low. The collision might generate about as much heat as the sun
radiates in eight or nine hours ; but the cometary particles would
pierce the photosphere, and their heat would be liberated mostly
below the solar surface, simply expanding by some slight amount
the diameter of the sun, but making no particular difference in the
amount of its radiation for the time being. There might be, and
very likely would be, a flash of some kind at the solar surface when
the shower of meteors' struck it, but probably nothing that the
astronomer would not take delight in observing.
REMARKABLE COMETS 273
311. Remarkable Comets. Our space does not permit
us to give full accounts of any considerable number. We
limit ourselves to three, which for various reasons are of
special interest.
Biela's comet is, or rather was, a small comet some 40,000
miles in diameter, at times barely visible to the naked eye,
and sometimes showing a short tail. It had a period of
6.6 years, and was the second comet of short period
known, having been discovered by Biela, an Austrian
officer, in 1826 (the periodicity of Encke's comet had
been discovered seven years earlier). Its orbit comes
within a few thousand miles of the earth's orbit, the dis-
tance varying somewhat, of course, on account of per-
turbations; but the approach is ^sometimes so close that
if the comet and the earth should happen to arrive at
the same time there would be a collision. At its return,
in 1846, it split into two. When first seen on Novem-
ber 28, it was one and single. On December 19 it was
distinctly pear-shaped, and ten days later it was divided.
The twin comets traveled along for four months at an almost
unchanging distance of about 165,000 miles, without any apparent
effect upon each other's motions, but both very active from the physical
point of view, and showing remarkable variations and alternations of
brightness entirely unexplained. In August, 1852, the twins were
again observed, then separated by a distance of about 1,500000
miles ; but it was impossible to tell which was which. Neither of
them has ever been seen again, though they must have returned
many times, and more than once in a very favorable position.
312. There remains, however, another remarkable chap-
ter in the story of this comet. In 1872, on November 27,
just as the earth was crossing the track of the lost comet,
274 LESSONS IN ASTRONOMY
but some millions of miles behind where the comet ought
to be, we encountered a wonderful meteoric shower. As
Miss Clerke expresses it, perhaps a little too positively,
" it became evident that Biela's comet was shedding over
us the pulverized products of its disintegration." A similar
meteoric shower occurred again in 1885 (see also Sec. 326),
when the earth once more crossed the track of the comet ;
and still again in 1892 and 1898, the last very feeble.
It is not certain whether the meteor swarms thus encountered
were the remains of the comet itself, or whether they were other small
bodies merely following in its path. The comet must have been several
millions of miles ahead of the place where these meteor swarms were
met, unless it has been set back in its orbit since 1852 by some unex-
plained and improbable perturbations. But the comet cannot be
found, and if it still exists and occupies the place it ought to, it must
have somehow lost the power of shining.
313. The Great Comet of 1882. This is the most recent
of the brilliant comets observed in the United States, and
will long be remembered not only for its magnificent beauty,
but for the great number of unusual phenomena which it
presented. It was first seen in the southern hemisphere
about September 3, but not in the northern until the 17th,
the day on which it arrived at perihelion. On that day it
was independently discovered within 2 or 3 of the sun, near
noon, by several observers, who had not before heard of its
existence. It was visible to the naked eye in full sunshine
for more than a week after its perihelion passage. It then
became a splendid object in the morning sky and continued
to be observed for six months.
That portion of the orbit visible from the earth coincides
almost exactly with the orbits of four other comets, those
THE GREAT COMET OF 1882 275
of 1668, 1843, 1880, and 1887, with which it forms a
"comet-group," as already mentioned (Sec. 294). The
perihelion distances of the comets of this group are all
less than 750,000 miles, so that they pass within 300,000
miles of the sun's surface, i.e., right through the corona,
and with a velocity exceeding 300 miles a second; and
yet this passage through the corona does not perceptibly
disturb their motion.
The orbit of the comet of 1882 turned out to be a very
elongated ellipse with a period of about 800 years. The
periods of the others are quite uncertain because they
could not be observed as long, but the orbits of all are
probably similar in every respect.
Early in October the comet presented the ordinary
features. The nucleus was round, a number of well-
marked envelopes were visible in the head, and the dark
stripe down the center of the tail was sharply defined.
Two weeks later the nucleus had been broken up and
transformed into a crooked stream some 50,000 miles in
length, of five or six bright points; the envelopes had
vanished from the head, and the dark stripe was replaced
by a bright central spine.
At the time of perihelion the comet's spectrum was
filled with countless bright lines. Those of sodium were
easily recognizable, and continued visible for weeks; the
other lines continued only a few days and were not
certainly identified, although the general aspect of the
spectrum indicated that iron, manganese, and calcium
were probably present. By the middle of October it
had become simply the normal comet spectrum with the
ordinary hydrocarbon bands.
276 LESSONS IN ASTROXOMY
The comet was so situated that the tail was directed
nearly away from the earth, and so was not seen to good
advantage, never having an apparent length exceeding 35.
The actual length, however, at one time was more than
100,000000 miles.
A unique, and still only doubtfully explained, phenom-
enon, was a faint, straight-edged " sheath " of light, which
FIG. 74. The " Sheath," and the Attendants of the Comet of 1882
enveloped the portions of the comet near the head and
projected 3 or 4 in front of it, as shown in Fig. 74.
Moreover, there were certain shreds of cometary matter
accompanying the comet, at a distance of 3 or 4 when
first seen, but gradually receding and growing fainter.
PHOTOGRAPHY OF COMETS 277
This also was something new in cometary history, though
the Lexell-B rooks comet, 1889 V, has since shown some-
thing much like it.
314. Halley's Comet. The most brilliant of the peri-
odic comets is Halley's, which was seen last in 1910 and is
due to appear again about 1985. This is undoubtedly the
same comet that was seen in 1066, the year of the Norman
Conquest, and was probably seen as early as 11 B.C.
Its path is very oval, extending beyond the orbit of the
planet Neptune. It reappears every 75 or 76 years, and
when near perihelion is usually a conspicuous object. On
May 18, 1910, it passed between the earth and the sun,
coming so near to us that the earth must have passed
through at least a part of its tail, but not the slightest
effect on the earth could be detected, nor could any trace
of the comet be seen when passing across the sun's face.
314*. Photography of Comets. It is now possible to
photograph comets, and the photographs bring out numer-
ous peculiarities and details, which are not visible to the
eye even with telescopic aid. This is especially the case
in the comet's tail. The figure on the next page is from
a magnificent photograph of Rordame's comet of 1893,
for which we are indebted to the kindness of Professor
Holden, director of the Lick Observatory. As the camera
was kept pointed at the head of the comet (which was mov-
ing pretty rapidly), the star images, during the hour's
exposure, are drawn out into parallel streaks, the little
irregularities being due to faults of the clockwork and
vibrations of the telescope. The knots and streamers,
which characterize the comet's tail, were none of them
visible in the telescope and are not the same shown upon
FIG. 75. Comet Rordame, July 13, 1893
Photographed by W. J. Hussey, at the Lick Observatory
278
PHOTOGRAPHY OF COMETS
279
plates taken the day before and the day after. Other
plates, made the same evening a few hours earlier and
later, indicate that the "knots" were swiftly receding
from the comet's head at a rate exceeding 150,000
miles an hour. It is to be noted also that the light
of a comet's
tail seems to
be specially
"actinic," so
that, as in the
case of the
nebulae, photo-
graphs show
features and
details which
are entirely
invisible in
telescopes.
Fig. 76 shows Swift's comet of 1892, at three different
dates as photographed by Barnard at the Lick Observa-
tory. The rapid changes in the structure of the tail 'are
very remarkable and significant.
In 1892 Barnard discovered a small comet by the streak, it left
upon one of his star plates, and several similar discoveries have since
been made by others.
FIG. 76. Swift's Comet of 1892
Photographed by Barnard
METEORS AND SHOOTINO-STARS
315. Meteorites. Occasionally bodies fall upon the
earth out of the sky. Such a body during its flight
through the air is called a " Meteor " or " Bolide," and the
280 LESSONS IN ASTRONOMY
pieces which fall to the earth are called " Meteorites,"
44 Aerolites," " Uranolites," or simply " meteoric stones."
If the fall occurs at night, a ball of fire is seen, which
moves with an apparent velocity depending upon the dis-
tance of the meteor and the direction of its motion. The
fire-ball is generally followed by a luminous train, which
sometimes remains visible for many minutes after the meteor
itself has disappeared. The motion is usually somewhat
irregular, and here and there along its path the meteor
throws off sparks and fragments and changes its course
more or less abruptly. Sometimes it vanishes by simply
fading out in the air, sometimes by bursting like a rocket.
If the observer is near enough, the flight is accompanied
by a heavy continuous roar, emphasized now and then by
violent detonations.
The observer must not expect to hear the explosion at the moment
when he sees it, since sound travels only about twelve miles a minute.
If the fall occurs by day, the luminous appearances are
mainly wanting, though sometimes a white cloud is seen,
and the train may be visible. In a few cases aerolites
have fallen almost silently, and without warning.
316. The Aerolites themselves. The mass that falls is
sometimes a single piece, but more usually there are many
fragments, sometimes numbering thousands; so that, as
the old writers say, " it rains stones." The pieces observed
to fall weigh from six hundred pounds to a few grains,
the aggregate mass sometimes amounting to a number of
tons. By far the greater number of aerolites are stones, but
a few perhaps three or four per cent of the whole num
ber are masses of nearly pure iron more or less alloyed
THE AEROLITES THEMSELVES 281
with nickel. There are also masses of so-called " meteoric
iron " which have been found (not seen to fall) in places
where it is not easy otherwise to account for their pres-
ence, and one of these (Peary's, from Greenland) weighs
nearly seventy tons. But their meteoric character is con-
sidered extremely doubtful by the highest authorities.
The total number of meteorites which have fallen and been gath-
ered into cabinets since 1800 is about 275, only 10 of which are
iron masses. Nearly all, however, contain a large percentage of iron,
either in the metallic form or as sulphide. Between 25 and 30 of
the 250 fell within the United States, the most remarkable being
those of Weston, Conn., in 1807; New Concord, Ohio, I860;
Amana, Iowa, 1875; Emmet County, Iowa, 1879 (mainly iron);
and Johnson County, Ark., 1886 (iron).
Twenty-five of the chemical elements have been found
in these bodies, including helium (Sec. 181), but not one
new element ; though a large number of new minerals (i.e.,
new compounds of known elements) appear in them, and
seem to be characteristic of aerolites.
The most distinctive external feature of a meteorite is
the thin, black, varnishlike crust that covers it. It is
formed by the melting of the surface during the meteor's
swift flight through the air, and in some cases penetrates
the mass in cracks and veins. The surface is generally
somewhat uneven, having " thumb-marks " upon it,
hollows, probably formed by the fusion of some of the
softer minerals. Fig. 77 is from a photograph of a mete-
orite weighing twenty-four pounds, which fell in Hungary
in 1837, one of several which fell together.
317. Path and Motion. When a meteor has been well
observed from a number of different stations, its path can
282 LESSONS IN ASTRONOMY
be computed. Tt usually is first seen at an altitude of
between 80 and 100 miles and disappears at an altitude of
between 5 and 10. The length of the path may be any-
where from 50 to 500 miles. In the earlier part of its
course the velocity ranges from 10 to 40 miles a second,
but this is greatly reduced before the meteor disappears.
In observing these bodies, the object should be to obtain as accu-
rate an estimate as possible of the altitude and azimuth of the meteor
FIG. 77. The Gross Divina Meteorite
at moments which can be identified, and also of the time occupied in
traversing definite portions of the path. The altitude and azimuth
will enable us to determine the height and position of the meteor,
while the observations of the time are necessary in computing its
velocity. By night the stars furnish the best reference points from
which to determine its position. By day one must take advantage
of natural objects or buildings to define the meteor's place, the
observer marking the precise spot where he stood. By taking the
proper instrument to the place afterwards it is then easy to ascer-
tain the bearings and altitude. As to the time of flight, it is usual
LIGHT AND HEAT OF METEORS 283
for the observer to begin to repeat rapidly some familiar verse of
doggerel when the meteor is first seen, reiterating it until the meteor
disappears. Then, by rehearsing the same before a clock, the
number of seconds can be pretty accurately determined.
318. The Light and Heat of Meteors. These are due
simply to the destruction of the meteor's velocity by the
friction, compression, and resistance of the air. When a
body moving with a high velocity is stopped by the resist-
ance of the air, the greater part of its energy is trans-
formed into heat. Lord Kelvin has demonstrated that the
heating effect in the case of a body moving through the
air with a velocity exceeding ten miles a second is
the same as if it were " immersed in a flame having a tem-
perature at least as high as the oxyhydrogen blowpipe " ;
and, moreover, this temperature is independent of the
density of the air, depending only on the velocity of the
meteor. Where the air is dense, the total quantity of
heat (i.e., the number of calories developed in a given time)
is, of course, greater than where the air is rarefied ; but the
virtual temperature of the air itself where it rubs against
the surface is the same in either case. During the
meteor's flight, its surface, therefore, is raised to a white
heat and melted, and the liquefied portions are swept off
by the rush of air, condensing as they cool to form the
train. In some cases this train remains visible for many
minutes, a fact not easily explained. It seems probable
that the material must be phosphorescent.
319. Origin of Meteors. They cannot be, as some have
maintained, the immediate product of eruptions from vol-
canoes, either terrestrial or lunar, since they reach our
atmosphere with a velocity which makes it certain that
284 LESSONS IN ASTRONOMY
they come to us from the depths of space. There is no
proof that they have originated in any way different from
the larger heavenly bodies. At the same time many of
them resemble each other so closely as almost to compel
the surmise that these, at least, must have had a common
source. It is not perhaps impossible that such may be
fragments which long ago were shot out from now extinct
lunar volcanoes with a velocity which made planets of
them for the time being. If so, they have since been
traveling in independent orbits until they encountered
the earth at the point where her orbit crosses theirs. Nor
is it impossible that some of them were thrown out by
terrestrial eruptions when the earth was young, or that
they have been ejected from other planets, or even from
the stars. It is only certain that during the period
immediately preceding their arrival upon the earth they
have been traveling in long ellipses or parabolas, around
the sun.
SHOOTING-STARS
320. Their Nature and Appearance. These are the
evanescent, swiftly moving, starlike points of light which
may be seen every few minutes on any clear moonless
night. They make no sound, nor has anything been
certainly known to reach the earth's surface from them.
For this reason it is probably best to retain, provisionally, at
least, the old distinction between them and the great meteors from
which aerolites fall. It is quite possible that the distinction has no
real ground, that shooting-stars, as is maintained by many, are
just like other meteors, except that being so small they are entirely
consumed in the air ; but then, on the other hand, there are some
things which rather favor the idea that the two classes differ in
SHOOTING-STARS 285
about the same way as asteroids do from comets. We know that an
aerolitic meteor is a compact mass of rock. It is possible, and not
even unlikely, that a shooting-star, on the contrary, is a little dust
cloud, like a puff of smoke.
321. Number of Shooting-Stars. Their number is enor-
mous. A single observer averages from four to eight an
hour; but if the observers are sufficiently numerous and
so placed as to be sure of noting all that are visible from
a given station, about eight times as many are counted.
From this it has been estimated that the total number
which enter our atmosphere daily must be between
10,000000 and 20,000000, the average distance between
them being some 200 miles.
Besides those which are visible to the naked eye, there is a still
larger number of meteors which are so small as to be observable
only with the telescope.
The average hourly number about six o'clock in the
morning is double the hourly number in the evening,
the reason being that in the morning we are in front
of the earth as regards its orbital motion, while in the
evening we are in the rear. In the evening we see only
such as overtake us ; in the morning we see all that we
either meet or overtake.
322. Elevation, Path, and Velocity. By observations
made at stations 30 or 40 miles apart it is easy to deter-
mine these data with some accuracy. It is found that on
the average the shooting-stars appear at a height of about
74 miles and disappear at an elevation of about 50 miles,
after traversing a course 40 or 50 miles long, with a velocity
from 10 to 50 miles a second, about 25 on the average.
They do not first become visible at so great a height as
286 LESSONS IN ASTRONOMY
the aerolitic meteors, and they are more quickly consumed
and therefore do not penetrate the atmosphere so deeply.
323. Brightness, Material, and Mass. Now and then
.a shooting-star rivals Jupiter or even Venus in bright-
ness. A considerable number are like first-magnitude
stars, but the great majority are faint. The bright ones
generally leave trains. Occasionally it has been possible
to get a "snap shot," so to speak, at the spectrum of a
meteor, and in it the bright lines of sodium and magne-
sium (probably) are fairly conspicuous among many others
which cannot be identified by such a hasty glance.
Since these bodies are consumed in the air, all that we
can hope to get of their material is their " ashes."
In most places its collection and identification is, of course, hope-
less ; but the Swedish naturalist Nordenskiold thought that it might
be found in the polar snows. In Spitzbergen he therefore melted
several tons of snow, and on filtering the water he actually detected
in it a sediment containing minute globules of oxide and sulphide
of iron. Similar globules have also been found in the products of
deep-sea dredging. They may be meteoric ; but what we now know
of the distance to which smoke and fine volcanic dust is carried
by the wind makes it not improbable that they may be of purely
terrestrial origin.
We have no way of determining the exact mass of a
shooting-star ; but from the light it emits, as seen from a
known distance, an approximate estimate can be formed,
since we know roughly how much energy corresponds to
the production of a given amount of light. It is likely,
on the whole, that an ordinary meteor and a good elec-
tric incandescent lamp do not differ widely in what is
called their "luminous efficiency," i.e.^ the percentage of
their total energy which is converted into visible light.
METEORIC SHOWERS
287
Calculations on this basis indicate that ordinary shooting-
stars are very minute, weighing only a small fraction of an
ounce, from less than a grain up to fifty or one hundred
grains for a very large one. Still this is hardly certain ;
the estimates of some investigators would make them
considerably larger.
324, Meteoric Showers. There are occasions when these
bodies, instead of showing themselves here and there in
FIG. 78. The Meteoric Kadiant in Leo, Nov. 13, 1867
the sky at intervals of several minutes, appear in showers
of thousands ; and at such times they do not move at
random, but all their paths diverge or radiate from a single
point in the sky, known as the radiant; i.e., their paths
produced backwards all pass through this point, though
they do not usually start there. Meteors which appear
288 LESSONS IN ASTRONOMY
near the radiant are apparently stationary, or describe
paths which are very short, while those in the more
distant regions of the sky pursue long courses. The
radiant keeps its place among the stars nearly unchanged
during the whole continuance of the shower, and the
shower is named according to the place of the radiant.
Thus, we have the " Leonids," or meteors whose radiant is
the constellation of Leo, the " Andromedes " (or Bielids),
the " Perseids," the " Lyrids," etc.
Fig. 78 represents the tracks of a large number of the Leonids of
1867, showing the position of the radiant near Zeta Leonis.
The radiant is explained as a mere effect of perspective.
The meteors are all moving in lines nearly parallel with
each other when encountered by the earth, and the radi-
ant is simply the perspective "vanishing point" of this
system of parallels. Its position depends entirely on
the direction of the motion of the meteors with respect
to the earth. For various reasons, however, the paths
of the meteors, after they enter the air, are not exactly
parallel, and in consequence the radiant is not a mathe-
matical point, but a "spot" in the sky, often covering an
area of 3 or 4 square.
Probably the most remarkable of all the meteoric showers
that ever occurred was that of the Leonids, on Nov. 12,
1833. The number of meteors at some stations was esti-
mated as high as 100,000 an hour for five or six hours.
" The sky was as full of them as it ever is of snowflakes
in a storm."
325. Dates of Meteoric Showers. Such meteoric showers
are caused by the earth's encounter with a swarm of little
DATES OF METEORIC SHOWERS 289
meteors, and since this swarm pursues a regular orbit
around the sun, the earth can meet it only when she is at
the point where her orbit cuts this path. The encounter,
therefore, must always happen on or near the same day
of the year, except as in time the meteoric orbits shift
their positions on account of perturbations. The Leonid
showers, therefore, appear about November 15, and the
Andromedes about the 27th or 28th of the same month.
But the Leonids since 1800 have-changed their date from Novem-
ber 12 to November 15, and the Andromedes from November 27
to November 23 since 1872, the effect of disturbance by the
planets.
In some cases the metebrs are distributed along their
whole orbit, forming a sort of elliptical ring and are
rather widely scattered. In that case the shower recurs
every year and may continue for several weeks, as is the
case with the Perseids, which appear in early August.
On the other hand, the flock may be concentrated, and
then the shower will occur only when the earth and the
meteor swarm both arrive at the orbit-crossing together.
This is the case with both the Leonids and the Androm-
edes. The showers then occur, not every year, but only
at intervals of several years, though always near the same
day of the month. For the Leonids the interval is about
thirty-three years, and for the Bielids about thirteen years,
though in this case there are some intermediate showers,
as in 1898.
326. The meteors which belong to the same group have
a marked family resemblance. The Perseids are yellow
and move with medium velocity. The Leonids are very
swift (we meet them), and they are of a bluish green tint,
290 LESSONS IN ASTRONOMY
i
with vivid trains. The Bielids are sluggish (they over-
take the earth), are reddish, being less intensely heated
than the others, and usually have only feeble trains.
During these showers no sound is heard, no sensible heat
perceived, nor do any masses of matter reach the ground ;
with one exception, however, that on Nov. 27, 1885, a
piece of meteoric iron fell at Mazapil, in northern Mexico,
during the shower of Andromedes, which occurred that even-
ing. The coincidence may be accidental, but is certainly
interesting. Some high authorities speak confidently of
this piece of iron as a piece of Biela's comet itself ; and
this brings us to one of the most important astronomical
discoveries of the last half-century.
327. The Connection between Comets and Meteors. At
the time of the great meteoric shower of 1833, Professors
Olmsted and Twining of New Haven were the first to
recognize the " radiant " and to point out its significance
as indicating that the meteors must be members of a swarm
of bodies revolving around the sun in a permanent orbit.
In 1864 Professor Newton of New Haven, taking up the
subject anew, showed by an examination of the old records
that there had been a number of great meteoric showers
about the middle of November, at intervals of thirty-
three or thirty-four years, and he predicted confidently
the repetition of the shower on Nov. 13 or 14, 1866. It
occurred as predicted and was observed in Europe; and
it was followed by another in 1867, which was visible in
America, the meteoric swarm being extended in so long a
procession as to require more than two years to cross the
earth's orbit. The researches of Newton and Adams
showed that the flock was moving in a long ellipse with a
RELATION BETWEEN COMETS AND METEORS 291
period of thirty-three years. Another shower was pretty
confidently expected in 1899 or 1900, but failed to appear;
in 1901 there was, however, a well-marked, but not very
abundant, display on the night of November 14-15. 1 The
failure to appear as expected is ascribed to the perturba-
tions produced by Jupiter and Saturn since 1866.
328. Identification of Meteoric and Cometary Orbits.
Within a few weeks after the shower of 1866 it was found
FIG. 79. Orbits of Meteoric Swarms
that the orbit pursued by these meteors was identical with
that of a comet, known as Tempel's, which had been visible
about a year before ; and about the same time Schiaparelli
showed that the Perseids, or August meteors, move in
an orbit identical with that of the bright comet of 1862.
Now a single coincidence might be accidental, but hardly
1 Similar minor showers occurred in 1902, 1903, and 1904.
292
LESSONS IN ASTRONOMY
two. Five years later came the shower of Andromedes,
following in the track of Bieia's comet, and among the
more than a hundred distinct meteor swarms now rec-
ognized Professor Alexander Herschel finds five others
which are similarly related each to its special comet. It
is no longer possible to doubt that there is a real and
u=place of Uranus 126 A.D.
FIG. 80. Origin of the Leonids
close connection between these comets and their attendant
meteors. Fig. 79 represents four of the orbits of these
cometo-meteoric bodies.
329, Nature of the Connection. This cannot be said to
be ascertained. In the case of the Leonids and Andro-
medes the meteoric swarm follows the comet, but this
does not seem to be so in the case of the Perseids, which
scatter along more or less abundantly every year. The
prevailing belief is that the comet itself is only the thickest
THE METEO1UT1C HYPOTHESIS 293
part of the meteoric swarm, and that the clouds of meteors
scattered along its paths are the result of its disintegration ;
but this is by no means certain.
It is easy to show that if the comet really is such a swarm it must
at each return to perihelion gradually break up more and more, and
disperse its constituent particles along its path until the compact
swarm has become a diffuse ring. The longer the comet has been
moving around the sun, the more uniformly the particles will be dis-
tributed. The Perseids, therefore, are supposed to have been in the
system for a long time, while the Leonids and Andromedes are
believed to be comparatively new-comers. Leverrier, indeed, has gone
so far as to indicate the year 126 A.D. as the time at which Uranus
captured Tempel's comet and brought it into the system, as illus-
trated by Fig. 80. But the theory that meteoric swarms are the
product of cometary disintegration assumes the premise that comets
enter the system as compact clouds, which, to say the least, is not
yet certain.
330. Lockyer's Meteoritic Hypothesis. Recently Sir Norman
Lockyer has been greatly enlarging the astronomical importance of
meteors. The probable meteoritic constitution of the zodiacal light,
as well as of Saturn's rings, and of the comets, has long been
recognized ; but he goes much farther, and maintains that all the
heavenly bodies are either meteoric swarms, more or less condensed,
or the final products of such condensation. Upon this hypothesis he
attempts to explain the evolution of the planetary system, the phe-
nomena of variable and colored stars, the various classes of stellar
spectra, and the forms and structure of the nebulae, indeed pretty
much everything in the heavens from the Aurora Borealis to the
sun. As a "working hypothesis," his theory is unquestionably
important and has attracted much attention, but it encounters serious
difficulties in many of its details.
CHAPTER XI
THE STARS
Their Nature, Number, and Designation Star-Catalogues and Charts
Proper Motions and the Motion of the Sun in Space Stellar Parallax
Star Magnitudes Variable Stars Stellar Spectra.
331. The solar system is surrounded by an immense void
peopled only by stray meteors. The nearest star, so far as
our present knowledge goes, is one whose distance is more
than 200,000 times as great as our distance from the sun,
so remote that from it the sun would look no brighter than
the Pole-star, and no telescope yet constructed would be
able to show a single one of all the planets. As to the
nature of the stars, their spectra indicate that they are
bodies resembling our sun, that is, incandescent, and
each shining with its own peculiar light. Some, are larger
and hotter than the sun, others smaller and cooler; some,
perhaps large, but hardly luminous at all. They differ
enormously among themselves, not being, as once thought,
as much alike as individuals of the same race, but differing
as widely as flies from elephants.
332. Number of Stars. Those which are visible to the
eye, though numerous, are by no means countless. If
we take a limited region, the bowl of the Dipper for
instance, we shall find that the number we can see within
it is not very large, hardly a dozen. In the whole
celestial sphere the number of stars bright enough to be
294
THE CONSTELLATIONS 295
distinctly seen by an average eye is only between 6000 and
7000, even in a perfectly clear and moonless sky; a little
haze or moonlight will cut down the number fully one-half.
At any one time not more than 2000 or 2500 are fairly
visible, since near the horizon the small stars (which are
vastly the more numerous) all disappear. The total number
which could be seen by the ancient astronomers well enough
to be observable with their instruments is not quite 1100.
With even the smallest telescope, however, the number
is enormously increased. A common opera-glass brings
out at least 100,000, and with a 2^-inch telescope Arge-
lander made his Durchmusterung of the stars north of the
equator, more than 300,000 in number. The Yerkes tele-
scope, 40 inches in diameter, probably makes visible at
least 100,000000.
333. Constellations. The stars are grouped in so-called
" constellations," many of which are extremely ancient.
All but one of those of the zodiac and most of those near
the north pole antedate history. Their names are, for the
most part, drawn from the Greek and Roman mythology,
many of them being connected in some way or other with
the Argonautic expedition. In some cases the eye, with
the help of a lively imagination, can trace in the arrange-
ment of the stars a vague resemblance to the object which
gives the name to the constellation, but generally no reason
is obvious for either name or boundaries.
We have already, in Chap. II, given a brief description
of those constellations which are visible in the United
States, with maps and directions for tracing them.
334, Designation of the Stars. In Sec. 24 we have
already indicated the different methods by which the
296 LESSONS IN ASTRONOMY
brighter stars are designated, by proper names, position
in the constellation, or by letters of the Greek and Roman
alphabets. But these methods do not apply to the tele-
scopic stars, at least to any considerable extent. Such
stars we identify by their catalogue number, that is, we
refer to them as number so-and-so in some star-catalogue.
Thus, LI., 21,185 is read "Lalande, 21,185," and means
the star so numbered in Lalande's catalogue. At present
more than 1,000000 stars are catalogued, so that, except
in the Milky Way, every star visible in a three-inch
telescope can be found and identified.
Of course all the bright stars which have names have
letters also and are sure to be found in every catalogue
which covers their part of the heavens. A conspicuous
star, therefore, has usually many " aliases," and sometimes
great care is necessary to avoid mistakes on this account.
335. Star-catalogues are carefully arranged lists of stars,
giving their positions (i.e., their right ascensions and decima-
tions, or latitudes and longitudes) for a given date, usually
also indicating their so-called magnitudes or brightness,
and often giving still other data. The earliest of these
star-catalogues was made about 125 B.C. by Hipparchus of
Bithynia, the first of the world's great astronomers, and
gives the latitudes and longitudes of 1080 stars. This
catalogue was republished by Ptolemy 250 years later, the
longitudes being corrected for precession; and during
the Middle Ages several other catalogues were made by
Arabic astronomers and those that followed them. The
last before the invention of the telescope was that of
Tycho Brahe, about 1580, containing 1005 stars. The
modern catalogues are numerous ; some, like Argelander's
STAR-CATALOGUES AND CHARTS 297
Durchmusterung, give the places of a great number of stars
rather roughly, merely as a means of ready identification.
Others are "catalogues of precision," like the Pulkowa
and Greenwich catalogues, which give the places of only
a few hundred so-called " fundamental " stars determined
as accurately as possible, each star by itself. Finally, we
have the so-called "zones," which give the place of many
thousands of stars determined accurately, but not independ-
ently ; that is, their positions are determined by reference
to the fundamental stars in the same region of the sky.
336. Mean and Apparent Places of the Stars. The modern
star-catalogue contains the mean right ascension and declination of
its stars at the beginning of some designated year, i.e., the place the
star would occupy if there were no nutation or aberration (Sec, 126,
and Appendix, 435). To get the actual (apparent) right ascension
and declination of a star for some given date, which is what we
always want in practice, the catalogue place must be " reduced " to
that date, i.e., it must be corrected for precession, etc. The opera-
tion is an easy one with modern formulae and tables, but tedious
when many stars are to be dealt with.
337. Star Charts and Stellar Photography. For some
purposes accurate star charts are even more useful than
catalogues. The old-fashioned and laborious way of mak-
ing such charts was by "plotting" the results of zone
observations, but at present it is being done, by means of
photography, vastly better and more rapidly. A coopera-
tive international campaign is now in progress, the object
of which is to secure a photographic chart of all the stars
down to the fourteenth magnitude. Eighteen different
observatories have participated in the work which is now
well advanced, although its completion will probably
require several years more.
298
LESSONS IN ASTRONOMY
One of the most remarkable things about the photo-
graphic method is that there appears to be no limit to the
faintness of the stars that can be photographed with a
good instrument. By increasing the time of exposure,
smaller and smaller stars
are continually reached.
With the ordinary plates
and exposure-times not
exceeding twenty min-
utes, it is now possible
to get distinct photo-
graphs of stars that the
eye cannot possibly see
with the same tele-
scope.
Fig. 81 represents the
photographic telescope
(fourteen inches diame-
ter and eleven f eet focus,
of the Paris Observa-
tory). The other instru-
ments engaged in the
star-chart campaign are
substantially like it in
FIG. 81. Photographic Telescope of the
Paris Observatory
diameter and length, though differing more or less in
mounting and in minor details.
Until very recently the most powerful instrument of this class was
the Bruce photographic telescope, which has a four-lens object-glass
of twenty-four inches diameter and eleven feet focus, taking plates
eighteen inches square. It belongs to the observatory of Harvard
College, but for some years has been at Arequipa, Peru. Within
PROPER MOTION 299
the last two or three years, however, other photographic telescopes
of equal or greater power have been mounted at Greenwich, the
Cape of Good Hope, Meudon, and Potsdam; the last has a photo-
graphic object-glass of 31 inches diameter.
STAR MOTIONS
338. The stars are ordinarily called " fixed," in distinc-
tion from the planets, or " wanderers," because they keep
their positions and configurations sensibly unchanged with
respect to each other for long periods of time. Delicate
observations, however, demonstrate that the fixity is not
absolute, but that the stars are really in motion. More-
over, by the spectroscope, their rate of motion towards or
from the earth can in some cases be approximately meas-
ured. In fact, it appears that the velocities of the stars
are of the same order as those of the planets: they are
flying through space far more swiftly than cannon-balls,
and it is only because of their enormous distance from us
that they appear to change their positions so slowly.
339. Proper Motion. If we compare a star's position
(right ascension and declination) as determined to-day with
that observed 100 years ago, it will always be found
to have changed considerably. The difference is due in
the main to precession (Sec. 125) ; but after allowing for
all such merely apparent motions of a star, it generally
turns out that during a century the star has really altered
its place more or less with reference to others near it, and
this shifting of its place is called its " proper motion." Of
two stars side by side in the same telescopic field of view
the proper motions may be directly opposite, while, of
course, the apparent motions will be sensibly the same.
300 LESSONS IN ASTRONOMY
Even the largest of these proper motions is very small.
For many years the so-called " runaway star," 1830 Groom-
bridge, headed the list with its annual drift of 7". But
in 1898 it was superseded by a little star designated as
"C. Z. (Cordova Zones), Hour V, No. 243," which has
a proper motion of 8". 7 yearly, and in 1916 a faint star
in Ophiuchus was found by Barnard to change its posi-
tion 10".4 a year. None of these stars is visible to the
naked eye.
About a dozen stars are known to have an annual proper
motion exceeding 3", and about 200, so far as known at
present, exceed V. The proper motions of the bright
stars average higher than those of the faint, as might be
expected, since, on the average, the bright ones are prob-
ably nearer. For the first-magnitude stars, the average
is about \" annually, and for the sixth-magnitude stars,
the smallest visible to the naked eye, it appears to be
about sV".
Motions of this kind were first detected in 1718 by Halley, who
found that since the time of Hipparchus the star Arcturus had
moved towards the south nearly a whole degree, and Sirius about
half as much.
340. Velocity of Star Motions. The proper motion of
a star gives us very little knowledge as to the star's real
motion in miles per second. The proper motion is derived
from the comparison of star-catalogues of different dates,
and is only the value in seconds of arc of that part of its
motion which is perpendicular to the line of sight. A star
moving straight towards us or from us has no proper
motion at all, i.e., no change of apparent place which can
be detected by comparing observations of its position.
VELOCITY OF STAR MOTION 301
We can, however, in some cases fix a minor limit to the
velocity of a star. We know, for instance, that the dis-
tance of the star, 1830 Groombridge, is certainly not less
than 1,400000 "astronomical units," and, therefore, since
its yearly path subtends an angle of 7" at the earth, the
length of the path must at least equal 48 astronomical
units a year, which corresponds to a velocity of over
140 miles a second. The real velocity must be more than
this, but how much greater we cannot determine until we
know how much the star's distance exceeds 1,400000 units,
and also how fast it is moving towards or from us.
In many cases a number of stars in the same region
of the sky have a motion practically identical, making it
almost certain that they are real neighbors and in some
way connected, probably by community of origin. In
fact, it seems to be the rule rather than the exception that
stars which are apparently near each other are real com-
rades ; they show, as Miss Clerke expresses it, a distinctly
" gregarious " tendency.
341. Radial Motion, or Motion in the Line of Sight.
Within the last fifty years a method l has been developed
by which any swift motion of a star, directly towards or
from us, may be detected by means of the spectroscope.
If a star is approaching us, the lines of its spectrum will
apparently be shifted towards the violet, according to
1 It is not, as students sometimes think, by changes in the apparent
size and brightness of a star. Theoretically, of course, a star which is
approaching us must grow brighter; but even the nearest star of all,
Alpha Centauri (Sec. 343), is so far away that if it were coming directly
towards us at the rate of 100 miles a second, it would require more than
8000 years to make the journey ; so that in a century its brightness would
only change about two per cent, far too little to be noticed.
302 LESSONS IN ASTRONOMY
Doppler's principle (Sec. 179), and vice versa if it is
receding from us. Visual observations of this sort, first
made by Huggins in 1868, and since then by many others,
succeeded in demonstrating the reality of these "radial
motions" (in the line of sight), and in roughly measur-
ing some of them. Later (in 1888), Vogel of Potsdam
took up the investigation photographically, and obtained
results that are far more satisfactory than any before
reached. He photographed the spectrum of the star and
the spectrum of hydrogen gas
Red (or some other substance whose
lines appear in the star spec-
Spectrum of Rigd trum) together upon the same
FIG. 82. -Displacement of Hy plate, the light from both being
Line in the Spectrum of Beta admitted through the same slit.
Orionis TJ, ., . , .
If the star is not approaching or
receding, its lines will coincide precisely with those of
the comparison spectrum ; otherwise they will deviate one
way or the other.
Fig. 82 is from one of his negatives of the spectrum of Beta
Orionis (Rigel), in which one of its dark lines is compared with the
corresponding bright lines in the spectrum of hydrogen. The dark
line of the stellar spectrum (bright in the negative) is shifted towards
the red by an amount which indicates that at the time the star was
rapidly receding.
Still more recently the work has been taken up at several observa-
tories in Europe and this country with instruments more powerful
than Vogel had at his command, and with great success, especially
by Keeler and Campbell at the Lick Observatory. Fig. 83 is enlarged
from a recent photograph made by Frost at the Yerkes Observatory,
showing part of the spectrum of Alpha Persei compared with that of
titanium ; the central strip is the spectrum of the star, and it will
THE SUN'S WAY 303
be seen that its dark lines are shifted towards the violet with respect
to the bright lines of the metal, indicating that the star and earth
were approaching each other at the rate of about 17 miles a second.
(Only a few of the lines in the star spectrum. are due to titanium,
and not all the lines of titanium are visible in the star.)
For the most part these radial motions of the stars, so
far as ascertained, range between zero and sixty miles
a second, with still higher speeds in a few exceptional
cases.
342. The " Sun's Way." The proper motions of the
stars are due partly to their own real motions, but partly
also to the motion of the sun, which, like the other stars,
12 3 4557
FIG. 83. Spectrum of Alpha Persei, compared with Titanium
Frost, Aug. 8, 1002
is traveling through space, taking with it its planets. Sir
William Herschel was the first to investigate and determine
the direction of this motion, a century ago. The principle
involved is this: on the whole, the stars must appear to
drift bodily in a direction opposite to the real motion of
the solar system.
Those in that quarter of the sky which we are approach-
ing open out from each other, and those in the rear close
up behind us. The motions of individual stars may lie in
all possible directions; but when we deal with them by
thousands the individual is lost in the general, and the
prevailing drift becomes obvious.
304 LESSONS IN ASTRONOMY
A number of different determinations of the point
towards which the sun's motion is directed have been
made by various astronomers. There is a reasonable and
almost surprising accordance of results, and they all show
that the sun is moving towards a point in the constella-
tion of Hercules, having a right ascension of about 267
(17 h 48 m ), and a declination of about 32 north. This
point is called the " apex of the sun's way." l As to the
velocity of this motion of the sun, it comes out as about
0".05 annually, seen from the average distance of a stand-
ard sixth-magnitude star. This would make the sun's
velocity about sixteen miles a second.
It can, however, be more accurately deduced from the
spectroscopic observations of radial motion. In the part
of the heavens toward which the sun is moving the stars
on the average seem to approach, and in the opposite
region to recede, and the difference of the two averages is
twice the sun's own motion, which comes out about eleven
miles a second, a result independent of all uncertainty
as to the distances of the stars.
THE PARALLAX AND DISTANCE OF STARS
343. When we speak of the " parallax " of the sun, of
the moon, or of a planet, we always mean the " diurnal "
or "geocentric" parallax (Sec. 139); i.e., the apparent
semi-diameter of the earth as seen from the body. In the
case of a star this kind of parallax is practically nothing,
1 If there are any predominant drifts among the stars whose motions
form the basis of this calculation, as recent investigations of Kapteyn
and others would indicate, this computed position would be affected.
ANNUAL OR HELIOCENTRIC PARALLAX 305
never reaching ^^^ of a second of arc. The expression
"parallax of a star" always refers, on the contrary, to
its " annual " or " heliocentric " parallax which is the appar-
ent semi-diameter of the earth's orbit, as seen from the
star. In Fig. 84 the angle at the star is its parallax.
Even this heliocentric parallax, in the case of most
stars, is far too small to be detected by our present
instruments, since it never reaches a single second of arc.
But in a few instances it has been actually measured by
operations the most refined and difficult in the whole range
of astronomical observation. Alpha Centauri, which is our
nearest neighbor so far as yet known, has a parallax of
E
FIG. 84. The Annual Parallax of a Star
about 0".9 according to the earlier observers, or only 0".75
according to the latest authorities. There are but four or
five other stars at present known which have a parallax
more than half as great as this, and perhaps fifty more
for which a sensible, but much smaller parallax has been
detected. (For the method of determining stellar parallax,
see Appendix, Sees. 441-443.)
344. Unit of Stellar Distance; the Light-Year. The
distances of the stars are so enormous that even the radius
of the earth's orbit, the "astronomical unit" hitherto
employed, is far too small for convenience. We may take
as the unit of stellar distance the parsec, the distance of
a star which has a parallax of 1", or we may use the
306 LESSONS IN ASTRONOMY
so-called light-year, the distance light travels in a year. This
is about 63,000 times the earth's distance from the sun.
This number is found by dividing the number of seconds in a year
by 499, the number of seconds required by light to make the journey
from the sun to the earth (Appendix, Sec. 432).
A star with a parallax of 1" is at a distance of 3.26
light-years, and in general the distance in light-years
3 26
equals ', where p rr is the parallax of the star expressed
in seconds.
So far as can be judged from the scanty data, it appears
that few, if any, stars are nearer than four light-years from
the solar system; that the naked-eye stars are probably,
for the most part, within 200 or 300 light-years ; and that
many of the remoter stars must be thousands, or even
tens of thousands, of light-years away.
For the parallaxes of a number of stars, see Table V,
Appendix.
THE LIGHT OF THE STARS
345, Star Magnitudes. As has already been mentioned
(Sec. 23), Hipparchus and Ptolemy arbitrarily divided the
stars into six " magnitudes " according to their brightness,
the stars of the sixth magnitude being those which are
barely perceptible by an ordinary eye, while the first class
comprise about twenty of the brightest. After the inven-
tion of the telescope the same system was extended to the
fainter stars, though without any special plan, so that
the magnitudes assigned to telescopic stars by different
observers are very discordant.
THE LIGHT-RATIO OF MAGNITUDES 307
Heis enumerates the stars clearly visible to the naked eye north
of the 35th parallel of south declination, as follows :
First magnitude, 14 Fourth magnitude, 313
Second " 48 Fifth " 854
Third 152 Sixth 2010
Total, 3391
It will be noticed how rapidly the numbers increase for the smaller
magnitudes. Nearly the same holds good also for the telescopic stars,
though below the tenth magnitude the rate of increase falls off.
346. Light-Ratio and Absolute Scale " of Star Mag-
nitudes. The scale of magnitudes ought to be such
that the " light-ratio," or number of times by which the
brightness of any star exceeds that of a star which is
one magnitude smaller, should be the same throughout
the whole extent of the scale. This relation was roughly,
but not accurately, observed by the older astronomers.. In
recent years photometric measurements have been made of
the brightness of all the naked-eye stars visible in our
latitude, and magnitudes have been published which are
based upon the so-called " absolute scale " first proposed
by Pogson about 1850, which uses a light-ratio equal to
the fifth root of 100 (2.51 +) ; i.e., upon this scale a star
of the third magnitude is 2.51 times brighter than one of
the fourth, one of the fourth 2.51 times as bright as one
of the fifth, and so on.
The scale is being extended rapidly to the fainter stars.
The ratio is based upon an old determination of Sir John Her-
schel, who found that the average first-magnitude star is just about
a hundred times as bright as a star of the sixth magnitude, five
magnitudes fainter, so that an increase of Jive in the " magnitude "
corresponds to a hundredfold decrease of brightness.
308 LESSONS IN ASTRONOMY
On this scale Altair (Alpha Aquilse) and Aldelaran
(Alpha Tauri) may be taken as standard first-magnitude
stars, while the Pole-star and the two Pointers are very
nearly of the standard second magnitude.
Of course, in indicating the brightness of stars with precision,
fractional numbers must be used, that is, we have stars of 2.4
magnitude, etc.
Stars that are brighter than Aldebaran or Altair have their bright-
ness denoted by a fraction, or even by a negative number ; thus the
absolute magnitude^f Vega is 0.2, and of Sirius 1.4. The neces-
sity of these negative and fractional magnitudes for bright stars is
rather unfortunate, but not really of much importance, as there are
too few of them to cause any practical inconvenience.
347. Magnitudes and Telescopic Power. If a good telescope
just shows a star of a certain magnitude, we must have a telescope
with its aperture larger in the ratio of 1.58 : 1, in order to show stars
one magnitude smaller (1.58 = V2.51). A tenfold increase in the
diameter of an object-glass theoretically carries the power of vision
just five magnitudes lower.
It is usually estimated that the twelfth magnitude is the limit of
vision for a four-inch glass. It would require, therefore, a forty-inch
glass to reach the seventeenth magnitude of the absolute scale.
Our space does not permit any extended discussion of the photo-
metric methods by which the brightness of stars is measured, a
subject which has of late attracted much attention. (See General
Astronomy, Arts. 823-829.)
348. Starlight compared with Sunlight. Zollner and
others have endeavored to determine the amount of light 2
1 The sun on this scale is about 26.3 magnitude.
2 The stars send us heat also, but probably the ratio of stellar heat to
solar does not differ much from that of starlight to sunlight. If so, the
heat from a star is beyond the reach of any ordinary instrument. Very
recently, however, Professor E. F. Nichols, at the Yerkes Observatory,
with a new "radiometer," has obtained distinct and measurable heat
effects from Arcturus and Vega.
STARLIGHT COMPARED WITH SUNLIGHT 309
received by us from certain stars, as compared with the
light of the sun. According to him, Sirius gives us about
YinnnfirffTnnr as mucn light as the sun does, and Capella
and Vega about -%-Q-Q-Q-Q ^-Q-O o o"o- At this rate, the standard
first-magnitude star, like Altair, should give us about
<JF<ro W^^> an( * it wou ld take, therefore, about nine mil-
lion million stars of the sixth magnitude to equal the sun.
These numbers, however, are very uncertain. The various
determinations for Vega vary more than fifty per cent.
Assuming what is only roughly true, that Argelander's magnitudes
agree with the absolute scale, it appears that the 324,000 stars of his
Durchmusterung, all of them north of the celestial equator, give
a light about equivalent to 240 or 250 first-magnitude stars. How
much light is given by stars smaller than the 9 magnitude (which was
his limit) is not certain. It must greatly exceed that given by the
larger stars. As a rough guess, we may estimate that the total star-
light of both the northern and southern hemispheres is equivalent to
about 3000 stars like Vega, or 1500 at any one time. According to
this, the starlight on a clear night is about ^ of the light of a full
moon, or about -SJ-Q-Q^-QTJV that of sunlight. Professor NeM^comb's
recent estimate of the total starlight is, however, only about one-
fourth as large ; the data do not warrant any exact conclusion.
More than ninety per cent of the light comes from stars not visible
by the naked eye.
349. Amount of Light emitted by Certain Stars. When
we know the distance of a star in astronomical units it is
easy to compute the amount of light it really emits as com-
pared with that given off by the sun. It is only necessary to
multiply the light we now get from it (expressed as a fraction
of sunlight) by the square of the star's distance in astro-
nomical units. Thus, the distance of Sirius is about 550,000
units, and the light we receive from it is
310 LESSONS IK ASTRONOMY
of sunlight. Multiplying this fraction by the square of
550,000, we find that Sirius is really radiating more than
forty times as much light as the sun. As for several other
stars whose distance and light have been measured, some
turn out brighter, and some darker, than the sun. The
range of variation is very wide, and in brilliance the sun
holds apparently about a medium rank among its kindred.
350. Why the Stars differ in Brightness. The appar-
ent brightness of a star, as seen from the earth, depends
both on its distance and on the quantity of light it emits,
and the latter depends on the extent of its luminous sur-
face and upon the brightness of that surface. As Bessel
long ago suggested, " there may be as many dark stars as
bright ones."
Taken as a class, the bright stars undoubtedly average
nearer to us than the fainter ones ; and just as undoubtedly
they also average larger in diameter and more intensely
luminous ; but when we compare any particular bright
star with another fainter one we can seldom say to which
of these different causes it owes its superiority. We can-
not assert that the faint star is smaller, or darker, or
more distant than that particular bright star, unless we
know something more about it than the simple fact that
it is fainter.
351. Dimensions of the Stars. The stars are so far
away that their apparent diameters are altogether too small
to be measured by any known form of micrometer. The
sun at the distance of the nearest star would measure l not
quite 0".01 across. Micrometers, therefore, do not help
1 This does not refer, of course, to the "spurious disk" of the star
(Appendix, Sec. 408), which is many times larger.
VARIABLE STARS 311
us in the matter, and until very recently we were abso-
lutely without any positive knowledge as to the real size
of a single one of the stars. But in 1889, by a spectro-
scopic method more fully explained in Sec. 360, Vogel
succeeded in showing that the bright variable star, Algol
(Beta Persei) (Sec. 358), must have a diameter of about
1,160000 miles, while its invisible companion is about
840,000 miles in diameter, or just about the size of the sun.
VARIABLE STARS
352. Classes of Variables. Many stars are found to
change their brightness more or less and are known as
"variable." They may be classed as follows:
I. Stars which change their brightness slowly and con-
tinuously.
II. Those that fluctuate irregularly.
III. Temporary stars which blaze out suddenly and then
disappear.
IV. Periodic stars of the type of " Omicron Ceti," usually
having a period more or less irregular, and usually of several
months.
V. Periodic stars having short periods, with a continu-
ous change of light.
VI. Periodic stars of the "Algol" type, in which the
period is usually short, and the variation is like what might
be produced if the star were periodically "eclipsed" by
some intervening object.
353. Gradual Changes. The number of stars which are
certainly known to be gradually changing in brightness is
surprisingly small. On the whole, the stars present, not
312 LESSONS IN ASTRONOMY
only in position, but in brightness also, sensibly the same
relations as in the catalogues of Hipparchus and Ptolemy.
There are, however, a few instances in which it can hardly be
doubted that considerable alteration has occurred, even within the
last two or three centuries. Thus, in 1610, Bayer lettered Castor as
Alpha Geminorum, while Pollux, which he called Beta Geminorum,
is now distinctly brighter. There are about a dozen other similar
cases known and a much larger number is suspected.
It is commonly believed that a considerable number of stars have
disappeared since the first catalogues were made, and that many new
ones have come into existence. While it is unsafe to deny absolutely
that such things may have happened, it can be said, on the other
hand, that not a single case of the kind is certainly known. The dis-
crepancies between the older and newer catalogues are nearly all
accounted for by some error that has already been discovered.
354. Irregular Fluctuations. The most conspicuous star
of the second class is Eta Argus (not visible in the United
States). It varies all the way from above the first magni-
tude (in 1843 it stood next to Sirius) down to the seventh
magnitude (invisible to the eye). This has been its status
ever since 1865, though some years ago it was reported as
slightly brightening. Alpha Orionis, Alpha Herculis, and
Alpha Cassiopeise behave in a similar way, except that their
variation is small, never reaching an entire magnitude.
355. Temporary Stars. There are several well-authenti-
cated instances (and a number of others more or less doubt-
ful) of stars which have blazed up 'suddenly, and then
gradually faded away. (See General Astronomy, Arts. 842-
845.) The most remarkable of these is that known as
Tycho's star, which appeared in the constellation of Cassi-
opeia (Sec. 28) in November, 1572, was for some days as
bright as Venus at her best, and then gradually faded away,
TEMPORARY STARS 313
until at the end of sixteen months it became invisible.
(There were 110 telescopes then.) It is not certain whether
it still exists as a telescopic star ; so far as we can judge,
it may be any one of half a dozen which are near the place
determined by Tycho.
It is a notable and probably significant fact, though as yet unex-
plained, that all these objects have appeared in or within a few
degrees of the Milky Way.
A temporary star, which appeared in the constellation
Corona Borealis, in May, 1866, is interesting as having
been the first spectroscopically examined. When near its
brightest (second magnitude) it showed the same bright
lines of hydrogen which are conspicuous in the solar promi-
nences. Before its outburst it was an eighth-magnitude
star of Argelander's catalogue, and within a few months
it returned to its former low estate, which it still retains.
Another instance is that of a sixth-magnitude star, which
in August, 1885, suddenly appeared in the midst of the great
nebula of Andromeda (Sec. 377). It showed no bright lines
in its spectrum and in a few months it totally disappeared,
even to the largest telescopes.
In 1892 a star of magnitude 4J appeared in the con-
stellation of Auriga. It showed what is now known to be
the characteristic spectrum of a temporary star, a combina-
tion of bright and dark lines of hydrogen and helium, the
dark lines always on the side toward the violet. It is thought
possible that this peculiar spectrum may be due to the
effect of intense explosive pressures in the luminous gases.
In April the star became invisible, but brightened up
again in the autumn, and then showed an entirely different
spectrum closely resembling that of a nebula (Sec. 380).
314 LESSONS IN ASTRONOMY
Later, in 1902, Campbell reported that its spectrum had
become continuous, the object having apparently become
a star again.
355*. Nova Persei. A recent and also one of the
most remarkable of temporary stars is that first seen on
Feb. 21, 1901, when it was already as bright as the Pole-
star. Photographs of the region made at Cambridge on
the 19th and previous dates prove that on the 19th it
must still have been fainter than the twelfth magnitude.
On the 24th it was for several hours the brightest star
then visible, Sirius alone excepted, having increased its
brilliance more than twenty-five thousand fold within five
days. It faded rapidly, with curious oscillations of light,
and before the end of the year had dropped below the
range of the eye. It is now visible only in large tele-
scopes. Its spectrum, when first photographed on Feb-
ruary 22, was simply dark lined, resembling that of the
Orion stars ; but by the 24th it was transfigured and had
become bright lined like that of Nova Aurigse. It then
gradually changed into the nebular type, but with the
peculiarity that its lines were extremely broad and hazy,
and still preserve this character, though very faint. Sev-
eral different observers have found that its proper motion
and parallax are insensible, its distance from us almost
certainly exceeding a hundred light-years.
Before the star became invisible to the eye an extensive
nebulosity had developed around it, and in November pho-
tographs made with the three-foot reflector of the Lick
Observatory, and confirmed by others from the Yerkes,
showed that certain knots and streaks of the nebula were
apparently moving swiftly away from the central star, -
LIGHT CURVES OF VARIABLES
315
at a rate of several thousand miles a second (!) unless the
star is much nearer than the parallax observations permit
us to assume. At present the explanation, first suggested
by Kapteyn, is generally, though not universally, accepted,
that the motion is purely apparent, and due to a
FIG. 85. Light Curves of Variable Stars
progressive illumination of denser portions of the nebula
as the light from the great explosion travels outward
186,000 miles a second. This would make the distance
of the star about three hundred light-years, which is not
at all improbable.
A brilliant "Nova" appeared in Aquila June 8, 1918. It was
nearly as bright as Vega when discovered, the next night rivaled
Sirius, then gradually faded.
356. Variables of the " Omicron Ceti" Type. These,
objects behave almost exactly like a temporary star in
remaining most of the time faint, rather suddenly increasing
816 LESSONS IN ASTRONOMY
in brightness, and then gradually fading away; but they
do it periodically. Omicron Ceti, or Mira (i.e., "the
wonderful") is the type. It was discovered in 1596 and
was the first variable star known. During most of the
time it is of the ninth magnitude; but at intervals of
about eleven months it runs up to the fourth, third, or even
second magnitude, and then back again, the whole change
occupying about three hundred days, and the rise being
much more rapid than the fall. It remains at its maxi-
mum about a week or ten days. The maximum bright-
ness varies very considerably ; and its period, while always
about eleven months, varies to the extent of two or three
weeks. The spectrum of the star when brightest is very
beautiful, showing a large number of intensely bright lines,
some of which are due to hydrogen and helium. Its light
curve is A in Fig. 85. 1
There are several hundred variables of this class, and
many of them have periods which do not differ very
widely from a year. Most of the periods, however, are
more or less irregular.
357. Class V. The variables of this class change their
light regularly and continuously, with an average range
of about one magnitude. The periods are short, from
several hours to a few weeks. Sometimes the light curve
is like that of Eta Aquilse, shown in B of Fig. 85, the
increase in brightness being much more rapid than the
decrease; sometimes, as in the case of Zeta Geminorum,
the ascending and descending branches of the curve are
alike.
1 The light-curve diagrams are not drawn to scale, and make no pre-
tensions to exact accuracy ; details differ for each star.
EXPLANATION OF VARIABLES 317
358. The " Algol' Type. In the stars of Class VI the
variation is precisely the reverse of that in Class IV. The
star remains bright for most of the time, but apparently
suffers a periodical eclipse. The periods are mostly very
short, ranging from ten hours to ten days.
Algol (Beta Persei) is the type star. During most of
the time it is of the second magnitude, and it loses about
five-sixths of its light at the time of obscuration. The fall
of brightness occupies about 4j hours. The minimum
lasts about 20 minutes, and the recovery of light takes
about 3^ hours. The period, a little less than three days, is
known with great precision, to a single second indeed,
and is given in connection with the light curve of the star
in Fig. 85. At present the period seems to be slowly
shortening. Above ninety variables of this class are now
known, and new ones are continually found.
359. Explanation of Variable Stars. No single explana-
tion will cover the whole ground. As to progressive changes,
no explanation need be looked for. The wonder rather is
that as the stars grow old such changes are not more rapid
and notable than they are. With few exceptions there has
been no obvious alteration since the days of Ptolemy.
As for irregular changes, no sure account can yet be
given. Where the range of variation is small (as it is in
most cases) one thinks of spots upon the surface of the
star, more or less like sun-spots ; and if we suppose these
spots to be much more extensive and numerous than are
the sun-spots, and also like them to have a regular period
of frequency, and also that the star revolves upon its axis,
we find in the combination a possible explanation of a
large proportion of all the variable stars.
318 LESSONS IN ASTRONOMY
For the temporary stars we may imagine either great
eruptions of glowing matter, like solar prominences on an
enormous scale, or, with Sir Norman Lockyer, we may
imagine that they, and most of the variable stars, are only
swarms of meteors, rather compact, but not yet having
reached the condensed condition of our own sun. Out-
bursts of brightness are, according to him, the result of
collisions between such swarms. Stars of the Mira type,
according to this theory, consist of two such swarms, the
smaller revolving around the larger in a long oval, so that
once in every revolution it brushes through the outer por-
tions of the larger one. But the great irregularity in the
periods of variables belonging to this class is hard to
reconcile with a true orbital revolution, which usually
keeps time accurately.
In the case of the short-period, " punctual variables," as
Miss Clerke calls them, of Class V, the spectroscopic phe-
nomena in many instances seem to indicate the mutual
interaction of two or more bodies revolving around their
common center of gravity ; this is certainly the case with
Beta Lyrae. Others admit of simpler explanation, as due
to the rotation of a body of irregular form or having large
spots on its surface.
360. Explanation of the Algol Type. The natural and
most probable explanation of the behavior of these stars is
that the periodical darkening is produced by the interposi-
tion of some opaque body between us and the star.
This eclipse theory, first proposed by Goodricke a hun-
dred years ago, received a striking confirmation from the
spectroscopic work of Vogel, who, in 1889, found by the
method indicated in Sec. 341 that about seventeen hours
EXPLANATION OF ALGOL 319
before the obscuration Algol is receding from us at the
rate of nearly twenty-seven miles a second, while seven-
teen hours after the minimum it approaches us at the same
rate. This, is just what it ought to do if it had a large
dark companion, and the two were revolving around their
common center of gravity in an orbit nearly edgewise to
the earth. When the dark star is rushing forward to
interpose itself between us and Algol, Algol itself must be
moving backwards, and vice versa when the dark star is
receding after the eclipse. Recently it has been proved that
the companion is not totally dark, but that there is a very
slight reduction of light halfway between minima, when the
darker star is eclipsed by the brighter one. The combined
mass of the two is about two-thirds that of the sun, and
their density is not much greater than that of cork. Russell,
and, simultaneously, Roberts of South Africa, have shown
that the phenomena of variables of this class determine a
maximum limit to the mean density of the pair ; and they
find in all cases this highest possible density to be far below
that of the sun. These stars seem to be hardly denser than
clouds.
361. Number and Designation of Variables and their
Range of Variation. Mr. Chandler's catalogue of known
variables, with its later supplements, includes 393 objects,
besides a considerable number of suspected variables.
About 275 of the 393 are distinctly periodic. The rest
of them are, some irregular, some temporary, and in respect
to many we have not yet certain knowledge whether the
variation is or is not periodic.
Table IV, Appendix, contains a list of the principal
naked-eye variables visible in the United States.
320 LESSONS IN ASTRONOMY
Such variable stars as had not names of their own before their
variability was discovered are at present generally indicated by the
letters R, S, T, etc. ; i.e., R Sagittarii is the first discovered variable
in the constellation of Sagittarius ; S Sagittarii is the second, etc.
In a considerable number of the earlier discovered vari-
ables the range of brightness is from two to eight magni-
tudes, that is, the maximum brightness exceeds the minimum
from 6 to 1000 times. In the majority, however, the range
is much less, only a fraction of a magnitude.
It is worth noting that a large proportion of the vari-
ables, especially those of Classes IV and V, are reddish in
their color. This is not true of the Algol type.
Since the publication of Chandler's last catalogue in 1896 there
has been a rapid increase in the number of known variables, largely
as the result of the examination of photographs made at Arequipa
on different dates. The total number known at the present time
probably exceeds 4000, and is continually growing. 1
The most remarkable discovery in this line, however, is that of
multitudes of variables in certain star clusters. The clusters known
as Messier 3, Messier 5, and Omega Centauri are especially notable ;
in the first, 132 variables have been detected, in the second, 85, and
in the last, 128. The changes are so rapid as to be obvious on
photographs taken only two hours apart.
STAR SPECTRA
362. As early as 1824 Fraunhofer observed the spectra
of a number of bright stars by looking at them with a
small telescope with a prism in front of the object-glass.
In 1864, as soon as the spectroscope had taken its place as
a recognized instrument of research, it was applied to the
stars by Huggins and Secchi. The former studied very
few spectra, but very thoroughly, with reference to the
1 See note on page 326.
CLASSES OF STELLAR SPECTRA
321
identification of the chemical elements in certain stars.
He found with certainty in their spectra the lines of sodium,
magnesium, calcium, iron, and hydrogen, and more or less
doubtfully a number of other metals. Secchi, on the
other hand, examined a great number of spectra, less in
detail, but with reference to a classification of the stars
from the spectroscopic point of view.
383. Secchi's Classes of Spectra. He made four classes,
as follows:
I. Those which have a spectrum characterized by great
intensity of
the dark lines
of hydrogen,
all other lines
being compara-
tively feeble or
absent. This
class comprises
more than half
of all the stars,
nearly all
the stars which
are white or
of a bluish tinge. Sirius and Vega are its types.
II. Those which show a spectrum resembling that of the
sun ; i.e., marked with a great number of fine dark lines.
Capella (Alpha Aurigse) and Pollux (Beta Geminorum)
are conspicuous examples. The stars of this class are
also numerous. The first and second classes together
comprise fully seven-eighths of all the stars whose spectra
are known.
FIG. 86. Secchi's Types of Stellar Spectra
Keeler
322 LESSONS IN ASTRONOMY
Certain stars, like Procyon and Altair, seem to be intermediate
between the first and second classes, and help us to trace the
probable order of evolution.
III. Stars which show a spectrum characterized by dark
bands, sharply defined at the upper or more refrangible edge
and shading out towards the red. Most of the red stars
and a large number of the variable stars belong to this
class. Some of them show also bright lines in their spectra.
IV. This class comprises only a few small stars, which,
like the preceding, show dark bands, but shading in the
opposite direction. Usually they also show a few bright
lines. There are not a few anomalous stars that will not
fall into any of these classes.
This classification is the basis of the Harvard system now very
generally used for detailed study. Different types are indicated by
letters, arranged so as to show a possible order of evolution based
upon increasing complexity of spectrum. Secchi's Type I is sub-
divided into Harvard Types B and A, II into F, G, K, while III
corresponds to M, IV to N.
364. Photography of Stellar Spectra. The observation
of these spectra by the eye is very tedious and difficult, and
photography comes in most effectively. Huggins in Eng-
land and Henry Draper in this country were the pioneers,
and fine results in this line have been obtained by E. C.
Pickering, of Cambridge, in connection with the Draper
Memorial Fund. Most observers use the prismatic spectro-
scope with a slit, photographing the spectra of stars one by
one, and having for comparison the spectra of known metals
upon the same plate. Pickering has recurred to the old
method of Fraunhofer, using a prism or prisms in front of
the object-glass of his photographic telescope, thus forming a
PHOTOGRAPHY OF STAR SPECTRA 323
44 slitless spectroscope." The edges of the prism or prisms
are placed east and west. If the clockwork of the instru-
ment followed the star exactly, the spectrum formed on
the sensitive plate would be a mere narrow streak ; but by
allowing the clock to gain or lose slightly, the image of the
star will move to the east or west by a very small quantity
during the exposure, converting the streak into a band.
The slitless spectroscope has three great advantages : (1) it saves
all the light which comes from the star, much of which, in the usual
JSirius
Procyon
Capella
FIG. 87. Star Spectra
Pickering
form of the instrument, is lost in the jaws of the slit ; (2) by taking
advantage of the length of a large telescope, it produces a long spec-
trum with even a single prism ; (3) and most important of all,
it gives on the same plate and with a single exposure the spectra of all
the many stars (sometimes more than a hundred) whose images fall upon
the plate.
On the other hand, the giving up of the slit precludes the usual
methods of identifying the lines and measuring their displacements
by actually confronting them with comparison spectra. For instance,
it has not yet been found possible to use the slitless spectroscope for
determining the radical velocities of stars, i.e., their absolute rates
of approach or recession (Sec. 341).
324 LESSONS IN ASTRONOMY
364*. With the eleven-inch telescope formerly belong-
ing to Dr. Draper, and a battery of four enormous prisms
placed in front of the object-glass, spectra are obtained
with an exposure of thirty minutes, which, before enlarge-
ment, are fully three inches long from the F line to the
ultra-violet extremity. They easily bear tenfold enlarge-
ment and show many hundreds of lines in the spectra of
the stars which belong to Secchi's second class. Fig. 87
shows the blue and violet portion of the spectra of Sirius,
Procyon, and Capella as thus photographed, and brings
out clearly the gradual transition between stars of the first
and second classes. The photographs fail to show the
lower portion of the spectrum, i.e., the red, yellow, and
green ; but within a few years the use of isochromatic
plates has made it possible to deal with these colors also.
The spectra of all the naked-eye stars in both of the
hemispheres have already been photographed and cata-
logued, and the classification of about 214,000 stars, which
will probably extend the work so as to include all down to
the ninth magnitude, will be given in the New Draper
Catalogue, prepared by Miss Cannon of the Harvard
College Observatory.
Photography of stellar spectra is now a part of the
regular program of nearly all large observatories, and its
importance is shown by the fact that from the spectrum
of a star we may tell with some certainty the speed with
which the star is moving toward or away from the earth,
the stage of physical development it has reached, and even,
in some cases, its order of distance from us.
365. Twinkling, or Scintillation, of the Stars. This phenomenon
is purely physical, and not in the least astronomical. It depends
SCINTILLATION OF THE STARS 325
both upon the irregularities of refraction in the air traversed by the
light on its way to the eye (due to winds and differences of tempera-
ture), and also on the fact that a star is optically a luminous point
without apparent size, a fact which, under the circumstances, gives
rise to the optical phenomenon known as interference. Planets which
have disks measurable with a micrometer do not sensibly twinkle.
The scintillation is of course greatest near the horizon, and on
a good night it practically disappears at the zenith. When the
image of a twinkling star is examined with the spectroscope, dark
interference bands are seen moving back and forth in its spectrum.
NOTE TO ARTICLE 361
Since 1902 several limited areas in the heavens have been discov-
ered abnormally rich in variable stars, tracts only a few degrees
square, in which variables are found by scores upon the photographic
negatives. The most notable are one discovered by Wolf in the con-
stellation of Aquila, and those discovered by the Harvard observers
around the great nebula of Orion, in Scorpio and Sagittarius, and in
the two " Magellanic clouds " near the south pole. Obviously they
indicate regions of space where conditions differ from those that
generally prevail, a peculiar stage of cosmic evolution.
Professor Pickering in his observatory report, dated Sept. 30, 1905,
states that since the Harvard photographic work began in 1886,
2750 variables have been discovered, about 555 elsewhere and
2197 at Cambridge. Mrs. Fleming has discovered 8 "novae" and
197 variables, mainly by bright hydrogen lines in their spectra;
Professor Bailey has detected 509 in globular star-clusters ; and
Miss Leavitt 1442, mostly in and near the Magellanic clouds. And
since that time the list has been considerably lengthened.
Of course nearly all of these new variables are extremely faint, ob-
servable only by great telescopes or by photography ; and for the great
majority nothing is yet known as to the period and type of variation.
The total number of variables which can be reached by our pres-
ent instruments must be hundreds of thousands, and not improbably
millions. Among the 6000 naked-eye stars about 70 variables are
already known, and there is no reason to suppose that the proportion
is different for the telescopic stars.
CHAPTER XII
THE STARS (Continued)
Double and Multiple Stars and Clusters Nebulae Distribution of Stars
and Constitution of the Stellar Universe Cosmogony and the Nebular
Hypothesis
366. Double Stars. The telescope shows numerous
cases in which two .stars lie so near each other that they
can be separated only by a high magnifying power. These
are double stars and at present at least 16,000 such
couples are known. There is also a considerable number
of triple stars and a few which are quadruple. Fig. 88
represents a few of the best known objects of each class.
The apparent distances generally range from 30" down-
wards, very few telescopes being able to separate stars
closer than a quarter of a second.
In a large proportion of cases (perhaps a third of all),
the two components are nearly equal in brightness ; but
in many they are very unequal : in that case (never when
they are equal), they often present contrasts of color, and
when they do the smaller star (for some reason not known)
always, or with very few and doubtful exceptions, has a
tint higher in the spectrum than that of the larger, if the
larger is reddish or yellow, the small star will be green,
blue, or purple.
Gamma Andromedae and Beta Cygni are fine examples of colored
doubles for a small telescope.
OPTICAL AND PHYSICAL DOUBLES 327
367. Stars optically and physically Double. Stars may
be double in two ways, optically or physically. In the
first case they are only approximately in line with each
other as seen from the earth ; in the second case, they are
really near each other. In the case of stars that are only
optically double it usually happens that after some years
FIG. 88. Double and Multiple Stars
we can detect their mutual independence by the fact that
their relative motion is in a straight line and uniform, i.e.,
one of them drifts by the other in a line which is perfectly
straight. TJiis is a simple consequence of the combina-
tion of their independent " proper motions." If they are
physically connected, we find, on the contrary, that the rel-
ative motion is hi a concave curve; i.e., taking either of
328 LESSONS IN ASTRONOMY
them as a center, the other one appears to move around
it in a curve.
The doctrine of chances shows, what direct observation
confirms, that optical pairs must be comparatively rare
and that the great majority of double stars must be really
physically connected, probably by the same attraction of
gravitation which controls the solar system.
368, Binary Stars. Stars thus physically connected
are also known as " binary " stars. They revolve in ellip-
tical orbits around their common center of gravity in
periods which range from 14 years to 1500 (so far as at
present known), while the apparent length of the ovals
ranges from 0".4 to 40". The elder Herschel, a little
more than a century ago, first discovered this orbital
motion of " binaries " in trying to ascertain the parallax
of some of the few double stars which were known at
his time. It was then supposed that they were simply
optical pairs, and he expected to detect an annual dis-
placement of one member of the pair with reference to
the other, from which he could infer its annual parallax
(Sec. 343). He failed in this, but found instead a true
orbital motion.
The apparent orbit is always an ellipse ; but this appar-
ent orbit is the true orbit seen more or less obliquely, so
that the larger star is not usually in the focus of the
relative orbit pursued by the smaller one. II we assume
what is probable (though certainly not proved as yet), that
the orbital motion of the pair is under the law of gravita-
tion, we know that the larger star must be in the focus
of the true relative orbit of the smaller, and, moreover,
that the latter must describe around it equal areas in equal
ORBITS OF BINARY STARS
329
times. By the help of these principles we can, if we have
observations sufficiently numerous and accurate, deduce
from the apparent oval the true orbital ellipse; but the
calculation is troublesome and delicate.
369. At present the number of pairs in which this kind of
motion has been certainly detected exceeds 200, and it is con-
tinually increasing as our study of the double stars goes on. About
fifty pairs have progressed so far, either having completed an entire
revolution or a large part of one, that it is possible to determine
their orbits with some accuracy.
The case of Sirius is peculiar. As long ago as 1844 it had been
found from meridian-circle observations to be moving, for no then
assignable reason, in a
small orbit with a period
of about fifty years. In
1862 Alvan G. Clark, a
member of the famous
Cambridgeport firm of
telescope makers, found
near it a minute compan-
ion, which explains every-
thing ; only we have to
admit that this faint
attendant, which does not
give a ten-thousandth as much light as Sirius itself, has a mass
nearly two-fifths as great. It seems to be one of Bessel's dark stars.
Fig. 89 represents the apparent orbits of two of the best determined
double-star systems, Gamma Virginis and Xi Ursse Majoris.
370. Size and Form of the Orbits. The dimensions of
a double-star orbit can easily be obtained if we know its
distance from us. Fortunately, a number of stars whose
parallaxes have been ascertained are also binary, and
assuming the best available data, we have the results given
in the little table which follows, the real semi-major
1
186^- \
61 Years V 856
2/1821
1718
7 Virginis
90
I o
Ursce Majoris
FIG. 89. Orbits of Binary Stars
330
LESSONS IN ASTRONOMY
axis of the orbit (in astronomical units) being always equal
a"
to the fraction in which a" is the angular semi-major
axis of the real (not apparent) orbit in seconds of arc, and
p n the parallax of the star. But it must not be forgotten
that there is still considerable uncertainty in the data,
especially in the parallaxes.
NAME
ASSUMED
PARALLAX
ANGULAR
SEMI-AXIS
REAL,
SEMI-AXIS
PERIOD
MASS
= 1
Eta Cassiopeia^ . .
Sirius .......
0".35
0.39
8". 21
8.03
23.5
20.6
195y.8
52.2
0.33
3.24
Alpha Centauri . .
70 Ophiuchi ....
0.75
0.16
17.70
4.54
23.6
30.3
81.1
88.4
2.00
3.56
These double-star orbits are evidently comparable in
magnitude with the larger orbits of the planetary system,
none of those given being smaller than the orbit of Uranus
and none much larger than that of Neptune. In form
they are much more eccentric than planetary orbits, and
it has been shown that this fact can be accounted for
as a result of "tidal evolution," operating upon a pair
of nebulous masses, formed by the separation of a parent
nebula into two portions which revolve around their
common center.
371. Masses of Binary Stars. If we assume that the
binary stars move under the law of gravitation, then, when
we know the semi-major axis of the orbit and the period
of revolution, we can easily find the mass of the pair as
compared with that of the sun, much more easily, indeed,
than we can determine the 'mass of Mercury or the
moon, strange as it may seem. It is done simply by the
MASSES OF BINARY STARS 331
following equation, which we give without demonstration
(see General Astronomy, Arts. 536 and 878):
in which (M + m) is the united mass of the two stars, S is
the mass of the sun, a is the semi -major axis of the orbit
of the double star in astronomical units, and t its period in
years. The final column of the preceding table gives the
masses of the star pairs resulting from the data given in
the table ; but the reader must bear in mind that the
margin of error is very considerable because of the uncer-
tainty of the orbits and parallaxes in question. A very
slight error in the parallax makes a very great error in the
resulting mass.
372. Planetary Systems attending Stars. It is a natural ques-
tion whether some of the small companions which we see near large
stars may not be the " Jupiters " of their planetary systems. We can
only say as to this that no telescope ever constructed could even come
near to making visible a planet which bears to its primary any such
relations of size, distance, and brightness as Jupiter bears to the sun.
Viewed from our nearest neighbor among the stars, Jupiter would be
a little star of about the twenty-first magnitude, not quite 5" distance
from the sun, which itself would look like a star of the second mag-
nitude. To render a star of the twenty-first magnitude barely visible
(apart from all the difficulties raised by the nearness of a larger star)
would require a telescope more than twenty feet in diameter. If any
of the stars have planetary systems accompanying them, we shall
never be likely to see them until our telescopes have attained a
magnitude and power as yet undreamed of.
373. Spectroscopic Binaries. One of the most interest-
ing of recent astronomical results is the detection by the
spectroscope of many pairs of double stars so close that no
332 LESSONS IN ASTRONOMY
telescope can separate them. In 1889 the bright com-
ponent of the well-known double star Mizar (Zeta Ursse
Majoris, Fig. 88) was found by Pickering to show the dark
lines double in the photographs of its spectrum, at regular
intervals of about fifty-two days. The obvious explana-
tion is that this star is composed of two, which revolve
around their common center of gravity in an orbit which
is turned nearly edgewise toward us. (If it was exactly
edgewise, the star would be variable like Algol.)
When the stars are at right angles to the line from them
to us, one of the two will be moving towards us, while the
other is moving in an opposite direction ; and as a con-
sequence, the lines in their spectra will be shifted opposite
ways, according to Doppler's principle (Sec. 179). Now
since the two stars are so close that their spectra overlie
each other, the result will be simply to make the lines in
the compound spectrum look double. From the distance
apart of the lines the relative velocity of the stars can be
found, and from this the size of the orbit and the mass of
the stars. Pickering inferred from his observations that
in the case of Mizar the relative velocity of the two com-
ponents is about 100 miles per second, the period about
104 days, and the distance between the two stars about the
same as the diameter of the orbit of Mars. Later observa-
tions by Vogel, while confirming the velocity observed by
Pickering, have shown that the period is only 20.6 days,
just one-fifth of Pickering's value, making the orbit
smaller than that of Mercury.
Mizar is really a quadruple star, both of the two which are seen
in a small telescope being spectroscopically double.
SPECTROSCOPIC BINARIES 333
The lines in the spectrum of Beta Aurigse exhibit the
same peculiarity, but the doubling occurs once in four
days, the velocity being about 150 miles a second and
the diameter of the orbit about 8,000000 miles, while the
united mass of the two stars is about two and a half times
that of the sun.
These observations of Professor Pickering's were made
by photographing the spectrum with the slitless spectro-
scope (Sec. 364), and are possible only where the stars
which compose the binary are both of them reasonably
bright.
374. With his slit-spectroscope, Vogel (Sec. 341), as has
already been stated (Sec. 360), has been able to detect a
similar orbital motion in Algol, although the companion
of the brighter star is itself invisible. A little later, in the
case of the bright star Alpha Virginis (Spica), he found
a result of the same kind. At first the photographic
observations of the spectrum of this star appeared very
discordant. Some days they indicated that the star was
moving towards us quite rapidly, and then again from
us ; but it is found that everything can be explained by
the simple supposition that the star is double, with a small
companion like that of Algol, not bright enough to show
itself by its light, but heavy enough to make its partner
swing around in an orbit about 6,000000 miles in diameter
once in four days, the orbit not being quite edgewise to
the earth, so that the dark companion does not eclipse
Spica as Algol is eclipsed by its attendant. Many such
systems are found, in which the presence of a darker com-
panion is made known only by the variable radial velocity
of the brighter star.
334 LESSONS IN ASTRONOMY
The most remarkable spectroscopic binaries thus far detected are,
however, two which were discovered in 1896 by spectrum photographs
made at Arequipa. The first is Mu 1 Scorpii, in which the relative
velocity of the components is nearly 300 miles a second. The other
is a little star of the fifth magnitude, known as " Lacaille 3105," in
which the relative velocity of the two stars is 385 miles a second (!),
and since the period is 74 hours, the mass must be about 77 times
that of the sun.
At present more than three hundred objects of this sort are known,
among them Capella and the Pole-star, the latter having a period of
3 d 23 h , and an apparent relative velocity of only four miles a second.
The catalogue of such objects is growing rapidly.
375. Multiple Stars (see Fig. 88). In a considerable
number of cases we find three or more stars connected in
one system. Zeta Cancri consists of a close pair revolving
in a nearly circular orbit, with a period somewhat less than
sixty years, while a third star revolves in the same direc-
tion around them at a much greater distance and with a
period not less than 500 years (not yet fully determined).
Moreover, this third star is subject to a peculiar irregularity
in its motion, which seems to indicate that it has an invisible
companion very near the system, the system being really
quadruple.
In Epsilon Lyrse we have a beautiful quadruple system,
composed of two pairs, each binary with a period of over
200 years. Moreover, since they have a common proper
motion, it is probable that the two pairs revolve around
each other in a period which can be reckoned only in
thousands of years.
In Theta Orionis we have a remarkable object in which
the six components are not organized in pairs, but are at
not very unequal distances from each other.
STAR-CLUSTERS
335
Asterope
376. Clusters. There are in the sky numerous groups
of stars, containing from a hundred to many thousand
members. A few of them are resolvable by the naked eye,
as, for instance, the Pleiades (Fig. 90) ; some, like Prsesepe
in Cancer, break up under the power of even an opera-
glass (Sec. 52) ; but most of them require a large telescope
to show the separate components. To the naked eye or
small telescopes, if
visible at all, they
look like faint
clouds of shining
haze, but in a great
telescope they are
among the most
magnificent objects
the heavens afford.
The cluster known
as "13 Messier,"
in the constellation
of Hercules, is one
of the finest.
The question at
once arises whether FlG ' 90 Ma P of the pleiades
the stars in such a cluster are comparable with our own sun
in magnitude and separated from each other by distances
like that between the sun and Alpha Centauri, or whether
they are really small (for stars) and closely packed ; whether
the swarm is no more distant than the rest of the stars or
far beyond them.
The Hercules cluster contains at least 30,000 stars
packed within an area less than 10' in diameter. While
PZeione*
Atlas?
336 LESSONS IN ASTRONOMY
the evidence may not be conclusive, recent investigations
seem to indicate that this cluster may be as distant as
100,000 light-years. If that be so, individual stars must
be more luminous than our sun, it may take 1000 years
for light to travel from one side to the other, and the
actual distances between members of the cluster must be
enormous, though perhaps less than that which separates
our sun from its nearest neighbor.
NEBULAE
377. Besides the luminous clouds which, under the tele-
scope, break up into separate stars, there are others which
no telescopic power resolves, and among them some which
are brighter than many of the clusters. These irresolvable
objects, of which about 10,000 are now catalogued, with
probably myriads more not yet entered on the list, are
" nebulae." Two or three of them are visible to the naked
eye, one, the brightest of all and the one in which the
temporary star of 1885 appeared, is in the constellation of
Andromeda (see Fig. 91). Another most conspicuous and
very beautiful nebula is that in the sword of Orion.
The larger and brighter nebulae are, for the most part,
irregular in form, sending out sprays and streams in all
directions and containing dark openings and "lanes."
Some of them are of enormous volume. The great nebula
of Orion (which includes within its boundary the mul-
tiple star Theta Orionis) covers several square degrees,
and photographs show that nearly the whole constellation
is enveloped in a faint nebulosity, the wisps attaching
themselves especially to the brighter stars.
THE NEBULAE 337
The nebula of Andromeda is not quite so extensive, but
is more regular in its form, a long oval with dark lanes
in it, and a bright nucleus much like a star in the center,
as seen in a small telescope.
The smaller nebulae are, for the most part, more or less
nearly oval and brighter in the center. In the so-called
FIG. 91. Nebula in Audromeda
Roberts
" nebulous stars " the central nucleus is like a star shining
through a fog. The " planetary nebulae " are about circular
and have a nearly uniform brightness throughout, while
the rare " annular" or "ring nebulae" are darker in the
center. Fig. 92 is from a photograph of the finest of these
ring nebulae, that in the constellation of Lyra. There
338
LESSONS IN ASTRONOMY
are a number of nebulae which exhibit a remarkable
spiral structure in large telescopes. There are several
double nebulae and a few that are variable in brightness,
though no regularity has yet been ascertained in their
variation. Many of the most conspicuous and interest-
ing are, how-
ever, extremely
irregular in
form and struc-
ture, as for In-
stance, the Tri-
fid Nebula and
the great nebula
of Orion (Figs.
93 and 94).
The great
majority of the
nebulae are ex-
tremely faint,
even in large
telescopes, but
the few that
are reasonably bright are very interesting objects.
378. Drawings and Photographs of Nebulae. Until very
lately the correct representation of a nebula was an extremely
difficult task. More or less elaborate engravings exist of
perhaps fifty of the more conspicuous of them, but pho-
tography has now taken possession of the field. The first
success in this line was by Henry Draper of New York, in
1880, in photographing the nebula of Orion. Since his
death in 1882 great progress has been made, both in Europe
FIG. 92. Annular Nebula in Lyra
Keeler
FIG. 93. Trifid Nebula
Keeler
FIG. 94. Great Nebula in Orion
Keeler
339
340
LESSONS IN ASTRONOMY
and in this country, and at present the photographs are
continually bringing out new and before unsuspected
features. Fig. 91, for instance, from a photograph of the
nebula of Andromeda, taken by Mr. Roberts of Liverpool
in 1 8 8 8, shows that
the so-called " dark
lanes," which hith-
erto had been seen
only as straight
and wholly myste-
rious markings,
are really curved
ovals, like the di-
visions in Saturn's
rings. The photo-
graph brings out
clearly a distinct
spiral structure
pervading the
whole nebula,
which as yet has
aever been made out satisfactorily by the eye with any
telescope. This spiral structure is found more or less evi-
dent in a great majority of the nebulae. Fig. 95, the so-
called "whirlpool nebula" in the constellation of Canes
Venatici, is its finest example.
The photographs not only show new features in old nebulae, but
they reveal numbers of new nebulae invisible to the eye with any tele-
scope. Thus, in the Pleiades, it has been found that almost all the
larger stars have wisps of nebulosity attached to them, as indicated
by the dotted lines in Fig. 90, and shown fully developed in the
Fia. 95. Spiral Nebula
Keeler
CHANGES IN NEBULA
341
photograph of Fig. 96 ; and in a small territory in and near the
constellation of Orion, Pickering, with an eight-inch telescope, found
upon his star plates nearly as large a number of new nebulae as of
those that were previously known within the same boundary.
The photographs of nebulae require generally an exposure of from
one to two hours. The images of all the brighter stars that fall upon
the plate are, therefore, always immensely overexposed, and seriously
injure the picture from an artistic point of view.
The photographic brightness of a nebula, to use such an expres-
sion, is many times greater than its brightness to the eye, owing to
the fact that its light consists mainly in rays which belong to the
upper or blue portion of the spectrum. It has very little red or
yellow in it. At least,
this is so with all the
nebulae whose spectra are
characterized by bright
lines.
379, Changes in
Nebulae. It cannot be
stated with certainty that
sensible changes have
occurred in any of the
nebulae since they first
began to be observed,
the early instruments
were so inferior to mod-
ern ones that the older
drawings cannot be
trusted ; but some of the
differences between the
older and more recent
representations make it
extremely likely that real changes are going on. Probably after
a reasonable interval of time photography will settle the question.
380. Spectra of Nebulae. One of the most important
of the early achievements of the spectroscope was the proof
FIG. 96. The Pleiades
Roberts
342 LESSONS IN ASTRONOMY
that the light of the irregular nebulae proceeds mainly
from glowing gas of low density, and not from aggregations
of stars. Huggins, in 1864, first made the decisive obser-
vation by finding bright lines in their spectra. Thus far the
spectra of all the nebulae that show lines at all appear to
be substantially the same. Four lines are usually easily
observed, two of which are due to hydrogen ; but the
other two, which are brighter than the hydrogen lines, are
not yet identified.
Fig. 97 shows the position of the principal lines so far visually
observed. In the brighter nebulae a number of others are also some-
times seen and photographs show nearly one hundred in all, among
FIG. 97. Spectrum of the Gaseous Nebulae
which are several of the lines of helium. Certain stars also show the
nebular lines in their spectra, and Mr. Campbell has found one or
two which show bright hydrogen lines extending out on each side
of the star spectrum in such a way as to indicate an immense
envelope of the gas surrounding the star itself. From the displace-
ment of the lines of their spectra it has been found that the irregu-
lar nebulae are moving very slowly, while the average radial velocity
of the planetary is 48 miles a second, and that of the spiral several
times as great as the planetary.
381. Not all nebulae show the bright-line spectrum.
Those which do (known as gaseous nebulae) are of a
greenish tint, at once recognizable in a large telescope.
DISTANCE AND DISTRIBUTION OF NEBULAE 343
The white nebulae are probably all spiral in form. Most
of them are intrinsically too faint to be studied with the
spectroscope, but the brightest ones (including the great
nebula of Andromeda) are found to present a spectrum
similar to that of our sun a bright band crossed by dark
absorption lines. This is just what we might expect from
a very distant cloud of stars, and has led to the suggestion
that the spiral nebulae may be other universes so far beyond
the limits of our own galaxy that none of the individual
stars can be distinguished.
We can, however, only speculate as to the real nature
of these bodies. That they are very different from the
irregular nebulae is shown not only by the difference in
form and spectrum but also by their remarkable radial
velocity. The average motion in line of sight for more
than a score of spirals is about 250 miles a second, and
occasionally it runs up to 600 miles.
382. Distance and Distribution of Nebulae Very little
is positively known as to the distance of nebulae, and the
method commonly used in finding the parallax of a star
cannot often be applied. However, photographs for this
purpose have been taken with the 60-inch reflector on
Mount Wilson, and the measures indicate that the parallax
of the nebula in Andromeda is about 0".004, and that the
ring nebula in Lyra is equally distant. The planetary
nebulae may be nearer, for the average parallax for six was
found in 1918 to be 0".018, corresponding to a distance
of about 180 light-years.
Most of the irregular nebulae are in the Milky Way,
and seem to be so closely connected with faint stars in the
vicinity as to leave little doubt that they lie at the same
344 LESSONS IN ASTRONOMY
order of distance as the stars. It seems probable that
apparently vacant spaces found in some parts of the sky
may be explained as due to the presence of dark nebulous
clouds obscuring the light from stars which lie beyond.
It seems certain that these nebulae are within the bound-
aries of our stellar system, but there is great uncertainty
as to the status of the spirals. These may, perhaps, be
very distant members of our universe, or, as has been sug-
gested, they may find their place in the space beyond. If
the distance could be known with certainty, much light
would be thrown upon the question of their constitution.
As to the distribution, we find the green, or gaseous,
nebulas confined almost entirely to the Milky Way, while
the white, or non-gaseous, are most numerous in the region
of the northern galactic pole.
THE SIDEREAL HEAVENS
383. The Galaxy, or Milky Way. This is a luminous
belt of irregular width and outline which surrounds the
heavens nearly in a great circle. It is very different in
brightness in different parts, and is marked here and there
by dark bars and patches which at night look like over-
lying clouds. For about a third of its length (between
Cygnus and Scorpio) it is divided into two roughly par-
allel streams. The telescope shows it to be made up almost
entirely of small stars from the eighth magnitude down;
it contains also numerous star-clusters, but very few true
nebulae.
The galaxy intersects the ecliptic at two opposite points
not far from the solstices and at an angle of nearly 60, the
DISTRIBUTION OF STARS IN THE HEAVENS 345
north " galactic pole " being, according to Herschel, in the
constellation of Coma Berenices. As Herschel remarks :
The galactic plane " is to the sidereal universe much what the
plane of the ecliptic is to the solar system, a plane of ultimate
reference, and the ground plan of the stellar system.
384, Distribution of Stars in the Heavens. It is obvi-
ous that the distribution of the stars is not even approxi-
mately uniform. They gather everywhere into groups
and streams; but, besides this, the examination of any
of the great star-catalogues shows that the average num-
ber to a square degree increases rapidly and pretty regu-
larly from the galactic pole to the galaxy itself, where
they are most thickly packed. This is best shown by
the " star-gauges " of the elder Herschel, each of which
consists merely in an enumeration of the stars visible in
a single field of view. He made 3400 of these gauges,
and his son followed up the work at the Cape of Good
Hope with 2300 more in the south circumpolar regions.
From these data it appears that near the pole of the
galaxy the average number of stars in a single field of
view is only about 4 ; at 45 from the galaxy, a little over
10; while on the galactic circle itself it is 122.
Herschel, starting from the unsound assumption that the stars are
all of about the same size and brightness and separated by approxi-
mately equal distances, drew from his observations numerous unten-
able conclusions as to the form and structure of the " galactic
cluster," to which the sun was supposed to belong, theories for
a time widely accepted and even yet more or less current in popular
text-books, though in many points certainly incorrect.
But although the apparent brightness of the stars does
not depend entirely, or even mainly, upon their distance,
346 LESSONS IN ASTRONOMY
it is certain that, as a class, the faint stars are really more
remote, as well as smaller and darker than the brighter
ones. We may, therefore, safely draw a few inferences,
which, so far as they go, in the main agree with Herschel.
385. Structure of the Stellar Universe. I. The great
majority of the stars we see are included within a space
having roughly the form of a rather thin flat disk, like a
watch, with a diameter eight or ten times as great as its
thickness, our sun being not very far from its center.
II. Within this space the naked-eye stars are dis-
tributed with some uniformity, but not without a tend-
ency to cluster, as shown in the Pleiades. The smaller
stars, on the other hand, are strongly "gregarious" and
are largely gathered into groups and streams which have
comparatively vacant spaces between them.
III. At right angles to the galactic plane the stars are
scattered more evenly and thinly than in it, and we find
on the sides of the disk the comparatively starless region
of the nebulae.
IV. As .to the Milky Way itself, it is not certain
whether the stars which compose it form a sort of thin,
flat, continuous sheet, or whether they are arranged in a
sort of ring with a comparatively empty space in the
middle, where the sun is situated, not far from its center.
As to the size of the disklike space which contains most of the
stars, very little can be said positively. Its diameter is probably as
great as 20,000 or 30,000 light-years, how much greater it may be
we cannot even guess, and as to the "beyond" we are still more
ignorant. It is possible that our galaxy, as seen from a great dis-
tance, would appear like a spiral nebula, the dark rifts being the
spaces between the arms of the spiral.
QUESTION" OF A STELLAR SYSTEM 347
386. Do the Stars form a System? It is probable
(though not certain) that gravitation operates between
the stars, as indicated by the motion of the binaries. The
stars are certainly moving very swiftly in various direc-
tions, and the question is whether these motions are
governed by gravitation, and are " orbital " in the ordinary
sense of the word.
There has been a very persistent belief that somewhere
there is an enormous central sun, around which the stars
are all circulating in the same way as the planets of the
solar system move about our own sun. This belief has
been abundantly proved to be unfounded. It is now
certain that there is no such great body dominating the
stellar universe.
387. Maedler's Hypothesis. Another less improbable
doctrine is that there is a general revolution of the mass
of stars around the center of gravity of the whole, a
revolution nearly in the plane of the Milky Way. Some
years ago Maedler, in his speculations, concluded (though
without sufficient reason) that this center of gravity of the
stellar system was not far from Alcyone, the brightest of
the Pleiades, and, therefore, that this star was in a sense
the " central sun " ; and the idea is frequently met with
in popular writings. It has no satisfactory basis, how-
ever, nor is there yet proof of any such general revolu-
tion, though some recent investigations rather tend to
make it probable.
388. On the whole, the most reasonable view seems to
be that the stars are moving much as bees do in a swarm,
each mainly under the control of the attraction of its
nearest neighbors, though influenced more or less, of
348 LESSONS IN ASTRONOMY
course, by that of the general mass. From a study of
both proper and radial motions it has been found that
there are apparently two such swarms mixed together in
what we call our universe. The stars in each swarm are
flying about in all directions, but all share in the motion
common to the swarm. The two swarms are moving in
nearly opposite directions.
Probably the paths of the stars are not " orbits " ; i.e.,
they are not paths which return into themselves. The
forces which at any moment act upon a given star are
so nearly balanced that its motion must be sensibly in a
straight line for thousands of years at a time.
COSMOGONY
389. One of the most interesting topics of speculation
relates to the process by which the present state of things
has come about. In a forest, to use an old comparison of
Herschel's, we see around us trees in all stages of their
life-history, from the sprouting seedlings to the prostrate
and decaying trunks of the dead. Is the analogy appli-
cable to the heavens, and can we hope by a study of the
present condition and behavior of the bodies around us to
come to an understanding of their past history and prob-
able future ? Possibly to some extent. But human life is
so short that the processes of change are hardly perceptible,
and our telescopes and spectroscopes reveal but little of
the "true inwardness" of things, so that speculation is
continually baffled and its results can seldom be accepted
as secure. Still, some general conclusions seem to have
been reached which are likely to be true; but the pupil
GENESIS OF THE PLANETARY SYSTEM 349
is warned that they are not to be regarded as established in
any such sense as the law of gravitation and the theory
of planetary motion.
In a general way we may say that the gathering of
clouds of rarefied matter or meteoritic swarms into more
compact masses under the force of gravitation, the produc-
tion of heat by this shrinkage, the effect of this heat upon
the mass itself and upon neighboring bodies, these prin-
ciples cover nearly all the explanations that can thus far
be given for the present condition of the heavenly bodies.
390. Genesis of the Planetary System. Our planetary
system is clearly no accidental aggregation of bodies.
Masses of matter coming haphazard to the sun would
move (as comets actually do move) in orbits which, though
necessarily conic sections, would have every degree of
inclination and eccentricity. In the planetary system
this is not so. Numerous relations exist for which gravi-
tation does not at all account, and for which the mind
demands an explanation.
We note the following as the principal:
1. The orbits of the planets are all nearly circular (i.e., never very
eccentric, asteroids excepted).
2. They are all nearly in one plane (excepting those of some
of the asteroids).
3. The revolution of all, without exception, is in the same
direction.
4. There is a curious and regular progression of distances (expressed
by Bode's law, which, however, breaks down with Neptune).
As regards the planets themselves :
5. The plane of every planet's rotation nearly coincides with that
of its orbit (probably excepting Uranus).
350 LESSONS IN ASTRONOMY
6. The direction of rotation is the same as that of the orbital
revolution (excepting probably Uranus and Neptune).
7. The plane of orbital revolution of the planet's satellites coin-
cides nearly with that of the planet's rotation, wherever this has
been ascertained.
8. The direction of the satellites' revolution also usually coincides
with that of the planet's rotation.
9. The largest planets rotate most swiftly.
391. Now this arrangement is certainly an admirable one
for a planetary system, and therefore some have argued that
the Deity constructed the system in that way, perfect from
the first. But to one who considers the way in which
other perfect works usually attain their perfection their
processes of growth and development this explanation
seems improbable. It appears far more likely that the
planetary system was formed by growth than that it was
built outright.
The theory which in its main features is now generally
accepted, as supplying an intelligible explanation of the
facts, is that known as the "nebular hypothesis." In a
more or less crude and unscientific form it was first sug-
gested by Swedenborg and Kant, and afterwards, about
the beginning of the present century, was worked out in
mechanical detail by Laplace.
It was formulated before the discovery of the great
principles of the " conservation of energy," and the equiva-
lence of heat to other forms of energy, so that in some
respects it is defective and doubtless wrong. The main
idea, however, that our system was once an incoherent
mass and has come to its present state by physical pro-
cesses, is almost certainly correct, and forms the foundation
of all current speculation upon the subject.
THE NEBULAR HYPOTHESIS 351
392. Laplace's Nebular Hypothesis. He maintained or
rather suggested:
(a) That at some time in the past l the matter which is
now gathered into the sun and planets was in the form of
a " nebula."
(b) This nebula, according to him, was a cloud of
intensely heated gas (questionable).
(c) Under the action of its own gravitation the nebula
assumed a form approximately globular, with a motion of
rotation, the whirling motion depending upon the acci-
dental differences in the original velocities and densities
of the different parts of the nebula. As the contraction
proceeded the swiftness of the rotation would necessarily
increase for mechanical reasons.
(d) In consequence of its whirling motion the globe
would necessarily become flattened at the poles and
ultimately, as the contraction went on, the centrifugal
force at the equator would there become equal to gravity
and rings of nebulous matter would be detached from the
central mass, like the rings of Saturn. In fact, Saturn's
rings suggested this feature of the theory.
(e) The ring thus formed would for a time revolve
as a whole, but would ultimately break, and the material
would collect into a globe revolving around the central nebula
as a planet.
1 As to the origin of the nebula itself he did not speculate. There was
no assumption on his part, as is often supposed, that the matter was first
created in the nebulous condition. He assumed only that, as the egg may
be taken as the starting-point in the life-history of an animal, so the
nebula is to be regarded as the starting-point of the life-history of the
planetary system. He did not raise the question whether the egg is, or
is not, older than the hen.
352 LESSONS IN ASTRONOMY
Laplace supposed that the ring would revolve as if it
were solid, the particles at the outer edge moving more
swiftly than those at the inner (questionable). If this
were always so, the planet formed would necessarily rotate
in the same direction in which the ring had revolved.
(/) The planet thus formed would throw off rings of its
own and so form for itself a system of satellites.
393. This theory obviously explains most of the facts
of the solar system, which were enumerated in the preced-
ing article, though some of the exceptional facts (such as
the short periods of the satellites of Mars and the retro-
grade motions of those of Uranus and Neptune) cannot be
explained by it alone in its original form. But even these
exceptions do not contradict it, as is sometimes supposed.
As to the modifications required by the theory, while
they alter the mechanism of the development in some
respects, they do not touch the main results. It is rather
more likely, for instance, that the original nebula was a
cloud of ice-cold dust than incandescent gas and "fire
mist," to use a favorite expression; and it is likely, as
suggested by the spiral nebulae, that planets and satellites
were often separated from the mother orb otherwise than
in the form of rings.
Nor is it possible that a thin wide ring could revolve in
the same way as a solid mass ; the particles near the inner
edge must make their revolution in periods much shorter
than those upon the circumference, or the ring would tear
to pieces. But this very fact makes it possible to account
for the peculiar backward motion of the satellites of
Uranus and Neptune, thus removing one of the main
objections to the theory in its original form,
THE METEORITIC HYPOTHESIS 353
Many things also make it questionable whether the
outer planets are so much older than the inner ones, as
Laplace's theory would indicate. It is not impossible that
they may even be younger.
Our limits do not permit us to enter into a discussion of Darwin's
" tidal theory " of satellite formation, which may be regarded as, in
a sense, supplementary to the nebular hypothesis ; nor can we more
than mention Faye's proposed modification of it. According to him,
the inner planets are the oldest.
394. Lockyer's Meteoritic Hypothesis. 1 Sir Norman
Lockyer has of late vigorously revived a theory which had
been from time to time suggested before, viz., that all the
heavenly bodies in their present state are mere clouds of
meteors, or have been formed by the condensation of such
clouds; and it is an interesting fact, as Professor G. H.
Darwin has recently shown, that a large swarm of meteors
in which the individuals move swiftly in all directions
would, in the long run and as a whole, behave almost
exactly, from a mechanical point of view, in the same way
as one of Laplace's hypothetical gaseous nebulae. 2
The spectroscopic observations upon which Sir Norman rests his
attempted demonstration are many of them very doubtful ; but that
does not really discredit the main idea, except so far as the question
of the origin and nature of the light of the heavenly bodies is
1 For planetesimal hypothesis see note on page 358.
2 This is not very strange, after all. According to the modern " kinetic
theory of gases" (Rolfe's "Physics," page 157), a meteor cloud is
mechanically just the same thing as a mass of gas magnified. The
kinetic theory asserts that gas is only a swarm of minute molecules, the
peculiar gaseous properties depending upon the collisions of these mole-
cules with each other and with the walls of the inclosing vessel.
354 LESSONS IN ASTRONOMY
concerned. He makes the light depend upon the collisions between
the meteors, and finds in the spectra of the heavenly bodies evidence
of the presence of materials with which we are familiar in the mete-
orites which fall upon the earth's surface. These identifications are
in many cases questionable, in some certainly incorrect, and it
seems much more likely that the luminosity depends to a great degree
upon other than mere mechanical actions, electrical and chemical
for instance.
395. Stars, Star-Clusters, and Nebulae. It is obvious
that the nebular hypothesis in all its forms applies to the
explanation of the relations of these different classes of
bodies to each other. In fact, Herschel, appealing only to
the "law of continuity," had concluded, before Laplace
published his theory, that the nebulae develop sometimes
into clusters, sometimes into double or multiple stars, and
sometimes into single stars. He showed the existence in
the sky of all the intermediate forms between the nebula
and the finished star. For a time, about the middle of the
last century, while it was generally believed that all the
nebulae were only star-clusters, too remote to be resolved
by existing telescopes, his views fell rather into abeyance ;
but they regained acceptance in their essential features
when the spectroscope demonstrated the substantial differ-
ence between gaseous nebulae and the star-clusters.
396, Conclusions from the Theory of Heat. Kant and
Laplace, as Newcomb says, seem to have reached their
results by reasoning forwards. Modern science comes to
very similar conclusions by working backwards from the
present state of things.
Many circumstances go to show that the earth was once
much hotter than it now is. As we penetrate below the
surface, the temperature rises nearly a degree (Fahrenheit)
CONCLUSIONS FROM THE THEORY OF HEAT 355
for every sixty feet, indicating a white heat at the depth
of a few miles ; the earth at present, as Lord Kelvin says,
" is in the condition of a stone that has been in the fire and
has cooled at the surface."
The moon bears apparently on its surface the marks of
the most intense igneous action, but seems now to be
entirely chilled.
The planets, so far as we can make out with the tele-
scope, exhibit nothing at variance with the view that
they were once intensely heated, while many things go
to establish it. Jupiter and Saturn, Uranus and Neptune,
do not seem yet to have cooled off to anything like the
earth's condition.
As to the sun, we have in it a body continuously pour-
ing forth an absolutely inconceivable quantity of heat with-
out any visible source of supply. As has been explained
already (Sec. 192), the only rational explanation of the
facts thus far presented is that which makes it a huge,
cloud-mantled ball of elastic substance slowly shrinking
under its own central gravity, and thus generating heat. 1
A shrinkage of about two hundred feet a year in the
sun's diameter will account for the whole annual output
of radiant heat and light.
397. Age of the System. Looking backward, then, and
trying to imagine the course of time and of events reversed,
We see the sun growing larger and larger, until at last it
has expanded to a huge globe that fills the largest orbit of
1 So far we have no decisive evidence whether the sun has passed its
maximum of temperature or not. Lockyer thinks its spectrum (resem-
bling as it does that of Capella and the stars of the second class) proves
that it is now on the downward grade and growing cooler ; but others do
not consider the evidence conclusive.
356 LESSONS IN ASTRONOMY
our system. How long ago this may have been we can-
not state with certainty. If we could assume that the
amount of heat yearly radiated by the solar surface had
remained constantly the same through all those ages, and,
moreover, that all the radiated heat came solely from the
slow contraction of the sun's mass, apart from any con-
siderable original capital in the form of a high initial
temperature, and without any reenforcement of energy
from outside sources, if we could assume these prem-
ises, it is easy to show that the sun's past history must
cover about 15,000000 or 20,000000 years. But such
assumptions are at least doubtful ; and if we discard
them, all that can be said is that the sun's age must be
greater, and probably many times greater, than the limit
we have named.
398. Future Duration of the System. Looking forward,
on the other hand, from the present towards the future, it
is easy to conclude with certainty that if the sun con-
tinues its present rate of radiation and contraction, and
if contraction is its only source of heat, it must within
5,000000 or 10,000000 years become so dense that its
constitution will be radically changed. Its temperature
will fall, and its function as a sun will end. Life on the
earth, as we know life, will be no longer possible when the
sun has become a dark, rigid, frozen globe. At least this
is the inevitable consequence of what now seems to be the
true account of the sun's condition and activity if nothing
interferes with its steady and inexorable course.
But there may be interference: catastrophes and par-
oxysms, sudden changes and reversals of the regular course
of events at critical moments, collisions and explosions,
THE SYSTEM NOT ETERNAL 357
are certainly possible and actually occur, as the phenom-
ena of the solar surface and temporary stars abundantly
make evident.
399, The System not Eternal. One conclusion seems
to be clear : that the present system of stars and worlds is
not an eternal one. We have before us everywhere evi-
dence of continuous, irreversible progress from a definite
beginning towards a definite end. Scattered particles and
masses are gathering together and condensing, so that the
great grow continually larger by capturing and absorbing
the smaller. At the same time the hot bodies are losing
their heat and distributing it to the colder ones, so that
there is an unremitting tendency towards a uniform, and
therefore useless, temperature throughout our whole uni-
verse ; for heat is available as energy (i.e., it can do work)
only when it can pass from a warmer body to a colder
one. The continual warming up of cooler bodies at the
expense of hotter ones always means a loss, therefore,
not of energy, for that is indestructible, but of available
energy. To use the ordinary technical term, energy is
continually dissipated by the processes which constitute
and maintain life on the universe. This dissipation of
energy can have but one ultimate result, that of absolute
stagnation when the temperature has become everywhere
the same.
If we carry our imagination backwards, we reach "a
beginning of things," which has no intelligible antecedent;
if forwards, we come to an end of things in dead stagnation.
That in some way this end of things will result in a " new
heavens and a new earth" is, of course, probable, but
science as yet can present no explanation of the method.
358 LESSONS IN ASTRONOMY
NOTE TO ARTICLE 394
The Planetesimal Hypothesis. A new form of the meteoric theory,
known as the " planetesimal hypothesis," has been recently proposed
and developed in this country by Chamberlin and Moulton, who
consider that they have demonstrated the falsity of Laplace's " ring
theory."
They assume as the origin of the solar system, instead of the gas-
eous globe of Laplace, a spiral nebula (like that shown by the figure
on page 340) composed of gas, carrying mingled with it multitudes
of little solid masses (planetesimals) moving around the center,
generally in the same direction, but in orbits that vary in inclina-
tion, eccentricity, and period, and are subject to continual perturba-
tion. There results a very slow accretion of the planetesimals into
planets, with very little development of heat, since the relative
velocities of the colliding bodies are very small.
A great advantage of this theory is that it allows time enough to
satisfy the most exorbitant demands of geology and biology, besides
evading nearly all, if not all, of the difficulties that embarrass the
original nebular hypothesis.
APPENDIX
ASTRONOMICAL INSTRUMENTS
The Celestial Globe The Telescope : Simple, Achromatic, and Reflecting
The Equatorial The Filar Micrometer The Transit-Instrument
The Clock and Chronograph The Meridian Circle The Sextant
400. The Celestial Globe. The celestial globe is a ball,
usually of papier-mache, upon which are drawn the circles of
the celestial sphere and a map of the stars. It is ordinarily
mounted in a framework which represents the horizon and
the meridian in the manner shown in Fig. 98.
The " horizon," HH' in the figure, is usually a wooden ring
three or four inches wide and perhaps three-quarters of an
inch thick, directly supported by the pedestal. It carries
upon its upper surface at the inner edge a circle marked with
degrees for measuring the azimuth of any heavenly body,
and outside this the so-called zodiacal circles, which give
the sun's longitude and the equation of time for every day
of the year.
The meridian ring, MM', is a circular ring of metal which
carries the bearings upon which the globe revolves. Things
are so arranged, or o.ught to be, that the mathematical axis
of the globe is exactly in the same plane as the graduated face
of the ring, which is divided into degrees. The meridian ring
is held underneath the globe by a support, with a clamp which
enables us to fix it securely in any desired position.
The surface of the globe is marked first with the celestial
equator, next with the ecliptic crossing the equator at an
359
360
APPENDIX
angle of 23| at X (as the figure is drawn, not the vernal), and
each of these circles is divided into degrees. The equinoctial
and solstitial colures X and PE are also always represented,
E being the pole of the ecliptic. As to the other circles,
usage differs. The ordinary way at present is to mark the
globe with twenty-four hour-circles 15 apart (the colures,
Sec. 117, being four of them), and with parallels of declina-
tion 10 apart. On the surface of the globe are plotted the
positions of the stars
and the outlines of
the constellations.
It is perhaps worth
noting that many of the
spirited figures of the
constellations upon our
present globes are copied
from designs drawn by
Albert Dtirer for a star-
map published in his
time.
The Hour-Index is
usually a small circle
of thin metal, about
four inches in diam-
eter, which is fitted
to the northern
pole of the globe
with a stiffish friction, so that it can be set like the hands
of a clock, and when once set will turn with the globe
without shifting.
On some globes a hand like a clock-hand is used, showing the hour
on a circle engraved on the surface of the globe itself. This is the
case with the globe shown in the figure.
FIG. 98. The Celestial Globe
THE CELESTIAL GLOBE 361
401, To " rectify " a Globe, i.e., to set it so as to show
the aspect of the heavens at any time :
1. Elevate the north pole P of the globe to an angle equal
to the observer's north latitude by means of the graduation on
the meridian ring, and clamp the ring securely.
If the observer is south of the equator, the south pole, of course,
must be elevated instead of the north.
2. Look up the day of the month on the horizon of the
globe, and opposite to the day find on the zodiacal circle the
sun's longitude for that day.
3. On the ecliptic (upon the surface of the globe) find
the degree of longitude thus indicated, and bring it to the
graduated face of the meridian ring. The globe is thus set
to correspond to apparent noon of the day in question.
It may be well to mark the place of the sun temporarily with a bit
of paper gummed on at the proper place in the ecliptic. It can easily
be wiped off after using.
4. Hold the globe fast so as to keep the place of the sun
exactly on the meridian, and turn the hour-index until it shows
the mean time of apparent noon (i.e., 12 h the equation of
time given on the wooden horizon for the day in question).
If standard time is used, the hour-index must be set to the standard
time for apparent noon instead of the local mean time.
5. Finally, turn the globe upon its axis until the hour-
index shows the hour for which it is to be set. The globe
will then represent the true aspect of the heavens at that time.
The hour-index ought to keep its position unchanged while the
globe is revolved, but the observer must watch to see that it does
not shift ; many globes are faulty in this respect.
The positions of the moon and planets are not given by this opera-
tion, since they have no fixed places in the sky and therefore cannot
362 APPENDIX
be put in by the globe maker. If one wants them represented, he
must look up their right ascensions and declinations in some almanac
and mark the proper places on the globe with bits of wax or paper.
TELESCOPES
402. Telescopes are of two kinds, refracting and reflecting.
The refractor was first invented early in the seventeenth
century and is much more used, but the largest instruments
ever made are reflectors. In both, the fundamental principle
is the same. The large lens of the instrument (or else its
concave mirror) forms a real image of the object looked at,
and this image is then examined and magnified by the eye-
piece, which in principle is only a magnifying-glass.
In the form of instrument, however, which was originally devised
by Galileo and is still used as the " opera-glass," the rays from the
object-glass are intercepted and brought to parallelism by a concave
lens which serves as an eye-glass, before they form the image. Tele-
scopes of this construction are never made of much power, being
inconvenient on account of the smallness of the field of view.
403. The Simple Refracting Telescope. This consists
essentially, as shown in Fig. 99, of two convex lenses : one,
the object-glass A, of large size and long focus ; the other, the
eye-glass B, of short focus, the two being set at a distance
nearly equal to the sum of their focal lengths. Kecalling the
optical principles relating to the formation of images by lenses,
we see that if the instrument is pointed towards the moon, for
instance, all the rays that strike the object-glass from the top
of the crescent will be collected to a focus at a, while those
from the bottom will come to a focus at b ; and correspondingly
with rays from the other points on the surface of the moon.
We shall, therefore, get in the " focal plane " of the object-
glass a small inverted " image " of the moon. The image is
a real one, i.e., the rays really meet at the focal points, so that
TELESCOPES 363
if we insert a photographic plate in the focal plane at ab and
properly expose it, we shall get a picture of the object. The
size of the picture will depend upon the apparent angular
diameter of the object and the distance from the object-glass
to the image ab.
If the focal length of the lens A is ten feet, then the image of
the moon (31' in apparent diameter) will be a little more than one
inch in linear diameter.
404, Magnifying Power. If we use the naked eye we
cannot see the image distinctly from a distance much less
than a foot, but if we use a magnifying-lens of, say, one inch
focus, we can view it from a distance of only an inch and
it will look correspondingly larger. Without stopping to
FIG. 99. The Simple Refracting Telescope
prove the principle, we may say that the magnifying power
is simply equal to the quotient obtained by dividing the focal
length of the object-glass by that of the eye-lens.
It is to be noted, however, that a magnifying power of unity is
sometimes spoken of as "no magnifying power at all," since the
image appears of the same size as the object.
The magnifying power of a telescope is changed at pleasure by
simply interchanging the eyepieces, of which every telescope of any
pretensions always has a considerable stock giving various powers.
These usually contain two or more lenses in order to give good
definition over a larger field than can be obtained with a single-lens
eyepiece. (See Sec. 409.)
405. Brightness of the Image. This depends not upon
the focal length of the object-glass, but upon its diameter, or,
364 APPENDIX
more strictly, its area. If we estimate the diameter of the
pupil of the eye at one-fifth of an inch, as it is usually reck-
oned, then (neglecting the loss from want of perfect transpar-
ency in the lenses) a telescope one inch in diameter collects
into the image of a star 25 times as much light as the naked
eye receives ; and the great Yerkes telescope of 40 inches in
diameter, 40,000 times as much, or about 35,000 after allow-
ing for the losses. The amount of light is proportional to
the square of the diameter of the object-glass.
The apparent brightness of an object which, like the moon
or a planet, shows a disk, is not, however, increased in any
such ratio, because the light gathered by the object-glass is
spread out by the magnifying power of the eyepiece. But
the total quantity of light in the image of the object greatly
exceeds that which is available for vision with the naked
eye, and objects which, like the stars, are mere luminous
points have their brightness immensely increased, so that
with the telescope millions otherwise invisible are brought
to light. With the telescope, also, the brighter stars are easily
seen in the daytime.
406. The Achromatic Telescope. A single lens cannot
bring the rays which emanate from a single point in the object
to any exact focus, since the rays of each different color are
differently refracted, the blue more than the green, and this
more than the red. In consequence of this so-called "chro-
matic aberration" the simple refracting telescope is a very
poor 1 instrument.
About 1760 it was discovered, in England, that by making
the object-glass of two or more lenses of different kinds of
1 By making it extremely long in proportion to its diameter, the indis-
tinctness of the image is considerably diminished ; and in the middle of the
seventeenth century instruments more than 100 feet in length were used
by Huyghens and others. Saturn's rings and several of his satellites were
discovered with instruments of this kind.
TELESCOPES 365
glass, the chromatic aberration can be nearly corrected.
Object-glasses so made none others are now in common
use are called achromatic. In practice, only two lenses are
ordinarily used in the construction of an astronomical glass,
a convex of crown-glass and a concave of ^m^-glass, the
curves of the two lenses and the distances between them being
so chosen as to give the best attainable correction of the
" spherical " aberration (see any Physics textbook), as well
as of the chromatic.
407. Achromatism not Perfect. It is not possible with
the kinds of glass ordinarily obtainable to get a perfect cor-
rection of color Even the best achromatic telescopes show a
purple halo around the image of a bright star, which, though
usually regarded as "very beautiful 7 ' by tyros, seriously
injures the definition and is especially obnoxious in large
instruments.
This imperfection of achromatism makes it impossible to get
satisfactory photographs with an ordinary visual telescope.
The rays of light most efficient in impressing the image upon the
photographic plate are the blue and violet, which in the visual
object-glass are left to wander wildly, their effect upon the eye being
slight as compared with that of the yellow rays.
For photographic purposes we may use an object-glass specially
figured for the photographic rays (but then the telescope is useless
for visual work) ; or we may combine with the visual object-glass a
third lens, known as a "photographic corrector," to be used only
with the camera; or we may use with the visual object-glass a
colored screen to cut out the violet rays, and photographic plates
which have been specially sensitized for the remaining light. The
last of these methods, while very convenient and inexpensive,
involves a great loss of light and cannot be used advantageously for
very faint objects.
408. Diffraction and Spurious Disks. Even if a lens were
absolutely perfect as regards the correction of aberrations,
366 APPENDIX
both spherical and chromatic, it would still be unable to give
vision absolutely distinct. Since light consists of waves of
finite length, the image of a luminous point can never be also
SL point) but must of mathematical necessity be a hazy-edged
disk of finite diameter surrounded by a series of " diffraction "
rings. The diameter of the " spurious disk " of a star, as it is
called, varies inversely with the diameter of the object-glass :
the larger the telescope, the smaller the image of a star with
a given magnifying power.
With a good telescope and a power of about 30 to thfc inch of
aperture (120 for a 4-inch telescope) the image of a star, when the
air is steady (a condition unfortunately seldom fulfilled), should be
a clean, round disk with a bright
rin g around it, separated from the
disk by a clear black space.
According to Dawes, the disk of
a star with a 4|-inch telescope
should be about 1" in diameter;
E Z2Z
^z^^^^lj
FIG. 100. -Telescope Eyepieces ^ a 9 - inch instrument 0".5,
and \" for a 36-inch glass. In a
4f-inch telescope, therefore, the two disks of a double star with
a distance of V between centers would be just in contact ; with the
Yerkes telescope this would be the case if the distance were 0".l ;
and in this fact lies much of the superiority of great telescopes.
409, Eyepieces. For some purposes the simple convex
lens is the best " eyepiece " possible ; but it performs well
only for a small object, like a close double star, placed exactly
in the center of the field of view. Generally, therefore, we
employ " eyepieces " composed of two or more lenses, which
give a larger field of view than a single lens, and define satis-
factorily over the whole extent of the field. They fall into
two general classes, the positive and the negative.
The positive eyepieces are much more generally useful. They act
as simple magnifying-glasses, and can be taken out of the telescope
TELESCOPES 367
and used as hand magnifiers if desired. The image of the object
formed by the object-glass lies outside o/this kind of eyepiece, between
it and the object-glass.
In the negative eyepiece, on the other hand, the rays from the
object-glass are intercepted by the so-called field-lens " before reach-
ing the focus, and the image is formed between the two lenses of the
eyepiece. It cannot, therefore, be used as a hand magnifier.
Fig. 100 shows the two most usual forms of eyepiece, but there
are many others.
These eyepieces show the object in an inverted position ; but
this is of no importance as regards astronomical observations.
410. Reticle. When the telescope is used for pointing
upon an object, as it is in most astronomical instruments, it
must be provided with a " reticle " of some sort. The simplest
form is a metallic frame with spider lines stretched across it,
the intersection of the spider lines being the point of reference.
This reticle is placed not at or near the object-glass, as is
often supposed, but in its focal plane, as ab in Fig. 99. Some-
times a glass plate with fine lines ruled upon it is used
instead of spider lines. Some provision must be made for
illuminating the lines, or " wires/ 7 as they are usually called,
by reflecting into the instrument a faint light from a lamp
suitably placed.
411. The Reflecting Telescope. About 1670, when the chro-
matic aberration of refractors first came to be understood (in
consequence of Newton's discovery of the " decomposition of
light"), the reflecting telescope was invented. For nearly
150 years it held its place as the chief instrument for star-
gazing, until about 1820, when large achromatics began to
be made. There are several varieties of reflecting telescope,
differing in the way in which the image formed by the mirror
is brought within reach of the magnifying eyepiece.
Until about 1870 the large mirror (technically " speculum ")
was always made of speculum metal, a composition of copper
368 APPENDIX
and tin. It is now usually made of glass, silvered on the
front by a chemical process. When new, these silvered films
reflect much more light than the old speculum metal : they
tarnish rather easily, but fortunately can be easily renewed.
412. Large Telescopes. The largest telescopes ever made have
been reflectors. At the head stands the enormous instrument of
the Mt. Wilson Solar Observatory, 100 inches in diameter, mounted
in 1917. At Victoria, B.C., there is a 72-inch mirror which was
completed in 1915, equal in size, but superior in power, to Lord
Rosse's great reflector, made in 1842, for many years the largest.
Keeler's work with the 3-foot Crossley reflector at the Lick Observ-
atory opened a new era in the photography of nebulae and star
clusters, and the still more wonderful photographs obtained at
Mt. Wilson with Rltchey's 5-foot mirror show the great possibilities
of the reflector in this line of work. One of the most famous
instruments of this class is the great 4-foot reflector at Paris.
Of the refractors, the largest is that of the Yerkes Observatory at
Williams Bay, Wisconsin, with an object-glass 40 inches in diameter
and a tube nearly 70 feet long. The next in size is the telescope of
the Lick Observatory, which has an aperture of 36 inches. Next
to this come the telescopes at Potsdam, Pulkowa, Meudon, Nice,
and Allegheny, with apertures of about 30 inches; the Greenwich
telescope, 28 inches; the Vienna telescope, 27 inches; the two tele-
scopes at Washington and the University of Virginia, 26 inches;
and four or five others with apertures of from 26 to 23 inches,
at Cambridge (England), Greenwich, Paris, and Princeton. More
than half of these large object-glasses were made by the Clarks of
Cambridge (U.S.).
413. Relative Advantages of Reflectors and Refractors. There
is no little discussion on this point, each form of instrument having
its earnest partisans.
In favor of the reflector we have first, its cheapness and compara-
tive ease of construction, since there is but one surface to grind and
polish, as against four in an achromatic object-glass ; second, the fact
that reflectors can be made larger than refractors ; third, the reflector
is absolutely achromatic, and this gives it an immense advantage in
THE EQUATORIAL
369
certain lines of astronomical photography (as, for instance, in that
of the nebulae) and of spectroscopy.
On the other hand, a refractor gives a much brighter image than
a reflector of the same size ; it also generally defines much better,
because, for optical reasons into which we cannot enter here, any
slight distortion or malformation of the speculum of a reflector dam-
ages the image many times more than the same amount of distortion
of an object-glass. Then a lens hardly deteriorates at all with age,
while a speculum soon tarnishes, and must be resilvered or repolished
every few years. The lens gives also a
wider field of good definition.
Finally, as a rule, refractors are T
lighter and more convenient than reflect-
ors of equal power.
414. Mounting of a Telescope,
the Equatorial. A telescope,
however excellent optically, is not
of much use unless firmly and con-
veniently mounted. 1
At present some form of equatorial
mounting is practically universal.
Fig. 101 represents schematically
the ordinary arrangement of the
instrument. Its essential feature
is that its " principal axis " (i.e., the
one which turns in fixed bearings attached to the pier, and is
called the polar axis) is placed parallel to the earth's axis,
pointing to the celestial pole, so that the circle H, attached to
it, is parallel to the celestial equator. This circle is some-
times called the hour-circle, sometimes the right-ascension
1 We may add that it must, of course, be mounted where it can be
pointed directly at the stars, without any intervening window-glass
between it and the object. We have known purchasers of telescopes to
complain bitterly because they could not see Saturn well through a closed
window.
FIG. 101. The Equatorial
370
APPENDIX
FIG. 102. Great Double Equatorial, Visual and Photographic, of the
Potsdam Astrophysical Observatory
circle. At the extremity of the polar axis a "sleeve" is
fastened, which carries within it the declination axis D, and
to this declination axis is attached the telescope tube T, and
also the declination circle C.
THE MICROMETER 371
The advantages of this mounting are very great. In the
first place, when the telescope is once pointed upon an object
it is not necessary to move the declination axis at all in order
to keep the object in the field, but only to turn the polar axis
with a perfectly uniform motion, which motion can be, and
usually is, given by clockwork (not shown in the figure).
In the next place, it is very easy to find an object even
if invisible to the eye (like a faint comet, or a star in the
FIG. 103. Filar-Position Micrometer
By Warner and Swasey
daytime) provided we know its right ascension and declination,
and have the sidereal time, a sidereal clock or chronometer
being an indispensable accessory of the instrument.
Fig. 81, Sec. 337, represents another form of equatorial mounting,
which has been adopted for some of the instruments of the photo-
graphic campaign.
415. The Micrometer. This is an instrument for meas-
uring small angles, usually not exceeding 15' or 20'. Various
372
APPENDIX
kinds are employed, all of them small pieces of apparatus,
which, when used, are secured to the eye end of a telescope.
The most common is the parallel-wire micrometer, which is a
pair of parallel spider threads,
one or both of which can be
moved with a fine screw with
a graduated head, so that the
distance between the two
"wires" can be varied at
pleasure and then "read off"
by looking at the micrometer
head. Fig. 103 represents such
an instrument to be attached
to a telescope ; the threads
are in the box BB, and are
viewed through the eyepiece.
FIG. 104. -The Transit-Instrument 416 The Transit-Instru-
ment (Fig. 104). This con-
sists of a telescope carrying at the eye end a reticle, and
mounted on a stiff axis with pivots
that are perfectly equal and cylindri-
cal. They turn in Y's which are
firmly set upon some sort of frame-
work or on the top of solid piers, and
so placed that the axis will be exactly
east and west and precisely level.
When the telescope is turned on its
axis, the middle " wire " of the reticle,
if everything is correctly adjusted,
will follow the celestial meridian,
and whenever a star crosses the wire
we know that it is exactly on the meridian. Instead of a
single wire the reticle generally contains a number of wires
equally spaced, as shown in Fig. 105. The observer notes
FIG. 105. Reticle of the
Transit-Instrument
TIMEPIECES 373
by his timepiece the instant at which the object crosses
each of the wires, and the mean of the observations is taken
as giving the moment when the star crossed the middle
wire.
A delicate spirit-level, to be placed on the pivots and test
the horizontality of the axis, is an indispensable accessory.
So far as the theory of the instrument is concerned, a gradu*
ated circle is not essential ; but practically it is necessary to
have one attached to the axis in order to enable the observer
to set the instrument to the proper altitude in preparing for
the observation of a star.
417. The Astronomical Clock, Chronometer, and Chrono-
graph. A good timepiece is an essential adjunct of the
transit-instrument, and equally so of most other astronom-
ical instruments. The invention of the pendulum clock by
Huyghens was almost as important an event in the history
of practical astronomy as that of the telescope itself.
The astronomical clock differs in no essential respect from
any other, except that it is made with extreme care and has a
" compensated " pendulum so constructed that the rate of the
clock will not be affected by changes of temperature. It is
almost invariably made to beat seconds, and usually has its
face divided into twenty-four hours instead of twelve.
Excellence in a clock consists essentially in the constancy
of its "rate" ; i.e., it should gain or lose precisely the same
amount each day, and as a matter of convenience the daily
rate should be small, not to exceed a second or two. The
rate is adjusted by slightly raising or lowering the pendulum
bob, or putting little weights upon a small shelf attached to
the rod; the "error," when necessary, is corrected by simply
setting the hands.
The error of a timepiece is the difference between the time shown
by the clock-face and the true time at the moment ; the rate is the
amount it gains or loses in twenty-four hours.
874
APPENDIX
The chronometer is simply a carefully made watch and
has the advantage of portability, though in accuracy it
cannot quite compete with a well made clock.
Formerly transit-instrument observations were made by
simply noting with eye and ear the time indicated by the
clock at the moment when
the star observed was
crossing the wire or reti-
cle. A skillful observer
can do this within about
a tenth of a second. At
present the observer usu-
ally presses a telegraph-
key at the moment of the
transit and so telegraphs
the instant to an instru-
ment called a chronograph,
which makes a permanent
record of the observation
upon a sheet of paper,
FIG. 106. The Meridian Circle (schematic)
thus making the observa-
tion much more accurate as well as easier.
For the description of the Chronograph, see General Astronomy,
Art. 56, or Manual, Sec. 59.
418. The Meridian Circle, or Transit Circle. In many
respects this is the fundamental instrument of a working
observatory. It is simply the transit-instrument plus a finely
graduated circle or circles attached to the axis and provided
with microscopes for reading the graduation with precision.
In the accurate construction of the pivots of the instru-
ment and of the circles, with their graduation, the utmost
resources of the mechanical art are taxed. Fig. 107 shows
THE MERIDIAN CIRCLE
375
the instrument in principle. Fig. 107 represents the new
meridian circle of the Washington Observatory with its acces-
sories. It has a telescope of 6 inches aperture and circles
27 inches in diameter.
FIG. 107. Transit, or Meridian, Circle in United States Naval Observatory
at Washington
By Warner and Swasey
Its main purpose is to determine the right ascension and
declination of objects as they cross the meridian. The
declination is determined by measuring how many degrees
376 APPENDIX
the object is north or south of the celestial equator at the
moment of transit. The " circle-reading " for the equator
must first be determined as a zero point; and this is done by
observing a star near the pole and getting the circle-reading as
it crosses the meridian above the pole, and, twelve hours later,
when it crosses again below it. The mean of these two read-
ings, corrected for refraction, will be the circle-reading for
the pole, or the polar point, which is, of course, just 90 from
the equatorial zero point.
419. The Nadir Point. To get the latitude of the observer
with this instrument (Sec. 81) it is necessary also to have
the nadir point as a zero, i.e., the circle-reading which corre-
sponds to the vertical position of the telescope. This is
found by pointing the telescope down towards a basin of
mercury beneath it, and setting it so that the image of the
east and west wire in the reticle coincides with itself. Then
the telescope will be exactly vertical. The horizontal point
is just 90 from the nadir point, and the difference between
the (north) horizontal point and the polar point is the latitude
of the observatory.
Obviously the instrument can also be used as a simple
transit-instrument in connection with a clock, so that (Sec. 99)
the observer can determine at one observation both the right
ascension and declination of any object which is visible when
it crosses the meridian.
420. The Sextant All the instruments so far mentioned,
except the chronometer, require firmly fixed supports, and
are, therefore, useless at sea. The sextant is the only instru-
ment for measurement upon which the mariner can rely. By
means of it he can measure the angular distance between any
two points (as, for instance, the sun and the visible horizon),
not by pointing first on one and afterwards on the other, but
by sighting them both simultaneously and in apparent coinci-
dence. This observation can be accurately made even if he
THE SEXTANT
377
has no stable footing, but is swinging about on the deck of a
vessel. Fig. 108 represents the instrument. (For a detailed
description and explanation, see General Astronomy, Arts.
76-80, or Manual, Sees. 73-75.)
421. Use of the Instrument. The principal use of the
instrument is in measuring the altitude of the sun. At sea,
an observer holding the instrument in his right hand and
S
S'
FIG. 108. The Sextant
keeping the plane of the arc vertical, looks directly towards
the visible horizon through the horizon-glass, H, at the point
under the sun. Then by moving the index, N, with his left
hand, he inclines the index mirror upward until he sees the
reflected image of the sun, and the lower edge of this image is
brought to touch the horizon line. The reading of the gradu-
ation, after due correction for refraction, etc., gives the sun's
true altitude at the moment. If the observation is made very
378 APPENDIX
near noon, for the purpose of determining the latitude, it will
not be necessary to read the chronometer at the same time.
If, however, the observation is made for the purpose of deter-
mining the longitude (Sec. 427), the instant of observation, as
shown by the chronometer, must be carefully noted.
The skillful use of the sextant requires considerable dex-
terity, and from the small size of the telescope the angles
measured are less precisely measured than with large fixed
instruments; but the portability of the instrument and its
applicability at sea render it absolutely invaluable. It was
invented by Godfrey of Philadelphia, in 1730, but an earlier
design of an instrument on the same principle has since been
found among the unpublished papers of Newton.
MISCELLANEOUS
Hour- Angle and Time Twilight Determination of Latitude Ship's Place
at Sea Finding the Form of the Earth's Orbit The Ellipse Illustra-
tions of Kepler's Third Law The Ecfuation of Light and the Sun's Dis-
tanceAberration of Light De 1'Isle's Method of getting the Solar
Parallax from the Transit of Venus The Conic Sections Stellar
Parallax
422. Hour-Angle and Time (supplementary to Sees. 89-91).
There is another way of looking at the matter of time
which has great advantages. If we face towards the north
pole and consider the star m (Fig. 109) as carried at the end
of the arc mP of the hour-circle which connects it to the pole,
we may regard this arc as a sort of clock-hand ; and if we
produce it to the celestial equator and mark off the equator
into 15-spaces, or "hours," the angle mQP, or the arc QY,
will measure the time which has elapsed since m was on the
meridian PQ. The angle mPQ is called the hour-angle of the
star m. It is the angle at the pole between the meridian and
the hour-circle which passes through the body.
HOUR-ANGLE AND TWILIGHT
379
Having now this definition of the hour-angle, we may
define sidereal time (Sec. 91) at any moment as the hour-angle
of the vernal equinox at that moment. In the same way, the
apparent solar time (Sec. 88) is the hour-angle of the sun's
center ; the mean solar time (Sec. 89) is the hour-angle of a
fictitious sun which moves around the heavens uniformly, once
a year, in the equator, keeping its right ascension equal to
the mean longitude of the real sun. For some purposes, as
in dealing with the tides,
it is convenient to use
lunar time, which is sim-
ply the hour-angle of the
moon at any moment.
423. Twilight is caused
by the reflection of sunlight
from the upper portions of
the earth's atmosphere. After
the sun has set, its rays still
continue to shine through the
air above the observer's head,
and twilight contin ues as long
as any portion of this illu-
minated air can be seen from
where he stands. It is considered to end when stars of the sixth
magnitude become visible near the zenith, which does not occur
until the sun is about 18 below the horizon ; but this is not strictly
the same for all places.
The duration of twilight varies with the season and with the
observer's latitude. In latitude 40 it is about ninety minutes on
March 1 and October 12, but more than two hours at the summer
solstice. In latitudes above 50, when the days are longest, twilight
never quite disappears, even at midnight, and in latitude 60 one
can read fair-sized type all night long. On the mountains of
Peru, on the other hand, it is said never to last more than half
an hour.
FIG. 109. Hour- Angle
380
APPENDIX
424. Methods of determining Latitude by Other Obser-
vations than those of Circumpolar Stars (supplementary to
Sec. 81). To determine the latitude by observations of a cir-
cumpolar star, the observer must remain at the same station
at least twelve hours. The latitude can be determined, how-
ever, with a good instrument, with almost equal precision by
observing the meridian altitude, or zenith distance, of a body
whose declination is accurately known. In Fig. 110 the circle
SQPN is the meridian, Q and P being respectively the equa-
tor and the pole, and Z the zenith. QZ is evidently the
declination of the zenith (i.e., the distance of the zenith from
the celestial equator) and is equal to PB, the latitude of the
observer, or height of the pole. Suppose now that we observe
Zs, i.e., the zenith distance of the star s, south of the zenith,
as it crosses the meridian, and
that we know Qs, the declina-
tion of the star. Evidently
QZ = Qs + sZ ; i.e., the latitude
equals the declination of the star
\ N plus its zenith distance. If the
star were at s', south of the
equator, the same equation would
hold good algebraically, because
the declination, Qs', is a minus quantity. If the star were at
n, between the zenith and the pole, we should have : latitude
equals the declination of the star minus the zenith distance.
This is the method actually used at sea (Sec. 426), the sun being
the object observed.
There are many other methods in use, as, for instance, that,
by the zenith telescope and that by the prime-vertical instru-
ment, which are practically more convenient and more accu-
rate than either of the two described, but they are more
complicated and their explanation would take us too far.
FIG. 110. Determination of
Latitude
MARINE ASTRONOMY 381
FINDING THE PLACE OF A SHIP
425. The determination of the place of a ship at sea is,
from the economic point of view, the most important problem
of Astronomy. National observatories and nautical almanacs
were established, and are maintained principally to supply
the mariner with the data needed to make this determination
accurately and promptly. The methods employed are neces-
sarily such that the required observations can be made with
the sextant and chronometer, since fixed instruments, like the
transit-instrument and meridian circle, are obviously out of
the question on board a vessel.
426. Latitude at Sea. This is obtained by observing with
the sextant the sun's maximum altitude, which is reached
when the sun is crossing the meridian.
Since at sea the sailor seldom knows beforehand the precise
time which will be shown by his chronometer at noon, he
takes care not to be too late, and begins to measure the sun's
altitude a little before noon, repeating his observations every
minute or two. At first the altitude will keep increasing, but
when noon comes the sun will cease rising, and then begin to
descend. The observer uses, therefore, the maximum altitude
obtained, which, with due allowance for refraction and some
other corrections (for details, see larger works), gives him the
true altitude of the sun's center. Taking this from 90, we
get its zenith distance.
Kef erring now to Fig. 110, in which the circle SQZPN is
the meridian, P the pole, Z the zenith, and OQ the celestial
equator seen edgewise, we see that PN, the altitude of the pole,
is necessarily equal to ZQ, the distance from the zenith to the
equator. Now, from the almanac, we find Qs, the declination
of the sun for the time when the observations are made. 1
1 If the sun happened to be south of the equator (in the winter), as at
s', we should have ZQ equals Zs' s'Q.
382 APPENDIX
We have only to add to this Zs, the distance of the sun from
the zenith (i.e., 90 Ss, the observed altitude of the sun), to
obtain QZ, which is the observer's latitude.
It is easy in this way, with a good sextant, to get the lati-
tude within about half a minute of arc, or, practically, about
half a mile, which is quite sufficiently accurate for nautical
purposes.
427. Determination of Local Time and Longitude at Sea.
- The usual method now employed for the longitude depends
upon the chronometer. This is carefully " rated " in port ;
i.e., its error and its daily gain or loss are determined by com-
parisons with an accurate clock for a week or two, the clock
itself being kept correct to Greenwich time by transit obser-
vations. By merely allowing for the gain or loss since leaving
port, and adding this gain or loss to the "error" (Sec. 417)
which the chronometer had when brought on board, the sea-
man at once obtains the error of the chronometer on Green-
wich time at any moment ; and allowing for this error, he has
the Greenwich time itself with an accuracy which depends
only on the constancy of the chronometer's rate : it makes no
difference whether it is gaining much or little, provided its
daily rate is steady.
He must also determine his own local time; and this must
be done with the sextant, since, as was said before, an instru-
ment like the transit cannot be used at sea. He does it by
measuring the altitude of the sun, not at or near noon, as often
supposed, but when the sun is as near due east or west as cir-
cumstances permit. From such an observation the sun's hour-
angle, i.e., the apparent solar time (Sec. 422), is easily found
by a trigonometrical calculation, provided the ship's latitude
is known. (For the method of calculation, see General
Astronomy, Art. 116, or Manual, Sec. 103.)
The longitude follows at once, being simply the difference
between the Greenwich time and the local time.
FORM OF THE EARTH'S ORBIT
383
In certain cases where the chronometers have been for
some reason disturbed, the mariner is obliged to get his Green-
wich time by observing with a sextant the distance of the
moon from some star or planet near the ecliptic, but the
results thus obtained are comparatively inaccurate.
428. To find the Form of the Earth's Orbit (supplementary
to Sec. 119). Take the point S (Fig. Ill) for the .sun, and
draw through it a line, OS f, directed towards the vernal
equinox, from which longitudes are measured. Lay off from S
lines indefinite in length, making angles with Sf equal to the
earth's longitude as seen
from the sun on each
of the days when the
observations are made
(earth's longitude equals
sun's longitude -f- 180).
We shall thus get a sort
of "spider" showing the
direction of the earth as
seen from the sun on
each of those days.
Next, as to the dis-
tances. While the ap-
parent diameter of the
sun does not tell us its absolute distance from the earth, unless
we know his diameter in miles, yet the changes in the appar-
ent diameter do inform us as to the relative distance at
different times, since the nearer we are to the sun, the larger
it looks. If, then, on the legs of the " spider " we lay off dis-
tances inversely proportional l to the number of seconds of arc
in the sun's measured diameter at each date, these distances
will be proportional to the true distance of the earth from the
10000"
ij.e., lay off Si, S 2 , etc., each equal to diameter
Fia. 111. Determination of the Form
of the Earth's Orbit
384
APPENDIX
sun, and the curve joining the points thus obtained will be a
true map of the earth's orbit, though without any scale of
miles. When the operation is performed we find that the
orbit is an ellipse of small eccentricity with the sun in one
of the two foci.
429. The Ellipse, and Definitions relating to it (supplemen-
tary to Sees. 119, 120). If we drive two pins into a board,
,as at F and S in Fig. 112, and put around the pins a looped
thread, attached to the point of a pencil, P, then, on carrying
the pencil around, it will mark out an ellipse. The pins, F
and S, are the " foci " of the
ellipse and C is its center.
From the manner in which
the ellipse is constructed it
\A is clear that at any point, P,
on its outline, the sum of
the two lines PS and PF will
always be the same, and equal
to the line A A'. The length
FIG. 112. The Ellipse . ,_ ... t . . _
of the ellipse, A A', is called
its major axis, and AC its semi-major axis, which is usually
designated by a, while the semi-minor axis, BC, is lettered b.
CS
The fraction, , is called the eccentricity of the ellipse and
A C
determines the shape of the oval. Its usual symbol is e. If e
is nearly unity, i.e., if CS is nearly equal to CA, the oval
will be very narrow compared with its length ; but if CS is
very small compared with CA, the ellipse will be almost round.
Taken together, a and e determine the size and form of the
oval. The ellipse is called a "conic " because when a cone is
cut across obliquely the section is an ellipse. (See Sec. 440.)
430. Problems illustrating the " Harmonic Law " (supplementary
to Sec. 220). To aid the student in apprehending the scope of
Kepler's third law, we give a few examples of its application.
PROBLEMS 385
1. What would be the period of a planet having a mean distance
from the sun of one hundred astronomical units, i.e., a distance a
hundred times that of the earth? _j_^
PMOO= I 2 (year): X* ;
whence X (in years) = VlOO 3 = 1000 years.
2. What would be the distance from the sun of a planet having a
period of 125 years ?
I 2 (year) : 125 2 = I 3 : X s ; whence X = VI25 2 = 25 astron. units.
3. What would be the period of a satellite revolving close to the
earth's surface ?
(Moon's Dist.) 3 : (Dist. of Satellite) 3 = (27.3 days) 2 : X 2 ,
or, 60 8 : I 3 = 27.3 2 : X 2 ;
whence X = 27 ^. days = O d .0587 = I h 24 m .5.
V60 3
4. How much would an increase of 10 per cent in the earth's
distance from the sun lengthen the year ?
100 3 : HO 3 = (365i) 2 : X*, whence X =
X being the new length of the year. X is found by computation
(most conveniently by the help of logarithms) to be 421.38 days.
The increase is 56.13 days.
5. What is the distance from the sun of an asteroid with a period
of 3 years?
I 2 (year) : 3.5 2 = I 3 : Dist. 8
-.- Dist. = V(3.5) 2 = \/12.25 = 2.305 astron. units.
431, The Equation of Light. When we observe a celestial
body, we see it not as it is at the moment of observation, but
as and where it was at the moment when the light which we
see left it. If we know its distance in astronomical units
and know how long light takes to traverse that unit, we can
at once correct our observation by simply dating it back to
the time when the light started from the object. The neces-
sary correction is called the " equation of light" and the time
386 APPENDIX
required by light to traverse the astronomical unit of distance
is called the " Constant of the Light-Equation " (not quite 500
seconds, as we shall see).
It was in 1675 that Roemer, the Danish astronomer (the inventor
of the transit-instrument, meridian circle, and prime-vertical instru-
ment, a man almost a century in advance of his day), found that
the eclipses of Jupiter's satellites show a peculiar variation in their
times of occurrence, which he explained as due to the time taken by
light to pass through space. His bold and original suggestion was
neglected for more than fifty years, until long after his death, when
Bradley's discovery of aberration (Sec. 435) proved the correctness
of his views.
432. Determination of the Constant of the Equation of
Light. Eclipses of the satellites of Jupiter recur at intervals
which are really almost exactly equal (the perturbations being
very slight), and the interval can easily be determined and the
times tabulated. But if we thus predict the times of the
eclipses during a whole synodic period of the planet, then,
beginning at the time of opposition, it is found that as the
planet recedes from the earth the eclipses, as observed, fall
constantly more and more behindhand and by precisely the
same amount for all four satellites. The difference between
the predicted and observed time continues to increase until
the planet is near conjunction, when the eclipses are about
16 m 38 8 later than the prediction. After the conjunction they
quicken their pace and make up the loss, so that when oppo-
sition is reached once more they are again on time.
It is easy to see from Fig. 113 that at opposition the planet
is nearer the earth than at conjunction by just two astronom-
ical units. At opposition the distance between Jupiter and
the earth is JA, while six and a half months later, at the
time of Jupiter's superior conjunction, it is JB. The differ-
ence between JA and JB is just twice the distance from S
to A.
THE EQUATION OF LIGHT
387
The whole apparent retardation of eclipses between opposi-
tion and conjunction must therefore be exactly twice the time 1
required for light to come from the sun to the earth. In this
way the " light-equation constant " is found to be very nearly
499 seconds, or 8 minutes 19 seconds, with a probable error
of perhaps two seconds.
433. Since these eclipses are gradual phenomena, the determina-
tion of the exact moment of a satellite's disappearance or reappear-
ance is very difficult, and this
renders the result somewhat
uncertain. Professor E. C.
Pickering of Cambridge has
proposed to utilize photometric
observations for the purpose
of making the determination
more precise, and two series
of observations of this sort,
and for this purpose, have
been made during recent
years, one of them in
Cambridge, U.S., and the
other at Paris under the direc-
tion of Cornu, who devised a FJQ 113> _ The Equation of Light
similar plan. The Cambridge
results are discussed in Vol. LII of the Harvard Annals.
Pickering has also applied photography to the observation of these
eclipses with encouraging success.
434. The Distance of the Sun determined by the " Light-
Equation." Until 1849, when Fizeau first succeeded in actu-
ally measuring it, our only knowledge of the velocity of light
1 The student's attention is specially directed to the point that the
observations of the eclipses of Jupiter's satellites give directly neither the
velocity of light nor the distance of the sun ; they give only the time
required by light to make the journey from the sun. Many elementary
text-books, especially the older ones, state the case carelessly.
388
APPENDIX
was obtained from such observations of Jupiter's satellites.
By assuming as known the earth's distance from the sun, the
velocity of light can be obtained when we know the time
occupied by light in coming from the sun.
At present, however, the case is reversed. We can deter-
mine the velocity of light by two independent experimental
methods, and with a surprising degree of accuracy. Then,
knowing this velocity and the " light-equation constant," we
can deduce the distance of the sun. According to the latest
determinations the velocity of light is 186,330 miles per
second. Multiplying this
by 499, we get 92,979000
miles for the sun's distance.
(Compare Sec. 436.)
435. Aberration of
Light. The fact that
light is not transmitted
instantaneously causes the
apparent displacement of
an object viewed from any
moving station, unless the
motion is directly towards
or from that object. If the motion of the observer is not
rapid, this displacement, or " aberration," is insensible ; but
the earth moves so swiftly in its orbit (18 miles per second)
that it is easily observable in the case of the stars. Astro-
nomical aberration may be defined, therefore, as the apparent
displacement of a heavenly body due to the combination of the
orbital motion of the earth with that of light the direction
in which we have to point our telescope in observing a star
is not the same as if the earth were at rest.
We may illustrate this by considering what would happen in the
case of falling raindrops. Suppose the observer standing with a
tube in his hand while the drops are falling straight down : if he
FIG. 114. Aberration
ABERRATION 389
wishes to have the drops descend through the middle of the tube
without touching the sides, he must keep it vertical so long as he
stands still ; but if he advances in any direction the drops will strike
the side of the tube, and he must thrust forward its upper end
(Fig. 114) by an amount which equals the advance he makes while
a drop is falling through it ; i.e., he must incline the tube forward at
an angle depending both upon the velocity of the raindrop and the
swiftness of his own motion, so that when the drop, which entered
the tube at J5, reaches A', the bottom of the tube will be there also.
It is true that this illustration is not a demonstration, because light
does not consist of particles coming towards us, but of waves trans-
mitted through the ether of space. But it has been shown (though
the proof is by no means elementary) that within very narrow limits
the apparent direction of a wave is affected in precisely the same way
as that of a moving projectile.
Observations on several hundred stars show that a star situ-
ated on a line at right angles to the direction of the earth's
motion is thus apparently displaced by an angle of about 20 ".5.
This is the so-called " CONSTANT OF ABERRATION."
The Astronomical Congress at Paris in 1896 adopted the
value 20".47, but a series of observations by Doolittle, extend-
ing from 1899 to 1911, carry it up to 20".525.
If the star is in a different part of the sky its displacement
will be less, the amount being easily calculated when the date
and the star's position are given.
436. Determination of the Sun's Distance by Means of the
Aberration of Light. The constant of aberration, a, and
the two velocities, that of the earth in its orbit, u, and the
velocity of light, V, are connected by the very simple equation
a = 206,265 x |; whence it = X V.
When, therefore, we have ascertained the value of a (20".52)
from observations of the stars, and of V (186,330 miles, accord-
ing to the most recent determinations by Michelson and
390 APPENDIX
Newcomb) by physical experiments, we can immediately find
u, the velocity of the earth in her orbit. The circumference of
the earth's orbit is then found by multiplying this velocity, u,
by the number of seconds in a sidereal year (Sec. 127) ; and
from this we get the radius of the orbit, or the earth's mean
distance from the sun, by dividing the circumference by 2 TT
(TT = 3.14159). Taking a = 20".52, the mean distance of the
sun comes out 93,104000 miles.
But the uncertainty of a is probably as much as 0".03, and
this affects the distance proportionally, say one part in 600,
or 150,000 miles. Still, the method is one of the very best
of all that we possess for determining in miles the value of
"the Astronomical Unit."
437. De 1'Isle's Method of determining the Sun's Parallax
by a Transit of Venus. We have thus (Sees. 434 and 436)
two methods by which the mean distance of the sun from the
FIG. 115. Transit of Venus
earth can be determined. They both depend upon a knowl-
edge of the velocity of light, and, of course, were unavailable
before 1849, when Fizeau first succeeded in actually measuring
it. Before that time it was necessary to rely entirely upon
observations of either Mars or Venus, made at times when
they come specially near us.
Most of the methods of getting the sun's parallax and dis-
tance from such observations depend upon our having a pre-
vious knowledge of the relative distances of the planets from
the sun. These relative distances were ascertained centuries
TRANSITS OF VENUS 391
ago. Copernicus knew them nearly as accurately as we have
them now ; but since we have not explained in this book how
they are found (the explanation involves a little Trigonom-
etry), we limit ourselves to giving here a single very simple
method, which requires a previous knowledge not of the rela-
tive distances of Venus and the earth from the sun, but only
of the synodic period of the planet (Sec. 228), i.e., the time in
which she gains one entire revolution upon the earth. This
is almost exactly 584 days (583.971), as has been known from
remote antiquity.
Fig. 115 represents things at a transit of Venus as they
would be seen by one looking down from an infinitely distant
point above the earth's north pole.
As seen from the earth itself,
Venus would appear to cross the
sun, striking the disk on the east .
side and moving straight across to
the west, making four " contacts "
with the edge of the sun, as shown
in Fig. 116.
438. Suppose, now, that two
observers, E and W (Fig. 115), FlG<116 ._ Contact8inaTransit
are stationed opposite each other of Venus
and near the earth's equator.
E will see Venus strike the sun's disk before W does, and if
they both observe the moment of contact in Greenwich time,
the difference between their records will be the time it takes
Venus to move over the arc from V\ to F 2 . From the figure
it is clear that the angle V[DV^ is the same as EDW, the
earth's apparent diameter seen from the sun, and this is at once
known when we have the time from V l to F 2 .
Since Venus gains one revolution in 584 days, in one day
she will gain ^ of a revolution, or 37' (very nearly), and
this will make her gain 1".54 in one minute. Now it is found
392
APPENDIX
that the difference between the moments of contact at two
stations situated like E and W is about H m 25 8 , and hence
that the diameter of the earth, as seen from the sun, is 17".6,
or the sun's horizontal parallax (Sec. 139) is 8".8 ; from which
its distance is easily found (Sec. 140).
The reader will see that the two observers must know their
longitudes accurately in order to be sure of the correct Green-
wich time. Moreover, the two stations can never be quite
exactly opposite
each other, but
stations a little
nearer together
must be taken
and proper al-
lowances made.
Finally, we are
3 very sorry to
add that the
necessary obser-
vations of the
moment when
Venus reaches
the edge of the
sun's disk can-
not be made
with the accu-
FIQ. 117. Ellipse, Parabola, and Hyperbola
racy which is desirable, owing to the effect of the planet's
atmosphere (see Sec. 248) ; so that practically the method
is less accurate than might be hoped. (For further details,
see General Astronomy, Chap. XVI.)
439. The Parabola (supplementary to Sees. 292-298).-
This differs from the ellipse in never coming around into itself.
In Fig. 117, the curves PA lt PA 2 , and PA 8 are ellipses of dif-
ferent length, all having S at one of their foci, but having F lt
THE CONICS
393
F 2 , and F 8 at the other. The first and smallest of the ellipses
is nearly circular and shaped about like the orbit of Mercury,
the two foci S and F l being pretty near together ; the next is
more eccentric than the orbit
of any asteroid ; and the third
still more so, about like the
orbit of Halley's comet. Now,
if we imagine the point F car-
ried farther and farther to the
right the ellipse will grow
larger and longer, until when
F is infinitely far away the
curve will become a parabola.
Of course if the point F is
very distant, even if not infi-
nitely so, the part of the curve
near S will agree with the parab-
ola so closely that no one could
distinguish between them.
All ellipses that have S for
the focus and P for the peri-
helion lie inside of the parab-
ola, while another set of
conic curves called hyperbolas,
with the same focus and peri-
helion, lie entirely outside of
it, which is, so to speak, a sort
of boundary or division line
between the ellipses and
hyperbolas which have this
focus and perihelion.
440. The Conic Sections. The way in which these curves
the ellipse, parabola, and hyperbola are formed by sec-
tions of the cone is shown by Fig. 118.
FIG. 118. The Conies
894 APPENDIX
(a) If the cone be cut by a plane which makes with its
axis, VC, an angle greater than BVC, the plane of the section
will cut completely across the cone and the section EF will
be an ellipse, which will vary in shape and size according to
the position of the plane. The circle is simply a special case
when the cutting plane is perpendicular to the axis, as NM.
(b) When the cutting plane makes with the axis an angle
less than BVC (the semi-angle of the cone), it plunges contin-
ually deeper and deeper into the cone and never comes out on
the other side (the cone is supposed to be indefinitely pro-
longed). The section in this case is an hyperbola, GHK. If
the plane of the section be produced upward, however, it
encounters the " cone produced," cutting out from it a second
hyperbola, G'H'K', precisely like the original one, but turned
in the opposite direction.
The axis of the hyperbola is always reckoned as negative,
lying outside of the curve itself ; in the figure, it is the line
HH'. The center of the hyperbola is the middle point of this
axis, a point also outside of the curve.
(c) When the angle made by the cutting plane with the
axis is exactly equal to the cone's semi-angle, the plane will
be parallel to the side of the cone, and we then get the special
case of the parabola, RPO, which forms a partition, so to
speak, between the infinite variety of ellipses and hyperbolas
which can be cut from a given cone. All parabolas are of the
same shape, just as all circles are, differing only in size. The
fact is by no means self-evident and we cannot stop to prove
it, but it is true.
441. Determination of the Parallax of a Star (supple-
mentary to Sec. 343). The determination of the parallax of
stars had been attempted over and over again from the time of
Tycho Brahe down, but without success until, in 1838, Bessel
at last demonstrated and measured the parallax of 61 Cygni ;
and the next year Henderson, of the Cape of Good Hope,
STELLAR PARALLAX 395
determined that of Alpha Centauri. The operation of measur-
ing the parallax of a star is, on the whole, the most delicate
in the whole range of practical Astronomy. Two methods have
been used so far, known as the absolute and the differential.
442. The Absolute Method consists in making the most
scrupulously precise observations of the star's right ascension
and declination with the meridian circle at different times
through the course of an entire year, applying rigidly all
known corrections (for precession, aberration, proper motion,
etc.), and then examining the deduced positions. If the star
is without parallax, these positions will all agree. If the star
has a sensible parallax, they will show, on the other hand,
when plotted on a chart, an apparent annual orbital motion of
the star in a little ellipse, the major axis of which is twice the
star's annual parallax, as can easily be shown.
Theoretically, the method is perfect ; practically, it seldom
gives satisfactory results, because the annual changes of tem-
perature and moisture disturb the instrument in such a way
that the instrumental errors intertwine themselves with the
parallax of a star in a manner that defies disentanglement.
No process of multiplying observations and taking averages
helps the matter very much, because the instrumental errors
are themselves periodic annually, just as is the parallax ; still,
in a few cases the method has proved successful, as in the
case of Alpha Centauri, above cited.
443. The Differential Method. This, the method which
has principally proved successful thus far, consists in meas-
uring the annual displacement of the star whose parallax we
are seeking, with respect to other small stars near it in appar-
ent position (i.e., within a few minutes of arc), but presumably
so far beyond as to have no sensible parallax of their own.
If, for instance, the observer notes the apparent place of an
object at no great distance from him with reference to the
trees on a distant hillside, and then moves a few feet one way
396 APPENDIX
or the other, he will see that the nearer object shifts its posi-
tion with reference to the trees. In the same way, on account
of the earth's orbital motion, those stars which are very near
the earth appear every year to shift slightly backwards and
forwards with respect to those that are far beyond them ; and
by measuring the amount of this shift it is possible to deduce
approximately the parallax and distance of the nearer stars.
We say approximately, because the shift thus measured is
not really the whole parallax of the nearer star, but only
the difference between that parallax and the parallax of the
remote objects with which it is compared ; so that observa-
tions, if accurately made, will always give us for the nearer
star a parallax too small, if anything, never too large ; and,
as a consequence, the distance of the nearer star determined
in this way will come out a little too large, and never too
small.
444. The necessary measurements, if the comparison stars
are within a minute or two of arc, may be made with the filar
micrometer (Sec. 415) ; but if the distance exceeds a few min-
utes, we must resort to the " heliometer " (see General Astron-
omy, Art. 677) with which Bessel first succeeded ; or- we may
employ photography, which the late Professor Pritchard at
Oxford and others still more recently have done with con-
siderable success.
On the whole, the differential method, notwithstanding the
fundamental objection to it that it never gives us the entire
parallax of the star, is at present more trustworthy than the
other.
It is obviously necessary to choose for observation by either
method those stars that are presumably near us. The most
important indication of the nearness of a star is a large proper
motion; brightness, also, is of course confirmatory. Still,
neither of these indications is certain. A star which happens
to be moving directly towards or from us shows no proper
STELLAR PARALLAX 397
motion at all, however near it may be ; and the faint stars
are so very much more numerous than the brighter ones that
among their millions it is quite likely that we shall ultimately
find individuals which are even nearer than Alpha Centauri.
445. Spectroscopic Method. In time it will be possible to
determine the distance of certain binary stars by the help of
the spectroscope. The velocity of one or both of the two
stars "in the line of sight" can be measured by the spectro-
scope at different parts of the star's orbit, and this will enable
us to compute the size of the orbit in miles when we know its
period and its inclination to the line of sight ; at the same
time the micrometer measures will give its angular dimen-
sions, and from these data the distance can be found. It will
probably be many years, however, before many results can
be obtained in this way, because the periods of most of the
binaries are very long.
Wright, of the Lick Observatory, tested the method in
1905 upon Alpha Centauri, using the spectroscopic observa-
tions of the star made by him in South America. He obtained
a parallax practically identical with that deduced from the
older methods.
There are also several indirect methods of finding the dis-
tances of stars. One of these is especially important because
it may be applied to those very far away. It has been found
that there is a definite relation between the intensity of certain
lines in the spectrum of a star and its so-called " absolute
magnitude." (By this we mean its magnitude if it were at a
certain standard distance from the earth.) Knowing the bright-
ness of the star as we really see it, and what its brightness
would be if it were at a given distance, we can find its actual
distance from us.
SUGGESTIVE QUESTIONS
FOR USE IN REVIEWS
To many of these questions direct answers will not be
found in the book ; but the principles upon which the answers
depend have been given and the student will have to use his
own thinking in order to make the proper application.
1. What point in the celestial sphere has both its right ascen-
sion and declination zero?
2. What angle does the (celestial) equator make with the hori-
zon at this place ?
3. Name the (fourteen) principal points in the celestial sphere
(zenith, etc.).
4. What important circles in the heavens have no correlatives
on the surface of the earth ?
5. What constellation of the zodiac rises at sunset to-day, and
which one is then on the meridian ? (Use the star-maps.)
6. If Vega comes to the meridian at 8 o'clock to-night, at what
time (approximately) will it transit eight days hence ?
7. What bright stars can I observe on the meridian between
4 and 5 P.M., in the middle of August ? (See star -maps.)
8. At what time of the year will Sirius be on the meridian at
midnight ?
9. The declination of Vega is 38 4 1/; does it pass the meridian
north of your zenith, or south of it?
10. What are the right ascension and declination of the north
pole of the ecliptic ?
11. What are the longitude and latitude (celestial) of the north
celestial pole (the one near the Pole-star) ?
12. Can the sun ever be directly overhead where you live ? If
not, why not ?
13. What is the zenith distance of the sun at noon on June 22
in New York City (lat. 40 42') ?
14. What are the greatest and least angles made at New York
by the ecliptic with the horizon at their point of intersection ? Why
does the angle vary ?
SUGGESTIVE QUESTIONS 399
15. If the obliquity of the ecliptic were 30, how wide would the
temperate zone be ? How wide if the obliquity were 50 ? What
must the obliquity be to make the two temperate zones each as wide
as the torrid zone ?
16. Does the equinox always occur on the same days of March and
September ? If not, why not ; and how much can the date vary ?
17. Was the sun's declination at noon on March 10, 1900, pre-
cisely the same as on the same date in 1903?
18. In what season of the year is New Year's Day in Chili ?
19. When the sun is in the constellation Taurus, in what sign of
the zodiac is he ?
20. In what constellation is the sun when he is vertically over the
tropic of Cancer ? Near what star ? (See star-map.)
21. When are day and night most unequal ?
22. In what part of the earth are the days longest on March 20 ?
On June 20 ? On December 20 ?
23. Why is it warmest in the United States when the earth is
farthest from the sun ?
24. What was the Russian date corresponding to Feb. 28, 1900,
of our calendar ? To May 28 ?
25. Why are the intervals from sunrise to noon and from noon to
sunset usually unequal as given in the almanac ? (For example, see
Feb. 20 and Nov. 20.)
26. If the earth were to shrink to half its present diameter, what
would be its mean density ?
27. Is it absolutely necessary, as often stated, to know the diam-
eter of the earth in order to find the distance of the sun from the
earth ?
28. How will a projectile fired horizontally on .the earth deviate
from the line it would follow if the earth did not rotate on its axis?
29. If the earth were to contract in diameter, how would the
weight of bodies on its surface be affected ?
30. What keeps up the speed of the earth in its motion around
the sun ?
31. Why is the sidereal month shorter than the synodic ?
32. Does the moon rise every day of the month ?
33. If the moon rises at H h 45 m Tuesday night, when will it rise
next?
34. How many times does the moon turn on its axis in a
year ?
35. What determines the direction of the horns of the moon?
36. Does the earth rise and set for an observer on the moon ? If
so, at what intervals ?
37. How do we know that the moon is not self-luminous ?
38. How do we know that there is no water on the moon?
400 APPENDIX
39. How much information does the spectroscope give us about
the moon ?
40. What conditions must concur to produce a lunar eclipse ?
41. Can an eclipse of the moon occur in the daytime ?
42. Why can there not be an annular eclipse of the moon ?
43. Which are most frequent at New York, solar eclipses or lunar ?
44. Can an occultation of Venus by the moon occur during a"
lunar eclipse ? Would an occultation of Jupiter be possible under
the same circumstances?
45. Which of the heavenly bodies are not self-luminous?
46. When is a planet an evening star ?
47. What planets have synodic periods longer than their sidereal
periods ?
48. When a planet is at its least distance from the earth, what is
its apparent motion in right ascension ?
49. A planet is seen 120 distant from the sun; is it an inferior
or a superior planet ?
50. Can there be a transit of Mars across the sun's disk ?
51. When Jupiter is visible in the evening, do the shadows of the
satellites precede or follow the satellites themselves as they cross the
planet's disk?
52. What would be the length of the month if the moon were
four times as far away as now ? (Apply Kepler's third law.)
53. What is the distance from the sun of an asteroid which has a
period of eight years,? (Kepler's third law.)
54. Upon what circumstances does the apparent length of a
comet's tail depend ?
55. How can the distance of a meteor from the observer, and its
height above the earth, be determined ?
56. What heavenly bodies are not included in the solar system?
57. How do we know that stars are suns? How much is meant
by the assertion that they are ?
58. Suppose that in attempting to measure the parallax of a bright
star by the differential method (Sec. 443) it should turn out that the
small star taken as the point to measure from, and supposed to be far
beyond the bright one, should really prove to be nearer. How would
the measures show the fact ?
59. If Alpha Centauri were to travel straight towards the sun
with a uniform velocity equal to that of the earth in its orbit, how
long would the journey take, on the assumption that the star's parallax
isO".75?
60. If Altair were ten times as distant from us, what would be
its apparent " magnitude " ? What, if it were a thousand times as
remote ? (See Sees. 346, 347 ; and remember that the apparent
brightness varies inversely with the square of the distance.)
TABLES OF ASTRONOMICAL DATA
TABLE I ASTRONOMICAL CONSTANTS
TIME CONSTANTS
The sidereal day = 23 h 56 m 4 8 .090 of mean solar time.
The mean solar day = 24 h 3 m 56 8 .56 of sidereal time.
To reduce a time-interval expressed in units of mean solar time to
units of sidereal time, multiply by 1.00273791 ; log. of 0.00273791
= [7.4374191].
To reduce a time-interval expressed in units of sidereal time to
units of mean solar time, multiply by 0.99726957 = (1 - 0.00273043);
log. 0.00273043 = [7.4362316].
Tropical year (Leverrier, reduced to 1900) . 365 d 5 h 48 m 45 8 .51.
Sidereal year " . 365 6 9-8.97.
Anomalistic year 365 6 13 48 .09.
Mean synodical month (new moon to new) . 29 d 12 h 44 m 2 8 .864.
Sidereal month . . . . . : ... 27 7 43 11 .545.
Tropical month (equinox to equinox) . . 27 7 43 4 .68.
Anomalistic month (perigee to perigee) . 27 13 18 37 .44.
Nodical month (node to node) . . . 27 5 5 35 .81.
Obliquity of the ecliptic (Newcomb),
23 27' 8".26 - 0".468 (t - 1900).
Constant of precession (Newcomb),
50".248 + 0.000222 (t - 1900).
Constant of nutation (Peters), 9".223.
Constant of aberration (Nyren), 20".492 ; (Chandler), 20".521.
Equatorial semi-diameter of the earth (Clarke's spheroid of 1878),
20,926202 feet = 6,378190 meters = 3963.296 miles.
Polar semi-diameter,
'20,854895 feet = 6,356456 meters = 3949.790 miles.
Ellipticity, or polar compression (Clarke), 293 \ 46 ; (Harkness),
401
402
APPENDIX
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is
C^l O iO
'
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2222
I
ll
igll
ASTRONOMICAL DATA
403
8S 88
S
If
OOOOOOO^rHJO rH OT
rH rH rH rH rH CO CO O WO
UJ rH O 10 rH * IN O
f. t~ to oo co re o
rH rH CO t> O
t^ o; 50 ec o IN o rH i-< IN iq *
10 i ^' ^ d a & ^ 53 s; a *
t-.eooorHiO'-ics^ ot-?ot-
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1 w 3 I
1 1 i i -
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I
- w
IP
I s
ie
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rH (N rH <N CO * IQ
3 -s 3 s *
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Itlllil-lifle
W-*lOOt-000> rHINcO-*
404
APPENDIX
TABLE IV THE PRINCIPAL VARIABLE STARS
A selection from S. C. Chandler's catalogue of variable stars, containing such as,
at the maximum, are easily visible to the naked eye, have a range of variation
exceeding half a magnitude, and can be seen in the United States.
No.
Name
Place, 1900
Range of
Variation
Period (days)
Remarks
a
S
1
2
3
R Andromedse
o Ceti . . t.
p Persei . .
18.8
2 14.3
2 58.7
+ 38 1'
- 3 26
+ 38 27
5.6tol3
1.7 to 9.5
3.4 to 4.2
410.7
331.6
33?
(Mira. Varia-
{ tions in length
( of period
4
5
6
ft Persei . .
X Tauri . . .
e Aurigae . .
3 1.6
3 55.1
454.8
+ 40 34
+ 12 12
+ 43 41
2.3 to 3.5
3.4 to 4.2
3 to 4.5
2* 20h 48> 55S.43
3d 22 1 * 52 12*
Irregular
( Algol. Period
( now shortening
( Algol type, but
\ irregular
7
a Orionis . .
549.7
+ 7 23
0.7 to 1.5
Irregular
8
>j Geminorum
6 8.8
+ 22 32
3.2 to 4.2
231.4
9
Geminorum
658.2
+ 20 43
3.7 to 4.5
IQd 3h 41m 3QS.6
10
R Canis Maj. .
7 14.9
-16 12
5.9 to 6.7
Id 3h i5m 46s
Algol type
11
R Leonis . .
9 42.2
+ 11 54
5.2 to 10
312.8
12
UHydrae . .
10 32.6
-12 52
4.5 to 6.3
194.65
13
RHydrae . .
13 24.2
22 46
3.5 to 5.5
425.15
Period short'ing
14
8 Librae . .
14 55.6
-87
5.0 to 6.2
24 7h 51m 22.8
Algol type
15
R Coronae . .
15 44.4
+ 28 28
5.8tol3
Irregular
16
RSerpentis .
15 46.1
+ 15 26
5. 6 to 13
357.0
17
a Herculis
17 10.1
+ 14 30
3.1 to 3.9
Two or three mon
the, but very irreg.
18
U Ophiuchi .
17 11.5
+ 1 19
6.0 to 6.7
20> 7> 42^.56
19
XSagittarii .
17 41.3
-27 48
4 to 6
7d 0^ 17 m 57"
20
WSagittarii .
1758.6
-29 35
5 to 6.5
7 d 14h 16m 1 3 3
21
22
23
R Scuti . . .
Lyrae . . .
X Cygni . .
18 42.1
18 46.4
19 46.7
- 5 49
+ 33 15
+ 32 40
4.7 to 9
3.4 to 4.5
4.0 to 13.5
71.10
12* 21* 47> 23'. 72
406.045
(Secondary mini-
j mum about mid-
Period length'ng
24
ij Aquilae . .
19 47.4
+ 45
3.5 to 4.7
7d 4h Urn 593
25
S Sagittae . .
19 51.4
+ 16 22
5. 6 to 6.4
gd gh urn 48s.5
26
T Vulpeculae .
2047.2
+ 27 52
5.5 to 6.5
4* 10" 27 50.4
27
TCephei . .
21 8.2
+ 68 5
5.6 to 9.9
387
28
/u. Cephei . .
21 40.4
+ 58 19
4 to 5
430?
29
6 Cephei . .
22 25.4
+ 57 54
3.7 to 4.9
5d g* 47- 39.3
30
/3 Pegasi . .
2258.9
+ 27 32
2.2 to 2.7
Irregular
31
R Cassiopeiae .
2353.3
+ 50 50
4.8 to 12
429.5
ASTRONOMICAL DATA
405
TABLE V PROPER MOTIONS AND PARALLAXES
(KAPTEYN, 1901)
No.
Name
Mag.
Proper
Motion
Annual
Parallax
Distance
(light-years)
1
a Centauri
0.7
3" 67
0" 76
4 3
2
LI 21158
75
4 75
047
69
3
61 Cveni
6.1
5 16
041
80
4
Sirius
1.4
1 31
038
8 6
5
4 9
16
032
10 2
6
7
C. Z.,V.,243
Procyon
8.5
7
8.70
1 25
0.32?
31
10.2
10 5
8
9
Groombridge, 34 ....
Lacaille 9352
7.9
7.1
2.80
7 00
0.30
29
10.9
11 1
10
e Indi . ...
4.8
4 68
028
11 6
11
12
Arg.-Oeltzen, 17415 . . .
LI. 21258
9.0
8.5
1.27
440
0.25
0.24
13.1
13 6
13
14
15
a Aquilse (Altair) ....
10 Ursae Major is ....
>j Cassiopeiae
1.0
4.2
3 8
0.65
0.50
1 20
0.24
0.20
0.19
13.6
16.3
17 2
16
17
Arg.-Oeltzen, 10603 . . .
e Eridani .... . .
7.0
4.4
1.43
3 03
0.18
0.16
18.1
204
18
a Lyra? (Vega) .....
0.4
036
0.15
21.7
19
Groombridge, 1830 . . . .
6.6
7.05
0.15?
21.7
20
Polaris
2 1
0" 045
0".074
44
The above contains with a single intentional exception, one interpolation (No. 6),
and the addition of Polaris, all the stars on Kapteyn's list having parallaxes exceed-
ing 0".14. There are about as many more on his list with parallaxes ranging
between CK'.IO and 0".14.
THE GREEK ALPHABET
Letters
Name
Letters
Name
Letters
Name
A, a,
Alpha.
I, i,
Iota.
P, p, g,
Rho.
B, A
Beta.
K, K,
Kappa.
S, o-, s,
Sigma.
r,y,
Gamma.
A, A,
Lambda.
T,r,
Tau.
A, 8,
Delta.
M, /*,
Mu.
Y, v,
Upsilon
E, e,
Epsilon.
N,v,
Nu.
^, <#>,
Phi.
z, ,
Zeta.
E, |,
Xi.
X, x
Chi.
H, 77,
Eta.
O, o,
Omicron.
*, ^
Psi.
@, 0, t), Theta.
n, IT, 5>, Pi.
Omega.
MISCELLANEOUS SYMBOLS
A.R,., or a, Right Ascension.
Decl., or 8, Declination..
X, Longitude (Celestial).
ft Latitude (Celestial).
<, Latitude (Terrestrial).
a), Angle between line of nodes and line of apsides of an orbit ;
also, sometimes the obliquity of the ecliptic.
Conjunction.
Quadrature.
Opposition.
Ascending Node.
Descending Node.
406
INDEX
[All references, unless expressly stated to the contrary, are to sections,
not to pages.]
Aberration, of light, 435; determin-
ing distance of sun, 436.
Absolute scale of star magnitudes,
346.
Acceleration of rotation at the sun's
equator, 163.
Achromatic telescope, 406, 407.
ADAMS, J. C. (and LEVEBRIER), dis-
covery of Neptune, 283; orbit of
the Leonids, 327.
Aerolite, see Meteorite.
Age of the sunand planetary system,
193, 397-399.
Albedo, defined, 149, 235; of the
moon (Zollner), 149; of the planets
(Zollner), 242, 247, 253, 268, 276,
281, 285.
Algol, or Beta Persei, 40, 351, 358,
360.
Alphabet, the Greek, page 406.
Altitude, defined, 11 ; parallels of,
11; of the pole equals latitude,
80.
Andromeda, constellation of, 35;
nebula of, 377, 378; temporary
star in nebula, 355.
Andromedes, or Bielids, 312, 326.
Angular measurements, units of, 8.
Annual or heliocentric parallax, de-
fined, 343 ; methods of determin-
ing it for the stars by observation,
441-444.
Annular eclipses, 201; nebula in
Lyra, 377, 382.
Anomalistic year, 127.
Anomalous phenomena in comets,
308.
Apex of the sun's way, 342.
Aphelion defined, 120.
Apogee defined, 137.
Apparent motion of a planet, 225-
229 ; motion of the sun, 115-117 ;
solar time, 88. A
Apsides, line of, defined, 120, 137 ^
the moon's orbit, 137.
Aquarius, 78, 118.
Aquila, 71.
Arcs of meridian, measurement of,
105, 110.
Areas, equal, law of, 121, 137, 220.
Argo Navis, 51.
Ariel, a satellite of Uranus, 282.
Aries, first of, defined, 17 ; constel-
lation of, 38, 118.
Asteroids, or minor planets, 260-263.
Astronomical constants, table of,
Table I, page 401 ; day, beginning
of, 90; symbols, page 40(5; unit,
see Distance of the sun.
Astronomy, utility of, 1.
Atmosphere of the moon, 148; of
Mars, 253; of Mercury, 242; of
Venus, 248.
Attraction of gravitation, its law,
221, 222.
407
408
LESSONS IN ASTRONOMY
Auriga, 41.
Axis of the earth, 13, 109 ; motions
of, 109.
Azimuth denned, 11.
BARNARD, E. E., measures of diam-
eters of planets, 262, 267, 275, 285 ;
seasonal changes on Mars, 256;
discovery of fifth satellite of Ju-
piter, 272; of comet by photog-
raphy, 314* ; photograph of Swift's
comet, 314*.
BAYER, J., his system of lettering
the stars, 24.
Beginning of the century, 130; of
the day, 90, 98.
BESSEL, F. W., dark stars, 350, 360 ;
first measures stellar parallax,
441,444.
Bethlehem, the star of, 355.
BIELA'S comet, 311, 312.
Bielids, or Andromedes, 312, 324, 328.
Binarystars, 368-371 ; spectroscopic,
373, 374.
Bissextile year, 129.
BODE, J. E., his law of planetary
distances, 219.
BOND, W. C., discovery of the
"gauze ring" of Saturn, 277;
discovery of Hyperion, 280.
Bootes, 59.
BOYS, C. V., determination of the
constant of gravitation and of the
density of the earth, 113.
BREDICHIN, TH., his theory of
comets' tails, 307.
Brightness, of comets, 291; of me-
teors, 318 ; of stars, and causes of
difference, 345-350.
BROOKS, W., his comets, 290, 299.
C2ESAR, JULIUS, reformation of the
calendar, 129.
Calcium, in the sun, 176 ; in f aculae,
165; in chromosphere and prom-
inences, 181, 182*.
Calendar, the, 128-130.
Calory, the, defined, 187.
Camelopardalis, 31.
CAMPBELL, W. W., spectrum of
Mars, 253 ; radial motion of stars,
341 ; spectra of nebulous stars, 380.
Canals of Mars, 256.
Cancer, 52, 118.
Canes Venatici, 58.
Canis Major, 49.
Canis Minor, 48.
Capricornus, 73, 118.
Capture theory of comets, 298.
Cardinal points defined, 16.
CARRINGTON, R., discovery of the
peculiar law of the sun's rotation,
163.
CASSINI, J. D., discovers division in
Saturn's ring, 277.
Cassiopeia, 28; temporary star in,
355.
Catalogues of stars, 335.
Celestial globe, described, 400, 401 ;
sphere, infinite, 6.
Centaurus, 62.
Centrifugal force due to earth's
rotation, 111.
Cepheus, 29.
Ceres, the first of the asteroids,
260, 262.
Cetus, 39.
CHANDLER, S. C., variation of lati-
tude, 109 ; investigation of Brooks'
comet, 1889-V, 299 ; his catalogue
of variable stars, 361.
Changes, gradual, in the brightness
of stars, 353; on the surface of
the moon, 155.
CHARLOIS, M., discoverer of aster-
oids by photography, 260.
Chemical constitution of the sun,
175, 176.
INDEX
409
Chromosphere of the sun, 180, 194 ;
and prominences made visible by
the spectroscope, 182; photog-
raphy of, 182*.
Chronograph, the, 417.
Chronometer, the, 417; longitude
by, 96, 427.
Circle, meridian, the, 81, 99, 418.
Circles, hour, defined, 15.
Circumpolar stars, latitude by, 81.
Civil day and astronomical day, 90.
CLARK, ALVAN, AND SONS, makers
of great telescopes, 412.
CLARK, A. G., discovers companion
of Sirius, 369.
Classification of the planets, Hum-
boldt, 217; of stellar spectra,
Secchi, 363; of variable stars, 352.
Clock, the astronomical, 417; its
rate and error, 92, 93, 417.
Clusters of stars, 361, 376.
Columba, 45.
Colures defined, 117.
Coma Berenices, 57.
Comet, Biela's, 311, 312; Donati's,
289; Encke's, 293, 311; Lexell-
Brooks, 299; Halley's, 293; of
1882, 313, 314.
Comets, anomalous phenomena
shown by, 308; attendant com-
panions, 314 ; brightness and visi-
bility, 291; capture theory of
their origin, 298 ; central stripe in
tail, 308 ; connection with meteors,
327-329 ; constitution of, 300 ; dan-
ger from, 310; density of, 303;
designation and nomenclature,
290 ; dimensions of, 301 ; elliptic,
293, 297 ; envelopes in head, 305 ;
families of, 297 ; formation of the
tail, 306; their light and spectra,
304; mass of, 302; nature of,
309; number of, 289; orbits of,
292, 293; periodic, their origin,
297, 298; photography of, 314*;
sheath of comet of 1882, 313 ; tails
or trains, 300, 306-308; visitors to
the solar system, 296.
Comet-groups, 294.
Conic sections, the, 440.
Conjunction, defined, 132, 227.
Constant, solar, defined and dis-
cussed, 187; of the equation of
light, 432 ; of aberration, 435.
Constellations, the, 4, 333. (For de-
tailed description, see Chap. II.)
Constitution of comets, 300 ; of the
sun, 194.
Contraction of a comet nearing the
sun, 301; of the sun, Helmholtz's
theory, 192, 396, 397.
COPERNICUS, rotation of the earth,
106 ; his system, 230.
Corona Borealis, 60.
Corona, the solar, 183-185.
Coronium, hypothetical element of
the corona, 184.
Correction of error of a timepiece,
92, 427.
Corvus, 55.
Cosmogony, 389-396.
Crater, 55.
Cygnus, 68.
Dark stars, 350, 360.
DARWIN, G. H., motion of the tides,
211 ; tidal evolution, 393 ; demon-
strates that a meteoric swarm
behaves like a gaseous nebula,
394.
Day, beginning of, 98; civil and
astronomical, 90.
Declination, defined, 14; determina-
tion of, 99, 100 ; parallels of, 14.
Degrees of latitude, length of, 110.
Deimos, a satellite of Mars, 258.
DE L'ISLE, J., his method of observ-
ing a transit of Venus, 437, 438.
Delphinus, 74.
410
LESSONS IN ASTRONOMY
Density, of comets, 303; of the
earth, 113; of the moon, 143; of
the sun, 161.
Designation and nomenclature of
comets, 290 ; of the stars, 24, 334 ;
of variable stars, 361.
DESLANDRES, H., photography of
solar prominences, 182*.
Diameter of a planet, how deter-
mined, 232.
Difference of brightness in stars, its
causes, 350.
Diffraction, telescopic, 408.
Diffraction grating, the, 171, note.
Dione, a satellite of Saturn, 280.
Disk, spurious, of a star, 408.
Displacement of spectrum lines by
motion in line of sight, 179, 341,
373.
Distance, of a body as depending on
its parallax, 140; of the moon,
141; of the nebulae, 382; of the
planets from the sun, Table II,
page 402; of the stars, 343, 441-
444; of the sun, by the equation
of light, 434 ; of the sun, by aber-
ration of light, 436; of the sun,
by its parallax, 437.
Distribution of the nebulas, 382 ; of
the stars in the heavens, 384 ; of
sun-spots, 169.
Diurnal or geocentric parallax de-
nned, 139 ; rotation of the heavens,
12.
DOPPLER, C., his principle, 179,
341, 373.
Double stars, 366, 367 ; optical and
physical, distinguished, 367.
Draco, 30.
DRAPER, H., photograph of the
nebula of Orion, 378 ; photographs
of star spectra, 364.
Duration of solar eclipses, 203 ; prob-
able, of the solar system, 193,
397-399.
E
Earth, the, astronomical facts re-
lating to it, 102 ; its density, 113 ;
dimensions of, 105, 110, Table I.
page 401 ; ellipticity or oblateness
determined, 110; its interior con-
stitution, 114; mass, 113; orbital
motion of, 115-122, 428; its orbit,
changes in, 122; its rotation, in-
variability of, 108; its rotation,
proofs of, 107; shadow of, its
dimensions, 196 ; surface area and
volume, 112 ; velocity in its orbit,
158.
Earth-shine on the moon* 147.
Ebb defined, 210.
Eccentricity of the earth's orbit,
119; of an ellipse, defined, 119,
429.
Eclipses, frequency of, 206 ; of Jupi-
ter's satellites, 273; lunar, 197-
199; Oppolzer's canon of, 205;
number in a year, 206; recur-
rence of, 207 ; solar, duration of,
203; solar, phenomena of, 204;
solar, varieties of, total, annu-
lar, and partial, 201, 202.
Ecliptic, the, defined, 116 ; obliquity
of, 116 ; poles of, 117.
Elements, chemical, recognized in
the stars, 362; chemical, recog-
nized in the sun, 176; of the
planets' orbits, Table II, page
402.
Ellipse, the, defined and described,
429, 439, 440.
Elliptic comets, 292, 293.
Ellipticity, or oblateness of the
earth, 110.
Elongation defined, 132, 227-.
Enceladus, a satellite of Saturn,
280.
ENCKE, J. F., his comet, 293, 311.
Energy of the solar radiation, 188,
189.
INDEX
411
Envelopes in the head of a comet,
305, 314.
Equation of light, 431-433 ; of time,
89.
Equator, celestial or equinoctial,
denned, 14.
Equatorial acceleration of the sun's
surface rotation, 163.
Equatorial telescope, the, 414; its
use in determining the place of a
heavenly hody, 100.
Equinoctial, the, or celestial equa-
tor, defined, 14.
Equinox, vernal, defined, 17, 11G.
Equinoxes, precession of, 125, 126.
Equuleus, 75.
Eridanus, 44.
Eros, asteroid, 261, 262*.
Error or correction of a timepiece,
92, 93, 417.
Eruptive prominences on the sun,
182.
Establishment of a port, 210.
Eyepieces, telescopic, various forms
of, 409.
Faculae, solar, 165.
Families of comets, 297.
FAYE, H., depth of sun-spots, 168;
modification of the nebular hy-
pothesis, 393.
Filar micrometer, the, 415.
FIZEAU, H. L., the Doppler-Fizeau
principle, 179 ; measure of velocity
of light, 434.
Flood tide, 210.
Force, repulsive, of light, 306.
Form of the earth's orbit deter-
mined, 428.
FOUCAUI/T, L., his pendulum experi-
ment, 107.
FRAUNHOFER, J., lines in the solar
spectrum, 175, note.
Frequency of eclipses, 206.
Galaxy, the, 383.
GALILEO, G., his discovery of Ju-
piter's satellites, 272 ; discovery of
phases of Venus, 247 ; discovery
of Saturn's ring, 277 ; discovery of
sun-spots, 169 ; his telescope, 402.
GALLE, J. G., the first to see Nep-
tune, 283, note.
Gemination of the canals of Mars,
256.
Gemini, 47, 118.
Genesis of the planetary system,
390, 391.
Geocentric parallax, 139.
Gibbous phase defined, 146.
Globe, the celestial, described, 400,
401.
Grating, diffraction, 171, note.
Gravitation, 221, 222.
Gravity, at the moon's surface, 143 ;
at the pole and equator of the
earth, 111; at the sun's surface,
161 ; superficial, of a planet, how
determined, 233.
Greek alphabet, the, page 406.
Gregorian calendar, the, 130.
Groups, cometary, 294.
Grus, 79.
Gyroscope illustrating the cause of
the seasons, 123.
H and K lines of calcium, 165, 176,
181,182*.
Habitability of Mars, 259.
HALE, G. E., photographs of the
moon, 156 * ; of solar prominences,
182*.
HALL, A., discovery of the satellites
of Mars, 258; mass of Saturn's
rings, 277.
HALLE Y, E., discovers the proper
motion of stars, 339 ; his periodic
comet, 293, 314
412
LESSONS IN ASTRONOMY
HARDING, C., discovers Juno, 260.
Harmonic law, Kepler's, 220, 430.
Harvest and hunter's moons, the,
136.
Heat, of meteors, its explanation,
318; from the moon, 150; from
the stars, 348, note; of the sun,
its constancy, 191 ; of the sun, its
intensity, 190; of the sun, its
maintenance, 192; of the sun, its
quantity, 187, 189.
Heavenly hodies, defined and enu-
merated, 2; apparent place of, 7.
Heliocentric or annual parallax,
defined, 139, 343.
Helium, hypothetical element in
the sun, 181 ; its identification
as a terrestrial element in uran-
inite, 181 ; in temporary and vari-
able stars, 355, 356; in nebulae,
380.
HELMHOLTZ, H. VON, his theory of
the sun's heat, 192.
HENCKE, L., discovers Astraea, 260.
Hercules, 66.
HERSCHEL, SIR J., illustration of
the solar system, 238 ; his names
for the satellites of Saturn and
Uranus, 280, 282.
HERSCHEL, SIR W., discovery of
Uranus, 281 ; his great telescope,
412 ; relation between nebulae and
stars, 395.
HERSCHELS, the, their star-gauges,
384.
HIPPARCHUS, 120, 125, 335, 345.
Horizon, defined, rational and visi-
ble, 10.
Horizontal parallax, 139.
Hour-angle defined, 422.
Hour-circles defined, 15.
Hourly number of meteors, 321.
HUGGINS, SIR WILLIAM, observes
spectrum of Mars, 253; observes
spectrum of Mercury, 242; ob-
serves spectrum of nebulas, 380;
observes spectrum of stars, 362;
observes spectrum of temporary
star of 1866, 355; spectroscopic
measures of star motions, 341.
HUMBOLDT, A. VON, his classifica-
tion of the planets, 217.
Hunter's moon, the, 136.
HUYGHENS, CHR., his discovery of
Saturn's ring, 277; discovery of
Titan, 280; invention of the pen-
dulum clock, 417.
Hydra, 55.
Hyperbola, the, 439, 440.
Hyperion, a satellite of Saturn, 280.
lapetus, the remotest satellite of
Saturn, 280.
Identification of helium, 181 ; of the
orbits of certain comets and
meteors, 328.
Illuminating power of a telescope,
405.
Illumination of the moon's disk
during a lunar eclipse, 198.
Illustration of the proportions of
the solar system, 238.
Influence of the moon on the earth,
151; of sun-spots on the earth,
170.
Intensity of the sun's heat, 189-190 ;
of the sun's light, 186.
Intramercurian planets, 264.
Invariability of the earth's rotation.
108 ; of the length of the year and
distance from the sun, 122.
Iron in comets, 314 ; in meteorites,
316 ; in stars, 362 ; in the sun, 175.
Julian calendar, the, 129.
Juno, the third asteroid, 260, 262.
Jupiter (the planet), 266-271; his
belts, red spot, and other
INDEX
413
markings, 268, 271 ; his rotation,
270; his satellites, and their
eclipses, 272, 273.
Jupiter's family of comets, 297.
KANT, I., a proposer of the nebular
hypothesis, 391.
KEELEB, J. E., spectroscopic obser-
vation of the rings of Saturn, 279;
radial motion of stars, 341 ; types
of stellar spectra, 363; photo-
graphs of nebulae, 378; spectra
and motions of nebulae, 380.
KELVIN, LORD, formerly Sir Wil-
liam Thomson, 114, 318, 396.
KEPLER, J., his laws of planetary
motion, 121, 220, 430.
KIRCHHOFF, G. R., fundamental
principles of spectrum analysis,
173.
L
Lacerta, 76.
LAGRANGE, J. L., stability of the
solar system, 288*.
LANGLEY, S. P., his value of the
solar constant, 187.
LAPLACE, P. S., his capture theory
of comets, 298; his nebular hy-
pothesis, 392, 393; stability of
the solar system, 288*.
LASSELL, W., his discovery of Ariel
and Umbriel, 282; his discovery
of the satellite of Neptune, 286.
Latitude (celestial) defined, 20;
(terrestrial) defined, 80 ; length of
degrees, 110; methods of deter-
mining, 81, 424, 426; variations
of, 109.
Law, Bode's, 219 ; of the earth's or-
bital motion, 121 ; of gravitation,
221, 222.
Laws, Kepler's, 121, 220, 430.
Leap year, 129, 130.
Leo, 53, 118.
Leo Minor, 54.
Leonids, the, 324, 325, 326, 329.
Lepus, 45.
LEVERRIER, J. U. (and ADAMS),
discovery of Neptune, 283 ; on the
origin of the Leonids, 329.
Libra, 61, 118.
Librations of the moon, 145.
Lick observatory, telescope, 412;
various observations, 156*, 253,
256, 262, 267, 272, 275, 279, 314*,
341, 380.
Light, aberration of, 435, 436; of
comets, 291 ; equation of, the,
431, 432; of the moon, 149 ; of the
sun, its intensity, 186; repulsive
force of, 306; of the stars, 348-
350; velocity of, used to deter-
mine the distance of the sun,
434, 436 ; the zodiacal, 265.
Light-ratio of the scale of stellar
magnitude, 346.
Light-year, the, 344.
Local time, 97 ; time from altitude
of the sun, 427 ; time by transit-
instrument, 93, 416.
LOCKYER, SIR J. N., his meteoritic
hypothesis, 330, 394; on spectra
of nebulae, 380.
Longitude and latitude (celestial),
20; (terrestrial), defined, 94; (ter-
restrial), methods of determining,
95, 96, 427.
LOWELL, P., observations on Mer-
cury, 243; on Venus, 249; on
Mars, 256.
Lunar, see Moon.
Lupus, 62.
Lynx, 46.
Lyra, 67.
Magnesium, in the sun, 176; in the
stars, 362.
Magnifying power of a telescope,
404.
414
LESSONS IN ASTRONOMY
Magnitudes, star, 345-347 ; star, ab-
solute scale of, 346; star, and
telescopic power, 347.
Mars (the planet), 251-257; habita-
bility of, 259; map of the planet,
257 ; satellites, 258 ; Schiaparelli's
observations, etc., 256; telescopic
aspect, rotation, etc., 253,254.
Mass, definition, 113; of comets,
302 ; of earth, 113 ; of moon, 143 ;
of a planet, how determined, 233 ;
of shooting-stars, how estimated,
323; of the sun, 161.
Masses of binary stars, 371.
Mazapil, meteorite of, 326.
Mean and apparent places of stars,
336 ; and apparent solar time, 88-
89.
Mercury (the planet), 239-244 ; rota-
tion of, 243 ; transits of, 244.
Meridian (celestial), defined, 11, 15,
16; (terrestrial), arcs of, meas-
ured, 105, 110; circle, the, 81, 99,
418.
Meteoritic hypothesis (Lockyer) ,
330, 394 ; showers, 324-326.
Meteorite of Mazapil, 326.
Meteorites, 315 ; their constituents,
316 ; their fall, 315.
Meteors, ashes of, 323; connection
with comets, 327-329; heat and
light, 318; observation of, 317;
origin of, 319 ; path and velocity,
317.
MICHELSON, A. A., the velocity of
light, 436.
Micrometer, the, 415.
Midnight sun, the, 86.
Milky Way, the, 383.
Mimas, the inner satellite of Saturn,
280.
Mira Ceti, 356.
Missing and new stars, 353.
Monoceros, 50.
Month, sidereal and synodic, 133.
Moon, its albedo, 149; its atmos-
phere discussed, 148; changes on
its surface, 155 ; character of its
surface, 153 ; density, 143 ; diam-
eter, surface area, and bulk,
142 ; distance and parallax, 141 ;
eclipses of, 195-199; heat, 150; in-
fluence on the earth, 151 ; libra-
tions, 145 ; light and albedo, 149 ;
maps, 154, 156; mass, density,
and gravity, 143; motion (in gen-
eral), 132-135; nomenclature of
objects on surface, 156; perturba-
tions of, 134 ; phases, 146 ; photog-
raphy of, 156*; rotation, 144;
shadow of, 200 ; surface structure,
153; telescopic appearance, 152;
temperature, 150 ; water not pres-
ent, 148.
Motion, apparent diurnal, of the
heavens, 12, 13; of the moon,
132-134; of a planet, 225, 226,
229; of the sun, 115-117; in line
of sight, or radial motion, effect
on spectrum, 179, 341, 373, 574;
of the sun in space, 342.
Motions of stars, 338-341..,
Mountains, lunar, 153. 156.
Mounting of a telescope, 414.
Multiple stars, 375.
N
Nadir defined, 10.
Nadir point of meridian circle, 419.
Names of planets, 218 ; of satellites
of the planets, 258, 280, 282, also
Table III, page 403.
Neap tide, 210.
Nebulae, the, 377-382; changes in,
379; distance and distribution,
382; drawings and photographs
of, 378; spectra of, 380, 381.
Nebular hypothesis, the, 392, 393.
Negative eyepieces, 409.
Neptune (the planet), 283-287.
INDEX
415
NEWCOMB, S., on the age and dura-
tion of the system, 193; and
MICHELSON, the velocity of light,
436.
NEWTON, H. A., estimate of the daily |
number of meteors, 321; investi-
gation of the orbit of the Leonids,
327 ; nature of comets, 309.
NEWTON, SIR ISAAC, law of gravi-
tation, 221, 222.
Nodes of the moon's orbit and their
regression, 134; of the planetary
orbits, 224.
NORDENSKIOLD, A. E. VON, ashes
of meteors, 323.
Norma, 64.
Novse, or temporary stars, 355, 355*.
Number, of comets, 289 ; of eclipses
in a saros, 207; of eclipses in a
year, 206 ; of the stars, 332.
Oases, on Mars, 256.
Oberon, a satellite of Uranus, 282.
Oblateness or ellipticity of the
earth, defined, 110.
Oblique sphere, 85.
Obliquity of the ecliptic^ 116.
OLBERS, H. W. M., DR., discovers
Pallas and Vesta, 260.
Ophiuchus, 65.
OPPOLZER, TH. VON, his canon of
eclipses, 205.
Opposition denned, 132, 227 v
Orbit, of the earth, its form, etc.,
115, 122, 428; of the moon, 137;
parallactic, of a star, 442.
Orbital motion of the earth, proof
of, 115.
Orbits, of binary stars, 370; of
comets, 292 ; of planets, 223.
Origin of the asteroids, 263; of
meteors, 319 ; of periodic comets,
297.
Orion, 43; nebula of, 378.
PALISA, J., discovery of asteroids,
260.
Pallas, the second asteroid, 260.
Parabola, the, 439, 440.
Parallax, annual or heliocentric, of
the stars, 139, 343, 441-444 ; diur-
nal or geocentric, 139 ; solar, by
transit of Venus, de 1'Isle's
method, 437; of a nebula, 382;
of stars, 343; stellar, how deter-
mined, 441-444.
Parallaxes, stellar, table of, Table
V, page 405.
Parallel sphere, 84.
Pegasus, 77.
Pendulum used to determine earth's
form, 111; Foucault, 107.
Perigee defined, 137.
Perihelion defined, 120.
Periodicity of sun-spots, 169.
Periods of the planets, 218 ; sidereal
and synodic, 133, 162, 228.
Persei, Nova (1901), 355*.
Perseids, the, 324-326, 328, 329.
Perseus, 40.
Perturbations, lunar, 134; plane-
tary, 122, 288*.
PETERS, C. H. F., asteroid dis-
coveries, 260.
Phase of Mars, 253.
Phases, of Mercury and Venus, 242,
247 ; of the moon, 146 ; of Saturn's
rings, 278.
Phobos, a satellite of Mars, 258.
Phoabe, name assigned to the ninth
satellite of Saturn, 280.
Phoenix, 39.
Photographic power of eclipsed
moon, 198; star charts, 337; tele-
scopes, 337.
Photographs, of solar prominences,
182* ; applied to discovery of aster-
oids, 260 ; of comets, 314* ; of neb-
ulae, 378 ; of star spectra, 341, 364.
416
LESSONS IN ASTRONOMY
Photography, solar, 164.
Photometry, stellar, 348, 349.
Photosphere, the, 165, 194.
PIAZZI, G., discovers Ceres, 260.
PICKERING, E. C., determination
of rotation period of Eros by
photometric observations, 262*;
photographs of star spectra, 364,
373; photometric observations of
eclipses of Jupiter's satellites,
433; photometric measures of
stellar magnitudes, 346.
PICKERING, W. H., observations on
moon, 155 ; on Jupiter's satellites,
272; announces a ninth satellite
of Saturn,' 280.
Pisces, 36, 118.
Piscis Australis, 79.
Place, of .a heavenly body, defined,
7 ; of a heavenly body, how deter-
mined by observation, 99, 100 ; of
a ship, how determined, 426, 427.
Planet, albedo of, defined, 231, 235 ;
apparent motion of, 225-229; di-
ameter and volume, how meas-
ured, 232 ; mass and density, how
determined, 233 ; rotation on axis
determined, 234, 262*; satellite
system, how investigated,' 236;
superficial gravity determined,
233.
Planetary data, their relative accu-
racy, 237 ; system, its genesis, age,
and duration, 390-398 ; its stabil-
ity, 288*.
Planetesimal hypothesis, page 358.
Planets, Humboldt's classification,
217; list of, 218; intramercurian,
264; minor, 260-263; possibly
attending stars, 372; table of
elements, Table II, page 402;
table of names, symbols, etc.,
218.
Pleiades, the, 42, 376.
Pointers, the, 12, 26.
Pole (celestial), altitude of, equals
latitude, 80 ; defined, 13 ; effect of
precession, 126 ; (terrestrial), diur-
nal phenomena near it, 83 ; mo-
tion of, 109.
Pole-star, former, Alpha Draconis,
126 ; how recognized, 12.
Positive eyepieces, 409.
Precession of the equinoxes, 125,
126.
Pressure, its effect on wave-length
of light, 179.
Prime vertical, the, 11.
PROCTOR, R. A., sun-spots, 168.
Prominences, the solar, 181, 182,
194.
Proper motion of stars, 339.
Ptolemaic system, the, 230.
PTOLEMY, CLAUDIUS, 4, 230.
Quadrature defined, 132, 227.
Quiescent prominences, 182.
R
Radial motion, or motion in line of
sight, measured by Poppler's
principle, 179, 341, 373, 374.
Radiant, the, of a meteoric shower,
324.
Radius vector defined, 120.
RAMSAY, W., identification of he-
lium, 181.
Rate of a timepiece defined, 417.
Rectification of a globe, 401.
Recurrence of eclipses, 207.
Red spot of Jupiter, 271.
Reflecting telescope, the, 411, 413.
Refracting telescope, the, 403-407,
413.
Refraction, astronomical, 82.
Repulsive force of light, 306.
Reticle, the, 410, 416.
Retrograde and retrogression de-
fined, 226.
INDEX
417
Reversing layer, 177.
Rhea, a satellite of Saturn, 280.
Right ascension, defined, 18, 93 ; how
determined by observation, 99,
100.
Right sphere, the, 83.
Rings of Saturn, the, 277-279.
ROBERTS, I., photographs of neb-
ulje, 378.
ROSSE, LORD, heat of the moon, 150 ;
his great reflector, 412.
Rotation, apparent diurnal, of the
heavens, 12 ; definition of , 144; dis-
tinguished from revolution, 106,
note ; of earth, its effect on grav-
ity, 111 ; of earth, proofs of, 107 ;
of earth, variability of, 108; of
the moon, 144 ; of the sun, 162, 163.
Rotation period, of Eros, 262*; of
Jupiter, 270 ; of Mars, 254 ; of Mer-
cury, 243 ; of a planet, how ascer-
tained, 234, 262*; of Saturn, 275;
of Venus, 249.
Sagitta, 70.
Sagittarius, 72, 118.
Saros, the, 207.
Satellite system, how investigated,
236 ; systems, table of, Table III,
page 403.
Satellites, of Jupiter, 272 ; of Mars,
258 ; of Neptune, 286 ; of Saturn,
280; of Uranus, 282.
Saturn (the planet), 274-280.
Scale of stellar magnitudes, 346.
SCHIAPARELLI, G. V., identification
of cometary and meteoric orbits,
328; observations of Mars, 256;
rotation of Mercury and Venus,
243, 249.
SCHMIDT, J., his map of the moon,
156.
SCHWABE, S. H., discovers perio-
dicity of sun-spots, 169.
Scintillation of the stars, 365.
Scorpio, 63, 118.
Sea, position of ship at, how found,
426, 427.
Seasons, explanation of, 123-124.
SECCHI, A., on stellar spectra, 363;
on sun-spots, 168.
Secondary spectrum of achromatic
object-glass, 407.
SEE, T. J. J., measures of planets'
diameters, 267, 281 ; evolution of
binary systems, 370.
Serpens, 65.
Serpentarius, 65.
Sextant, the, 420, 421.
Shadow, of the earth, its dimensions,
196 ; of the moon, its dimensions,
200 ; of the moon, its velocity, 203.
Ship at sea, determination of its
position, 426, 427.
Shooting-stars (see also Meteors),
320-324 ; ashes of, 323 ; brightness
of, 323; elevation and path, 322;
mass of, 323; materials of, 323;
nature of, 320; number, daily
and hourly, 321; radiant, 324;
showers of, 324-326 ; spectrum o2,
323 ; velocity of, 322.
Showers, meteoric, 324-326.
Sidereal, and synodic months, 133 ;
and synodic periods of planets,
228 ; time defined, 91 ; year, 127.
Signs of the zodiac, 118; effect of
precession on them, 126.
Sirius, its companion, 369; light
compared with that of the sun,
349 ; its mass compared with that
of the sun, 370.
Solar, constant, the, 187 ; parallax,
158; time, mean and apparent,
88, 89.
Solstice defined, 117.
SOSIGENES and the calendar, 129.
Spectroscope, its principle and con-
struction, 171, 172; slitless, 364,
418
LESSONS IN ASTRONOMY
445; used to observe the solar
prominences, 182; used to meas-
ure motions in line of sight, 178,
179, 341, 373, 374.
Spectroscopic binaries, 360, 373, 374.
Spectrum, of the chromosphere and
prominences, 181; of comets in
general, 304; of the comet of
1882, 314; of meteors, 323; of
nebulae, 380, 381; of a shooting-
star, 323; of stars, 362-364; the
solar, 172-175 ; of the solar corona,
184; of a sun-spot, 178.
Spectrum analysis, fundamental
principles, 173.
Speculum of a reflecting telescope,
411.
Sphere, celestial, the, 6 ; doctrine of
the, 9-20.
SPOERER, G., peculiar law of sun-
spot latitude, 169.
Spots, solar, see Sun-spots.
Spring tide denned, 210.
Stability of the planetary system,
288*.
Standard time, 97.
Stars, binary, 368-371, 373, 374;
catalogues of, 335; charts of,
337; clusters of, 361, 376; dark,
350, 360 ; designation and nomen-
clature, 24, 334; dimensions of,
351, 360; distance of, 343, 344;
distribution of, 384 ; double, 366,
367; gravitation among them,
368, 371, 386; heat from them,
348, note; light of certain stars
compared with sunlight, 348, 349 ;
magnitudes and brightness, 345-
350 ; mean and apparent places of,
336 ; missing and new, 353 ; mo-
tions of, 338-342; multiple, 375;
new, 353, 355, 355*; number of,
332; parallax of, 343, 441-444,
Table V, page 405 ; shooting (see
Shooting-stars, also Meteors) ;
spectra of, 362-364; system of
the, 386; temporary, 355, 355*;
total amount of light from the,
348 ; twinkling of, 365 ; variable,
352-361, Table IV, page 404.
Star-gauges of the Herschels, 384.
Starlight, its total amount, 348.
Stellar parallaxes, table of, Table
V, page 405; photometry, 348,
349.
Structure of the stellar universe,
385.
STRUVE, H., mass, of Saturn's
ring, 277; measures of Neptune,
285.
Sun, age and duration of, 193,
397, 398 ; apparent motion in the
heavens, 115-117; its chromo-
sphere, 180 ; its constitution, 194 ;
its corona, 183-185; its density,
161 ; dimensions of, 160 ; distance
of, 158, 159, 434-438; elements
recognized in it, 176 ; faculae, 165 ;
gravity on its surface, 161 ; heat
of, quantity, intensity, and main-
tenance, 187-192; light of, its
intensity, 186 ; mass of, 161 ; mo-
tion in space, 342; parallax of,
159, 434-^38; prominences, 181,
182, 194; reversing layer, the,
177, 194; rotation of, 162, 163;
spectrum of, 172, 175; tempera-
ture of, 190; temperature dimin-
ishing, Lockyer, 396, note.
Sun-spots, appearance and nature,
166, 167 ; cause of, 168 ; distribu-
tion of, 169; Spoerer's law of
latitude, 169; influence on the
earth, 170; periodicity of, 169;
spectrum of, 178.
Superficial gravity of a planet, how
determined, 233.
Surface structure of the moon, 153,
154.
Swarms, meteoric, 324-329.
INDEX
419
Synodic and sidereal months, 133;
and sidereal periods of planets,
228.
System, planetary, its age and dura-
tion, 397-399; its genesis and
evolution, 390-393; its stability,
288* ; stellar, its probable nature,
386-388.
Syzygy denned, 132.
Tables : astronomical constants,
Table I, page 401; astronomical
symbols, page 406 ; 'binary stars,
orbits and masses, 370; Bode's
law, 219; constellations, show-
ing place in heavens, page 63;
Greek alphabet, page 406 ; moon,
names of principal objects, 156;
planet's elements, Table II, page
402; planets' names, distances,
etc., approximate, 218; satellite
systems, Table III, page 403;
stellar parallaxes and proper mo-
tions, Table V, page 405 ; variable
stars, Table IV, page 404.
Tails of comets, 300, 301, SOS-
SOS.
Taurus, 42.
Telegraph, longitude by, 95.
Telescope, achromatic, 406, 407;
eyepieces of, 409; general prin-
ciples of, 402 ; illuminating power,
405 ; magnifying power, 404 ; mag-
nitude of stars visible with a
given aperture, 347 ; mounting of,
414; reflecting, 411; simple re-
fracting, 403.
Telescopes, great, 412.
TEMPEL, E. W., his comet, 329, 330.
Temperature of the moon, 150; of
the sun, 190.
Temporary stars, 355, 355*.
Terminator, the, defined and de-
scribed, 146.
Tethys, a satellite of Saturn, 280.
THOMSON, SIB W. (now LORD
KELVIN), internal heat of the
earth, 396 ; heat of meteors, 318 ;
rigidity of the earth, 114.
Tidal wave, course of, 213.
Tides; definitions relating to, 210;
due mainly to moon's action, 209;
explanation of, 208, 209, 211, 212;
height of, 214; in rivers, 215;
motion of, 211^213.
Time, equation of, 89; local, from
sun's altitude, 427; methods of
determining, 92, 93, 427 ; relation
to hour-angle, 422; sidereal, de-
fined, 91; solar mean and ap-
parent, 88, 89; standard, defined,
97.
Titan, satellite of Saturn, 280.
Titania, satellite of Uranus, 282^
Total and annular eclipses, 197, 198,
201.
Trains of meteors, 315.
Transit or meridian circle, 81, 99,
418.
Transit-instrument, the, 92, 416.
Transits, of Mercury, 244 ; of Venus,
250.
Triangulum, 37.
Tropical year, the, 127.
Twinkling of the stars, 365.
TYCHO BRAKE, his temporary star
in Cassiopeia, 355.
Ultra-Neptunian planet, 288.
Umbriel, a satellite of Uranus,
282.
Universe, stellar, its structure, 385.
Uranography defined, 5.
Uranolite, see Meteorite.
Uranus (the planet), 281, 282.
Ursa Major, 26.
Ursa Minor, 27.
Utility of astronomy, 1.
420
LESSONS IN ASTKONOMY
Vanishing point, 6, note.
Variable stars, 352-361; in star
clusters, 361 ; table of, Table IV,
page 404.
Velocity, of earth in its orbit, 102,
158; of light, 436; of moon's
shadow, 203; of meteors and
shooting-stars, 317, 322; of star
motions, 340, 341.
Venus (the planet), 245-250; phases
of, 247 ; transits of, 250.
Vernal equinox, the, 17, 36, 116.
Vertical circles, 11.
VERY, F. W., measures of lunar
heat, 150.
Vesta, the fourth asteroid, 260.
Virgo, 56, 118.
Visible horizon defined, 10.
VOGEL, H. C., spectroscopic deter-
mination of star motions in the
line of sight, 341 ; spectroscopic
observations of Algol, Spica, and
Mizar, 360, 373, 374.
Volcanoes on the moon, 153.
Vulcan, the hypothetical intramer-
curian planet, 264.
Vulpecula, 69.
W
Water absent from the moon, 148.
Wave-length of a light-ray affected
by motion in the line of sight,
Doppler's principle, 179, 341;
affected by pressure, 179.
Wave, tidal, its course, 213.
Way, the sun's, 342.
Weather, the moon's influence on,
151.
Weight, loss of, between pole and
equator, 111.
WILSON and GRAY, temperature of
the sun, 190.
WOLF, MAX, introduces photo-
graphic method of discovering-
asteroids, 260.
WOLF, R., sun-spot curve, 169.
Year, the sidereal, tropical, and
anomalistic, 127, and Table I,
page 401.
Z
Zenith, the, defined, 10.
Zenith distance denned, 11.
Zero points of the meridian circle,
418, 419.
Zodiac, the, and its signs, 118; its
signs as affected by precession,
126.
Zodiacal light, the, 265.
ZOLLNER, J. C. F., determination
of planet's albedoes, 242, 247, 253,
268, 276, 281, 285; measurement
of moonlight, 149; measures of
light of stars, 348.
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THIS BOOK IS DUE ON THE LAST DATE
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1944
THE UNIVERSITY OF CALIFORNIA LIBRARY