A text-book of astronomy

UNIVERSITY OF CALIFORNIA

DEPARTMFNT OF

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TWENTIETH CENTURY TEXT-BOOKS

A TEXT-BOOK OF

ASTRONOMY

BY

GEORGE C. COMSTOCK

DIRECTOR OF THE WASHBURN OBSERVATORY AND

PROFESSOR OF ASTRONOMY IN THE

UNIVERSITY OF WISCONSIN

NEW YORK

D. APPLETON AND COMPANY
1901

COPYRIGHT, 1901
BY D. APPLETON AND COMPANY

EDUCATION

PREFACE

THE present work is not a compendium of astronomy
or an outline course of popular reading in that science. It
has been prepared as a text-book, and the author has pur-
posely omitted from it much matter interesting as well as
important to a complete view of the science, and has en-
deavored to concentrate attention upon those parts of the
subject that possess special educational value. From this
point of view matter which permits of experimental treat-
ment with simple apparatus is of peculiar value and is
given a prominence in the text beyond its just due in a
well-balanced exposition of the elements of astronomy,
while topics, such as the results of spectrum analysis,
which depend upon elaborate apparatus, are in the experi-
mental part of the work accorded much less space than
their intrinsic importance would justify.

Teacher and student are alike urged to magnify the
observational side of the subject and to strive to obtain in
their work the maximum degree of precision of which their
apparatus is capable. The instruments required are few
and easily obtained. With exception of a watch and a pro-
tractor, all of the apparatus needed may be built by any
one of fair mechanical talent who will follow the illustra-
tions and descriptions of the text. In order that proper
opportunity for observations may be had, the study should
be pursued during the milder portion of the year, between
April and November in northern latitudes, using clear

V

54. in 34

vi ASTRONOMY

weather for a direct study of the sky and cloudy days for
book work.

The illustrations contained in the present work are
worthy of as careful study as is the text, and many of
them are intended as an aid to experimental work and
accurate measurement, e. g., the star maps, the diagrams
of the planetary orbits, pictures of the moon, sun, etc. If
the school possesses a projection lantern, a set of astro-
nomical slides to be used in connection with it may be
made of great advantage, if the pictures are studied as an
auxiliary to Nature. Mere display and scenic effect are of
little value.

A brief bibliography of popular literature upon astron-
omy may be found at the end of this book, and it will be
well if at least a part of these works can be placed in the
school library and systematically used for supplementary
reading. An added interest may be given to the study if
one or more of the popular periodicals which deal with
astronomy are taken regularly by the school and kept
within easy reach of the students. From time to time
the teacher may well assign topics treated in these peri-
odicals to be read by individual students and presented
to the class in the form of an essay.

The author is under obligations to many of his profes-
sional friends who have contributed illustrative matter for
his text, and his thanks are in an especial manner due to
the editors of the Astrophysical Journal, Astronomy and
Astrophysics, and Popular Astronomy for permission to
reproduce here plates which have appeared in those peri-
odicals, and to Dr. Charles Boynton, who has kindly read
and criticised the proofs.

GEOKGE C. COMSTOCK.

UNIVERSITY OF WISCONSIN, February, 1901.

CONTENTS

CHAPTER PAGE

I. — DIFFERENT KINDS OF MEASUREMENT . .... . 1

The measurement of angles and time.

II. — THE STARS AND THEIR DIURNAL MOTION . . . 10

Finding the stars — Their apparent motion — Latitude — Direc-
tion of the meridian — Sidereal time — Definitions.

III. — FlXED AND WANDERING STARS . . . ... 29

Apparent motion of the sun, moon, and planets— Orbits of the
planets — How to find the planets.

IV. — CELESTIAL MECHANICS . . ..... . .46

Kepler's laws — Newton's laws of motion — The law of gravita-
tion— Orbital motion — Perturbations — Masses of the planets —
Discovery of Neptune — The tides.

V. — THE EARTH AS A PLANET . . • . .^ -. . . 70

Size — Mass — Precession — The warming of the earth — The
atmosphere — Twilight.

VI. — THE MEASUREMENT OF TIME '. -..". . . . . 86

Solar and sidereal time— Longitude— The calendar— Chro-
nology.

VII. — ECLIPSES . . . .".... .101

Their cause and nature — Eclipse limits — Eclipse maps — .Re-
currence and prediction of eclipses.

. — INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE 121

The clock — Radiant energy — Mirrors and lenses — The tele-
scope—Camera—Spectroscope—Principles of spectrum analysis.

IX.— THE MOON . . . . . . "... . . .150

Numerical data — Phases— Motion — Librations — Lunar topog-
raphy— Physical condition.

viii ASTRONOMY

CHAPTER PAGE

X.— THE SUN . _.-'••. . . -, . * .. . 178

Numerical data— Chemical nature — Temperature — Visible
and invisible parts — Photosphere — Spots — Faculae — Chromo-
sphere— Prominences — Corona — The sun-spot period — The sun's
rotation — Mechanical theory oi the sun.

XI. — THE PLANETS . ...... . . . 212

Arrangement of the solar system — Bode's law — Physical con-
dition of the planets — Jupiter — Saturn — Uranus and Neptune —
Venus — Mercury — Mars — The asteroids.

XII. — COMETS AND METEORS . . . " . . . . . 251

Motion, size, and mass of comets— Meteors — Their number
and distribution — Meteor showers — Relation of comets and me-
teors— Periodic comets — Comet families and groups — Comet tails
— Physical nature of comets — Collisions.

XIII.— THE FIXED STARS . . . i . . ... .291

Number of the stars — Brightness — Distance — Proper motion
— Motion in line of sight — Double stars — Variable stars— New
stars.

XIV. — STARS AND NEBULA . V *. ; . . . . 330

Stellar colors and spectra — Classes of stars— Clusters — Nebu-
lae— Their spectra and physical condition— The Milky Way —
Construction of the heavens — Extent of the stellar system.

XV. — GROWTH AND DECAY . . . . . . ... . . 358

Logical bases and limitations— Development of the sun— The
nebular hypothesis — Tidal friction — Roche's limit — Development
of the moon — Development of stars and nebulae — The future.

APPENDIX : . . . " . . v . . . ; . .'. . 383
INDEX 387

LIST OF LITHOGRAPHIC PLATES

FACING PAGE

I. — Northern Constellations . . .... . 124

II. — Equatorial Constellations . '. , _. . , . . 190

III.— Map of Mars . . ... : . . . V .. 246

IV.— The Pleiades . . ~ . ... . . . V . . 344

Protractor •:'.'-. In pocket at back of book

LIST OF FULL-PAGE ILLUSTRATIONS

FACING PAGE

A Total Solar Eclipse . . . .."-'/ / . Frontispiece

The Harvard College Observatory, Cambridge. Mass. . . . 24

Isaac Xewton . ... ... .. •* . . . • . 46

Galileo Galilei . . . ." ..',". . . . 52

The Lick Observatory, Mount Hamilton, Cal. . ... 60

The Yerkes Observatory, Williams Bay, Wis 100

The Moon, one day after First Quarter . . . ... 150

William Herschel . . . ..... . .234

Pierre Simon Laplace . . . 364

ASTRONOMY

CHAPTER I

DIFFERENT KINDS OF MEASUREMENT

1. Accurate measurement. — Accurate measurement is the
foundation of exact science, and at the very beginning of
his study in astronomy the student should learn something
of the astronomer's kind of measurement. He should prac-
tice measuring the stars with all possible care, and should
seek to attain the most accurate results of which his instru-
ments and apparatus are capable. The ordinary affairs of
life furnish abundant illustration of some of these measure-
ments, such as finding the length of a board in inches or
the weight of a load of coal in pounds and measurements
of both length and weight are of importance in astronomy,
but of far greater astronomical importance than these are
the measurement of angles and the measurement of time.
A kitchen clock or a cheap watch is usually thought of as
a machine to tell the " time of day," but it may be used to
time a horse or a bicycler upon a race course, and then it
becomes an instrument to measure the amount of time
required for covering the length of the course. Astrono-
mers use a clock in both of these ways — to tell the time at
which something happens or is done, and to measure the
amount of time required for something ; and in using a
clock for either purpose the student should learn to take
the time from it to the nearest second or better, if it has a

1

ASTRONOMY

seconds hand,' 6r' to1 'a small fraction of a minute, by esti-
mating the position of the minute hand between the min-
ute marks on the dial. Estimate the fraction in tenths of
a minute, not in halves or quarters.

EXERCISE 1. — If several watches are available, let one
person tap sharply upon a desk with a pencil and let each
of the others note the time by the minute hand to the
nearest tenth of a minute 'and record the observations as
follows :

2h. 44.5m. First tap. 2h. 46.4m. 1.9m.
2h. 44.9m. Second tap. 2h. 46.7m. 1.8m.
2h. 40.6m. Third tap. 2h. 48.6m. 2.0m.

The letters h and m are used as abbreviations for hour and
minute. The first and second columns of the table are the
record made by one student, and second and third the rec-
ord made by another. After all the observations have been
made and recorded they should be brought together and
compared by taking the differences between the times re-
corded for each tap, as is shown in the last column. This
difference shows how much faster one watch is than the
other, and the agreement or disagreement of these differ-
ences shows the degree of accuracy of the observations.
Keep up this practice until tenths of a minute can be esti-
mated with fair precision.

2. Angles and their use. — An angle is the amount of
opening or difference of direction between two lines that
cross each other. At twelve o'clock the hour and minute
hand of a watch point in the same direction and the angle
between them is zero. At one o'clock the minute hand is
again at XII, but the hour hand has moved to I, one
twelfth part of the circumference of the dial, and the angle
between the hands is one twelfth of a circumference. It is
customary to imagine the circumference of a dial to be cut
up into 360 equal parts — i. e., each minute space of an ordi-
nary dial to be subdivided into six equal parts, each of

DIFFERENT KINDS OF MEASUREMENT 3

which is called a degree, and the measurement of an angle
consists in finding how many of these degrees are included
in the opening between its sides. At one o'clock the angle
between the hands of a watch is thirty degrees, which is
usually written 30°, at three o'clock it is 90°, at six o'clock
180°, etc.

A watch may be used to measure angles. How? But
a more convenient instrument is the protractor, which is
shown in Fig. 1, applied to the angle ABC and showing
that A BC = 85° as near-
ly as the protractor scale
can be read.

The student should
have and use a protrac-
tor, such as is fur-
nished with this book,
for the numerous exer-
cises which are to follow.

EXEECISE 2. — Draw B A

neatly a triangle with FIG. I.-A protractor.

sides about 100 millimeters long, measure each of its an-
gles and take their sum. No matter what may be the
shape of the triangle, this sum should be very nearly 180°
— exactly 180° if the work were perfect — but perfection
can seldom be attained and one of the first lessons to
be learned in any science which deals with measurement
is, that however careful we may be in our work some
minute error will cling to it and our results can be only
approximately correct. This, however, should not be
taken as an excuse for careless work, but rather as a stim-
ulus to extra effort in order that the unavoidable errors
may be made as small as possible. In the present case
the measured angles may be improved a little by adding
(algebraically) to each of them one third of the amount by
which their sum falls short of 180°, as in the following
example :

4 ASTRONOMY

Measured angles. Correction. Corrected angles.

A 73^4 +0.1 73.°5

B 49.3 +0.1 49.4

C 57.0 +0.1 57.1

Sum 179.7 180.0

Defect +0.3

This process is in very common use among astronomers,
and is called " adjusting " the observations.

3. Triangles. — The instruments used by astronomers for
the measurement of angles are usually provided with a
telescope, which may be pointed at different objects, and
with a scale, like that of the protractor, to measure the
angle through which the telescope is turned in passing
from one object to another. In this way it is possible to
measure the angle between lines drawn from the instru-
ment to two distant ob-
jects, such as two church
steeples or the sun and
moon, and this is usually
called the angle between
the objects. By meas-
uring angles in this way
it is possible to deter-
mine the distance to an

inaccessible point, as shown in Fig. 2. A surveyor at A
desires to know the distance to C\ on the opposite side of a
river which he can not cross. He measures with a tape line
along his own side of the stream the distance A B — 100
yards and then, with a suitable instrument, measures the
angle at A between the points C and B, and the angle at
B between <?and A, finding BAC = 73.4°, A B C= 49.3°.
To determine the distance A C he draws upon paper a line
100 millimeters long, and marks the ends a and b ; with a
protractor he constructs at a the angle ~b a c = 73.4°, and at
b the anglr abc = 49.3°, and marks by c the point where

DIFFERENT KINDS OF MEASUREMENT 5

the two lines thus drawn meet. With the millimeter scale
he now measures the distance a c = 90.2 millimeters, which
determines the distance A C across the river to be 90.2
yards, since the triangle on paper has been made simi-
lar to the one across the river, and millimeters on the one
correspond to yards on the other. What is the proposition
of geometry upon which this depends? The measured
distance A B in the surveyor's problem is called a base line.
EXERCISE 3. — With a foot rule and a protractor meas-
ure a base line and the angles necessary to determine the
length of the schoolroom. After the length has been thus
found, measure it directly with the foot rule and compare

FIG. 3.— Finding the moon's distance from the earth.

the measured length with the one found from the angles.
If any part of the work has been carelessly done, the stu-
dent need not expect the results to agree.

In the same manner, by sighting at the moon from
widely different parts of the earth, as in Fig. 3, the moon's
distance from us is found to be about a quarter of a million
miles. What is the base line in this case ?

4. The horizon — altitudes. — In their observations astron-
omers and sailors make much use of the plane of the hori-
zon, and practically any flat and level surface, such as that
of a smooth pond, may be regarded as a part of this plane
and used as such. A very common observation relating to

6 ASTRONOMY

the plane of the horizon is called " taking the sun's alti-
tude," and consists in measuring the angle between the
sun's rays and the plane of the horizon upon which they
fall. This angle between a line and a plane appears slightly
different from the angle between two lines, but is really the
same thing, since it means the angle between the sun's rays
and a line drawn in the plane of the horizon toward the
point directly under the sun. Compare this with the defi-
nition given in the geographies, " The latitude of a point
on the earth's surface is its angular distance north or south
of the equator," and note that the latitude is the angle
between the plane of the equator and a line drawn from
the earth's center to the given point on its surface.

A convenient method of obtaining a part of the plane
of the horizon for use in observation is as follows : Place
a slate or a pane of glass upon a table in the sunshine.
Slightly moisten its whole surface and then pour a little
more water upon it near the center. If the water runs
toward one side, thrust the edge of a thin wooden wedge
under this side and block it up until the water shows no
tendency to run one way rather than another ; it is then
level and a part of the plane of the horizon. Get several
wedges ready before commencing the experiment. After
they have been properly placed, drive a pin or tack behind
each one so that it may not slip.

5. Taking the sun's altitude. EXERCISE 4. — Prepare a
piece of board 20 centimeters or more square, planed
smooth on one face and one edge. Drive a pin perpen-
dicularly into the face of the board, near the middle of the
planed edge. Set the board on edge on the horizon plane
and turn it edgewise toward the sun so that a shadow of
the pin is cast on the plane. Stick another pin into the
board, near its upper edge, so that its shadow shall fall
exactly upon the shadow of the first pin, and with a watch
or clock observe the time at which the two shadows coin-
cide. Without lifting the board from the plane, turn it

DIFFERENT KINDS OF MEASUREMENT 7

around so that the opposite edge is directed toward the sun
and set a third pin just as the second one was placed, and
again take the time. Remove the pins and draw fine pencil
lines, connecting the holes, as shown in Fig. 4, and with
the protractor measure the an-
gle thus marked. The student
who has studied elementary ge-
ometry should be able to dem-
onstrate that at the mean of the
two recorded times the sun's alti-
tude was equal to one half of the

angle measured in the figure. FlG- 4. -Taking the sun's

When the board is turned

edgewise toward the sun so that its shadow is as thin as
possible, rule a pencil line alongside it on the horizon plane.
The angle which this line makes with a line pointing due
south is called the sun's azimuth. When the sun is south,
its azimuth is zero ; when west, it is 90° ; when east,
270°, etc.

EXERCISE 5. — Let a number of different students take
the sun's altitude during both the morning and afternoon
session and note the time of each observation, to the near-
est minute. Verify the setting of the plane of the horizon
from time to time, to make sure that no change has occurred
in it.

6. Graphical representations. — Make a graph (drawing)
of all the observations, similar to Fig. 5, and find by bisect-
ing a set of chords g to #, e to e^ d to d, drawn parallel to
B B, the time at which the sun's altitude was greatest. In
Fig. 5 we see from the intersection of M M with B B that
this time was llh. 50m.

The method of graphs which is here introduced is of
great importance in physical science, and the student
should carefully observe in Fig. 5 that the line B B is a
scale of times, which may be made long or short, provided
only the intervals between consecutive hours 9 to 10, 10 to

ASTRONOMY

11, 11 to 12, etc., are equal. The distance of each little
circle from B B is taken proportional to the sun's altitude,
and may be upon any desired scale — e. g., a millimeter to
a degree — provided the same scale is used for all observa-

d ,-ff>— — -&-• — ~-^-.,d

ST.

'<£k

B 9 10 11 -trl.2 1 SB

FIG. 5. — A graph of the sun's altitude.

tions. Each circle is placed accurately over that part of
the base line which corresponds to the time at which the
altitude was taken. Square ruled paper is very convenient,
although not necessary, for such diagrams. It is especially
to be noted that from the few observations which are rep-
resented in the figure a smooth curve has been drawn
through the circles which represent the sun's altitude, and
this curve shows the altitude of the sun at every moment
between 9 A. M. and 3 P. M. In Fig. 5 the sun's altitude at
noon was 57°. What was it at half past two ?

7. Diameter of a distant object. — By sighting over a pro-
tractor, measure the angle between imaginary lines drawn
from it to the opposite sides of a window. Carry the pro-
tractor farther away from the window and repeat the ex-
periment, to see how much the angle changes. The angle
thus measured is called " the angle subtended " by the win-
dow at the place where the measurement was made. If
this place was squarely in front of the window we may
draw upon paper an angle equal to the measured one and
lay off from the vertex along its sides a distance propor-
tional to the distance of the window— e. g., a millimeter for

DIFFERENT KINDS OF MEASUREMENT 9

each centimeter of real distance. If a cross line be now
drawn connecting the points thus found, its length will be
proportional to the width of the window, and the width
may be read oil to scale, a centimeter for every millimeter
in the length of the cross line.

The astronomer who measures with an appropriate in-
strument the angle subtended by the moon may in an
entirely similar manner find the moon's diameter and has,
in fact, found it to be 2,163 miles. Can the same method
be used to find the diameter of the sun ? A planet ? The
earth ?

.

\J

CHAPTEE II

THE STARS AND THEIR DIURNAL MOTION

8. The stars. — From the very beginning of his study in
astronomy, and as frequently as possible, the student should
practice watching the stars by night, to become acquainted
with the constellations and their movements. As an intro-
duction to this study he may face toward the north, and
compare the stars which he sees in that part of the sky with
the map of the northern heavens, given on Plate I, oppo-
site page 124. Turn the map around, upside down if
necessary, until the stars upon it match the brighter ones
in the sky. Note how the stars are grouped in such con-
spicuous constellations as the Big Dipper (Ursa Major), the
Little Dipper (Ursa Minor), and Cassiopea. These three
constellations should be learned so that they can be recog-
nized at any time.

The names of the stars.— Facing the star map is a key
which contains the names of the more important constella-
tions and the names of the brighter stars in their constella-
tions. These names are for the most part a Greek letter
prefixed to the genitive case of the Latin name of the con-
stellation. (See the Greek alphabet printed at the end of
the book.)

9. Magnitudes of the stars. — Nearly nineteen centuries
ago St. Paul noted that " one star diff ereth from another
star in glory," and no more apt words can be found to mark
the difference of brightness which the stars present. Even
prior to St. Paul's day the ancient Greek astronomers had
divided the stars in respect of brightness into six groups,

10

THE STARS AND THEIR DIURNAL MOTION H

which the modern astronomers still use, calling each group
a magnitude. Thus a few of the brightest stars are said to
be of the first magnitude, the great mass of faint ones
which are just visible to the unaided eye are said to be of
the sixth magnitude, and intermediate degrees of brilliancy
are represented by the intermediate magnitudes, second,
third, fourth, and fifth. The student must not be misled
by the word magnitude. It has no reference to the size of
the stars, but only to their brightness, and on the star maps
at the beginning and end of this book the larger and smaller
circles by which the stars are represented indicate only the
brightness of the stars according to the system of magni-
tudes. Following the indications of these maps, the stu-
dent should, in learning the principal stars and constella-
tions, learn also to recognize how bright is a star of the/
second, fourth, or other magnitude.

10. Observing the stars. — Find on the map and in the
sky the stars a Ursae Minoris, a Ursae Majoris, ft Ursae Ma-
joris. What geometrical figure will fit on to these stars ?
In addition to its regular name, a Ursae Minoris is frequent-
ly called by the special name Polaris, or the pole star.
Why are the other two stars called " the Pointers " ? What
letter of the alphabet do the five bright stars in Cassiopea

EXERCISE 6. — Stand in such a position that Polaris is
just hidden behind the corner of a building or some other
vertical line, and mark upon the key map as accurately as
possible the position of this line with respect to the other
stars, showing which stars are to the right and which are
to the left of it. Kecord the time (date, hour, and minute)
at which this observation was made. An hour or two later
repeat the observation at the same place, draw the line and
note the time, and you will find that the line last drawn
upon the map does not agree with the first one. The stars
have changed their positions, and with respect to the verti-
cal line the Pointers are now in a different direction from

12 ASTRONOMY

Polaris. Measure with a protractor the angle between the
two lines drawn in the map, and use this angle and the
recorded times of the observation to find how many degrees
per hour this direction is changing. It should be about 15°
per hour. If the observation were repeated 12 hours after
the first recorded time, what would be the position of the
vertical line among the stars ? What would it be 24 hours
later ? A week later ? Kepeat the observation on the next
clear night, and allowing for the number of whole revolu-
tions made by the stars between the two dates, again deter-
mine from the time interval a more accurate value of the
rate at which the stars move.

The motion of the stars which the student has here de-
tected is called their u diurnal " motion. What is the sig-
nificance of the word diurnal ?

In the preceding paragraph there is introduced a method
of great importance in astronomical practice — i. e., determin-
ing something — in this case the rate per hour, from obser-
vations separated by a long interval of time, in order to get
a more accurate value than could be found from a short
interval. Why is it more accurate? To determine the
rate at which the planet Mars rotates about its axis, astron-
omers use observations separated by an interval of more
than 200 years, during which the planet made more than
75,000 revolutions upon its axis. If we were to write out
in algebraic form an equation for determining the length
of one revolution of Mars about its axis, the large number,
75,000, would appear in the equation as a divisor, and in
the final result would greatly reduce whatever errors existed
in the observations employed.

Kepeat Exercise 6 night after night, and note whether
the stars come back to the same position at the same hour
and minute every night.

11. The plumb-line apparatus. — This experiment, and
many others, may be conveniently and accurately made
with no other apparatus than a plumb line, and a device

THE STARS AND THEIR DIURNAL MOTION

13

for sighting past it. In Figs. 6 and 7 there is shown a
simple form of such apparatus, consisting essentially of a
board which rests in a horizontal position upon the points
of three screws that pass through it. This board carries

FIG. 6.

The plumb-line apparatus.

FIG. 7.

a small box, to one side of which is nailed in vertical posi-
tion another board 5 or 6 feet long to carry the plumb line.
This consists of a wire or fish line with any heavy weight —
e. g., a brick or flatiron — tied to its lower end and immersed
in a vessel of water placed inside the box, so as to check
any swinging motion of the weight. In the cover of the
box is a small hole through which the wire passes, and by
turning the screws in the baseboard the apparatus may be
readily leveled, so that the wire shall swing freely in the
center of the hole without touching the cover of the box.

14 ASTRONOMY

Guy wires, shown in the figure, are applied so as to stiffen
the whole apparatus. A board with a screw eye at each
end may be pivoted to the upright, as in Fig. 6, for measur-
ing altitudes ; or to the box, as in Fig. 7, for observing the
time at which a star in its diurnal motion passes through
the plane determined by the plumb line and the center of
the screw eye through which the observer looks.

The whole apparatus may be constructed by any person
of ordinary mechanical skill at a very small cost, and it or
something equivalent should be provided for every class be-
ginning observational astronomy. To use the apparatus for
the experiment of § 10, it should be leveled, and the board
with the screw eyes, attached as in Fig. 7, should be turned
until the observer, looking through the screw eye, sees
Polaris exactly behind the wire. Use a bicycle lamp to
illumine the wire by night. The apparatus is now adjusted,
and the observer has only to wait for the stars which he
desires to observe, and to note by his watch the time at
which they pass behind the wire. It will be seen that the
wire takes the place of the vertical edge of the building,
and that the board with the screw eyes is introduced solely
to keep the observer in the right place relative to the
wire.

12. A sidereal clock. — Clocks are sometimes so made and
regulated that they show always the same hour and minute
when the stars come back to the same place, and such a
timepiece is called a sidereal clock — i. e., a star-time clock.
Would such a clock gain or lose in comparison with an ordi-
nary watch ? Could an ordinary watch be turned into a
sidereal watch by moving the regulator ?

13. Photographing the stars.— EXERCISE 7. — For any stu-
dent who uses a camera. Upon some clear and moonless
night point the camera, properly focused, at Polaris, and
expose a plate for three or four hours. Upon developing
the plate you should find a series of circular trails such as
are shown in Fig. 8, only longer. Each one of these is pro-

THE STARS AND THEIR DIURNAL MOTION 15

duced by a star moving slowly over the plate, in conse-
quence of its changing position in the sky. The center
indicated by these curved trails is called the pole of the
heavens. It is that part of the sky toward which is pointed
the axis about which the earth rotates, and the motion of
the stars around the center is only an apparent motion due
to the rotation of the earth which daily carries the observer
and his camera around this axis while the stars stand still,
just as trees and fences and telegraph poles stand still,

FIG. 8.— Photographing the circumpolar star?.— BARNARD.

although to the passenger upon a railway train they appear
to be in rapid motion. So far as simple observations are
concerned, there is no method by which the pupil can tell
for himself that the motion of the stars is an apparent
rather than a real one, and, following the custom of astron-
omers, we shall habitually speak as if it were a real move-
ment of the stars. How long was the plate exposed in
photographing Fig. 8 ?

16 ASTRONOMY

14. Finding the stars, — On Plate I, opposite page 124,
the pole of the heavens is at the center of the map, near
Polaris, and the heavy trail near the center of Fig. 8 is
made by Polaris. See if you can identify from the map
any of the stars whose trails show in the photograph. The
brighter the star the bolder and heavier its trail.

Find from the map and locate in the sky the two bright
stars Capella and Vega, which are on opposite sides of
Polaris and nearly equidistant from it. Do these stars
share in the motion around the pole ? Are they visible on
every clear night, and all night ?

Observe other bright stars farther from Polaris than
are Vega and Capella and note their movement. Do they
move like the sun and moon ? Do they rise and set ?

In what part of the sky do the stars move most rapidly,
near the pole or far from it ?

How long does it take the fastest moving stars to make
the circuit of the sky and come back to the same place ?
How long does it take the slow stars ?

15. Rising and setting of the stars. — A study of the sky
along the lines indicated in these questions will show that
there is a considerable part of it surrounding the pole
whose stars are visible on every clear night. The same
star is sometimes high in the sky, sometimes low, some-
times to the east of the pole and at other times west of it,
but is always above the horizon. Such stars are said to
be circumpolar. A little farther from the pole each star,
when at the .lowest point of its circular path, dips for a
time below the horizon and is lost to view, and the farther
it is away from the pole the longer does it remain invisible,
until, in the case of stars 90° away from the pole, we find
them hidden below the horizon for twelve hours out of
every twenty-four (see Fig. 9). The sun is such a star,
and in its rising and setting acts precisely as does every
other star at a similar distance from the pole — only, as we
shall find later, each star keeps always at (nearly) the same

THE STARS AND THEIR DIURNAL MOTION 17

distance from the pole, while the sun in the course of a
year changes its distance from the pole very greatly, and
thus changes the amount of time it spends above and be-

FIG. 9. -Diurnal motion of the northern constellations.

low the horizon, producing in this way the long days of
summer and the short ones of winter.

How much time do stars which are more than 90° from
the pole spend above the horizon ?

We say in common speech that the sun rises in the
east, but this is strictly true only at the time when it is 90°
distant from the pole — i. e., in March and September. At
other seasons it rises north or south of east according as
its distance from the pole is less or greater than 90°, and
the same is true for the stars.

18 ASTRONOMY

16. The geography of the sky, — Find from a map the
latitude and longitude of your schoolhouse. Find on the
map the place whose latitude is 39° and longitude 77° west
of the meridian of Greenwich. Is there any other place in
the world which has the same latitude and longitude as
your schoolhouse ?

The places of the stars in the sky are located in exactly
the manner which is illustrated by these geographical
questions, only different names are used. Instead of lati-
tude the astronomer says declination, in place of longitude
he says right ascension, in place of meridian he says hour
circle, but he means by these new names the same ideas
that the geographer expresses by the old ones.

Imagine the earth swollen up until it fills the whole
sky ; the earth's equator would meet the sky along a line
(a great circle) everywhere 90° distant from the pole, and
this line is called the celestial equator. Trace its posi-
tion along the middle of the map opposite page 190 and
notice near what stars it runs. Every meridian of the
swollen earth would touch the sky along an hour circle —
i. e., a great circle passing through the pole and therefore
perpendicular to the equator. Xote that in the map one of
these hour circles is marked 0. It plays the same part in
measuring right ascensions as does the meridian of Green-
wich in measuring longitudes ; it is the beginning, from
which they are reckoned. Xote also, at the extreme left
end of the map, the four bright stars in the form of a
square, one side of which is parallel and close to the hour
circle, which is marked 0. This is familiarly called the
Great Square in Pegasus, and may be found high up in the
southern sky whenever the Big Dipper lies below the pole.
Why can it not be seen when Ursa Major is above the
pole?

Astronomers use the right ascensions of the stars not
only to tell in what part of the sky the star is placed, but
also in time reckonings, to regulate their sidereal clocks, and

THE STARS AND THEIR DIURNAL MOTION 19

with regard to this use they find it convenient to express
right ascension not in degrees but in hours, 24 of which
fill up the circuit of the sky and each of which is equal to
15° of arc, 24 X 15 = 360. The right ascension of Capella
is 5h. 9m. = 77.2°, but the student should accustom him-
self to using it in hours and minutes as given and not to
change it into degrees. He should also note that some

FIG. 10.— From a photograph of the Pleiades.

stars lie on the side of the celestial equator toward Polaris,
and others are on the opposite side, so that the astronomer
has to distinguish between north declinations and south
declinations, just as the geographer distinguishes between
north latitudes and south latitudes. This is done by the
use of the + and — signs, a 4- denoting that the star lies
north of the celestial equator — i. e., toward Polaris.

Find on Plate II, opposite page 190, the Pleiades

20 ASTRONOMY

(Pleades), E. A. = 3h. 42m., Dec. = + 23.8°. Why do
they not show on Plate I, opposite page 124? In what
direction are they from Polaris ? This is one of the
finest star clusters in the sky, but it needs a telescope to
bring out its richness. See how many stars you can count
in it with the naked eye, and afterward examine it with
an opera glass. Compare what you see with Fig. 10. Find
Antares, E. A. = 16h. 23m. Dec. = — 26.2°. How far is
it, in degrees, from the pole ? Is it visible in your sky ?
If so, what is its color ?

Find the E. A. and Dec. of a Ursse Majoris ; of j3 Ursae
Majoris ; of Polaris. Find the Northern Crown, Corona
Borealis, E. A. = 15h. 30m., Dec. = -f 27.0° ; the Beehive,
Prmepe, E. A. = 8h. 33m., Dec. = + 20.4°.

These should be looked up, not only on the map, but
also in the sky.

17. Reference lines and circles. — As the stars move across
the sky in their diurnal motion, they carry the framework
of hour circles and equator with them, so that the right
ascension and declination of each star remain unchanged
by this motion, just as longitudes and latitudes remain un-
changed by the earth's rotation. They are the same when
a star is rising and when it is setting ; when it is above the
pole and when it is below it. During each day the hour
circle of every star in the heavens passes overhead, and at
the moment when any particular hour circle is exactly
overhead all the stars which lie upon it are said to be " on
the meridian " — i. e., at that particular moment they stand
directly over the observer's geographical meridian and upon
the corresponding celestial meridian.

An eye placed at the center of the earth and capable of
looking through its solid substance would see your geograph-
ical meridian against the background of the sky exactly cov-
ering your celestial meridian and passing from one pole
through your zenith to the other pole. In Fig. 11 the inner
circle represents the terrestrial meridian of a certain place,

THE STARS AND THEIR DIURNAL MOTION

21

0, as seen from the center of the earth, (7, and the outer
circle represents the celestial meridian of 0 as seen from
C, only we must imagine, what can not be shown on the
figure, that the outer circle is so large that the inner one
shrinks to a mere point in
comparison with it. i$s#P z

represents the direction IB.
which the earth's axis passes
through the center, then C E
at right angles to it must
be the direction of the equa-
tor which we suppose to be
turned edgewise toward us ;
and if C 0 is the direction of
some particular point on the
earth's surface, then Z di-
rectly overhead is called the
zenith of that point, upon

the celestial sphere. The line C H represents a direction
parallel to the horizon plane at 0, and HOP is the angle
which the axis of the earth makes with this horizon plane.
The arc 0 E measures the latitude of 0, and the arc Z E
measures the declination of Z, and since by elementary
geometry each of these arcs contains the same number of
degrees as the angle E O Z, we have the

Theorem. — The latitude of any place is equal to the~~\
declination of its zenith.

Corollary. — Any star whose declination is equal to your
latitude will once in each day pass through your zenith.

18. Latitude. — From the construction of the figure

Z ECZ+ Z
LHCP+ Z

FIG. 11. — Reference lines and circles.

from which we find by subtraction and transposition

Z ECZ= Z HCP
and this gives the further

22 ASTRONOMY

Theorem. — The latitude of any place is equal to the
elevation of the pole above its horizon plane.

"" An observer who travels north or south over the earth
changes his latitude, and therefore changes the angle be-
tween his horizon plane and the axis of the earth. What
effect will this have upon the position of stars in his sky ?
If you were to go to the earth's equator, in what part of
the sky would you look for Polaris ? Can Polaris be seen
from Australia ? From South America ? If you were to
go from Minnesota to Texas, in what
respect would the appearance of
stars in the northern sky be changed ?
How would the appearance of stars
in the southern sky be changed ?

EXEKCISE 8. — Determine your
latitude by taking the altitude of
Polaris when it is at some one of the
four points of its diurnal path, shown

FIG. 12.-Diurnal path of j Fj ^ ^ ifc j t 1 jt j
Polaris.

said to be at upper culmination, and

the star £ Ursae Minoris in the handle of the Big Dipper
will be directly below it. When at 2 it is at western elon-
gation, and the star Castor is near the meridian. When it
is at S it is at lower culmination, and the star Spica is on
the meridian. When it is at 4 it is at eastern elongation,
and Altair is near the meridian. All of these stars are
conspicuous ones, which the student should find upon the
map and learn to recognize in the sky. The altitude ob-
served at either 2 or 4 may be considered equal to the lati-
tude of the place, but the altitude observed when Polaris
is at the positions marked 1 and 8 must be corrected for
the star's distance from the pole, which may be assumed
equal to 1.3°.

The plumb-line apparatus described at page 12 is shown
in Fig. 6 slightly modified, so as to adapt it to measuring
the altitudes of stars. Note that the board with the screw

THE STARS AND THEIR DIURNAL MOTION 23

eye at one end has been transferred from the box to the
vertical standard, and has a screw eye at each end. When
the apparatus has been properly leveled, so that the plumb
line hangs at the middle of the hole in the box cover, the
board is to be pointed at the star by sighting through the
centers of the two screw eyes, and a pencil line is to be
ruled along its edge upon the face of the vertical standard.
After this has been done turn the apparatus halfway around
so that what was the north side now points south, level it
again and revolve the board about the screw which holds it
to the vertical standard, until the screw eyes again point to
the star. Rule another line along the same edge of the
board as before and with a protractor measure the angle
between these lines. Use a bicycle lamp if you need artifi-
cial light for your work. The student who has studied
plane geometry should be able to prove that one half of the
angle between these lines is equal to the altitude of the
star.

After you have determined your latitude from Polaris,
compare the result with your position as shown upon the
best map available. With a little practice and considerable
care the latitude may be thus determined within one tenth
of a degree, which is equivalent to about 7 miles. If
you go 10 miles north or south from your first station you
should find the pole higher up or lower down in the sky by
an amount which can be measured with your apparatus.

19. The meridian line. — To establish a true north and
south line upon the ground, use the apparatus as described
at page 13, and when Polaris is at upper or lower culmina-
tion drive into the ground two stakes in line with the star
and the plumb line. Such a meridian line is of great con*
venience in observing the stars and should be laid out and
permanently marked in some convenient open space from
which, if possible, all parts of the sky are visible. June and
November are convenient months for this exercise, since
Polaris then comes to culmination early in the evening.

24 ASTRONOMY

20. Time. — What is the time at which school begins in
the morning ? What do you mean by " the time " ?

The sidereal time at any moment is the right ascension
of the hour circle which at that moment coincides with the
meridian. When the hour circle passing through Sirius
coincides with the meridian, the sidereal time is 6h. 40m.,
since that is the right ascension of Sirius, and in astronom-
ical language Sirius is " on the meridian " at 6h. 40m.
sidereal time. As may be seen from the map, this 6h. 40m.
is the right ascension of Sirius, and if a clock be set to in-
dicate 6h. 40m. when Sirius crosses the meridian, it will
show sidereal time. If the clock is properly regulated,
every other star in the heavens will come to the meridian
at the moment when the time shown by the clock is equal
to the right ascension of the star. A clock properly reg-
ulated for this purpose will gain about four minutes per
day in comparison with ordinary clocks, and when so reg-
ulated it is called a sidereal clock. The student should
be provided with such a clock for his future work, but
one such clock will serve for several persons, and a nut-
meg clock or a watch of the cheapest kind is quite suffi-
cient.

EXERCISE 9. — Set such a clock to sidereal time by
means of the transit of a star over your meridian. For this
experiment it is presupposed that a meridian line has been
marked out on the ground as in § 19, and the simplest
mode of performing the experiment required is for the
observer, having chosen a suitable star in the southern part
of the sky, to place his eye accurately over the northern end
of the meridian line and to estimate as nearly as possible
the beginning and end of the period during which the star
appears to stand exactly above the southern end of the
line. The middle of this period may be taken as the time
at which the star crossed the meridian and at this moment
the sidereal time is equal to the right ascension of the star.
The difference between this right ascension and the ob-

THE STARS AND THEIR DIURNAL MOTION 25

served middle instant is the error of the clock or the
amount by which its hands must be set back or forward in
order to indicate true sidereal time.

A more accurate mode of performing the experiment
consists in using the plumb-line apparatus carefully ad-
justed, as in Fig. 7, so that the line joining the wire to
the center of the screw eye shall be parallel to the meridian
line. Observe the time by the clock at which the star dis-
appears behind the wire as seen through the center of the
screw eye. If the star is too high up in the sky for con-
venient observation, place a mirror, face up, just north of
the screw eye and observe star, wire and screw eye by re-
flection in it.

The numerical right ascension of the observed star is
needed for this experiment, and it may be measured from
the star map, but it will usually be best to observe one of
the stars of the table at the end of the book, and to obtain
its right ascension as follows: The table gives the right
ascension and declination of each star as they were at the
beginning of the year 1900, but on account of the preces-
sion (see Chapter V), these numbers all change slowly with
the lapse of time, and on the average the right ascension of
each star of the table must be increased by one twentieth
of a minute for each year after 1900 — i. e., in 1910 the
right ascension of the second star of the table will be
Oh. 38.6m. + i#m. — Oh. 39.1m. The declinations also
change slightly, but as they are only intended to help in
finding the star on the star maps, their change may be
ignored.

Having set the clock approximately to sidereal time,
observe one or two more stars in the same way as above.
The difference between the observed time and the right
ascension, if any is found, is the " correction " of the
clock. This correction ought not to exceed a minute if due
care has been taken in the several operations prescribed.
The relation of the clock to the right ascension of the stars
3

26 ASTRONOMY

is expressed in the following equation, with which the
student should become thoroughly familiar :

A = T± U

T stands for the time by the clock at which the star crossed
the meridian. A is the right ascension of the star, and U
is the correction of the clock. Use the -j- sign in the equa-
tion whenever the clock is too slow, and the — sign when
it is too fast. U may be found from this equation when A
and T are given, or A may be found when T and U are
given. It is in this way that astronomers measure the right
ascensions of the stars and planets.

Determine U from each star you have observed, and
note how the several results agree one with another.

21. Definitions.— To define a thing or an idea is to give
a description sufficient to identify it and distinguish it
from every other possible thing or idea. If a definition
does not come up to this standard it is insufficient. Any-
thing beyond this requirement is certainly useless and
probably mischievous.

Let the student define the following geographical terms,
and let him also criticise the definitions offered by his fel-
low-students : Equator, poles, meridian, latitude, longitude,
north, south, east, west.

Compare the following astronomical definitions with
your geographical definitions, and criticise them in the
same way. If you are not able to improve upon them, com-
mit them to memory :

The Poles of the heavens are those points in the sky
toward which the earth's axis points. How many are
there ? The one near Polaris is called the north pole.

The Celestial Equator is a great circle of the sky distant
90° from the poles.

The Zenith is that point of the sky, overhead, toward
which a plumb line points. Why is the word overhead
placed in the definition ? Is there more than one zenith ?

THE STARS AND THEIR DIURNAL MOTION 27

The Horizon is a great circle of the sky 90° distant
from the zenith.

An Hour Circle is any great circle of the sky which
passes through the poles. Every star has its own hour
circle.

The Meridian is that hour circle which passes through
the zenith.

A Vertical Circle is any great circle which passes
through the zenith. Is the meridian a vertical circle ?

The Declination of a star is its angular distance north
or south of the celestial equator.

The Right Ascension of a star is the angle included be-
tween its hour circle and the hour circle of a certain point
on the equator which is called the Vernal Equinox. From
spherical geometry we learn that this angle is to be meas-
ured either at the pole where the two hour circles inter-
sect, as is done in the star map opposite page 124, or
along the equator, as is done in the map opposite page
190. Eight ascension is always measured from the ver-
nal equinox in the direction opposite to that in which the
stars appear to travel in their diurnal motion — i. e., from
west toward east.

The Altitude of a star is its angular distance above the
horizon.

The Azimuth of a star is the angle between the meridian
and the vertical circle passing through the star. A star
due south has an azimuth of 0°. Due west, 90°. Due
north, 180°. Due east, 270°.

What is the azimuth of Polaris in degrees ?

What is the azimuth of the sun at sunrise ? At sunset ?
At noon ? Are these azimuths the same on different days ?

The Hour Angle of a star is the angle between its hour
circle and the meridian. It is measured from the meridian
in the direction in which the stars appear to travel in their
diurnal motion — i. e., from east toward west.

What is the hour angle of the sun at noon ? What is

28 ASTRONOMY

the hour angle of Polaris when it is at the lowest point in
its daily motion ?

22. Exercises.— The student must not be satisfied with
merely learning these definitions. He must learn to see
these points and lines in his mind as if they were visibly
painted upon the sky. To this end it will help him to note
that the poles, the zenith, the meridian, the horizon, and
the equator seem to stand still in the sky, always in the
same place with respect to the observer, while the hour
circles and the vernal equinox move with the stars and
keep the same place among them. Does the apparent mo-
tion of a star change its declination or right ascension ?
What is the hour angle of the sun when it has the greatest
altitude ? "Will your answer to the preceding question be
true for a star ? What is the altitude of the sun after sun-
set ? In what direction is the north pole from the zenith ?
From the vernal equinox ? Where are the points in which
the meridian and equator respectively intersect the horizon ?

CHAPTER III

FIXED AND WANDERING STARS

23. Star maps, — Select from the map some conspicuous
constellation that will be conveniently placed for observa-
tion in the evening, and make on a large scale a copy of all
the stars of the constellation that are shown upon the map.
At night compare this copy with the sky, and mark in upon
your paper all the stars of the constellation which are not
already there. Both the original drawing and the addi-
tions made to it by night should be carefully done, and foi
the latter purpose what is called the method of allineations
may be used with advantage — i. e., the new star is in line
with two already on the drawing and is midway between
them, or it makes an equilateral triangle with two otherss
or a square with three others, etc.

A series of maps of the more prominent constellations,
such as Ursa Major, Cassiopea, Pegasus, Taurus, Orion,
Gemini, Canis Major, Leo, Corvus, Bootes, Virgo, Hercules,
Lyra, Aquila, Scorpius, should be constructed in this man-
ner upon a uniform scale and preserved as a part of the
student's work. Let the magnitude of the stars be repre-
sented on the maps as accurately as may be, and note the
peculiarity of color which some stars present. For the
most part their color is a very pale yellow, but occasionally
one may be found of a decidedly ruddy hue — e. g., Alde-
baran or Antares. Such a star map, not quite complete, is
shown in Fig. 13.

So, too, a sharp eye may detect that some stars do not
remain always of the same magnitude, but change their

30 ASTRONOMY

brightness from night to night, and this not on account of
cloud or mist in the atmosphere, but from something in the

FIG. 13. — Star map of the region about Orion.

star itself. Algol is one of the most conspicuous of these
variable stars, as they are called.

24. The moon's motion among the stars. — Whenever the
moon is visible note its position among the stars by allinea-
tions, and plot it on the key map opposite page 190. Keep
a record of the day and hour corresponding to each such
observation. You will find, if the work is correctly done,
that the positions of the moon all fall near the curved line
shown on the map. This line is called the ecliptic.

FIXED AND WANDERING STARS 31

After several such observations have been made and
plotted, find by measurement from the map how many
degrees per day the moon moves. How long would it re-
quire to make the circuit of the heavens and come back to
the starting point ?

On each night when you observe the moon, make on a
separate piece of paper a drawing of it about 10 centime-
ters in diameter and show in the drawing every feature of
the moon's face which you can see — e. g., the shape of the
illuminated surface (phase) ; the direction among the stars
of the line joining the horns ; any spots which you can see
upon the moon's face, etc. An opera glass will prove of
great assistance in this work.

Use your drawings and the positions of the moon plot-
ted upon the map to answer the following questions : Does
the direction of the line joining the horns have any special
relation to the ecliptic ? Does the amount of illuminated
surface of the moon have any relation to the moon's angular
distance from the sun ? Does it have any relation to the
time at which the moon sets ? Do the spots on the moon
when visible remain always in the same place ? Do they
come and go ? Do they change their position with relation
to each other? Can you determine from these spots that
the moon rotates about an axis, as the earth does? In
what direction does its axis point ? How long does it take
to make one revolution about the axis ? Is there any day
and night upon the moon ?

Each of these questions can be correctly answered from
the student's own observations without recourse to any
book.

25. The sun and its motion. — Examine the face of the
sun through a smoked glass to see if there is anything
there which you can sketch.

By day as well as by night the sky is studded with stars,
only they can not be seen by day on account of the over-
whelming glare of sunlight, but the position of the sun

32 ASTRONOMY

among the stars may be found quite as accurately as was
that of the moon, by observing from day to day its right
ascension and declination, and this should be practiced at
noon on clear days by different members of the class.

EXERCISE 10. — The right ascension of the sun may be
found by observing with the sidereal clock the time of its
transit over the meridian. Use the equation in § 20, and
substitute in place of U the value of the clock correction
found from observations of stars on a preceding or fol-
lowing night. If the clock gains or loses with respect to
sidereal time, take this into account in the value of U.

EXEECISE 11. — To determine the sun's decimation,
measure its altitude at the time it crosses the meridian.
Use either the method of Exercise 4, or that used with
Polaris in Exercise 8. The student should be able to show
from Fig. 11 that the declination is equal to the sum of
the altitude and the latitude of the place diminished by
90°, or in an equation

Declination = Altitude -j- Latitude — 90°.

If the declination as found from this equation is a negative
number it indicates that the sun is on the south side of the
equator.

The right ascension and declination of the sun as ob-
served on each day should be plotted on the map and the
date, written opposite it. If the work has been correctly
done, the plotted points should fall upon the curved line
(ecliptic) which runs lengthwise of the map. This line, in
fact, represents the sun's path among the stars.

Note that the hours of right ascension increase from 0
up to 24, while the numbers on the clock dial go only from
0 to 12, and then repeat 0 to 12 again during the same
day. When the sidereal time is 13 hours, 14 hours, etc.,
the clock will indicate 1 hour, 2 hours, etc., and 12 hours
must then be added to the time shown on the dial.

If observations of the sun's right ascension and declina-

FIXED AND WANDERING STARS 33

tion are made in the latter part of either March or Septem-
ber the student will find that the sun crosses the equator
at these times, and he should determine from his observa-
tions, as accurately as possible, the date and hour of this
crossing and the point on the equator at which the sun
crosses it. These points are called the equinoxes, Vernal
Equinox and Autumnal Equinox for the spring and autumn
crossings respectively, and the student will recall that the
vernal equinox is the point from which right ascensions
are measured. Its position among the stars is found by
astronomers from observations like those above described,
only made with much more elaborate apparatus.

Similar observations made in June and December show
that the sun's midday altitude is about 47° greater in sum-
mer than in winter. They show also that the sun is as far
north of the equator in June as he is south of it in Decem-
ber, from which it is easily inferred that his path, the
ecliptic, is inclined to the equator at an angle of 23°. 5, one
half of 47°. This angle is called the obliquity of the eclip-
tic. The student may recall that in the geographies the
torrid zone is said to extend 23°. 5 on either side of the
earth's equator. Is there any connection between these
limits and the obliquity of the ecliptic ? Would it be cor-
rect to define the torrid zone as that part of the earth's
surface within which the sun may at some season of the
year pass through the zenith ?

EXERCISE 12. — After a half dozen observations of the
sun have been plotted upon the map, find by measurement
the rate, in degrees per day, at which the sun moves along
the ecliptic. How many days will be required for it to
move completely around the ecliptic from vernal equinox
back to vernal equinox again ? Accurate observations with
the elaborate apparatus used by professional astronomers
show that this period, which is called a tropical year, is 365
days 5 hours 48 minutes 46 seconds. Is this the same as
the ordinary year of our calendars ?

34: ASTRONOMY

26. The planets. — Any one who has watched the sky and
who has made the drawings prescribed in this chapter can
hardly fail to have fonnd in the course of his observations
some bright stars not set down on the printed star maps,
and to have fonnd also that these stars do not remain fixed
in position among their fellows, bnt wander about from
one constellation to another. Observe the motion of one
of these planets from night to night and plot its posi-
tions on the star map, precisely as was done for the moon.
What kind of path does it follow ?

Both the ancient Greeks and the modern Germans have
called these bodies wandering stars, and in English we name
them planets, which is simply the Greek word for wanderer,
bent to our use. Besides the sun and moon there are in
the heavens five planets easily visible to the naked eye and,
as we shall see later, a great number of smaller ones visible
only in the telescope. More than 2,000 years ago astron-
omers began observing the motion of sun, moon, and
planets among the stars, and endeavored to account for
these motions by the theory that each wandering star
moved in an orbit about the earth. Classical and mediaeval
literature are permeated with this idea, which was displaced
only after a long struggle begun by Copernicus (1543 A. D.),
who taught that the moon alone of these bodies revolves
about the earth, while the earth and the other planets re-
volve around the sun. The ecliptic is the intersection of
the plane of the earth's orbit with the sky, and the sun ap-
pears to move along the ecliptic because, as the earth moves
around its orbit, the sun is always seen projected against
the opposite side of it. The moon and planets all appear
to move near the ecliptic because the planes of their orbits
nearly coincide with the plane of the earth's orbit, and a
narrow strip on either side of the ecliptic, following its
course completely around the sky, is called the zodiac, n
word which may be regarded as the name of a narrow street
(16° wide) within which all the wanderings of the visible

FIXED AND WANDERING STARS 35

planets are confined and outside of which they never ven-
ture. Indeed, Mars is the only planet which ever approaches
the edge of the street, the others traveling near the middle
of the road.

27. A typical case of planetary motion. — The Copernican
theory, enormously extended and developed through the

*/3 Ariet is

*7 Arietis

+ 1] Piscium
* *

I Arietis

% TT Piscium
Dec. 31 ,

-~^5-^J>

Piscium

*-

£ Arietis ^.^-"Oct.2 ___________ <D

* f<¥- ----- -O ------ O ---------- Z£~« Aug. 3

Sept. 12 Sept. 2 Aug. 23

V Piscium

%• £ Piscium

if- a Piscium
FIG. 14.— The apparent motion of a planet.

Newtonian law of gravitation (see Chapter IV), has com-
pletely supplanted the older Ptolemaic doctrine, and an
illustration of the simple manner in which it accounts for
the apparently complicated motions of a planet among the
stars is found in Figs. 14 and 15, the first of which repre-
sents the apparent motion of the planet Mars through the
constellations Aries and Pisces during the latter part of the

36 ASTRONOMY

year 1894, while the second shows the true motions of Mars
and the earth in their orbits about the sun during the same
period. The straight line in Fig. 14, with cross ruling upon
it, is a part of the ecliptic, and the numbers placed opposite
it represent the distance, in degrees, from the vernal equi-
nox. In Fig. 15 the straight line represents the direction
from the sun toward the vernal equinox, and the angle
which this line makes with the line joining earth and sun is
called the earth's longitude. The imaginary line joining
the earth and sun is called the earth's radius vector, and
the pupil should note that the longitude and length of the
radius vector taken together show the direction and dis-
tance of the earth from the sun — i. e., they fix the relative
positions of the two bodies. The same is nearly true for
Mars and would be wholly true if the orbit of Mars lay in
the same plane with that of the earth. How does Fig. 14
show that the orbit of Mars does not lie exactly in the same
plane with the orbit of the earth ?

EXERCISE 13. — Find from Fig. 15 what ought to have
been the apparent course of Mars among the stars during
the period shown in the two figures, and compare what you
find with Fig. 14. The apparent position of Mars among
the stars is merely its direction from the earth, and this
direction is represented in Fig. 14 by the distance of the
planet from the ecliptic and by its longitude.

The longitude of Mars for each date can be found from
Fig. 15 by measuring the angle between the straight line
S V and the line drawn from the earth to Mars. Thus for
October 12th we may find with the protractor that the angle
between the line S V and the line joining the earth to Mars
is a 4ittle more than 30°, and in Fig. 14 the position of
Mars for this date is shown nearly opposite the cross line
corresponding to 30° on the ecliptic. Just how far below
the ecliptic this position of Mars should fall can not be
told from Fig. 15, which from necessity is constructed as if
the orbits of Mars and the earth lay in the same plane, and

FIXED AND WANDERING STARS 37

Mars in this case would always appear to stand exactly on
the ecliptic and to oscillate back and forth as shown in Fig.
14, but without the up-and-down motion there shown. In
this way plot in Fig. 14 the longitudes of Mars as seen from

;>q

^
^-'' ^

if,* -^

*- CP

*4 ^ '<»

** ^ ^
o'''\J^'

o'"

FIG. 15.— The real motion of a planet.

the earth for other dates and observe how the forward mo-
tion of the two planets in their orbits accounts for the appar-
ently capricious motion of Mars to and fro among the stars.

38

ASTRONOMY

28. The orbits of the planets.— Each planet, great or
small, moves in its own appropriate orbit about the sun,
and the exact determination of these orbits, their sizes,
shapes, positions, etc., has been one of the great problems

FIG. 16.— The orbits of Jupiter and Saturn.

of astronomy for more than 2,000 years, in which succes-
sive generations of astronomers have striven to push to a
still higher degree of accuracy the knowledge attained by
their predecessors. Without attempting to enter into the
details of this problem we may say, generally, that every

FIXED AND WANDERING STARS 39

planet moves in a plane passing through the sun, and for
the six planets visible to the naked eye these planes nearly
coincide, so that the six orbits may all be shown without
much error as lying in the flat surface of one map. It is,
however, more convenient to use two maps, such as Figs. 16
and 17, one of which shows the group of planets, Mercury,
Venus, the earth, and Mars, which are near the sun, and
on this account are sometimes called the inner planets,
while the other shows the more distant planets, Jupiter and
Saturn, together with the earth, whose orbit is thus made
to serve as a connecting link between the two diagrams.
These diagrams are accurately drawn to scale, and are in-
tended to be used by the student for accurate measure-
ment in connection with the exercises and problems which
follow.

In addition to the six planets shown in the figures the
solar system contains two large planets and several hundred
small ones, for the most part invisible to the naked eye,
which are omitted in order to avoid confusing the dia-
grams.

29. Jupiter and Saturn. — In Fig. 16 the sun at the center
is encircled by the orbits of the three planets, and inclosing
all of these is a circular border showing the directions from
the sun of the constellations which lie along the zodiac.
The student must note carefully that it is only the direc-
tions of these constellations which are correctly shown, and
that in order to show them at all they have been placed
very much too close to the sun. The cross lines extending
from the orbit of the earth toward the sun with Eoman
numerals opposite them show the positions of the earth in
its orbit on the first day of January (7), first day of Feb-
ruary (//), etc., and the similar lines attached to the orbits
of Jupiter and Saturn with Arabic numerals show the posi-
tions of those planets on the first day of January of each
year indicated, so that the figure serves to show not only
the orbits of the planets, but their actual positions in their

4:0

ASTKONOMY

orbits for something more than the first decade of the twen-
tieth century.

The line drawn from the sun toward the right of the
figure shows the direction to the vernal equinox. It forms
one side of the angle which measures a planet's longitude.

FIG. 17.— The orbits of the inner planets.

EXERCISE 14. — Measure with your protractor the longi-
tude of the earth on January 1st. Is this longitude the
same in all years ? Measure the longitude of Jupiter on
January 1, 1900; on July 1, 1900; on September 25, 1906.

FIXED AND WANDERING STARS 41

Draw neatly on the map a pencil line connecting the
position of the earth for January 1, 1900, with the position
of Jupiter for the same date, and produce the line beyond
Jupiter until it meets the circle of the constellations. This
line represents the direction of Jupiter from the earth, and
points toward the constellation in which the planet appears
at that date. But this representation of the place of Jupi-
ter in the sky is not a very accurate one, since on the scale
of the diagram the stars are in fact more than 100,000 times
as far off as they are shown in the figure, and the pencil
mark does not meet the line of constellations at the same
intersection it would have if this line were pushed back
to its true position. To remedy this defect we must draw
another line from the sun parallel to the one first drawn,
and its intersection with the constellations will give very
approximately the true position of Jupiter in the sky.

EXERCISE 15. — Find the present positions of Jupiter
and Saturn, and look them up in the sky by means of your
star maps. The planets will appear in the indicated con-
stellations as very bright stars not shown on the map.

Which of the planets, Jupiter and Saturn, changes its
direction from the sun more rapidly ? Which travels the
greater number of miles per day ? When will Jupiter and
Saturn be in the same constellation ? Does the earth move
faster or slower than Jupiter ?

The distance of Jupiter or Saturn from the earth at any
time may be readily obtained from the figure. Thus, by
direct measurement with the millimeter scale we find for
January 1, 1900, the distance of Jupiter from the earth is 6.1
times the distance of the sun from the earth, and this may
be turned into miles by multiplying it by 93,000,000, which
is approximately the distance of the sun from the earth.
For most purposes it is quite as well to dispense with this
multiplication and call the distance 6.1 astronomical units,
remembering that the astronomical unit is the distance of
the sun from the earth.
4

42 ASTRONOMY

EXEKCISE 16. — What is Jupiter's distance from the earth
at its nearest approach ? What is the greatest distance it
ever attains? Is Jupiter's least distance from the earth
greater or less than its least distance from Saturn ?

On what day in the year 1906 will the earth be on
line between Jupiter and the sun? On this day Jupiter
is said to be in opposition— -i. e., the planet and the sun
are on opposite sides of the earth, and Jupiter then comes
to the meridian of any and every place at midnight. When
the sun is between the earth and Jupiter (at what date in
1906?) the planet is said to be in conjunction with the
sun, and of course passes the meridian with the sun at
noon. Can you determine from the figure the time at
which Jupiter comes to the meridian at other dates than
opposition and conjunction? Can you determine when it
is visible in the evening hours ? Tell from the figure what
constellation is on the meridian at midnight on January
1st. Will it be the same constellation in every year ?

30. Mercury, Venus, and Mars.— Fig. 17, which repre-
sents the orbits of the inner planets, differs from Fig. 16
only in the method of fixing the positions of the planets
in their orbits at any given date. The motion of these plan-
ets is so rapid, on account of their proximity to the sun, that
it would not do to mark their positions as was done for
Jupiter and Saturn, and with the exception of the earth they
do not always return to the same place on the same day in
each year. It is therefore necessary to adopt a slightly dif-
ferent method, as follows : The straight line extending from
the sun toward the vernal equinox, F, is called the prime
radius, and we know from past observations that the earth
in its motion around the sun crosses this line on September
23d in each year, and to fix the earth's position for Septem-
ber 23d in the diagram we have only to take the point at
which the prime radius intersects the earth's orbit. A
month later, on October 23d, the earth will no longer be at
this point, but will have moved on along its orbit to the

FIXED AND WANDERING STARS

point marked 30 (thirty days after September 23d). Sixty
days after September 23d it will be at the point marked 60,
etc., and for any date we have only to find the number of
days intervening between it and the preceding September
23d, and this number will show at once the position of the
earth in its orbit. Thus for the date July 4, 1900, we find

1900, July 4 — 1899, September 23 = 284 days,
and the little circle marked upon the earth's orbit between
the numbers 270 and 300 shows the position of the earth on
that date.

In what constellation was the sun on July 4, 1900?
What zodiacal constellation came to the meridian at mid-
night on that date? What other constellations came to
the meridian at the same time ?

The positions of the other planets in their orbits are
found in the same manner, save that they do not cross the
prime radius- on the same date in each year, and the times
at which they do cross it must be taken from the following
table :

TABLE OF EPOCHS

A. D.

Mercury.

Venus.

Earth.

Mars.

Period . . .
1900
1901

88.0 days.
Feb. 18th.
Feb 5th

224. 7 days.
Jan. llth.
\pril 5th

365.25 days.
Sept. 23d.
Sept 23d

687.1 days.
April 28th.

1902
1903

Jan. 23d.
April 8th

June 29th.
Feb. 8th.

Sept, 23d.
Sept 23d

March 16th.

1904.

March 25th

May 3d.

Sept. 23d.

Feb. 1st.

1905
1906

March 12th.
Feb 27th

July 26th.
March 8th

Sept. 23d.
Sept 23d

Dec. 19th.

1907

Feb 14th

May 31st.

Sept 23d

Nov. 6th.

1908

Feb. 1st

Jan. llth.

Sept. 23d.

1909
1910

Jan. 18th.
Jan 5th

April 4th.
June 28th.

Sept. 23d.
Sept 23d

Sept, 23d.

The first line of figures in this table shows the num-
ber of days that each of these planets requires to make
a complete revolution about the sun, and it appears from
these numbers that Mercury makes about four revolutions

44 ASTRONOMY

in its orbit per year, and therefore crosses the prime radius
four times in each year, while the other planets are decid-
edly slower in their movements. The following lines of
the table show for each year the date at which each planet
first crossed the prime radius in that year; the dates of
subsequent crossings in any year can be found by adding
once, twice, or three times the period to the given date,
and the table may be extended to later years, if need be, by
continuously adding multiples of the period. In the case
of Mars it appears that there is only about one year out of
two in which this planet crosses the prime radius.

After the date at which the planet crosses the prime
radius has been determined its position for any required
date is found exactly as in the case of the earth, and the
constellation in which the planet will appear from the
earth is found as explained above in connection with Jupi-
ter and Saturn.

The broken lines in the figure represent the construc-
tion for finding the places in the sky occupied by Mercury,
Venus, and Mars on July 4, 1900. Let the student make a
similar construction and find the positions of these planets
at the present time. Look them up in the sky and see if
they are where your work puts them.

31. Exercises. — The "evening star" is a term loosely
applied to any planet which is visible in the western sky
soon after sunset. It is easy to see that such a planet must
be farther toward the east in the sky than is the sun, and
in either Fig. 16 or Fig. 17 any planet which viewed from
the position of the earth lies to the left of the sun and
not more than 50° away from it will be an evening star.
If to the right of the sun it is a morning star, and may be
seen in the eastern sky shortly before sunrise.

What planet is the evening star now 9 Is there more
than one evening star at a time? What is the morning
star now ?

Do Mercury, Venus, or Mars ever appear in opposition ?

FIXED AND WANDERING STARS 45

What is the maximum angular distance from the sun at
which \7enus can ever be seen ? Why is Mercury a more
difficult planet to see than Venus? In what month of the
year does Mars come nearest to the earth? Will it always
be brighter in this month than in any other ? Which of
all the planets comes nearest to the earth ?

The earth always comes to the same longitude on the
same day of each year. Why is not this true of the other
planets ?

The student should remember that in one respect Figs.
16 and 17 are not altogether correct representations, since
they show the orbits as all lying in the same plane. If this
were strictly true, every planet would move, like the sun,
always along the ecliptic ; but in fact all of the orbits are
tilted a little out of the plane of the ecliptic and every
planet in its motion deviates a little from the ecliptic, first
to one side then to the other ; but not even Mars, which is
the most erratic in this respect, ever gets more than eight
degrees away from the ecliptic, and for the most part all
of them are much closer to the ecliptic than this limit.

A . >->^

V

CHAPTEE IV

CELESTIAL MECHANICS

32. The beginnings of celestial mechanics.— From the ear-
liest dawn of civilization, long before the beginnings of
written history, the motions of sun and moon and planets
among the stars from constellation to constellation had
commanded the attention of thinking men, particularly of
the class of priests. The religions of which they were the
guardians and teachers stood in closest relations with the
movements of the stars, and their own power and influence
were increased by a knowledge of them.

Out of these professional needs, as well as from a spirit
of scientific research, there grew up and flourished for
many centuries a study of the motions of the planets, sim-
ple and crude at first, because the observations that could
then be made were at best but rough ones, but growing
more accurate and more complex as the development of the
mechanic arts put better and more precise instruments into
the hands of astronomers and enabled them to observe with
increasing accuracy the movements of these bodies. It was
early seen that while for the most part the planets, includ-
ing the sun and moon, traveled through the constellations
from west to east, some of them sometimes reversed their
motion and for a time traveled in the opposite way. This
clearly can not be explained by the simple theory which
had early been adopted that a planet moves always in the
same direction around a circular orbit having the earth at
its center, and so it was said to move around in a small
circular orbit, called an epicycle, whose center was situated
46

ISAAC NEWTON ( 1643-1727 ).

CELESTIAL MECHANICS 47

upon and moved along a circular orbit, called the deferent,
within which the earth was placed, as is shown in Fig. 18,
where the small circle is the epicycle, the large circle is the
deferent, P is the planet, and E the earth. When this
proved inadequate to account for the really complicated
movements of the planets, another epicycle was put on top
of the first one, and then another and another, until the
supposed system became so complicated that Copernicus, a
Polish astronomer, repudiated
its fundamental theorem and
taught that the motions of
the planets take place in cir-
cles around the sun instead
of about the earth, and that
the earth itself is only one of
the planets moving around
the sun in its- own appropri-
ate orbit and itself largely re-
sponsible for the seemingly

& J FIG. 18.— Epicycle and deferent.

erratic movements of the

other planets, since from day to day we see them and ob-
serve their positions from different points of view.

33. Kepler's laws. — Two generations later came Kepler
with his three famous laws of planetary motion :

I. Every planet moves in an ellipse which has the sun
at one of its foci.

II. The radius vector of each planet moves over equal
areas in equal times.

III. The squares of the periodic times of the planets
are proportional to the cubes of their mean distances from
the sun.

These laws are the crowning glory, not only of Kepler's
career, but of all astronomical discovery from the begin-
ning up to his time, and they well deserve careful study
and explanation, although more modern progress has shown
that they are only approximately true.

48 ASTRONOMY

EXERCISE 17. — Drive two pins into a smooth board an
inch apart and fasten to them the ends of a string a foot
long. Take up the slack of the string with the point of a
lead pencil and, keeping the string drawn taut, move the
pencil point over the board into every possible position.
The curve thus traced will be an ellipse having the pins at
the two points which are called its foci.

In the case of the planetary orbits one focus of the
ellipse is vacant, and, in accordance with the first law, the
center of the sun is at the other focus. In Fig. 17 the dot,
inside the orbit of Mercury, which is marked «, shows the
position of the vacant focus of the orbit of Mars, and the
dot b is the vacant focus of Mercury's orbit. The orbits of
Venus and the earth are so nearly circular that their vacant
foci lie very close to the sun and are not marked in the
figure. The line drawn from the sun to any point of the
orbit (the string from pin to pencil point) is a radius vector.
The point midway between the pins is the center of the
ellipse, and the distance of either pin from the center meas-
ures the eccentricity of the ellipse.

Draw several ellipses with the same length of string,
but with the pins at different distances apart, and note that
the greater the eccentricity the flatter is the ellipse, but
that all of them have the same length.-

If both pins were driven into the same hole, what kind
of an ellipse would you get ?

The Second Law was worked out by Kepler as his answer
to a problem suggested by the first law. In Fig. 17 it is
apparent from a mere inspection of the orbit of Mercury
that this planet travels much faster on one side of its orbit
than on the other, the distance covered in ten days between
the numbers 10 and 20 being more than fifty per cent greater
than that between 50 and 60. The same difference is found,
though usually in less degree, for every other planet, and
Kepler's problem was to discover a means by which to
mark upon the orbit the figures showing the positions of

CELESTIAL MECHANICS 49

the planet at the end of equal intervals of time. His solu-
tion of this problem, contained in the second law, asserts
that if we draw radii vectores from the sun to each of the
marked points taken at equal time intervals around the
orbit, then the area of the sector formed by two adjacent
radii vectores and the arc included between them is equal
to the area of each and every other such sector, the short
radii vectores being spread apart so as to include a long
arc between them while the long radii vectores have a short
arc. In Kepler's form of stating the law the radius vector
is supposed to travel with the planet and in each day to
sweep over the same fractional part of the total area of the
orbit. The spacing of the numbers in Fig. 17 was done by
means of this law.

For the proper understanding of Kepler's Third Law we
must note that the " mean distance " which appears in it is
one half of the long diameter of the orbit and that the
"periodic time" means the number of days or years re-
quired by the planet to make a complete circuit in its orbit.
Representing the first of these by a and the second by T,
we have, as the mathematical equivalent of the law,

where the quotient, (7, is a number which, as Kepler found,
is the same for every planet of the solar system. If we take
the mean distance of the earth from the sun as the unit of
distance, and the year as the unit of time, we shall find by
applying the equation to the earth's motion, C = 1. Ap-
plying this value to any other planet we shall find in the
same units, a = T , by means of which we may determine
the distance of any planet from the sun when its periodic
time, I7, has been learned from observation.

EXERCISE 18. — Uranus requires 84 years to make a
revolution in its orbit. What is its mean distance from the
sun ? What are the mean distances of Mercury, Venus, and
Mars ? (See Chapter III for their periodic times.) Would

50 ASTRONOMY

it be possible for two planets at different distances from
the sun to move around their orbits in the same time ?

A circle is an ellipse in which the two foci have been
brought together. Would Kepler's laws hold true for such
an orbit ?

34. Newton's laws of motion, — Kepler studied and de-
scribed the motion of the planets. Newton, three genera-
tions later (1727 A. D.), studied and described the mechan-
ism which controls that motion. To Kepler and his age the
heavens were supernatural, while to Newton and his suc-
cessors they are a part of Nature, governed by the same
laws which obtain upon the earth, and we turn to the ordi-
nary things of everyday life as the foundation of celestial
mechanics.

Every one who has ridden a bicycle knows that he can
coast farther upon a level road if it is smooth than if it is
rough ; but however smooth and hard the road may be and
however fast the wheel may have been started, it is sooner
or later stopped by the resistance which the road and the
air offer to its motion, and when once stopped or checked
it can be started again only by applying fresh power. We
have here a familiar illustration of what is called

The first law of motion.—" Every body continues in its
state of rest or of uniform motion in a straight line except
in so far as it may be compelled by force to change that
state." A gust of wind, a stone, a careless movement of
the rider may turn the bicycle to the right or the left, but
unless some disturbing force is applied it will go straight
ahead, and if all resistance to its motion could be removed
it would go always at the speed given it by the last power
applied, swerving neither to the one hand nor the other.

When a slow rider increases his speed we recognize at
once that he has applied additional power to the wheel, and
when this speed is slackened it equally shows that force has
been applied against the motion. It is force alone which
can produce a change in either velocity or direction of

CELESTIAL MECHANICS 51

motion ; but simple as this law now appears it required the
genius of Galileo to discover it and of Newton to give it the
form in which it is stated above.

35. The second law of motion, which is also due to Gali-
leo and Newton, is :

" Change of motion is proportional to force applied and
takes place in the direction of the straight line in which
the force acts." Suppose a man to fall from a balloon at
some great elevation in the air ; his own weight is the force
which pulls him down, and that force operating at every
instant is sufficient to give him at the end of the first sec-
ond of his fall a downward velocity of 32 feet per second —
i. e., it has changed his state from rest, to motion at this
rate, and the motion is toward the earth because the force
acts in that direction. During the next second the cease-
less operation of this force will have the same effect as in
the first second and will add another 32 feet to his ve-
locity, so that two seconds from the time he commenced to
fall he will be moving at the rate of 64 feet per second, etc.
The column of figures marked v in the table below shows
what his velocity will be at the end of subsequent seconds.
The changing velocity here shown is the change of motion
to which the law refers, and the velocity is proportional to
the time shown in the first column of the table, because the
amount of force exerted in this case is proportional to the
time during which it operated. The distance through
which the man will fall in each second is shown in the col-
umn marked d, and is found by taking the average of his
velocity at the beginning and end of this second, and the
total distance through which he has fallen at the end of
each second, marked s in the table, is found by taking the
sum of all the preceding values of d. The velocity, 32 feet
per second, which measures the change of motion in each
second, also measures the accelerating force which produces
this motion, and it is usually represented in formulae by
the letter g. Let the student show from the numbers in

52 ASTRONOMY

the table that the accelerating force, the time, ^, during
which it operates, and the space, s, fallen through, satisfy
the relation

s = | g t2,

which is usually called the law of falling bodies. How does
the table show that g is equal to 32 ?

TABLE

t

V

d

s

0

0

0

0

1

32

16

16

2

64

48

64

3

96

80

144

4

128

112

256

5

160

144

400

etc. etc. etc. etc.

If the balloon were half a mile high how long would it
take to fall to the ground ? What would be the velocity
just before reaching the ground ?

Fig. 19 shows the path through the air of a ball which
has been struck by a bat at the point A, and started off in
the direction A B with a velocity of 200 feet per second.
In accordance with the first law of motion, if it were acted
upon by no other force than the impulse given by the bat,
it should travel along the straight line A S at the uniform
rate of 200 feet per second, and at the end of the fourth
second it should be 800 feet from A, at the point marked 4,
but during these four seconds its weight has caused it to
fall 256 feet, and its actual position, 4', is 256 feet below
the point 4. In this way we find its position at the end of
each second, 1', 2', 3', 4', etc., and drawing a line through
these points we shall find the actual path of the ball under
the influence of the two forces to be the curved line A C.
No matter how far the ball may go before striking the
ground, it can not get back to the point A, and the curve

GALILEO GALILEI (1564-1642).

CELESTIAL MECHANICS

53

A C therefore can not be a part of a circle, since that curve
returns into itself. It is, in fact, a part of a parabola,
which, as we shall see later, is a kind of orbit in which
comets and some other heavenly bodies move. A skyrocket

FIG. 19.— The path of a ball.

moves in the same kind of a path, and so does a stone, a
bullet, or any other object hurled through the air.

36. The third law of motion. — " To every action there is
always an equal and contrary reaction ; or the mutual ac-
tions of any two bodies are always equal and oppositely
directed." This is well illustrated in the case of a man
climbing a rope hand over hand. The direct force or action
which he exerts is a downward pull upon the rope, and it is
the reaction of the rope to this pull which lifts him along
it. We shall find in a later chapter a curious application
of this law to the history of the earth and moon.

54 ASTRONOMY

It is the great glory of Sir Isaac Newton that he first of
all men recognized that these simple laws of motion hold
true in the heavens as well as upon the earth ; that the
complicated motion of a planet, a comet, or a star is de-
termined in accordance with these laws by the forces
which act upon the bodies, and that these forces are
essentially the same as that which we call weight. The
formal statement of the principle last named is in-
cluded in —

37. Newton's law of gravitation, — " Every particle of
matter in the universe attracts every other particle with a
force whose direction is that of a line joining the two, and
whose magnitude is directly as the product of their masses,
and inversely as the square of their distance from each
other." We know that we ourselves and the things about
us are pulled toward the earth by a force (weight) which is
called, in the Latin that Newton wrote, gravitas, and the
word marks well the true significance of the law of gravita-
tion. Newton did not discover a new force in the heavens,
but he extended an old and familiar one from a limited
terrestrial sphere of action to an unlimited and celestial
one, and furnished a precise statement of the way in which
the force operates. Whether a body be hot or cold, wet or
dry, solid, liquid, or gaseous, is of no account in deter-
mining the force which it exerts, since this depends solely
upon mass and distance.

The student should perhaps be warned against straining
too far the language which it is customary to employ in
this connection. The law of gravitation is certainly a far-
reaching one, and it may operate in every remotest corner
of the universe precisely as stated above, but additional
information about those corners would be welcome to sup-
plement our rather scanty stock of knowledge concerning
what happens there. We may not controvert the words of_J>-
a popular preacher who says, " When I lift my hand I move
the stars in Ursa Major," but we should not wish to stand

CELESTIAL MECHANICS 55

sponsor for them, even though they are justified by a rigor-
ous interpretation of the Newtonian law.

The word mass, in the statement of the law of gravita-
tion, means the quantity of matter contained in the body,
and if we represent by the letters m' and m" the respective
quantities of matter contained in the two bodies whose dis-
tance from each other is r, we shall have, in accordance
with the law of gravitation, the following mathematical
expression for the force, F, which acts between them :

This equation, which is the general mathematical ex-
pression for the law of gravitation, may be made to yield
some curious results. Thus, if we select two bullets, each
having a mass of 1 gram, and place them so that their qen-
ters are 1 centimeter apart, the above expression for the
force exerted between them becomes

from which it appears that the coefficient Ic is the force
exerted between these bodies. This is called the gravita-
tion constant, and it evidently furnishes a measure of the
specific intensity with which one particle of matter attracts
another. Elaborate experiments which have been made to
determine the amount of this force show that it is sur-
prisingly small, for in the case of the two bullets whose
mass of 1 gram each is supposed to be concentrated into
an indefinitely small space, gravity would have to operate
between them continuously for more than forty minutes in
order to pull them together, although they were separated
by only 1 centimeter to start with, and nothing save their
own inertia opposed their movements. It is only when one
or both of the masses m\ m" are very great that the force
of gravity becomes large, and the weight of bodies at the

56 ASTRONOMY

surface of the earth is considerable because of the great
quantity of matter which goes to make up the earth.
Many of th'e heavenly bodies are much more massive than
the earth, as the mathematical astronomers have found by
applying the law of gravitation to determine numerically
their masses, or, in more popular language, to " weigh "
them.

The student should observe that the two terms mass
and weight are not synonymous ; mass is defined above as
the quantity of matter contained in a body, while weight
is the force with which the earth attracts that body, and
in accordance with the law of gravitation its weight de-
pends upon its distance from the center of the earth, while
its mass is quite independent of its position with respect
to the earth.

By the third law of motion the earth is pulled toward a
falling body just as strongly as the body is pulled toward
the earth — i. e., by a force equal to the weight of the body.
How much does the earth rise toward the body ?

38. The motion of a planet. — In Fig. 20 /S represents the
sun and P a planet or other celestial body, which for the
moment is moving along the straight line P 1. In accord-
ance with the first law of motion it would continue to move
along this line with uniform velocity if no external force
acted upon it; but such a force, the sun's attraction, is
acting, and by virtue of this attraction the body is pulled
aside from the line P 1.

Knowing the velocity and direction of the body's motion
and the force with which the sun attracts it, the mathema-
tician is able to apply Newton's laws of motion so as to
determine the path of the body, and a few of the possible
orbits are shown in the figure where the short cross stroke
marks the point of each orbit which is nearest to the sun.
This point is called the perihelion.

Without any formal application of mathematics we may
readily see that the swifter the motion of the body at P

CELESTIAL MECHANICS

the shorter will he the time during which it is subjected to
the sun's attraction at close range, and therefore the force
exerted by the sun, and the resulting change of motion, will
be small, as in the orbits P 1 and P 2.

On the other hand, P 5 and P 6 represent orbits in which
the velocity at P was comparatively small, and the resulting
change of motion greater
than would be possible for
a more swiftly moving body.

What would be the or_
bit if the velocity at P were
reduced to nothing at all ?

What would be the effect
if the body starting at P
moved directly away from 1?

The student should not
fail to observe that the sun's
attraction tends to pull the
body at P forward along its
path, and therefore increas-
es its velocity, and that this
influence continues until

the planet reaches perihelion, at which point it attains its
greatest velocity, and the force of the sun's attraction is
wholly expended in changing the direction of its motion.
After the planet has passed perihelion the sun begins to
pull backward and to retard the motion in just the same
measure that before perihelion passage it increased it, so
that the two halves of the orbit on opposite sides of a line
drawn from the perihelion through the sun are exactly
alike. We may here note the explanation of Kepler's sec-
ond law : when the planet is near the sun it moves faster,
and the radius vector changes its direction more rapidly
than when the planet is remote from the sun on account
of the greater force with which it is attracted, and the ex-
act relation between the rates at which the radius vector

FIG. 20.— Different kinds of orbits.

58 ASTRONOMY

turns in different parts of the orbit, as given by the second
law, depends upon the changes in this force.

When the velocity is not too great, the sun's backward
pull, after a planet has passed perihelion, finally overcomes
it and turns the planet toward the sun again, in such a way
that it comes back to the point P, moving in the same di-
rection and with the same speed as before — i. e., it has gone
around the sun in an orbit like P 6 or P 4, an ellipse, along
which it will continue to move ever after. But we must
not fail to note that this return into the same orbit is a
consequence of the last line in the statement of the law of
gravitation (p. 54), and that, if the magnitude of this force
were inversely as the cube of the distance or any other pro-
portion than the square, the orbit would be something very
different. If the velocity is too great for the sun's attrac-
tion to overcome, the orbit will be a hyperbola, like P 2,
along which the body will move away never to return, while
a velocity just at the limit of what the sun can control gives
an orbit like P 3, a parabola, along which the body moves
with parabolic velocity, which is ever diminishing as the
body gets farther from the sun, but is always just sufficient
to keep it from returning. If the earth's velocity could be
increased 41 per cent, from 19 up to 27 miles per second, it
would have parabolic velocity, and would quit the sun's
company.

The summation of the whole matter is that the orbit in
which a body moves around the sun, or past the sun, de-
pends upon its velocity and if this velocity and the direc-
tion of the motion at any one point in the orbit are known
the whole orbit is determined by them, and the position of
the planet in its orbit for past as well as future times can
be determined through the application of Newton's laws ;
and the same is true for any other heavenly body — moon,
comet, meteor, etc. It is in this way that astronomers are
able to predict, years in advance, in what particular part of
the sky a given planet will appear at a given time.

CELESTIAL MECHANICS 59

It is sometimes a source of wonder that the planets
move in ellipses instead of circles, but it is easily seen from
Fig. 20 that the planet, P, could not by any possibility
move in a circle, since the direction of its motion at P is
not at right angles with the line joining it to the sun as it
must be in a circular orbit, and even if it were perpen-
dicular to the radius vector the planet must needs have
exactly the right velocity given to it at this point, since
either more or less speed would change the circle into an
ellipse. In order to produce circular motion there must be
a balancing of conditions as nice as is required to make a
pin stand upon its point, and the really surprising thing is
that the orbits of the planets should be so nearly circular
as they are. If the orbit of the earth were drawn accu-
rately to scale, the untrained eye would not detect the
slightest deviation from a true circle, and even the orbit of
Mercury (Fig. 17), which is much more
eccentric than that of the earth, might al-
most pass for a circle.

The orbit P 2, which lies between the
parabola and the straight line, is called in
geometry a hyperbola, and Newton suc-
ceeded in proving from the law of gravita-
tion that a body might move under the
sun's attraction in a hyperbola as well as
in a parabola or ellipse ; but it must move
in some one of these curves ; no other or-
bit is possible.* Thus it would not be An orbit.
possible for a body moving under the law
of gravitation to describe about the sun any such orbit
as is shown in Fig. 21. If the body passes a second time
through any point of its orbit, such as P in the figure, then
it must retrace, time after time, the whole path that it first

* The circle and straight line are considered to be special cases of
these curves, which, taken collectively, are called the conic sections.

60 ASTRONOMY

traversed in getting from P around to P again — i. e., the
orbit must be an ellipse.

Newton also proved that Kepler's three laws are mere
corollaries from the law of gravitation, and that to be
strictly correct the third law must be slightly altered so as
to take into account the masses of the planets. These are,
however, so small in comparison with that of the sun, that
the correction is of comparatively little moment.

39. Perturbations. — In what precedes we have considered
the motion of a planet under the influence of no other
force than the sun's attraction, while in fact, as the law of
gravitation asserts, every other body in the universe is in
some measure attracting it and changing its motion. The
resulting disturbances in the motion of the attracted ,body
are called perturbations, but for the most part these are
insignificant, because the bodies by whose disturbing attrac-
tions they are caused are either very small or very remote,
and it is only when our moving planet, P, comes under the
influence of some great disturbing power like Jupiter or
one of the other planfets that the perturbations caused by
their influence need to be taken into account.

The problem of the motion of three bodies — sun, Jupiter,
planet — which must then be dealt with is vastly more com-
plicated than that which we have considered, and the ablest
mathematicians and astronomers have not been able to fur-
nish a complete solution for it, although they have worked
upon the problem for two centuries, and have developed an
immense amount of detailed information concerning it.

In general each planet works ceaselessly upon the orbit
of every other, changing its size and shape and position,
backward and forward in accordance with the law of gravi-
tation, and it is a question of serious moment how far this
process may extend. If the diameter of the earth's orbit
were very much increased or diminished by the perturbing
action of the other planets, the amount of heat received
from the sun would be correspondingly changed, and the

CELESTIAL MECHANICS 61

earth, perhaps, be rendered unfit for the support of life.
The tipping of the plane of the earth's orbit into a new
position might also produce serious consequences ; but the
great French mathematician of a century ago, Laplace,
succeeded in proving from the law of gravitation that al-
though both of these changes are actually in progress they
can not, at least for millions of years, go far enough to
prove of serious consequence, and the same is true for all
the other planets, unless here and there an asteroid may
prove an exception to the rule.

The precession (Chapter V) is a striking illustration
of a perturbation of slightly different character from the
above, and another is found in connection with the plane
of the moon's orbit. It will be remembered that the moon
in its motion among the stars never goes far from the
ecliptic, but in a complete circuit of the heavens crosses it
twice, once -in going from south to north and once in the
opposite direction. The points at which it crosses the
ecliptic are called the nodes, and under the perturbing in-
fluence of the sun these nodes move westward along the
ecliptic about twenty degrees per year, an extraordinarily
rapid perturbation, and one of great consequence in the
theory of eclipses.

40. Weighing the planets. — Although these perturbations
can not be considered dangerous, they are interesting since
they furnish a method for weighing the planets which pro-
duce them. From the law of gravitation we learn that the
ability of a planet to produce perturbations depends di-
rectly upon its mass, since the force F which it exerts con-
tains this mass, m', as a factor. So, too, the divisor r2 in
the expression for the force shows that the distance be-
tween the disturbing and disturbed bodies is a matter of
great consequence, for the smaller the distance the greater
the force. When, therefore, the mass of a planet such as
Jupiter is to be determined from the perturbations it pro-
duces, it is customary to select some such opportunity as

62

ASTRONOMY

FIG. 22. — A planet subject to great per-
turbations by Jupiter.

is presented in Fig. 22, where one of the small planets,
called asteroids, is represented as moving in a very eccen-
tric orbit, which at one point approaches close to the orbit
of Jupiter, and at another place comes near to the orbit of

the earth. For the most part
Jupiter will not exert any
very great disturbing influ-
ence upon a planet moving in
such an orbit as this, since it
is only at rare intervals that
the asteroid and Jupiter ap-
proach so close to each other,
as is shown in the figure.
The time during which the
asteroid is little aifected by
the attraction of Jupiter is
used to study the motion giv-
en to it by the sun's attrac-
tion— that is, to determine carefully the undisturbed orbit
in which it moves ; but there comes a time at which the
asteroid passes close to Jupiter, as shown in the figure, and
the orbital motion which the sun imparts to it will then be
greatly disturbed, and when the planet next comes round
to the part of its orbit near the earth the effect of these
disturbances upon its apparent position in the sky will be
exaggerated by its close proximity to the earth. If now
the astronomer observes the actual position of the asteroid
in the sky, its right ascension and declination, and com-
pares these with the position assigned to the planet by the
law of gravitation when the attraction of Jupiter is ignored,
the differences between the observed right ascensions and
declinations and those computed upon the theory of undis-
turbed motion will measure the influence that Jupiter has
had upon the asteroid, and the amount by which Jupiter has
shifted it, compared with the amount by which the sun has
moved it — that is, with the motion in its orbit — furnishes

CELESTIAL MECHANICS 63

the mass of Jupiter expressed as a fractional part of the
mass of the sun.

There has been determined in this manner the mass of
every planet in the solar system which is large enough to
produce any appreciable perturbation, and all these masses
prove to be exceedingly small fractions of the mass of the
sun, as may be seen from the following table, in which is
given opposite the name of each planet the number by
which the mass of the sun must be divided in order to
get the mass of the planet :

Mercury 7,000,000 (?)

Venus 408,000

Earth 329,000

Mars 3,093,500

Jupiter 1,047.4

Saturn 3,502

Uranus 22,800

Neptune 19,700

It is to be especially noted that the mass given for each
planet includes the mass of all the satellites which attend
it, since their influence was felt in the perturbations from
which the mass was derived. Thus the mass assigned to
the earth is the combined mass of earth and moon.

41. Discovery of Neptune. — The most famous example of
perturbations is found in connection with the discovery,
in the year 1846, of Neptune, the outermost planet of the
solar system. For many years the motion of Uranus, his
next neighbor, had proved a puzzle to astronomers. In
accordance with Kepler's first law this planet should move
in an ellipse having the sun at one of its foci, but no ellipse
could be found which exactly fitted its observed path among
the stars, although, to be sure, the misfit was not very pro-
nounced. Astronomers surmised that the small deviations
of Uranus from the best path which theory combined with
observation could assign, were due to perturbations in its

64 ASTRONOMY

motion caused by an unknown planet more remote from
the sun — a thing easy to conjecture but hard to prove, and
harder still to find the unknown disturber. But almost
simultaneously two young men, Adams in England and
Le Verrier in France, attacked the problem quite inde-
pendently of each other, and carried it to a successful so-
lution, showing that if the irregularities in the motion of
Uranus were indeed caused by an unknown planet, then
that planet must, in September, 1846, be in the direction
of the constellation Aquarius ; and there it was found on
September 23d by the astronomers of the Berlin Observatory
whom Le Verrier had invited to search for it, and found
within a degree of the exact point which the law of gravi-
tation in his hands had assigned to it.

This working backward from the perturbations experi-
enced by Uranus to the cause which produced them is justly
regarded as one of the greatest scientific achievements of
the human intellect, and it is worthy of note that we are
approaching the time at which it may be repeated, for Nep-
tune now behaves much as did Uranus three quarters of a
century ago, and the most plausible explanation which can
be offered for these anomalies in its path is that the bounds
of the solar system must be again enlarged to include an-
other disturbing planet.

42. The shape of a planet, — There is an effect of gravita-
tion not yet touched upon, which is of considerable interest
and wide application in astronomy — viz., its influence in de-
termining the shape of the heavenly bodies. The earth is
a globe because every part of it is drawn toward the center
by the attraction of the other parts, and if this attraction
on its surface were everywhere of equal force the material
of the earth would be crushed by it into a truly spherical
form, no matter what may have been the shape in which it
was originally made. But such is not the real condition of
the earth, for its diurnal rotation develops in every particle
of its body a force which is sometimes called centrifugal,

CELESTIAL MECHANICS 65

but which is really nothing more than the inertia of its
particles, which tend at every moment to keep unchanged
the direction of their motion and which thus resist the at-
traction that pulls them into a circular path marked out
by the earth's rotation, just as a stone tied at the end of
a string and swung swiftly in a circle pulls upon the
string and opposes the constraint which keeps it moving
in a circle. A few experiments with such a stone will
show that the faster it goes the harder does it pull upon
the string, and the same is true of each particle of the
earth, the swiftly moving ones near the equator having
a greater centrifugal force than the slow ones near the
poles. . At the equator the centrifugal force is directly
opposed to the force of gravity, and in effect diminishes it,
so that, comparatively, there is an excess of gravity at the
poles which compresses the earth along its axis and causes
it to bulge out at the equator until a balance is thus re-
stored. As we have learned from the study of geography,
in the case of the earth, this compression amounts to about
27 miles, but in the larger planets, Jupiter and Saturn, it
is much greater, amounting to several thousand miles.

But rotation is not the only influence that tends to
pull a planet out of shape. The attraction which the earth
exerts upon the moon is stronger on the near side and
weaker on the far side of our satellite than at its center,
and this difference of attraction tends to warp the moon, as
is illustrated in Fig. 23 where ./, #, and 8 represent pieces
of iron of equal mass placed in line on a table near a horse-
shoe magnet, H. Each piece of iron is attracted by the
magnet and is held back by a weight to which it is
fastened by means of a cord running over a pulley, P,
at the edge of the table. These weights are all to be
supposed equally heavy and each of them pulls upon its
piece of iron with a force just sufficient to balance the
attraction of the magnet for the middle piece, No. 2.
It is clear that under this arrangement No. 2 will move

66

ASTRONOMY

neither to the right nor to the left, since the forces exerted
upon it by the magnet and the weight just balance each
other. Upon No. 1, however, the magnet pulls harder
than upon No. #, because it is nearer and its pull there-

FIG. 23. — Tide-raising forces.

fore more than balances the force exerted by the weight,
so that No. 1 will be pulled away, from No. 2 and will
stretch the elastic cords, which are represented by the
lines joining 1 and #, until their tension, together with the
force exerted by the weight, just balances the attraction
of the magnet. For No. 8, the force exerted by the magnet
is less than that of the weight, and it will also be pulled
away from No. 2 until its elastic cords are stretched to the
proper tension. The net result is that the three blocks
which, without the magnet's influence, would be held close
together by the elastic cords, are pulled apart by this out-
side force as far as the resistance of the cords will permit.
An entirely analogous set of forces produces a similar
effect upon the shape of the moon. The elastic cords of
Fig. 23 stand for the attraction of gravitation by which all
the parts of the moon are bound together. The magnet
represents the earth pulling with unequal force upon differ-
ent parts of the moon. The weights are the inertia of the
moon in its orbital motion which, as we have seen in a

CELESTIAL MECHANICS

67

previous section, upon the whole just balances the earth's
attraction and keeps the moon from falling into it. The
effect of these forces is to stretch out the moon along a line
pointing toward the earth, just as the blocks were stretched
out along the line of the magnet, and to make this diam-
eter of the moon slightly but permanently longer than
the others.

The tides. — Similarly the moon and the sun attract op-
posite sides of the earth with different forces and feebly
tend to pull it out of shape. But here
a new element comes into play : the
earth turns so rapidly upon its axis
that its solid parts have no time in
which to yield sensibly to the strains,
which shift rapidly from one diameter
to another as different parts of the
earth are turned toward the moon, and
it is chiefly the waters of the sea which
respond to the distorting effect of the
sun's and moon's attraction. These are
heaped up on opposite sides of the
earth so as to produce a slight elonga-
tion of its diameter, and Fig. 24 shows
how by the earth's rotation this swell-
ing of the waters is swept out from
under the moon and is pulled back by
the moon until it finally takes up some
such position as that shown in the fig-
ure where the effect of the earth's rota-
tion in carrying it one way is just bal-
anced by the moon's attraction urging
it back on line with the moon. This heaping up of the
waters is called a tide. If /in the figure represents a little
island in the sea the waters which surround it will of
course accompany it in its diurnal rotation about the
earth's axis, but whenever the island comes back to the

FIG. 24.— The tides.

68 ASTRONOMY

position /, the waters will swell up as a part of the tidal
wave and will encroach upon the land in what is called
high tide or flood tide. So too when they reach 7", half a
day later, they will again rise in flood tide, and midway
between these points, at /', the waters must subside, giv-
ing low or ebb tide.

The height of the tide raised by the moon in the open
sea is only a very few feet, and the tide raised by the sun is
even less, but along the coast of a continent, in bays and
angles of the shore, it often happens that a broad but low
tidal wave is forced into a narrow corner, and then the rise
of the water may be many feet, especially when the solar
tide and the lunar tide come in together, as they do twice
in every month, at new and full moon. Why do they come
together at these times instead of some other ?

Small as are these tidal effects, it is worth noting that
they may in certain cases be very much greater — e. g., if
the moon were as massive as is the sun its tidal effect
would be some millions of times greater than it now is and
would suffice to grind the earth into fragments. Although
the earth escapes this fate, some other bodies are not so
fortunate, and we shall see in later chapters some evidence
of their disintegration.

43. The scope of the law of gravitation.— In all the do-
main of physical science there is no other law so famous as
the Newtonian law of gravitation ; none other that has been
so dwelt upon, studied, and elaborated by astronomers and
mathematicians, and perhaps none that can be considered
so indisputably proved. Over and over again mathemat-
ical analysis, based upon this law, has pointed out conclu-
sions which, though hitherto unsuspected, have afterward
been found true, as when Newton himself derived as a corol-
lary from this law that the earth ought to be flattened at
the poles — a thing not known at that time, and not proved
by actual measurement until long afterward. It is, in fact,
this capacity for predicting the unknown and for explain-

CELESTIAL MECHANICS 69

ing in minutest detail the complicated phenomena of the
heavens and the earth that constitutes the real proof of the
law of gravitation, and it is therefore worth while to note
that at the present time there are a very few points at
which the law fails to furnish a satisfactory account of
things observed. Chief among these is the case of the planet
Mercury, the long diameter of whose orbit is slowly turning
around in a way for which the law of gravitation as yet fur-
nishes no explanation. Whether this is because the law itself
is inaccurate or incomplete, or whether it only marks a case
in which astronomers have not yet properly applied the
law and traced out its consequences, we do not know ; but
whether it be the one or the other, this and other simila-r
cases show that even here, in its most perfect chapter,
astronomy still remains an incomplete science.

CHAPTER V

THE EARTH AS A PLANET

44. The size of the earth, — The student is presumed to
have learned, in his study of geography, that the earth is a
globe about 8,000 miles in diameter and, without dwelling
upon the " proofs " which are commonly given for these
statements, we proceed to consider the principles upon

which the measurement of
the earth's size and shape
are based.

In Fig. 25 the circle rep-
resents a meridian section
of the earth ; P P' is the
axis about which it rotates,
and the dotted lines repre-
sent a beam of light com-
ing from a star in the plane
of the meridian, and so dis-
tant that the dotted lines
are all practically parallel

Pio. 25,-Measuring the size of the earth. ^ ^ ^^ ^ ^^

radii drawn through the points -/, #, #, represent the direc-
tion of the vertical at these points, and the angles which
these radii produced, make with the rays of starlight are
each equal to the angular distance of the star from the
zenith of the place at the moment the star crosses the me-
ridian. We have already seen, in Chapter II, how these
angles may be measured, and it is apparent from the figure
that the difference between any two of these angles — e. g.,
70

THE EARTH AS A PLANET 71

the angles at 1 and 2 — is equal to the angle at the center,
0, between the points 1 and 2. By measuring these angu-
lar distances of the star from the zenith, the astronomer
finds the angles at the center of the earth between the sta-
tions 1, 2, 3, etc., at which his observations are made. If
the meridian were a perfect circle the change of zenith dis-
tance of the star, as one traveled along a meridian from the
equator to the pole, would be perfectly uniform — the same
number of degrees for each hundred miles traveled — and
observations made in many parts of the earth show that
this is very nearly true, but that, on the whole, as we ap-
proach the pole it is necessary to travel a little greater dis-
tance than is required for a given change in the angle at
the equator. The earth is, in fact, flattened at the poles to
the amount of about 27 miles in the length of its diameter,
and by this -amount, as well as by smaller variations due to
mountains and valleys, the shape of the earth differs from
a perfect sphere. These astronomical measurements of the
curvature of the earth's surface furnish by far the most sat-
isfactory proof that it is very approximately a sphere, and
furnish as its equatorial diameter 7,926 miles.

Neglecting ths compression, as it is called, i. e., the 27
miles by which the equatorial diameter exceeds the polar,
the size of the earth may easily be found by measuring the
distance 1 — 2 along the surface and by combining with this
the angle 102 obtained through measuring the meridian
altitudes of any star as seen from 1 and 2. Draw on paper
an angle equal to the measured difference of altitude and
find how far you must go from its vertex in order to have
the distance between the sides, measured along an arc of
a circle, equal to the measured distance between 1 and 2.
This distance from the vertex will be the earth's radius.

EXERCISE 19. — Measure the diameter of the earth by
the method given above. In order that this may be done
satisfactorily, the two stations at which observations are
made must be separated by a considerable distance — i. e.,

ASTBONOMY

200 miles. They need not be on the same meridian, but if
they are on different meridians in place of the actual dis-
tance between them, there must be used the projection of
that distance upon the meridian — i. e., the north and south
part of the distance.

By co-operation between schools in the Northern and
Southern States, using a good map to obtain the required
distances, the diameter of the earth
may be measured with the plumb-
line apparatus described in Chapter
II and determined within a small
percentage of its true value.

45. The mass of the earth.— We
have seen in Chapter IV the possi-
bility of determining the masses of
the planets as fractional parts of
the sun's mass, but nothing was
there shown, or could be shown,
about measuring these masses after
the common fashion in kilogrammes
or tons. To do this we must first
get the mass of the earth in tons or
kilogrammes, and while the princi-
ples involved in this determination
are simple enough, their actual ap-
. 26. -illustrating the prin- plication is delicate and difficult.

In Fig. 26 we suppose a long
plumb line to be suspended above
the surface of the earth and to be attracted toward the
center of the earth, (7, by a force whose intensity is (Chap-
ter IV)

1C

ciples involved in weighing
the earth.

where E denotes the mass of the earth, which is to be de-
termined by experiment, and R is the radius of the earth,
3,963 miles. If there is no disturbing influence present,

THE EARTH AS A PLANET 73

the plumb line will point directly downward, but if a mas-
sive ball of lead or other heavy substance is placed at one
side, ^, it will attract the plumb line with a force equal to

/ = k m^ ,

where r is the distance of its center from the plumb bob
and B is its mass which we may suppose, for illustration,
to be a ton. In consequence of this attraction the plumb
line will be pulled a little to one side, as shown by the dot-
ted line, and if we represent by I the length of the plumb
line and by d the distance between the original and the
disturbed positions of the plumb bob we may write the pro-
portion

and introducing the values of F and / given above, and
solving for J^the proportion thus transformed, we find

T7T ~D v / -iV

J]j =T £} . — .

d \ T

In this equation the mass of the ball, B, the length of the
plumb line, I, the distance between the center of the ball
and the center of the plumb bob, r, and the radius of the
earth, R, can all be measured directly, and d, the amount
by which the plumb bob is pulled to one side by the ball, is
readily found by shifting the ball over to the other side, at
2) and measuring with a microscope how far the plumb
bob moves. This distance will, of course, be equal to 2 d.

By methods involving these principles, but applied in a
manner more complicated as well as more precise, the mass
of the earth is found to be, in tons, 6,642 X 1018 — i. e., 6,642
followed by 18 ciphers, or in kilogrammes 60,258 X 1020.
The earth's atmosphere makes up about a millionth part
of this mass.

If the length of the plumb line were 100 feet, the
weight of the ball a ton, and the distance between the two
6

74 ASTRONOMY

positions of the ball, 1 and #, six feet, how many inches, d,
would the plumb bob be pulled out of place ?

Find from the mass of the earth and the data of § 40
the mass of the sun in tons. Find also the mass of Mars.
The computation can be very greatly abridged by the use
of logarithms.

46. Precession,— That the earth is isolated in space and
has no support upon which to rest, is sufficiently shown by
the fact that the stars are visible upon every side of it, and
no support can be seen stretching out toward them. We
must then consider the earth to be a globe traveling freely
about the sun in a circuit which it completes once every
year, and rotating once in every twenty-four hours about
an axis which remains at all seasons directed very nearly
toward the star Polaris. The student should be able to
show from his own observations of the sun that, with refer-
ence to the stars, the direction of the sun from the earth
changes about a degree a day. Does this prove that the
earth revolves about the sun ?

But it is only in appearance that the pole maintains its
fixed position among the stars. If photographs are taken
year after year, after the manner of Exercise 7, it will be
found that slowly the pole is moving (nearly) toward Po-
laris, and making this star describe a smaller and smaller
circle in its diurnal path, while stars on the other side of
the pole (in right ascension 12h.) become more distant
from it and describe larger circles in their diurnal motion ;
but the process takes place so slowly that the space of a
lifetime is required for the motion of the pole to equal the
angular diameter of the full moon.

Spin a top and note how its rapid whirl about its axis
corresponds to the earth's diurnal rotation. When the axis
about which the top spins is truly vertical the top " sleeps " ;
but if the axis is tipped ever so little away from the verti-
cal it begins to wabble, so that if we imagine the axis pro-
longed out to the sky and provided with a pencil point as

THE EARTH AS A PLANET 75

a marker, this would trace a circle around the zenith, along
which the pole of the top would move, and a little observa-
tion will show that the more the top is tipped from the
vertical the larger does this circle become and the more
rapidly does the wabbling take place. Were it not for the
spinning of the top about its axis, it would promptly fall
over when tipped from the vertical position, but the spin
combines with the force which pulls the top over and pro-
duces the wabbling motion. Spin the top in opposite
directions, with the hands of a watch and contrary to the
hands of a watch, and note the effect which is produced
upon the wabbling.

The earth presents many points of resemblance to the
top. Its diurnal rotation is the spin about the axis. This
axis is tipped 23.5° away frojn the perpendicular to its
orbit (obliquity of the ecliptic) just as the axis of the top
is tipped away from the vertical line. In consequence of
its rapid spin, the body of the earth bulges out at the equa-
tor (27 miles), and the sun and moon, by virtue of their at-
traction (see Chapter IV), lay hold of this protuberance and
pull it down toward the plane of the earth's orbit, so that if
it were not for the spin this force would straighten the axis
up and set it perpendicular to the orbit plane. But here, as
in the case of the top, the spin and the tipping force com-
bine to produce a wabble which is called precession, and
whose effect we recognize in the shifting position of the
pole among the stars. The motion of precession is very
much slower than the wabbling of the top, since the tip-
ping force for the earth is relatively very small, and a pe-
riod of nearly 26,000 years is required for a complete cir-
cuit of the pole about its center of motion. Friction ulti-
mately stops both the spin and the wabble of the top, but
this influence seems wholly absent in the case of the earth,
and both rotation and precession go on unchanged from
century to century, save for certain minor forces which for
a time change the direction or rate of the precessional

76 ASTRONOMY

motion, first in one way and then in another, without in
the long run producing any results of consequence.

The center of motion, about which the pole travels in a
small circle having an angular radius of 23.5°, is at that
point of the heavens toward which a perpendicular to the
plane of the earth's orbit points, and may be found on the
star map in right ascension 18h. Om. and declination 66.5°.

EXERCISE 20. — Find this point on the map, and draw
as well as you can the path of the pole about it. The mo-
tion of the pole along its path is toward the constellation
Cepheus. Mark the position of the pole along this path
at intervals of 1,000 years, and refer to these positions in
dealing with some of the following questions :

Does the wabbling of the top occur in the same direc-
tion as the motion of precession ? Do the tipping forces
applied to the earth and top act in the same direction ?
What will be the polar star 12,000 years hence? The
Great Pyramid of Egypt is thought to have been used
as an observatory when Alpha Draconis was the bright star
nearest the pole. How long ago was that ?

The motion of the pole of course carries the equator
and the equinoxes with it, and thus slowly changes the
right ascensions and declinations of all the stars. On this
account it is frequently called the precession of the equi-
noxes, and this motion of the equinox, slow though it is,
is a matter of some consequence in connection with chro-
nology and the length of the year.

Will the precession ever bring back the right ascen-
sions and declinations to be again what they now are ?

In what direction is the pole moving with respect to
the Big Dipper ? Will its motion ever bring it exactly to
Polaris ? How far away from Polaris will the precession
carry the pole ? What other bright stars will be brought
near the pole by the precession ?

47. The warming of the earth. — Winter and summer alike
the day is on the average warmer than the night, and it is

THE EARTH AS A PLANET ff

easy to see that this surplus of heat comes from the sun by
day and is lost by night through radiation into the void
which surrounds the earth ; just as the heat contained in a
mass of molten iron is radiated away and the iron cooled
when it is taken out from the furnace and placed amid
colder surroundings. The earth's loss of heat by radiation
goes on ceaselessly day and night, and were it not for the
influx of solar heat this radiation would steadily diminish
the temperature toward what is called the " absolute zero "
— i. e., a state in which all heat has been taken away and
beyond which there can be no greater degree of cold. This
must not be confounded with the zero temperatures shown
by our thermometers, since it lies nearly 500° below the zero
of the Fahrenheit scale (—273° Centigrade), a temperature
which by comparison makes the coldest winter weather
seem warm, although the ordinary thermometer may regis-
ter many degrees below its zero. The heat radiated by the
sun into the surrounding space on every side of it is another
example of the same cooling process, a hot body giving up
its hea.t to the colder space about it, and it is the minute
fraction of this heat poured out by the sun, and in small
part intercepted by the earth, which warms the latter and
produces what we call weather, climate, the seasons, etc.

Observe the fluctuations, the ebb and flow, which are
inherent in this process. From sunset to sunrise there is
nothing to compensate the steady outflow of heat, and
air and ground grow steadily colder, but with the sunrise
there comes an influx of solar heat, feeble at first' because
it strikes the earth's surface very obliquely, but becoming
more and more efficient as the sun rises higher in the sky.
But as the air and the ground grow warm during the morn-
ing hours they part more and more readily and rapidly with
their store of heat, just as a steam pipe or a cup of coffee
radiates heat more rapidly when very hot. The warmest
hour of the day is reached when these opposing tendencies
of income and expenditure of heat are just balanced ; and

78 ASTRONOMY

barring such disturbing factors as wind and clouds, the gain
in temperature usually extends to the time — an hour or two
beyond noon — at which the diminishing altitude of the sun
renders his rays less efficient, when radiation gains the
upper hand and the temperature becomes for a short time
stationary, and then commences to fall steadily until the
next sunrise.

We have here an example of what is called a periodic
change — i. e., one which, within a definite and uniform
period (24 hours), oscillates from a minimum up to a
maximum temperature and then back again to a minimum,
repeating substantially the same variation day after day.
But it must be understood that minor causes not taken
into account above, such as winds, water, etc., produce
other fluctuations from day to day which sometimes ob-
scure or even obliterate the diurnal variation of tempera-
ture caused by the sun.

Expose the back of your hand to the sun, holding the
hand in such a position that the sunlight strikes perpen-
dicularly upon it; then turn the hand so that the light
falls quite obliquely upon it and note how much more vig-
orous is the warming effect of the sun in the first position
than in the second. It is chiefly this difference of angle
that makes the sun's warmth more effective when he is
high up in the sky than when he is near the horizon, and
more effective in summer than in winter.

We have seen in Chapter III that the sun's motion
among the stars takes place along a path which carries it
alternately north and south of the equator to a distance
of 23.5°, and the stars show by their earlier risings and
later settings, as we pass from the equator toward the
north pole of the heavens, that as the sun moves north-
ward from the equator, each day in the northern hemi-
sphere will become a little longer, each night a little shorter,
and every day the sun will rise higher toward the zenith
until this process culminates toward the end of June, when

THE EARTH AS A PLANET 79

the sun begins to move southward, bringing shorter days
and smaller altitudes until the Christmas season, when
again it is reversed and the sun moves northward. "We
have here another periodic variation, which runs its com-
plete course in a period of a year, and it is easy to see that
this variation must have a marked effect on the warming
of the earth, the long days and great altitudes of summer
producing the greater warmth of that season, while the
shorter days and lower altitudes of December, by diminish-
ing the daily supply of solar heat, bring on the winter's
cold. The succession of the seasons, winter following sum-
mer and summer winter, is caused by the varying altitude
of the sun, and this in turn is due to the obliquity of the
ecliptic, or, what is the same thing, the amount by which
the axis of the earth is tipped from being perpendicular to
the plane of its orbit, and the seasons are simply a periodic
change in the warming of the earth, quite comparable with
the diurnal change but of longer period.

It is evident that the period within which the succession
of winter and summer is completed, the year, as we com-
monly call it, must equal the time required by the sun to
go from the vernal equinox around to the vernal equinox
again, since this furnishes a complete cycle of the sun's
motions north and south from the equator. On account
of the westward motion of the equinox (precession) this
is not quite the same as the time required for a com-
plete revolution of the earth in its orbit, but is a little
shorter (20m. 23s.), since the equinox moves back to meet
the sun.

48. Relation of the sun to climate,— It is clear that both
the northern and southern hemispheres of the earth must
have substantially the same kind of seasons, since the mo-
tion of the sun north and south affects both alike ; but
when the sun is north of the equator and warming our
hemisphere most effectively, his light falls more obliquely
upon the other hemisphere, the days there are short and

80 ASTRONOMY

winter reigns at the time we are enjoying summer, while
six months later the conditions are reversed.

In those parts of the earth near the equator — the torrid
zone —there is no such marked change from cold to warm
as we experience, because, as the sun never gets more than
23.5° away from the celestial equator, on every day of the
year he mounts high in the tropic skies, always coming
within 23.5° of the zenith, and usually closer than this, so
that there is no such periodic change in the heat supply as
is experienced in higher latitudes, and within the tropics
the temperature is therefore both higher and more uniform
than in our latitude.

In the frigid zones, on the contrary, the sun never rises
high in the sky ; at the poles his greatest altitude is only
23.5°, and during the winter season he does not rise at all,
so that the temperature is here low the whole year round,
and during the winter season, when for weeks or months at
a time the supply of solar light is entirely cut off, the tem-
perature falls to a degree unknown in more favored climes.

If the obliquity of the ecliptic were made 10° greater,
what would be the effect upon the seasons in the temperate
zones ? What if it were made 10° less ?

Does the precession of the equinoxes have any effect
upon the seasons or upon the climate of different parts of
the earth ?

If the axis of the earth pointed toward Arcturus instead
of Polaris, would the seasons be any different from what
they are now ?

49. The atmosphere. — Although we live upon its surface,
we are not outside the earth, but at the bottom of a sea of
air which forms the earth's outermost layer and extends
above our heads to a height of many miles. The study of
most of the phenomena of the atmosphere belongs to that
branch of physics called meteorology, but there are a few
matters which fairly come within oar consideration of the
earth as a planet.

THE EARTH AS A PLANET 81

We can not see the stars save as we look through this
atmosphere, and the light which comes through it is bent
and oftentimes distorted so as to present serious obstacles
to any accurate telescopic study of the heavenly bodies.
Frequently this disturbance is visible to the naked eye, and
the stars are said to twinkle — i. e., to quiver and change
color many times per second, solely in consequence of a dis-
turbed condition of the air and not from anything which
goes on in the star. This effect is more marked low down
in the sky than near the zenith, and it is worth noting that
the planets show very little of it because the light they
send to the earth comes from a disk of sensible area, while
a star, being much smaller and farther from the earth, has
its disk reduced practically to a mere point whose light is
more easily affected by local disturbances in the atmosphere
than is the broader beam which comes from the planets'
disk.

50. Refraction. — At all times, whether the stars twinkle
or not, their light is bent in its passage through the atmos-
phere, so that the stars appear to stand higher up in the
sky than their true positions. This effect, which the as-
tronomer calls refraction, must be allowed for in observa-
tions of the more precise class, although save at low alti-
tudes its amount is a very small fraction of a degree, but
near the horizon it is much exaggerated in amount and
becomes easily visible to the naked eye by distorting the
disks of the sun and moon from circles into ovals with
their long diameters horizontal. The refraction lifts both
upper and lower edge of the sun, but lifts the lower edge
more than the upper, thus shortening the vertical diameter.
See Fig. 27, which shows not only this effect, but also the
reflection of the sun from the curved surface of the sea,
still further flattening the image. If the surface of the
water were flat, the reflected image would have the same
shape as the sun's disk, and its altered appearance is some-
times cited as a proof that the earth's surface is curved.

82

ASTRONOMY

The total amount of the refraction at the horizon is a
little more than half a degree, and since the diameters of
the sun and moon subtend an angle of about half a degree,
we have the remarkable result that in reality the whole

BF

FIG. 2?.— Flattening of the sun's disk by refraction and by reflection from the
surface of the sea.

disk of either sun or moon is below the horizon at the
instant that the lower edge appears to touch the horizon
and sunset or moonset begins. The same effect exists at
sunrise, and as a consequence the duration of sunshine or
of moonshine is on the average about six minutes longer
each day than it would be if there were no atmosphere and
no refraction. A partial offset to this benefit is found in
the fact that the atmosphere absorbs the light of the heav-
enly bodies, so that stars appear much less bright when
near the horizon than when they are higher up in the sky,
and by reason of this absorption the setting sun can be
looked at with the naked eye without the discomfort which
its dazzling luster causes at noon.

51. The twilight.— Another effect of the atmosphere,
even more marked than the preceding, is the twilight. As

THE EARTH AS A PLANET 83

at sunrise the mountain top catches the rays of the coming
sun before they reach the lowland, and at sunset it keeps
them after they have faded from the regions below, so the
particles of dust and vapor, which always float in the atmos-
phere, catch the sunlight and reflect it to the surface of the
earth while the sun is still below the horizon, giving at the
beginning and end of day that vague and diffuse light which
we call twilight.

Fig. 28 shows a part of the earth surrounded by such a
dust-laden atmosphere, which is illuminated on the left by
the rays of the sun, but which, on the right of the figure,
lies in the shadow cast
by the earth. To an
observer placed at 1 the
sun is just setting, and
all the atmosphere
above 'him is illumined
with its rays, which

furnish a bright twi- FIG. 28.-Twilight phenomena.

light. When, by the earth's rotation, this observer has been
carried to #, all the region to the east of his zenith lies in
the shadow, while to the west there is a part of the atmos-
phere from which there still comes a twilight, but now com-
paratively faint, because the lower part of the atmosphere
about our observer lies in the shadow, and it is mainly
its upper regions from which the light comes, and here the
dust and moisture are much less abundant than in the lower
strata. Still later, when the observer has been carried by the
earth's rotation to the point 3, every vestige of twilight will
have vanished from his sky, because all of the illuminated
part of the atmosphere is now below his horizon, which is
represented by the line 8 L. In the figure the sun is rep-
resented to be 78° below this horizon line at the end of twi-
light, but this is a gross exaggeration, made for the sake of
clearness in the drawing — in fact, twilight is usually said
to end when the sun is 18° below the horizon.

84 ASTRONOMY

Let the student redraw Fig. 28 on a large scale, so that
the points 1 and 2 shall be only 18° apart, as seen from the
earth's center. He will find that the point L is brought
down much closer to the surface of the earth, and measur-
ing the length of the line 2 L, he should find for the " height
of the atmosphere " about one-eightieth part of the radius
of the earth — i. e., a little less than 50 miles. This, how-
ever, is not the true height of the atmosphere. The air
extends far beyond this, but the particles of dust and vapor
which are capable of sending sunlight down to the earth
seem all to lie below this limit.

The student should not fail to watch the eastern sky
after sunset, and see the shadow of the earth rise up and
fill it while the twilight arch retreats steadily toward the
west.

Duration of tivilight. — Since twilight ends when the sun
is 18° below the horizon, any circumstance which makes

FIG. 29.— The cause of long and short twilights.

the sun go down rapidly will shorten the duration of twi-
light, and anything which retards the downward motion
of the sun will correspondingly prolong it. Chief among
influences of this kind is the angle which the sun's course
makes with the horizon. If it goes straight down, as at
a, Fig. 29, a much shorter time will suffice to carry it to
a depression of 18° than is needed in the case shown at
I in the same figure, where the motion is very oblique to
the horizon. If we consider different latitudes and differ-
ent seasons of the year, we shall find every possible variety

THE EARTH AS A PLANET 85

of circumstance from a to #, and corresponding to these,
the duration of twilight varies from an all-night duration
in the summers of Scotland and more northern lands to a
half hour or less in the mountains of Peru.

Coleridge does not much exaggerate the shortness of
tropical twilight in the lines,

" The sun's rim dips ; the stars rush out :
At one stride comes the dark."

The, Ancient Mariner.

In the United States the longest twilights come at the
end of June, and last for a little more than two hours,
while the shortest ones are in March and September,
amounting to a little more than an hour and a half ; but
at all times the last half hour of twilight is hardly to be
distinguished from night, so small is the quantity of re-
flecting matter in the upper regions of the atmosphere.
For practical convenience it is customary to assume in
the courts of law that twilight ends an hour after sunset.

How long does twilight last at the north pole ?

The Aurora. — One other phenomenon of the atmos-
phere may be mentioned, only to point out that it is not
of an astronomical character. The Aurora, or northern
lights, is as purely an affair of the earth as is a thunder-
storm, and its explanation belongs to the subject of ter-
restrial magnetism.

CHAPTER VI

THE MEASUREMENT OP TIME

52. Solar time. — To measure any quantity we need a unit
in terms of which it must be expressed. Angles are meas-
ured in degrees, and the degree is the unit for angular meas-
urement. For most scientific purposes the centimeter is
adopted as the unit with which to measure distances, and
similarly a day is the fundamental unit for the measure-
ment of time. Hours, minutes, and seconds are aliquot
parts of this unit convenient for use in dealing with shorter
periods than a day, and the week, month, and year which
we use in our calendars are multiples of the day.

Strictly speaking, a day is not the time required by the
earth to make one revolution upon its axis, but it is best
defined as the amount of time required for a particular part
of the sky to make the complete circuit from the meridian
of a particular place through west and east back to the
meridian again. The day begins at the moment when this
specified part of the sky is on the meridian, and " the time "
at any moment is the hour angle of this particular part of
the sky — i. e., the number of hours, minutes, etc., tha£ have
elapsed since it was on the meridian.

The student has already become familiar with the kind
of day which is based upon the motion of the vernal equi-
nox, and which furnishes sidereal time, and he has seen
that sidereal time, while very convenient in dealing with
the motions of the stars, is decidedly inconvenient for the
ordinary affairs of life since in the reckoning of the hours
it takes no account of daylight and darkness. One can not

THE MEASUREMENT OF TIME §7

tell off-hand whether 10 hours, sidereal time, falls in the day
or in the night. We must in some way obtain a day and a
system of time reckoning based upon the apparent diurnal
motion of the sun, and we may, if we choose, take the sun
itself as the point in the heavens whose transit over the
meridian shall mark the beginning and the end of the day.
In this system " the time " is the number of hours, minutes,
etc., which have elapsed since the sun was on the meridian,
and this is the kind of time which is shown by a sun dial,
and which was in general use, years ago, before clocks and
watches became common. Since the sun moves among the
stars about a degree per day, it is easily seen that the rotat-
ing earth will have to turn farther in order to carry any
particular meridian from the sun around to the sun again,
than to carry it from a star around to the same star, or
from the vernal equinox around to the vernal equinox
again; just as the minute hand of a clock turns farther
in going from the hour hand round to the hour hand again
than it turns in going from XII to XII. These solar days
and hours and minutes are therefore a little longer than
the corresponding sidereal ones, and this furnishes the ex-
planation why the stars come to the meridian a little ear-
lier, by solar time, every night than on the night before, and
why sidereal time gains steadily upon solar time, this gain
amounting to approximately 3m. 56.5s. per day, or exactly
one day per year, since the sun makes the complete circuit
of the constellations once in a year.

With the general introduction of clocks and watches
into use about a century ago this kind of solar time went
out of common use, since no well-regulated clock could
keep the time correctly. The earth in its orbital motion
around the sun goes faster in some parts of its orbit than
in others, and in consequence the sun appears to move
more rapidly among the stars in winter than in summer ;
moreover, on account of the convergence of hour circles
as we go away from the equator, the same amount of mo-

88 ASTRONOMY

tion along the ecliptic produces more effect in winter and
summer when the sun is north or south, than it does in the
spring and autumn when the sun is near the equator, and
as a combined result of these causes and other minor ones
true solar time, as it is called, is itself not uniform, but
falls behind the uniform lapse of sidereal time at a variable
rate, sometimes quicker, sometimes slower. A true solar
day, from noon to noon, is 51 seconds linger in September
than in December.

53. Mean solar time. — To remedy these inconveniences
there has been invented and brought into common use

+/5JW

+fOm

Om
—5m
—10m.

z

^-^

\

/
/
I

\

/

/

I

>

\

/

'

\

f

\

* X

/

'

\

I

—

\

/

1

\

/

Ja

i
n.f Fcb.i Ma

r.t Apr.fMa

V 1 Jin

e 1 Jv

y 1 Ji,

g.ffept.f Oc

t.1 Nor.f DC

c.i Jaw./

FIG. 30.— The equation of time.

what is called mean solar time, which is perfectly uniform
in its lapse and which, by comparison with sidereal time,
loses exactly one day per year. " The time " in this system
never differs much from true solar time, and the difference
between the two for any particular day may be found in
any good almanac, or may be read from the curve in Fig.
30, in which the part of the curve above the line marked
Om shows how many minutes mean solar time is faster than
true solar time. The correct name for this difference be-
tween the two kinds of solar time is the equation of time, but
in the almanacs it is frequently marked " sun fast " or " sun
slow." In sidereal time and true solar time the distinction

THE MEASUREMENT OF TIME 89

between A. M. hours (ante meridiem = before the sun reaches
the meridian) and p. M. hours (post meridiem = after the
sun has passed the meridian) is not observed, " the time "
being counted from 0 hours to 24 hours, commencing when
the sun or vernal equinox is on the meridian. Occasion-
ally the attempt is made to introduce into common use
this mode of reckoning the hours, beginning the day
(date) at midnight and counting the hours consecutively
up to 24, when the next date is reached and a new start
made. Such a system would simplify railway time tables
and similar publications ; but the American public is slow
to adopt it, although the system has come into practical
use in Canada and Spain.

54. To find (approximately) the sidereal time at any mo-
ment. — RULE I. When the mean solar time is known. Let
W represent the time shown by an ordinary watch, and
represent by S the corresponding sidereal time and by D
the number of days that have elapsed from March 23d to
the date in question. Then

S= W+ftxDX*.

The last term is expressed in minutes, and should be re-
duced to hours and minutes. Thus at 4 p. M. on July 4th —

D = 103 days.
f J X D X 4 = 406m.

= 6h. 46m.
W=4h. Om.

46m.

The daily gain of sidereal upon mean solar time is f§- of 4
minutes, and March 23d is the date on which sidereal and
mean solar time are together, taking the average of one year
with another, but it varies a little from year to year on
account of the extra day introduced in leap years.

RULE II. When the stars in the northern sky can be
seen. Find (3 Cassiopeiae, and imagine a line drawn from it
7

90 ASTRONOMY

to Polaris, and another line from Polaris to the zenith.
The sidereal time is equal to the angle between these lines,
provided that that angle must be measured from the zenith
toward the west Turn the angle from degrees into hours
by dividing by 15.

55. The earth's rotation. — We are familiar with the fact
that a watch may run faster at one time than at another,
and it is worth while to inquire if the same is not true of
our chief timepiece — the earth. It is assumed in the sec-
tions upon the measurement of time that the earth turns
about its axis with absolute uniformity, so that mean solar
time never gains or loses even the smallest fraction of a
second. Whether this be absolutely true or not, no one has
ever succeeded in finding convincing proof of a variation
large enough to be measured, although it has recently been
shown that the axis about which it rotates is not perfectly
fixed within the body of the earth. The solid body of the
earth wriggles about this axis like a fish upon a hook, so
that the position of the north pole upon the earth's sur-
face changes within a year to the extent of 40 or 50 feet
(15 meters) without ever getting more than this distance
away from its average position. This is probably caused
by the periodical shifting of masses of air and water from
one part of the earth to another as the seasons change,
and it seems probable that these changes will produce
some small effect upon the rotation of the earth. But in
spite of these, for any such moderate interval of time as a
year or a century, so far as present knowledge goes, we may
regard the earth's rotation as uniform and undisturbed.
For longer intervals— e. g., 1,000,000 or 10,000,000 years—
the question is a very different one, and we shall have to
meet it again in another connection.

56. Longitude and time.— In what precedes there has
been constant reference to the meridian. The day begins
when the sun is on the meridian. Solar time is the angu-
lar distance of the sun past the meridian. Sidereal time

THE MEASUREMENT OF TIME

91

FIG. 31. — Longitude and time.

was determined by observing transits of stars over a me-
ridian line actually laid out upon the ground, etc. But
every place upon the earth has its own meridian from
which " the time " may be reckoned, and in Fig. 31, where
the rays of sunlight
are represented as
falling upon a part
of the earth's equa-
tor through which
the meridians o1
New York, Chicago,
and San Francisco
pass, it is evident
that these rays make
different angles with
the meridians, and
that the sun is farther from the meridian of New York;
than from that of San Francisco by an amount just equal
to the angle at 0 between these meridians. This angle is
called by geographers the difference of longitude between
the two places, and the student should note that the word
longitude is here used in a different sense from that on
page 36. From Fig. 31 we obtain the

Theorem. — The difference between " the times " at any
two meridians is equal to their difference of longitude, and
the time at the eastern meridian is greater than at the
western meridian. Astronomers usually express differences
of longitude in hours instead of degrees. Ih. = 15°.

The name given to any kind of time should distinguish
all the elements which enter into it — e. g., New York
sidereal time means the hour angle of the vernal equinox
measured from the meridian of New York, Chicago true
solar time is the hour angle of the sun reckoned from the
meridian of Chicago, etc.

57. Standard time. — The requirements of railroad traffic
have led to the use throughout the United States and

THE MEASUREMENT OF TIME 93

Canada of four " standard times," each of which is a mean
solar time some integral number of hours slower than the
time of the meridian passing through the Royal Observa-
tory at Greenwich, England.

Eastern time is 5 hours slower than that of Greenwich.
Central " 6 "
Mountain " 7 "
Pacific " 8 "

In Fig. 32 the broken lines indicate roughly the parts of
the United States and Canada in which these several kinds
of time are used, and illustrate how irregular are the bound-
aries of these parts.

Standard time is sent daily into all of the more impor-
tant telegraph offices of the United States, and serves to
regulate watches and clocks, to the almost complete exclu-
sion of local time.

58. To determine the longitude. — With an ordinary watch
observe the time of the sun's transit over your local me-
ridian, and correct the observed time for the equation of
time by means of the curve in Fig. 30. The difference
between the corrected time and 12 o'clock will be the cor-
rection of your watch referred to local mean solar time.
Compare your watch with the time signals in the nearest
telegraph office and find its correction referred to standard
time. The difference between the two corrections is the
difference between your longitude and that of the standard
meridian.

X. B. — Don't tamper with the watch by trying to " set it
right." No harm will be done if it is wrong, provided you
take due account of the correction as indicated above.

If the correction of the watch changed between your
observation and the comparison in the telegraph office,
what effect would it have upon the longitude determina-
tion ? How can you avoid this effect ?

59. Chronology, — The Century Dictionary defines chro-
nology as " the science of time " — that is, " the method of

94: ASTRONOMY

measuring or computing time by regular divisions or pe-
riods according to the revolutions of the sun or moon."

We have already seen that for the measurement of short
intervals of time the day and its subdivisions — hours,
minutes, seconds — furnish a very complete and convenient
system. But for longer periods, extending to hundreds and
thousands of days, a larger unit of time is required, and for
the most part these longer units have in all ages and among
all peoples been based upon astronomical considerations.
But to this there is one marked exception. The week is a
simple multiple of the day, as the dime is a multiple of the
cent, and while it may have had its origin in the changing
phases of the moon this is at best doubtful, since it does
not follow these with any considerable accuracy. If the
still longer units of time— the month and the year — had
equally been made to consist of an integral number of days
much confusion and misunderstanding might have been
avoided, and the annals of ancient times would have pre-
sented fewer pitfalls to the historian than is now the case.
The month is plainly connected with the motion of the
moon among the stars. The year is, of course, based upon
the motion of the sun through the heavens and the change
of seasons which is thus produced ; although, as commonly
employed, it is not quite the same as the time required by
the earth to make one complete revolution in its orbit.
This time of one revolution is called a sidereal year, while,
as we have already seen in Chapter V, the year which
measures the course of the seasons is shorter than this on
account of the precession of the equinoxes. It is called a
tropical year with reference to the circuit which the sun
makes from one tropic to the other and back again.

We can readily understand why primitive peoples should
adopt as units of time these natural periods, but in so
doing they incurred much the same kind of difficulty that
we should experience in trying to use both English and
American money in the ordinary transactions of life. How

THE MEASUREMENT OF TIME 95

many dollars make a pound sterling ? How shall we make
change with English shillings and American dimes, etc. ?
How much is one unit worth in terms of the other ?

One of the Greek poets * has left us a quaint account of
the confusion which existed in his time with regard to the*
place of months and moons in the calendar :

" The moon by us to you her greeting sends,
But bids us say that she's an ill-used moon
And takes it much amiss that you will still
Shuffle her days and turn them topsy-turvy,
So that when gods, who know their feast days well,
By your false count are sent home supperless,
They scold and storm at her for your neglect."

60. Day, month, and year. — If the day, the month, and
the year are to be used concurrently, it is necessary to
determine how many days are contained in the month and
year, and when this has been done by the astronomer the
numbers are found to be very awkward and inconvenient
for daily use ; and much of the history of chronology
consists in an account of the various devices by which in-
genious men have sought to use integral numbers to replace
the cumbrous decimal fractions which follow.

According to Professor Harkness, for the epoch 1900
A. D. —

One tropical year = 365.242197 mean solar days.

" = 365d. 5h. 48m. 45.8s.
One lunation = 29.530588 mean solar days.
= 29d. 12h. 44m. 2.8s.

The word lunation means the average interval from one
new moon to the next one — i. e., the time required by the
moon to go from conjunction with the sun round to con-
junction again.

A very ancient device was to call a year equal to 365

* Aristophanes, The Clouds, WhewelPs translation.

96 ASTRONOMY

days, and to have months alternately of 29 and 30 days in
length, but this was unsatisfactory in more than, one way.
At the end of four years this artificial calendar would be
about one day ahead of the true one, at the end of forty
years ten days in error, and within a single lifetime the
seasons would have appreciably changed their position in
the year, April weather being due in March, according to
the calendar. So, too, the year under this arrangement
did not consist of any integral number of months, 12
months of the average length of 29.5 days being 354 days,
and 13 months 383.5 days, thus making any particular
month change its position from the beginning to the mid-
dle and the end of the year within a comparatively short
time. Some peoples gave up the astronomical year as an
independent unit and adopted a conventional year of 12
lunar months, 354 days, which is now in use in certain
Mohammedan countries, where it is known as the wander-
ing year, with reference to the changing positions of the
seasons in such a year. Others held to the astronomical
year and adopted a system of conventional months, such
that twelve of them would just make up a year, as is done
to this day in our own calendar, whose months of arbitrary
length we are compelled to remember by some such jingle
as the following :

" Thirty days hath September,
April, June, and November ;
All the rest have thirty-one
Save February,

Which alone hath twenty-eight,
Till leap year gives it twenty-nine."

61. The calendar. — The foundations of our calendar may
fairly be ascribed to Julius Caesar, who, under the advice
of the Egyptian astronomer Sosigines, adopted the old
Egyptian device of a leap year, whereby every fourth year
was to consist of 366 days, while ordinary years were only
365 days long. He also placed the beginning of the year

THE MEASUREMENT OF TIME 97

at the first of January, instead of in March, where it had
formerly been, and gave his own name, Julius, to the month
which we now call July. August was afterward named in
honor of his successor^ Augustus. The names of the earlier
months of the year are drawn from Eoman mythology;
those of the later months, September, October, etc., mean-
ing seventh month, eighth month, represent the places of
these months in the year, before Caesar's reformation, and
also their places in some of the subsequent calendars, for
the widest diversity of practice existed during mediaeval
times with regard to the day on which -the new year should
begin, Christmas, Easter, March 25th, and others having been
employed at different times and places.

The system of leap years introduced by Caesar makes
the average length of a year 365.25 days, which differs by
about eleven minutes from the true length of the tropical
year, a difference so small that for ordinary purposes no
better approximation to the true length of the year need
be desired. But any deviation from the true length, how-
ever small, must in the course of time shift the seasons, the
vernal and autumnal equinox, to another part of the year,
and the ecclesiastical authorities of mediaeval Europe found
here ground for objection to Caesar's calendar, since the
great Church festival of Easter has its date determined
with reference to the vernal equinox, and with the lapse of
centuries Easter became more and more displaced in the
calendar, until Pope Gregory XIII, late in the sixteenth
century, decreed another reformation, whereby ten days
were dropped from the calendar, the day after March llth
being called March 21st, to bring back the vernal equinox
to the date on which it fell in A. D. 325, the time of the
Council of Nicaea, which Gregory adopted as the funda-
mental epoch of his calendar.

The calendar having thus been brought back into agree-
ment with that of old time, Gregory purposed to keep it in
such agreement for the future by modifying Caesar's leap-

98 ASTRONOMY

year rule so that it should run : Every year whose number
is divisible by 4 shall be a leap year except those years
whose numbers are divisible by 100 but not divisible by
400. These latter years — e. g., 1900 — are counted as com-
mon years. The calendar thus altered is called Gregorian
to distinguish it from the older, Julian calendar, and it
found speedy acceptance in those civilized countries whose
Church adhered to Rome ; but the Protestant powers were
slow to adopt it, and it was introduced into England and
her American colonies by act of Parliament in the year
1752, nearly two centuries after Gregory's time. In Rus-
sia the Julian calendar has remained in common use to
our own day, but in commercial affairs it is there cus-
tomary to write the date according to both calendars —
e. g., July T\, and at the present time strenuous exertions
are making in that country for the adoption of the Gre-
gorian calendar to the complete exclusion of the Julian
one.

The Julian and Gregorian calendars are frequently rep-
resented by the abbreviations 0. S. and N". S., old style,
new style, and as the older historical dates are usually ex-
pressed in 0. S., it is sometimes convenient to transform a
date from the one calendar to the other. This is readily
done by the formula

0 = ./•+(.»•- 2) -J

where G and J are the respective dates, N is the number
of the century, and the remainder is to be neglected in the
division by 4. For September 3, 1752, 0. S., we have

,7= Sept. 3

N-2 = +15

G = Sept. 14

THE MEASUREMENT OF TIME 99

and September 14 is the date fixed by act of Parliament to
correspond to September 3, 1752, 0. S. Columbus discovered
America on October 12, 1492, 0. S. What is the corre-
sponding date in the Gregorian calendar ?

62. The day of the week, — A problem similar to the
above but more complicated consists in finding the day of
the week on which any given date of the Gregorian cal-
endar falls— e. g., October 21, 1492.

The formula for this case is

Y-l Y-l Y-l

where Y denotes the given year, D the number of the day
(date) in that year, and q and r are respectively the quo-
tient and the remainder obtained by dividing the second
member of the equation by 7. If r — 1 the date falls on
Sunday, etc., and if r = 0 the day is Saturday. For the
example suggested above we have

Jan. 31 Y = 1492

Feb. 29 -\-D — +295

Mch. 31 +(;r_i)_±- 4= + 373

April 30 - ( r - 1) -^ 100 = 14

May 31 + (Y — 1) -f- 400 = + 3

June 30 ~*j~^L48

July 31

Aug. 31 0= 306

Sept. 30 r = 6 = Friday.

Oct. 21

Find from some history the day of the week on which
Columbus first saw America, and compare this with the
above.

On what day of the week did last Christmas fall ? On
what day of the week were you born ? In the formula for
the day of the week why does q have the coefficient 7 ?

100 ASTRONOMY

What principles in the calendar give rise to the divisors 4,
100,400?

For much curious and interesting information about
methods of reckoning the lapse of time the student may
consult the articles Calendar and Chronology in any good
encyclopaedia.

CHAPTEE VII

ECLIPSES

63. The nature of eclipses. — Every planet has a shadow
which travels with the planet along its orbit, always point-
ing directly away from the sun, and cutting off from a cer-
tain region of space the sunlight which otherwise would fill
it. For the most part these shadows are invisible, but occa-
sionally one of them falls upon a planet or some other body
which shines by reflected sunlight, and, cutting off its sup-
ply of light, produces the striking phenomenon which we
call an eclipse. The satellites of Jupiter, Saturn, and Mars
are eclipsed whenever they plunge into the shadows cast by
their respective planets, and Jupiter himself is partially
eclipsed when one of his own satellites passes between him
and the sun, and casts upon his broad surface a shadow too
small to cover more than a fraction of it.

But the eclipses of most interest to us are those of the
sun and moon, called respectively solar and lunar eclipses.
In Fig. 33 the full moon, M' , is shown immersed in the
shadow cast by the earth, and therefore eclipsed, and in the
same figure the new moon, Jf, is shown as casting its shadow
upon the earth and producing an eclipse of the sun. From
a mere inspection of the figure we may learn that an eclipse
of the sun can occur only at new moon — i. e., when the
moon is on line between the earth and sun — and an eclipse
of the moon can occur only at full moon. Why ? Also, the
eclipsed moon, M' , will present substantially the same ap-
pearance from every part of the earth where it is at all vis-
ible— the same from North America as from South Amer-

101

ASTRONOMY

§, ica — but the eclipsed sun will present very
.different aspects from different parts of
the earth. Thus, at L, within the moon's
shadow, the sunlight will be entirely cut
off, producing what is called a total eclipse.
At points of the earth's surface near J and
K there will be no interference whatever
with the sunlight, and no eclipse, since the
moon is quite off the line joining these re-
gions to any part of the sun. At places be-
tween J and L or K and L the moon will
cut off a part of the sun's light, but not all
of it, and will produce what is called a par-
\ tial eclipse, which, as seen from the north-
i ern parts of the earth, will be an eclipse of
the lower (southern) part of the sun, and
as seen from the southern hemisphere will
be an eclipse of the northern part of the

sun.

The moon revolves around the earth in
a plane, which, in the figure, we suppose to
be perpendicular to the surface of the pa-
per, and to pass through the sun along the
line M' M produced. But it frequently
happens that this plane is turned to one
side of the sun, along some such line as
P Q, and in this case the full moon would
cut through the edge of the earth's shadow
without being at any time wholly immersed
in it, giving a partial eclipse of the moon,
as is shown in the figure.

In what parts of the earth would this
eclipse be visible? What kinds of solar
eclipse would be produced by the new moon
at Q? In what parts of the earth would
they be visible ?

ECLIPSES 103

64. The shadow cone. — The shape and position of the
earth's shadow are indicated in Fig. 33 by the lines drawn
tangent to the circles which represent the sun and earth,
since it is only between these lines that the earth interferes
with the free radiation of sunlight, and since both sun and
earth are spheres, and the earth is much the smaller of the
two, it is evident that the earth's shadow must be, in geo-
metrical language, a cone whose base is at the earth, and
whose vertex lies far to the right of the figure — in other
words, the earth's shadow, although very long, tapers off
finally to a point and ends. So, too, the shadow of the
moon is a cone, having its base at the moon and its vertex
turned away from the sun, and, as shown in the figure, just
about long enough to reach the earth.

It is easily shown, by the theorem of similar triangles in
connection with the known size of the earth and sun, that
the distance from the center of the earth to the vertex of
its shadow is always equal to the distance of the earth from
the sun divided by 108, and, similarly, that the length of
the moon's shadow is equal to the distance of the moon
from the sun divided by 400, the moon's shadow being the
smaller and shorter of the two, because the moon is smallei
than the earth. The radius of the moon's orbit is just about
T£¥th part of the radius of the earth's orbit — i. e., the dis-
tance of the moon from the earth is ¥i^th part of the dis-
tance of the earth from the sun, and it is this " chance "
agreement between the length of the moon's shadow and
the distance of the moon from the earth which makes the
tip of the moon's shadow fall very near the earth at the
time of solar eclipses. Indeed, the elliptical shape of the
moon's orbit produces considerable variations in the dis-
tance of the moon from the earth, and in consequence of
these variations the vertex of the shadow sometimes falls
short of reaching the earth, and sometimes even projects
considerably beyond its farther side. When the moon's
distance is too great for the shadow to bridge the space be-

104 ASTRONOMY

tween earth and moon there can be no total eclipse of the
sun, for there is no shadow which can fall upon the earth,
even though the moon does come directly between earth
and sun. But there is then produced a peculiar kind of
partial eclipse called annular, or ring-shaped, because the
moon, although eclipsing the central parts of the sun, is
not large enough to cover the whole of it, but leaves the
sun's edge visible as a ring of light, which completely sur-
rounds the moon. Although, strictly speaking, this is only
a partial eclipse, it is customary to put total and annular
eclipses together in one class, which is called central eclipses,
since in these eclipses the line of centers of sun and moon
strikes the earth, while in ordinary partial eclipses it passes
to one side of the earth without striking it. In this latter
case we have to consider another cone called the penumbra
— i. e., partial shadow — which is shown in Fig. 33 by the
broken lines tangent to the sun and moon, and crossing at
the point F, which is the vertex of this cone. This penum-
bral cone includes within its surface all that region of space
within which the moon cuts off any of the sunlight, and
of course it includes the shadow cone which produces total
eclipses. Wherever the penumbra falls there will be a solar
eclipse of some kind, and the nearer the place is to the axis
of the penumbra, the more nearly total will be the eclipse.
Since the moon stands about midway between the earth and
the vertex of the penumbra, the diameter of the penumbra
where it strikes the earth will be about twice as great as
the diameter of the moon, and the student should be able
to show from this that the region of the earth's surface
within which a partial solar eclipse is visible extends in a
straight line about 2,100 miles on either side of the region
where the eclipse is total. Measured along the curved
surface of the earth, this distance is frequently much
greater.

Is it true that if at any time the axis of the shadow cone
comes within 2,100 miles of the earth's surface a partial

ECLIPSES 105

eclipse will be visible in those parts of the earth nearest the
axis of the shadow ?

65. Different characteristics of lunar and solar eclipses. —
One marked difference between lunar and solar eclipses
which has been already suggested, may be learned from Fig.
33. The full moon, M' , will be seen eclipsed from every
part of the earth where it is visible at all at the time of the
eclipse — that is, from the whole night side of the earth ;
while the eclipsed sun will be seen eclipsed only from those
parts of the day side of the earth upon which the moon's
shadow or penumbra falls. Since the point of the shadow
at best but little more than reaches to the earth, the
amount of space upon the earth which it can cover at any
one moment is very small, seldom more than 100 to 200
miles in length, and it is only within the space thus ac-
tually covered by the shadow that the sun is at any given
moment totally eclipsed, but within this region the sun
disappears, absolutely, behind the solid body of the moon,
leaving to view only such outlying parts and appendages as
are too large for the moon to cover. At a lunar eclipse, on
the other hand, the earth coming between sun and moon
cuts off the light from the latter, but, curiously enough,
does not cut it off so completely that the moon disappears
altogether from sight even in mid-eclipse. The explana-
tion of this continued visibility is furnished by the broken
lines extending, in Fig. 33, from the earth through the
moon. These represent sunlight, which, entering the
earth's atmosphere near the edge of the earth (edge as seen
from sun and moon), passes through it and emerges in a
changed direction, refracted, into the shadow cone and
feebly illumines the moon's surface with a ruddy light like
that often shown in our red sunsets. Eclipse and sunset
alike show that when the sun's light shines through dense
layers of air it is the red rays which come through most
freely, and the attentive observer may often see at a clear
sunset something which corresponds exactly to the bending
8

106 ASTRONOMY

of the sunlight into the shadow cone ; just before the sun
reaches the horizon its disk is distorted from a circle into
an oval whose horizontal diameter is longer than the verti-
cal one (see § 49).

QUERY. — At a total lunar eclipse what would be the
effect upon the appearance of the moon if the atmosphere
around the edge of the earth were heavily laden with
clouds ?

66. The track of the shadow. — We may regard the moon's
shadow cone as a huge pencil attached to the moon, mov-
ing with it along its orbit in the direction of the arrow-
head (Fig. 34), and as it moves drawing a black line across
the face of the earth at the time of total eclipse. This black
line is the path of the shadow and marks out those regions
within which the eclipse will be total at some stage of its
progress. If the point of the shadow just reaches the
earth its trace will have no sensible width, while, if the
moon is nearer, the point of the cone will be broken off,
and, like a blunt pencil, it will draw a broad streak across
the earth, and this under the most favorable circumstances
may have a breadth of a little more than 160 miles and a
length of 10,000 or 12,000 miles. The student should
be able to show from the known distance of the moon
(240,000 miles) and the known interval between consecutive
new moons (29.5 days) that on the average the moon's
shadow sweeps past the earth at the rate of 2,100 miles per
hour, and that in a general way this motion is from west
to east, since that is the direction of the moon's motion in
its orbit. The actual velocity with which the moon's shadow
moves past a given station may, however, be considerably
greater or less than this, since on the one hand when the
shadow falls very obliquely, as when the eclipse occurs near
sunrise or sunset, the shifting of the shadow will be very
much greater than the actual motion of the moon which
produces it, and on the other hand the earth in revolving
upon its axis carries the spectator and the ground upon

ECLIPSES 107

which he stands along the same direction in which the
shadow is moving. At the equator, with the sun and moon
overhead, this motion of the earth subtracts about 1,000
miles per hour from the velocity with which the shadow
passes by. It is chiefly on this account, the diminished
velocity with which the shadow passes by, that total solar
eclipses last longer in the tropics than in higher latitudes,
but even under the most favorable circumstances the dura-
tion of totality does not reach eight minutes at any one
place, although it may take the shadow several hours to
sweep the entire length of its path across the earth.

According to Whitmell the greatest possible duration of
a total solar eclipse is 7m. 40s., and it can attain this limit
only when the eclipse occurs near the beginning of July
and is visible at a place 5° north of the equator.

The duration of a lunar eclipse depends mainly upon
the position of the moon with respect to the earth's shadow.
If it strikes the shadow centrally, as at Jf' , Fig. 33, a total
eclipse may last for about two hours, with an additional
hour at the beginning and end, during which the moon is
entering and leaving the earth's shadow. If the moon
meets the shadow at one side of the axis, as at P, the total
phase of the eclipse may fail altogether, and between these
extremes the duration of totality may be anything from
two hours downward.

67. Relation of the lunar nodes to eclipses. — To show why
the moon sometimes encounters the earth's shadow cen-
trally and more frequently at full moon passes by without
touching it at all, we resort to Fig. 34, which represents a
part of the orbit of the earth about the sun, with dates
showing the time in each year at which the earth passes
the part of its orbit thus marked. The orbit of the moon
about the earth, M M', is also shown, with the new moon,
Jf, casting its shadow toward the earth and the full moon,
Jfaf', apparently immersed in the earth's shadow. But here
appearances are deceptive, and the student who has made

108 ASTRONOMY

the observations set forth in Chapter III has learned for
himself a fact of which careful account must now be taken.
The apparent paths of the moon and sun among the stars
are great circles which lie near each other, but are not
exactly the same ; and since these great circles are only the
intersections of the sky with the planes of the earth's orbit

FIG. 34.— Relation of the lunar nodes to eclipses.

and the moon's orbit, we see that these planes are slightly
inclined to each other and must therefore intersect along
some line passing through the center of the earth. This
line, N' N" ', is shown in the figure, and if we suppose the
surface of the paper to represent the plane of the earth's
orbit, we shall have to suppose the moon's orbit to be tipped
around this line, so that the left side of the orbit lies above
and the right side below the surface of the paper. But
since the earth's shadow lies in the plane of its orbit — i. e.,
in the surface of the paper — the full moon of March, Jf' ,
must have passed below the shadow, and the new moon, J/,
must have cast its shadow above the earth, so that neither
a lunar nor a solar eclipse could occur in that month. But
toward the end of May the earth and moon have reached
a position where the line N' N" points almost directly
toward the sun, in line with the shadow cones which hide
it. Note that the line N' N" remains very nearly parallel
to its original position, while the earth is moving along

ECLIPSES 109

its orbit. The full moon will now be very near this line
and therefore very close to the plane of the earth's orbit, if
not actually in it, and must pass through the shadow of the
earth and be eclipsed. So also the new moon will cast its
shadow in the plane of the ecliptic, and this shadow, falling
upon the earth, produced the total solar eclipse of May 28, '
1900.

N1 N" is called the line of nodes of the moon's orbit (§ 39),
and the two positions of the earth in its orbit, diametrically
opposite each other, at which N' N" points exactly toward
the sun, we shall call the nodes of the lunar orbit. Strictly
speaking, the nodes are those points of the sky against
which the moon's center is projected at the moment when
in its orbital motion it cuts through the plane of the earth's
orbit. Bearing in mind these definitions, we may condense
much of what precedes into the proposition : Eclipses of
either sun or moon can occur only when the earth is at or
near one of the nodes of the moon's orbit. Corresponding
to these positions of the earth there are in each year two
seasons, about six months apart, at which times, and at
these only, eclipses can occur. Thus in the year 1900 the
earth passed these two points on June 2d and November
24th respectively, and the following list of eclipses which
occurred in that year shows that all of them were within a
few days of one or the other of these dates :

Eclipses of the Year 1900

Total solar eclipse May 28th.

Partial lunar eclipse June 12th.

Annular (solar) eclipse November 21st.

68. Eclipse limits. — If the earth is exactly at the node at
the time of new moon, the moon's shadow will fall cen-
trally upon it and will produce an eclipse visible within the
torrid zone, since this is that part of the earth's surface
nearest the plane of its orbit. If the earth is near but not
at the node, the new moon will stand a little north or south

110 ASTRONOMY

of the plane of the earth's orbit, and its shadow will strike
the earth farther north or south than before, producing an
eclipse in the temperate or frigid zones ; or the shadow may
even pass entirely above or below the earth, producing no
eclipse whatever, or at most a partial eclipse visible near
the north or south pole. Just how many days' motion the
earth may be away from the node and still permit an eclipse
is shown in the following brief table of eclipse limits, as
they are called :

Solar Eclipse Limits
If at any new moon the earth is

Less than 10 days away from a node, a central eclipse is certain.

Between 10 and 16 days " " " some kind of eclipse is certain.

Between 16 and 19 days " " " a partial eclipse is possible.

More than 19 days " " " no eclipse is possible.

Lunar Eclipse Limits
If at any full moon the earth is

Less than 4 days away from a node, a total eclipse is certain.
Between 4 and 10 days " " " some kind of eclipse is certain.
Between 10 and 14 days " " " a partial eclipse is possible.
More than 14 days " " " no eclipse is possible.

From this table of eclipse limits we may draw some
interesting conclusions about the frequency with which
eclipses occur.

69. Number of eclipses in a year. — Whenever the earth
passes a node of the moon's orbit a new moon must occur at
some time during the 2 X 16 days that the earth remains
inside the limits where some kind of eclipse is certain, and
there must therefore be an eclipse of the sun every time the
earth passes a node of the moon's orbit. But, since there
are two nodes past which the earth moves at least once in
each year, there must be at least two solar eclipses every
year. Can there be more than two ? On the average, will
central or partial eclipses be the more numerous ?

A similar line of reasoning will not hold true for
eclipses of the moon, since it is quite possible that no full

ECLIPSES HI

moon should occur during the 20 days required by the
earth to move past the node from the western to the east-
ern limit. This omission of a full moon while the earth is
within the eclipse limits sometimes happens at both nodes
in the same year, and then we have a year with no eclipse
of the moon. The student may note in the list of eclipses
for 1900 that the partial lunar eclipse of June 12th oc-
curred 10 days after the earth passed the node, and was
therefore within the doubtful zone where eclipses may
occur and may fail, and corresponding to this position the
eclipse was a very small one, only a thousandth part of the
moon's diameter dipping into the shadow of the earth.
By so much the year 1900 escaped being an illustration of
a year in which no lunar eclipse occurred.

A partial eclipse of the moon will usually occur about a
fortnight before or after a total eclipse of the sun, since
the full moon will then be within the eclipse limit at the
opposite node. A partial eclipse of the sun will always
occur about a fortnight before or after a total eclipse of the
moon.

70. Eclipse maps. — It is the custom of astronomers to
prepare, in advance of the more important eclipses, maps
showing the trace of the moon's shadow across the earth,
and indicating the times of beginning and ending of the
eclipses, as is shown in Fig. 35. While the actual construc-
tion of such a map requires much technical knowledge, the
principles involved are simple enough : the straight line
passed through the center of sun and moon is the axis of
the shadow cone, and the map contains little more than a
graphical representation of when and where this cone meets
the surface of the earth. Thus in the map, the " Path of
Total Eclipse " is the trace of the shadow cone across the
face of the earth, and the width of this path shows that the
earth encountered the shadow considerably inside the ver-
tex of the cone. The general direction of the path is from
west to east, and the slight sinuosities which it presents

ECLIPSES 113

are for the most part due to unavoidable distortion of the
map caused by the attempt to represent the curved surface
of the earth upon the flat surface of the paper. On either
side of the Path of Total Eclipse is the region within which
the eclipse was only partial, and the broken lines marked Be-
gins at 3h., Ends at 3h., show the intersection of the penum-
bral cone with the surface of the earth at 3 P. M., Green*-
wich time. These two lines inclose every part of the earth's
surface from which at that time any eclipse whatever could
be seen, and at this moment the partial eclipse was just be-
ginning at every point on the eastern edge of the penumbra
and just ending at every point on the western edge, while
at the center of the penumbra, on the Path of Total Eclipse,
lay the shadow of the moon, an oval patch whose greatest
diameter was but little more than 60 miles in length, and
within which lay every part of the earth where the eclipse
was total at that moment.

The position of the penumbra at other hours is also
shown on the map, although with more distortion, because
it then meets the surface of the earth more obliquely, and
from these lines it is easy to obtain the time of beginning
and end of the eclipse at any desired place, and to estimate
by the distance of the place from the Path of Total Eclipse
how much of the sun's face was obscured.

Let the student make these " predictions " for Washing-
ton, Chicago, London, and Algiers.

The points in the map marked First Contact, Last Con-
tact, show the places at which the penumbral cone first
touched the earth and finally left it. According to compu-
tations made as a basis for the construction of the map the
Greenwich time of First Contact was Oh. 12.5m. and of Last
Contact 5h. 35.6m., and the difference between these two
times gives the total duration of the eclipse upon the earth
— i. e., 5 hours 23.1 minutes.

71. Future eclipses. — An eclipse map of a different kind
is shown in Fig. 36, which represents the shadow paths of

114

ASTRONOMY

all the central eclipses of the sun, visible during the period
1900-1918 A. D., in those parts of the earth north of the
south temperate zone. Each continuous black line shows
the path of the shadow in a total eclipse, from its begin-

FIG. 36.— Central eclipses for the first two decades of the twentieth century.
OPPOLZEB.

ning, at sunrise, at the western end of the line to its end,
sunset, at the eastern end, the little circle near the mid-
dle of the line showing the place at which the eclipse
was total at noon. The broken lines represent similar
data for the annular eclipses. This map is one of a se-
ries prepared by the Austrian astronomer, Oppolzer, show-
ing the path of every such eclipse from the year 1200

ECLIPSES 115

B. c. to 2160 A. D., a period of more than three thousand
years.

If we examine the dates of the eclipses shown in this
map we shall find that they are not limited to the particu-
lar seasons, May and N ovember, in which those of the year
1900 occurred, but are scattered through all the months of
the year, from January to December. This shows at once
that the line of nodes, N' N", of Fig. 34, does not remain
in a fixed position, but turns round in the plane of the
earth's orbit so that in different years the earth reaches the
node in different months. The precession has already fur-
nished us an illustration of a similar change, the slow rota-
tion of the earth's axis, producing a corresponding shifting
of the line in which the planes of the equator and ecliptic
intersect ; and in much the same way, through the disturb-
ing influence of the sun's attraction, the line N' N" is made
to revolve westward, opposite to the arrowheads in Fig.
34, at the rate of nearly 20° per year, so that the earth
comes to each node about 19 days earlier in each year than
in the year preceding, and the eclipse season in each year
comes on the average about 19 days earlier than in the year
before, although there is a good deal of irregularity in the
amount of change in particular years.

72. Recurrence of eclipses.— Before the beginning of the
Christian era astronomers had found out a rough-and-ready
method of predicting eclipses, which is still of interest and
value. The substance of the method is that if we start
with any eclipse whatever — e. g., the eclipse of May 28, 1900
—and reckon forward or backward from that date a period of
18 years and 10 or 11 days, we shall find another eclipse quite
similar in its general characteristics to the one with Avhich
we started. Thus, from the map of eclipses (Fig. 36), we
find that a total solar eclipse will occur on June 8, 1918,
18 years and 11 days after the one illustrated in Fig. 35.
This period of 18 years and 11 days is called saros, an
ancient word which means cycle or repetition, and since

116 ASTRONOMY

every eclipse is repeated after the lapse of a saros, we may
find the dates of all the eclipses of 1918 by adding 11
days to the dates given in the table of eclipses for 1900
(§ 67), and it is to be especially noted that each eclipse of
1918 will be like its predecessor of 1900 in character —
lunar, solar, partial, total, etc. The eclipses of any year
may be predicted by a similar reference to those which
occurred eighteen years earlier. Consult a file of old
almanacs.

The exact length of a saros is 223 lunar months, each of
which is a little more than 29.5 days long, and. if we multi-
ply the exact value of this last number (see § 60) by 223,
we shall find for the product 6,585.32 days, which is equal
to 18 years 11.32 days when there are four leap years in-
cluded in the 18, or 18 years 10.32 days when the num-
ber of leap years is five ; and in applying the saros to the
prediction of eclipses, due heed must be paid to the number
of intervening leap years. To explain why eclipses are
repeated at the end of the saros, we note that the occurrence
of an eclipse depends solely upon the relative positions of
the earth, moon, and node of the moon's orbit, and the
eclipse will be repeated as often as these three come back
to the position which first produced it. This happens at
the end of every saros, since the saros is, approximately, the
least common multiple of the length of the year, the length
of the lunar month, and the length of time required by the
line of nodes to make a complete revolution around the
ecliptic. If the saros were exactly a multiple of these
three periods, every eclipse would be repeated over and
over again for thousands of years ; but such is not the
case, the saros is not an exact multiple of a year, nor
is it an exact multiple of the time required for a revo-
lution of the line of nodes, and in consequence the
restitution which comes at the end of the saros is not a
perfect one. The earth at the 223d new moon is in fact
about half a day's motion farther west, relative to the node,

ECLIPSES

117

than it was at the beginning, and the re-
sulting eclipse, while very similar, is not
precisely the same as before. After another
18 years, at the second repetition, the earth
is a day farther from the node than at first,
and the eclipse differs still more in charac-
ter, etc. This is shown in Fig. 37, which
represents the apparent positions of the
disks of the sun and moon as seen from the
center of the earth at the end of each sixth
saros, 108 years, where the upper row of
figures represents the number of repetitions
of the eclipse from the beginning, marked
0, to the end, 72. The solar eclipse limits,
10, 16, 19 days, are also shown, and all those
eclipses which fall between the 10-day lim-
its will be central as seen from some part of
the earth, those between 16 and 19 partial
wherever seen, while between 10 and 16
they may be either total or partial. Com-
pare the figure with the following descrip-
tion given by Professor Newcomb : " A se-
ries of such eclipses commences with a very
small eclipse near one pole of the earth.
Gradually increasing for about eleven recur-
rences, it will become central near the same
pole. Forty or more central eclipses will
then recur, the central line moving slowly
toward the other pole. The series will then
become partial, and finally cease. The en-
tire duration of the series will be more than
a thousand years. A new series commences,
on the average, at intervals of thirty years."
A similar figure may be constructed to
represent the recurrence of lunar eclipses ;
but here, in consequence of the smaller

118 ASTRONOMY

eclipse limits, we shall find that a series is of shorter dura-
tion, a little over eight centuries as compared with twelve
centuries, which is the average duration of a series of solar
eclipses.

One further matter connected with the saros deserves
attention. During the period of 6,585.32 days the earth
has 6,585 times turned toward the sun the same face upon
which the moon's shadow fell at the beginning of the saros,
but at the end of the saros the odd 0.32 of a day gives the
earth time to make about a third of a revolution more
before the eclipse is repeated, and in consequence the
eclipse is seen in a different region of the earth, on the
average about 116° farther west in longitude. Compare in
Fig. 36 the regions in which the eclipses of 1900 and 1918
are visible.

Is this change in the region where the repeated eclipse
is visible, true of lunar eclipses as well as solar ?

73. Use of eclipses.— At all times and among all peoples
eclipses, and particularly total eclipses of the sun, have
been reckoned among the most impressive phenomena of
Nature. In early times and among uncultivated people
they were usually regarded with apprehension, often amount-
ing to a terror and frenzy, which civilized travelers have
not scrupled to use for their own purposes with the aid of
the eclipse predictions contained in their almanacs, threat-
ening at the proper time to destroy the sun or moon, and
pointing to the advancing eclipse as proof that their
threats were not vain. In our own day and our own land
these feelings of awe have not quite disappeared, but for
the most part eclipses are now awaited with an interest and
pleasure which, contrasted with the. former feelings of man-
kind, furnish one of the most striking illustrations of the
effect of scientific knowledge in transforming human fear
and misery into a sense of security and enjoyment.

But to the astronomer an eclipse is more than a beau-
tiful illustration of the working of natural laws ; it is in

ECLIPSES 119

varying degree an opportunity of adding to his store of
knowledge respecting the heavenly bodies. The region
immediately surrounding the sun is at most times closed to
research by the blinding glare of the sun's own light, so
that a planet as large as the moon might exist here unseen
were it not for the occasional opportunity presented by a
total eclipse which shuts off the excessive light and permits
not only a search for unknown planets but for anything
and everything which may exist around the sun. More
than one astronomer has reported the discovery of such
planets, and at least one of these has found a name and a
description in some of the books, but at the present time
most astronomers are very skeptical about the existence of
any such object of considerable size, although there is
some reason to believe that an enormous number of little
bodies, ranging in size from grains of sand upward, do
move in this region, as yet unseen and offering to the
future problems for investigation.

But in other directions the study of this region at the
times of total eclipse has yielded far larger returns, and in
the chapter on the sun we shall have to consider the mar-
velous appearances presented by the solar prominences and
by the corona, an appendage of the sun which reaches out
from his surface for millions of miles but is never seen
save at an eclipse. Photographs of the corona are taken
by astronomers at every opportunity, and reproductions of
some of these may be found in Chapter X.

Annular eclipses and lunar eclipses are of comparatively
little consequence, but any recorded eclipse may become of
value in connection with chronology. We date our letters
in a particular year of the twentieth century, and commonly
suppose that the years are reckoned from the birth of
Christ ; but this is an error, for the eclipses which were ob-
served of old and by the chroniclers have been associated
with events of his life, when examined by the astronomers
are found quite inconsistent with astronomic theory.

120 ASTRONOMY

They are, however, reconciled with it if we assume that our
system of dates has its origin four years after the birth of
Christ, or, in other words, that Christ was born in the
year 4 B. c. A mistake was doubtless made at £he time
the Christian era was introduced into chronology. At
many other points the chance record of an eclipse in
the early annals of civilization furnishes a similar means of
controlling and correcting the dates assigned by the histo-
rian to events long past.

CHAPTEE VIII

INSTRUMENTS AND THE PRINCIPLES INVOLVED
IN THEIR USE

74. Two familiar instruments. — In previous chapters we
have seen that a clock and a divided circle (protractor) are
needed for the observations which an astronomer makes,
and it is worth while to note here that the geography of
the sky and the science of celestial motions depend funda-
mentally upon these two instruments. The protractor is a
simple instrument, a humble member of the family of
divided circles, but untold labor and ingenuity have been
expended on this family to make possible the construction
of a circle so accurately divided that with it angles may be
measured to the tenth of a second instead of to the tenth
of a degree — i. e., 3,600 times as accurate as the protractor
furnishes.

The building of a good clock is equally important and
has cost a like amount of labor and pains, so that it is a far
cry from Galileo and his discovery that a pendulum " keeps
time " to the modern clock with its accurate construction
and elaborate provision against disturbing influences of
every kind. Every such timepiece, whether it be of the
nutmeg variety which sells for a dollar, or whether it be the
standard clock of a great national observatory, is made up
of the same essential parts which fall naturally into four
classes, which we may compare with the departments of a
well-ordered factory : I. A timekeeping department, the
pendulum or balance spring, whose oscillations must all be
of equal duration. II. A power department, the weights or
9 121

122 ASTRONOMY

mainspring, which, when wound, store up the power applied
from outside and give it out piecemeal as required to keep
the first department running. III. A publication depart-
ment, the dial and hands, which give out the time furnish-
ed by Department I. IV. A transportation department,
the wheels, which connect the other three and serve as a
means of transmitting power and time from one to the
other. The case of either clock or watch is merely the
roof which shelters it and forms no department of its in-
dustry. Of these departments the first is by far the most
important, and its good or bad performance makes or mars
the credit of the clock. Beware of meddling with the
balance wheel of your watch.

75. Radiant energy, — But we have now to consider other
instruments which in practice supplement or displace the
simple apparatus hitherto employed. Among the most im-
portant of these modern instruments are the telescope, the
spectroscope, and the photographic camera ; and since all
these instruments deal with the light which comes from
the stars to the earth, we must for their proper understand-
ing take account of the nature of that light, or, more strictly
speaking, we must take account of the radiant energy emit-
ted by the sun and stars, which energy, coming from the
sun, is translated by our nerves into the two different sen-
sations of light and heat. The radiant energy which comes
from the stars is not fundamentally different from that of
the sun, but the amount of energy furnished by any star is
so small that it is unable to produce through our nerves
any sensible perception of heat, and for the same reason
the vast majority of stars are invisible to the unaided eye ;
they do not furnish a sufficient amount of energy to affect
the optic nerves. A hot brick taken into the hand reveals
its presence by the two different sensations of heat and
pressure (weight) ; but as there is only one brick to produce
the two sensations, so there is only one energy to produce
through its action upon different nerves the two sensations

INSTRUMENTS USED AND PRINCIPLES INVOLVED 123

of light and heat, and this energy is called radiant because
it appears to stream forth radially from everything which
has the capacity of emitting it. For the detailed study
of radiant energy the student is referred to that branch
of science called physics ; but some of its elementary prin-
ciples may be learned through the following simple experi-
ment, which the student should not fail to perform for
himself :

Drop a bullet or other similar object into a bucket
of water and observe the circular waves which spread
from the place where it enters the water. These waves
are a form of radiant energy, but differing from light or
heat in that they are visibly confined to a single plane,
the surface of the water, instead of filling the entire sur-
rounding space. By varying the size of the bucket, the
depth of the water, the weight of the bullet, etc., differ-
ent kinds of waves, big and little, may be produced ; but
every such set of waves may be described and defined in
all its principal characteristics by means of three num-
bers— viz., the vertical height of the waves from hollow
to crest ; the distance of one wave from the next ; and
the velocity with which the waves travel across the water.
The last of these quantities is called the velocity of propa-
gation ; the second is called the wave length ; one half
of the first is called the amplitude ; and all these terms
find important applications in the theory of light and
heat.

The energy of the falling bullet, the disturbance which
it produced on entering the water, was carried by the
waves from the center to the edge of the bucket but not
beyond, for the wave can go only so far as the water
extends. The transfer of energy in this way requires a
perfectly continuous medium through which the waves
may travel, and the whole visible universe is supposed to
be filled with something called ether, which serves every-
where as a medium for the transmission of radiant energy

124 ASTRONOMY

just as the water in the experiment served as a medium
for transmitting in waves the energy furnished to it by the
falling bullet. The student may think of this energy as be-
ing transmitted in spherical waves through the ether, every
glowing body, such as a star, a candle flame, an arc lamp, a
hot coal, etc., being the origin and center of such systems
of waves, and determining by its own physical and chem-
ical properties the wave length and amplitude of the wave
systems given off.

The intensity of any light depends upon the amplitude
of the corresponding vibration, and its color depends upon
the wave length. By ingenious devices which need not be
here described it has been found possible to measure the
wave length corresponding to different colors — e. g., all of
the colors of the rainbow, and some of these wave lengths
expressed in tenth meters are as follows : A tenth meter is
the length obtained by dividing a meter into 1010 equal
parts. 1010 = 10,000,000,000.

Color. Wave length.

Extreme limit of visible violet 3.900

Middle of the violet : 4,060

blue 4,730

green 5,270

yellow 5,810

orange 5,970

red 7,000

Extreme limit of visible red 7,600

The phrase " extreme limit of visible violet " or red
used above must be understood to mean that in general the
eye is not able to detect radiant energy having a wave
length less than 3,900 or greater than 7,600 tenth meters.
Radiant energy, however, exists in waves of both greater
and shorter length than the above, and may be readily
detected by apparatus not subject to the limitations of the
human eye — e. g., a common thermometer will show a rise
of temperature when its bulb is exposed to radiant energy
of wave length much greater than 7,600 tenth meters, and

PLATE I.

THE NOETHEEN

CONSTELLATIONS

31

INSTRUMENTS USED AND PRINCIPLES INVOLVED 125

a photographic plate will be strongly affected by energy of
shorter wave length than 3,900 tenth meters.

76. Reflection and condensation of waves.— When the
waves produced by dropping a bullet into a bucket of
water meet the sides of the bucket, they appear to rebound
and are reflected back toward the center, and if the bullet is
dropped very near the center of the bucket the reflected
waves will meet simultaneously at this point and produce
there by their combined action a wave higher than that
which was reflected at the walls of the bucket. There has
been a condensation of energy produced by the reflection,
and this increased energy is shown by the greater amplitude
of the wave. The student should not fail to notice that
each portion of the wave has traveled out and back over
the radius of the bucket, and that they meet simultaneously
at the center because of this equality of the paths over which
they travel, and the resulting equality of time required to
go out and back. If the bullet were dropped at one side of
the center, would the reflected waves produce at any point
a condensation of energy ?

If the bucket were of elliptical instead of circular cross
section and the bullet were dropped at one focus of the
ellipse there would be produced a condensation of reflected
energy at the other focus, since the sum of the paths trav-
ersed by each portion of the wave before and after reflec-
tion is equal to the sum of the paths traversed by every
other portion, and all parts of the wave reach the second
focus at the same time. Upon what geometrical principle
does this depend ?

The condensation of wave energy in the circular and
elliptical buckets are special cases under the general prin-
ciple that such a condensation will be produced at any
point which is so placed that different parts of the wave
front reach it simultaneously, whether by reflection or by
some other means, as shown below.

The student will note that for the sake of greater pre-

126 ASTRONOMY

cision we here say wave front instead of wave. If in any
wave we imagine a line drawn along the crest, so as to touch
every drop which at that moment is exactly at the crest, we
shall have what is called a wave front, and similarly a line
drawn through the trough between two waves, or through
any set of drops similarly placed on a wave, constitutes a
wave front.

77. Mirrors and lenses. — That form of radiant energy
which we recognize as light and heat may be reflected and
condensed precisely as are the waves of water in the exer-
cise considered above, but owing to the extreme shortness
of the wave length in this case the reflecting surface should
be very smooth and highly polished. A piece of glass hol-
lowed out in the center by grinding, and with a light film
of silver chemically deposited upon the hollow surface and
carefully polished, is often used by astronomers for this pur-
pose, and is called a concave mirror.

The radiant energy coming from a star or other distant
object and falling upon the silvered face of such a mirror
is reflected and condensed at a point a little in front of the
mirror, and there forms an image of the star, which may be
seen with the unaided eye, if it is held in the right place, or
may be examined through a magnifying glass. Similarly,
an image of the sun, a planet, or a distant terrestrial object
is formed by the mirror, which condenses at its appropriate
place the radiant energy proceeding from each and every
point in the surface of the object, and this, in common
phrase, produces an image of the object.

Another device more frequently used by astronomers
for the production of images (condensation of energy) is a
lens which in its simplest form is a round piece of glass,
thick in the center and thin at the edge, with a cross sec-
tion, such as is shown at A B in Fig. 38. If we suppose
E G D to represent a small part of a wave front coming from
a very distant source of radiant energy, such as a star, this
wave front will be practically a plane surface represented

INSTRUMENTS USED AND PRINCIPLES INVOLVED 127

by the straight line ED, but in passing through the lens
this surface will become warped, since light travels slower
in glass than in air, and the central part of the beam, 0,
in its onward motion will be retarded by the thick center

FIG. 38.— Illustrating the theory of lenses.

of the lens, more than E or D will be retarded by the com-
paratively thin outer edges of A B. On the right of the
lens the wave front therefore will be transformed into a
curved surface whose exact character depends upon the
shape of the lens and the kind of glass of which it is made.
By properly choosing these the new wave front may be
made a part of a sphere having its center at the point F and
the whole energy of the wave front, E G D, will then be con-
densed at F, because this point is equally distant from all
parts of the warped wave front, and therefore is in a posi-
tion to receive them simultaneously. The distance of F
from A B is called the focal length of the lens, and ^itself
is called the focus. The significance of this last word
(Latin, focus = fireplace) will become painfully apparent to
the student if he will hold a common reading glass between
his hand and the sun in such a way that the focus falls
upon his hand.

All the energy transmitted by the lens in the direc-
tion GFis concentrated upon a very small area at F, and
an image of the object — e. g., a star, from which the light
came — is formed here. Other stars situated near the one in
question will also send beams of light along slightly differ-
ent directions to the lens, and these will be concentrated,
each in its appropriate place, in the focal plane, F H, passed
through the focus, F, perpendicular to the line, F G, and

128

ASTRONOMY

we shall find in this plane a picture of all the stars or other
objects within the range of the lens.

78. Telescopes. — The simplest kind of telescope consists
of a concave mirror to produce images, and a magnifying
glass, called an eyepiece, through which to examine them ;

but for convenience'
sake, so that the observ-
er may not stand in his
own light, a small mir-
ror is frequently added
to this combination, as
at H in Fig. 39, where
the lines represent the
directions along which
the energy is propagated.
By reflection from this mirror the focal plane and the
images are shifted to F, where they may be examined from
one side through the magnifying glass E.

Such a combination of parts is called a reflecting tele-
scope, while one in which the images are produced by a
lens or combination of lenses is called a refracting tele-
scope, the adjective having reference to the bending, re-
fraction, produced by the glass upon the direction in which
the energy is propagated. The customary arrangement of
parts in such a telescope is shown in Fig. 40, where the

FIG.

). — Essential parts of
telescope.

reflecting

FIG. 40.— A simple form of refracting telescope.

part marked 0 is called the objective and V E (the mag-
nifying glass) is the eyepiece, or ocular, as it is sometimes
called.

Most objects with which we have to deal in using a
telescope send to it not light of one color only, but a mix-

INSTRUMENTS USED AND PRINCIPLES INVOLVED 129

ture of light of many colors, many different wave lengths,
some of which are refracted more than others by the glass
of which the lens is composed, and in consequence of these
different amounts of refraction a single lens does not fur-
nish a single image of a star, but gives a confused jumble of
red and yellow and blue images much inferior in sharpness
of outline (definition) to the images made by a good con-
cave mirror. To remedy this defect it is customary to
make the objective of two or more pieces of glass of differ-
ent densities and ground to different shapes as is shown at 0
in Fig. 40. The two pieces of glass thus mounted in one
frame constitute a compound lens having its own focal
plane, shown at F in the figure, and similarly the lenses
composing the eyepiece have a focal plane between the
eyepiece and the objective which must also fall at F, and
in the use of a telescope the eyepiece must be pushed out
or in until its focal plane coincides with that of the objec-
tive. This process, which is called focusing, is what is
accomplished in the ordinary opera glass by turning a screw
placed between the two tubes, and it must be carefully
done with every telescope in order to obtain distinct vision.
79. Magnifying power.— The amount by which a given
telescope magnifies depends upon the focal length of the ob-
jective (or mirror) and the focal length of the eyepiece, and
is equal to the ratio of these two quantities. Thus in lig.
40 the distance of the objective from the focal plane J^is
about 16 times as great as the distance of the eyepiece
from the same plane, and the magnifying power of this
telescope is therefore 16 diameters. A magnifying power
of 16 diameters means that the diameter of any object seen
in the telescope looks 16 times as large as it appears with-
out the telescope, and is nearly equivalent to saying that
the object appears only one sixteenth as far off. Some-
times the magnifying power is assumed to be the number
of times that the area of an object seems increased ; and
since areas are proportional to the squares of lines, the

130 ASTRONOMY

magnifying power of 16 diameters might be called a power
of 256. Every large telescope is provided with several eye-
pieces of different focal lengths, ranging from a quarter of
an inch to two and a half inches, which are used to fur-
nish different magnifying powers as may be required for
the different kinds of work undertaken with the instru-
ment. Higher powers can be used with large telescopes
than with small ones, but it is seldom advantageous to
use with any telescope an eyepiece giving a higher power
than 60 diameters for each inch of diameter of the ob-
jective.

The part played by the eyepiece in determining magni-
fying power will be readily understood from the following
experiment :

Make a pin hole in a piece of cardboard. Bring a
printed page so close to one eye that you can no longer see
the letters distinctly, and then place the pin hole between
the eye and the page. The letters which were before
blurred may now be seen plainly through the pin hole,
even when the page is brought nearer to the eye than be-
fore. As it is brought nearer, notice how the letters seem
to become larger, solely because they are nearer. A pin
hole is the simplest kind of a magnifier, and the eyepiece
in a telescope plays the same part as does the pin hole in
the experiment ; it enables the eye to be brought nearer to
the image, and the shorter the focal length of the eyepiece
the nearer is the eye brought to the image and the higher
is the magnifying power.

80. The equatorial mounting,— Telescopes are of all sizes,
from the modest opera glass which may be carried in the
pocket and which requires no other support than the hand,
to the giant which must have a special roof to shelter it
and elaborate machinery to support and direct it toward
the sky. But for even the largest telescopes this machinery
consists of the following parts, which are illustrated, with
exception of the last one, in the small equatorial telescope

INSTRUMENTS USED AND PRINCIPLES INVOLVED 131

shown in Fig. 41. It is not customary to place a driving
clock on so small a telescope as this :

(a) A supporting pier or tripod.

(b) An axis placed parallel to the axis of the earth.

(c) Another axis at
right angles to b and
capable of revolving
upon b as an axle.

(d) The telescope
tube attached to c and ca-
pable of revolving about c.

(e) Graduated circles
attached to c and d to
measure the amount by
which the telescope is
turned on these axes.

(/) A driving clock so
connected with b as to
make c (and d) revolve
about b with an angular
velocity equal and opposite
to that with which the
earth turns upon its axis.

Such a support is called
an equatorial mounting,
and the student should
note from the figure that
the circles, e, measure the
hour angle and declination
of any star toward which FlG 41 _A simp7e eqn^orial mounting.
the telescope is directed,

and conversely if the telescope be so set that these circles
indicate the hour angle and declination of any given star,
the telescope will then point toward that star. In this
way it is easy to find with the telescope any moderately
bright star, even in broad daylight, although it is then

INSTRUMENTS USED AND PRINCIPLES INVOLVED 133

absolutely invisible to the naked eye. The rotation of the
earth about its axis will speedily carry the telescope away
from the star, but if the driving clock be started, its effect
is to turn the telescope toward the west just as fast as the
earth's rotation carries it toward the east, and by these
compensating motions
to keep it directed to-
ward the star. In Fig.
42, which represents
the largest and one of
the most perfect re-
fracting telescopes
ever built, let the stu-
dent pick out and iden-
tify the several parts
of the mounting above
described. A part of
the driving clock may
be seen within the head
of the pier. In Fig.
43 trace out the cor-
responding parts in
the mounting of a re-
flecting telescope.

A telescope is often
only a subordinate part
of some instrument or
apparatus, and then its
style of mounting is
determined by the requirements of the special case ; but
when the telescope is the chief thing, and the remainder
of the apparatus is subordinate to it, the equatorial mount-
ing is almost always adopted, although sometimes the ar-
rangement of the parts is very different in appearance from
any of those shown above. Beware of the popular error that
an object held close in front of a telescope can be seen by an

FIG. 43.— The reflecting telescope of the
Paris Observatory.

134

ASTRONOMY

observer at the eyepiece. The numerous stories of astrono-
mers who saw spiders crawling over the objective of their
telescope, and imagined they were beholding strange ob-
jects in the sky, are all fictitious, since nothing on or near
the objective could possibly be seen through the telescope.
81. Photography. — A photographic camera consists of a
lens and a device for holding at its focus a specially pre-
pared plate or film. This
plate carries a chemical
deposit which is very
sensitive to the action
of light, and which may
be made to preserve the
imprint of any picture
which the lens forms
upon it. If such a sen-
sitive plate is placed at
the focus of a reflecting
telescope, the combina-
tion becomes a camera
available for astronom-
ical photography, and at
the present time the
tendency is strong in
nearly every branch of
astronomical research to
substitute the sensitive
plate in place of the ob-
server at a telescope. A
refracting telescope may also be used for astronomical pho-
tography, and is very much used, but some complications
occur here on account of the resolution of the light into
its constituent colors in passing through the objective.
Fig. 44 shows such a telescope, or rather two telescopes, one
photographic, the other visual, supported side by side upon
the same equatorial mounting.

FIG. 44.— Photographic telescope of the Paris
Observatory.

INSTRUMENTS USED AND PRINCIPLES INVOLVED 135

One of the great advantages of photography is found in
connection with what is called —

82. Personal equation, — It is a remarkable fact, first in-
vestigated by the German astronomer Bessel, three quar-
ters of a century ago, that where extreme accuracy is re-
quired the human senses can not be implicitly relied upon.
The most skillful observers will not agree exactly in their
measurement of an angle or in estimating the exact instant
at which a star crossed the meridian ; the most skillful
artists can not draw identical pictures of the same ob-
ject, etc.

These minor deceptions of the senses are included in
the term personal equation, which is a famous phrase in
astronomy, denoting that the observations of any given
person require to be corrected by means of some equation
involving his personality.

General health, digestion, nerves, fatigue, all influence
the personal equation, and it was in reference to such mat-
ters that one of the most eminent of living astronomers has
given this description of his habits of observing :

" In order to avoid every physiological disturbance, I
"~Tiave adopted the rule to abstain for one or two hours be-
fore commencing observations from every laborious occupa-
tion ; never to go to the telescope with stomach loaded with
food ; to abstain from everything which could affect the
nervous system, from narcotics and alcohol, and especially
from the abuse of coffee, which I have found to be exceed-
ingly prejudicial to the accuracy of observation."* A
regimen suggestive of preparation for an athletic contest
thanj&rthe more quiet labors of an astronomer.

83. Visual and photographic work. — The photographic
plate has no stomach and no nerves, and is thus free from
many of the sources of error which inhere in visual observa-
tions, and in special classes of work it possesses other

* Schiaparelli, Osservazioni sulle Stelle Doppie.

136 ASTRONOMY

marked advantages, such as rapidity when many stars are
to he dealt with simultaneously, permanence of record, and
owing to the cumulative effect of long exposure of the plate
it is possible to photograph with a given telescope stars far
too faint to be seen through it. On the other hand, the
eye has the advantage in some respects, such as studying
the minute details of a fairly bright object — e. g., the sur-
face of a planet, or the sun's corona and, for the present at
least, neither method of observing can exclude the other.
For a remarkable case of discordance between the results
of photographic and visual observations compare the pic-
tures of the great nebula in the constellation Andromeda,
which are given in Chapter XIV. A partial explanation
of these discordances and other similar ones is that the
eye is most strongly affected by greenish-yellow light,
while the photographic plate responds most strongly to
violet light ; the photograph, therefore, represents things
which the eye has little capacity for seeing, and vice versa.
84. The spectroscope. — In some respects the spectroscope
is the exact counterpart of the telescope. The latter con-
denses radiant energy and the former disperses it. As a
measuring instrument the telescope is mainly concerned
with the direction from which light comes, and the differ-
ent colors of which that light is composed affect it only as
an obstacle to be overcome in its construction. On the
other hand, with the spectroscope the direction from which
the radiant energy comes is of minor consequence, and the
all-important consideration is the intrinsic character of
that radiation. What colors are present in the light and
in what proportions ? What can these colors be made to
tell about the nature and condition of the body from which
they come, be it sun, or star, or some terrestrial source of
light, such as an arc lamp, a candle flame, or a furnace in
blast ? These are some of the characteristic questions of
the spectrum analysis, and, as the name implies, they are
solved by analyzing the radiant energy into its component

INSTRUMENTS USED AND PRINCIPLES INVOLVED 137

parts, setting down the blue light in one place, the yellow
in another, the red in still another, etc., and interpreting
this array of colors by means of principles which we shall
have to consider. Something of this process of color
analysis may be seen in the brilliant hues shown by a soap
bubble, or reflected from a piece of mother-of-pearl, and
still more strikingly exhibited in the rainbow, produced by

FIG. 45.— Resolution of light into its component colors.

raindrops which break up the sunlight into its component
colors and arrange them each in its appropriate place.
Any of these natural methods of decomposing light might
be employed in the construction of a spectroscope, but in
spectroscopes which are used for analyzing the light from
feeble sources, such as a star, or a candle flame, a glass
prism of triangular cross section is usually employed to re-
solve the light into its component colors, which it does by
refracting it as shown at the edges of the lens in Fig. 38.

The course of a beam of light in passing through such
a prism is shown in Fig. 45. Note that the bending of the
light from its original course into a new one, which is here
shown as produced by the prism, is quite similar to the
bending shown at the edges of a lens and comes from the
10

138 ASTRONOMY

same cause, the slower velocity of light in glass than in
air. It takes the light-waves as long to move over the
path A B in glass as over the longer path 1, 2, 3, 4, of
which only the middle section lies in the glass.

'Not only does the prism bend the beam of light trans-
mitted by it, but it bends in different degree light of differ-
ent colors, as is shown in the figure, where the beam at the
left of the prism is supposed to be made up of a mixture of
blue and red light, while at the right of the prism the
greater deviation imparted to the blue quite separates the
colors, so that they fall at different places on the screen,
S S. The compound light has been analyzed into its con-
stituents, and in the same way every other color would be
put down at its appropriate place on the screen, and a beam
of white light falling upon the prism would be resolved by
it into a sequence of colors, falling upon the screen in the
order red, orange, yellow, green, blue, indigo, violet. The
initial letters of these names make the word RoygMv, and
by means of it their order is easily remembered.

If the light which is to be examined comes from a star
the analysis made by the prism is complete, and when
viewed through a telescope the image of the star is seen to
be drawn out into a band of light, which is called a spec-
trum, and is red at one end and violet or blue at the other,
with all the colors of the rainbow intervening in proper
order between these extremes. Such a prism placed in
front of the objective of a telescope is called an objec-
tive prism, and has been used for stellar work with marked
success at the Harvard College Observatory. But if the
light to be analyzed comes from an object having an ap-
preciable extent of surface, such as the sun or a planet,
the objective prism can not be successfully employed,
since each point of the surface will produce its own spec-
trum, and these will appear in the view telescope super-
posed and confused one with another in a very objection-
able manner. To avoid this difficulty there is placed

INSTRUMENTS USED AND PRINCIPLES INVOLVED 139

between the prism and the source of light an opaque
screen, $, with a very narrow slit cut in it, through which all
the light to be analyzed must pass and must also go through
a lens, J, placed between the slit and the prism, as shown
in Fig. 46. The slit and lens, together with the tube in

FIG. 46.— Principal parts of a spectroscope.

which they are usually supported, are called a collimator,
By this device a very limited amount of light is permitted
to pass from the object through the slit and lens to the
prism and is there resolved into a spectrum, which is in
effect a series of images of the slit in light of different
colors, placed side by side so close as to make practically a
continuous ribbon of light whose width is the length of
each individual picture of the slit. The length of the ribbon
(dispersion) depends mainly upon the shape of the prism
and the kind of glass of which it is made, and it may be
very greatly increased and the efficiency of the spectro-
scope enhanced by putting two, three, or more prisms in
place of the single one above described. When the amount
of light is very great, as in the case of the sun or an elec-
tric arc lamp, it is advantageous to alter slightly the ar-
rangement of the spectroscope ' and to substitute in place
of the prism a grating — i. e., a metallic mirror with a great
number of fine parallel lines ruled upon its surface at equal
intervals, one from another. It is by virtue of such a sys-
tem of fine parallel grooves that mother-of-pearl displays

140

ASTRONOMY

its beautiful color effects, and a brilliant spectrum of great
purity and high dispersion is furnished by a grating ruled
with from 10,000 to 20,000 lines to the inch. Fig. 47 rep-
resents, rather crudely, a part of the spec-
trum of an arc light furnished by such a
grating, or rather it shows three different
spectra arranged side by side, and looking
something like a rude ladder. The sides
of the ladder are the spectra furnished by
, the incandescent carbons of the lamp, and
the cross pieces are the spectrum of the
electric arc filling the space between the
carbons. Fig. 48 shows a continuation of
the same spectra into a region where the
radiant energy is invisible to the eye, but
is capable of being photographed.

It is only when a lens is placed be-
• tween the lamp and the slit of the spec-
troscope that the three spectra are shown
distinct from each other as in the figure.
The purpose of the lens is to make a pic-
ture of the lamp upon the slit, so that
all the radiant energy from any one point
of the arc may be brought to one part of
the slit, and thus appear in the resulting
spectrum separated from the energy
which comes from every other part of
the arc. Such an instrument is called
an analyzing spectroscope while one with-
out the lens is called an integrating spec-
troscope, since it furnishes to each point
of the slit a sample of the radiant energy
coming from every part of the source of
light, and thus produces only an average
spectrum of that source without distinction of its parts.
When a spectroscope is attached to a telescope, as is often

INSTRUMENTS USED AND PRINCIPLES INVOLVED

done (see Fig. 49), the eyepiece is removed to make way
for it, and the telescope objective takes the part of the
analyzing lens. A camera is frequently combined with

FIG. 48.— Violet and ultraviolet parts of spectrum of an arc lamp.

such an apparatus to photograph the spectra it furnishes,
and the whole instrument is then called a spectrograph.

85. Spectrum analysis, — Having seen the mechanism of
the spectroscope by which the light incident upon it is
resolved into its constituent parts and drawn out into a
series of colors arranged in the order of their wave lengths,
we have now to consider the interpretation which is to be
placed upon the various kinds of spectra which may be
seen, and here we rely upon the experience of physicists
and chemists, from whom we learn as follows :

The radiant energy which is analyzed by the spectro-
scope has its source in the atoms and molecules which make
up the luminous body from which the energy is radiated,
and these atoms and molecules are able to impress upon
the ether their own peculiarities in the shape of waves of
different length and amplitude. We have seen that by
varying the conditions of the experiment different kinds of
waves may be produced in a bucket of water; and as a
study of these waves might furnish an index to the condi-
tions which produced them, so the study of the waves
peculiar to the light which comes from any source may be
made to give information about the molecules which make
up that source. Thus the molecules of iron produce a
system of waves peculiar to themselves and which can be
duplicated by nothing else, and every other substance
gives off its own peculiar type of energy, presenting a

142

ASTRONOMY

limited and definite number of wave lengths dependent
upon the nature and condition of its molecules. If these
molecules are free to behave in their own characteristic
fashion without disturbance or crowding, they emit light of
these wave lengths only, and we find in the spectrum a
series of bright lines, pictures of the slit produced by light
of these particular wave lengths, while between these bright
lines lie dark spaces showing the absence from the radiant
energy of light of intermediate wave lengths. Such a
spectrum is shown in the central portion of Fig. 47, which,

FIG. 49. — A spectroscope attached to the Yerkes telescope.

as we have already seen, is produced by the space between
the carbons of the arc lamp. On the other hand, if the
molecules are closely packed together under pressure they
so interfere with each other as to give off a jumble of
energy of all wave lengths, and this is translated by the
spectroscope into a continuous ribbon of light with no dark
spaces intervening, as in the upper and lower parts of Figs.

INSTRUMENTS USED AND PRINCIPLES INVOLVED 143

47 and 48, produced by the incandescent solid carbons of
the lamp. These two types are known as the continuous
and discontinuous spectrum, and we may lay down the fol-
lowing principle regarding them :

A discontinuous spectrum, or bright-line spectrum as
it is familiarly called, indicates that the molecules of the
source of light are not crowded together, and therefore the
light must come from an incandescent gas. A continuous
spectrum shows only that the molecules are crowded to-
gether, or are so numerous that the body to which they
belong is not transparent and gives no further informa-
tion. The body may be solid, liquid, or gaseous, but in
the latter case the gas must be under considerable pres-
sure or of great extent.

A second principle is : The lines which appear in a spec-
trum are characteristic of the source from which the light
came— e. g., the double line in the yellow part of the spec-
trum at the extreme left in Fig. 47 is produced by sodium
vapor in and around the electric arc and is never pro-
duced by anything but sodium. When by laboratory ex-
periments we have learned the particular set of lines
corresponding to iron, we may treat the presence of these
lines in another spectrum as proof that iron is present
in the source from which the light came, whether that
source be a white-hot poker in the next room or a star
immeasurably distant. The evidence that iron is pres-
ent lies in the nature of the light, and there is no reason
to suppose that nature to be altered on the way from
star to earth. It may, however, be altered by something
happening to the source from which it comes — e. g., chang-
ing temperature or pressure may affect, and does affect, the
spectrum which such a substance as iron emits, and we must
be prepared to find the same substance presenting different
spectra under different conditions, only these conditions
must be greatly altered in order to produce radical changes
in the spectrum.

144

ASTRONOMY

86. Wave lengths.— To identi-
fy a line as belonging to and pro-
duced by iron or any other sub-
stance, its position in the spec-
trum— i. e., its wave length — must
be very accurately determined,
and for the identification of a sub-
stance by means of its spectrum it
is often necessary to determine ac-
curately the wave lengths of many
lines. A complicated spectrum
may consist of hundreds or thou-
sands of lines, due to the presence
of many different substances in
the source of light, and unless
great care is taken in assigning
the exact position of these lines
in the spectrum, confusion and
wrong identifications are sure to
result. For the measurement of
the required wave length a tenth
meter (§ 75) is the unit employed,
and a scale of wave lengths ex-
pressed in this unit is presented
in Fig. 50. The accuracy with
which some of these wave lengths
are determined is truly astound-
ing ; a ten-billionth of an inch !
These numerical wave lengths
save all necessity for referring to
the color of any part of the spec-
trum, and pictures of spectra for
scientific use are not usually
printed in colors.

87. Absorption spectra.— There
is another kind of spectrum, of

INSTRUMENTS USED AND PRINCIPLES INVOLVED 145

greater importance than either of those above considered,
which is well illustrated by the spectrum of sunlight (Fig.
50). This is a nearly continuous spectrum crossed by nu-
merous dark lines due to absorption of radiant energy in a
comparatively cool gas through which it passes on its way
to the spectroscope. Fraunhofer, who made the first care-
ful study of spectra, designated some of the more conspicu-
ous of these lines by letters of the alphabet which are shown
in the plate, and which are still in common use as names
for the lines, not only in the spectrum of sunlight but
wherever they occur in other spectra. Thus the double
line marked Z>, wave length 5893, falls at precisely the same
place in the spectrum as does the double (sodium) line
which we have already seen in the yellow part of the arc-
light spectrum, which line is also called D and bears a very
intimate relation to the dark D line of the solar spectrum.

The student who has access to colored crayons should
color one edge of Fig. 50 in accordance with the lettering
there given and, so far as possible, he should make the
transition from one color to the next a gradual one, as it is
in the rainbow.

Fig. 50 is far from being a complete representation of
the spectrum of sunlight. Xot only does this spectrum ex-
tend both to the right and to the left into regions invisible
to the human eye, but within the limits of the figure, in-
stead of the seventy-five lines there shown, there are liter-
ally thousands upon thousands of lines, of which only the
most conspicuous can be shown in such a cut as this.

The dark lines which appear in the spectrum of sun-
light can, under proper conditions, be made to appear in
the spectrum of an arc light, and Fig. 51 shows a magnified
representation of a small part of such a spectrum adjacent
to the D (sodium) lines. Down the middle of each of these
lines runs a black streak whose position (wave length) is
precisely that of the D lines in the spectrum of sunlight,
and whose presence is explained as follows :

146 ASTRONOMY

The very hot sodium vapor at the center of the arc gives
off its characteristic light, which, shining through the outer
and cooler layers of sodium vapor, is partially absorbed by
these, resulting in a fine dark line corresponding exactly in
position and wave length to the bright lines, and seen
against these as a background, since the higher tempera-
ture at the center of the arc tends to broaden the bright
lines and make them diffuse. Similarly the dark lines in
the spectrum of the sun (Fig. 50) point to the existence of

D

FIG. 51.— The lines reversed.

a surrounding envelope of relatively cool gases, which absorb
from the sunlight precisely those kinds of radiant energy
which they would themselves emit if incandescent. The
resulting dark lines in the spectrum are to be interpreted
by the same set of principles which we have above applied
to the bright lines of a discontinuous spectrum, and they
may be used to determine the chemical composition of the
sun, just as the bright lines serve to determine the chemi-
cal elements present in the electric arc. With reference to
the mode of their formation, bright-line and dark-line spec-
tra are sometimes called respectively emission and absorp-
tion spectra.

88. Types of spectrum, — The sun presents by far the
most complex spectrum known, and Fig. 50 shows only a
small number of the more conspicuous lines which appear

INSTRUMENTS USED AND PRINCIPLES INVOLVED 147

in it. Spectra of stars, per contra, appear relatively simple,
since their feeble light is insufficient to bring out faint
details. In Chapters XIII and XIV there are shown types
of the different kinds of spectra given by starlight, and
these are to be interpreted by the principles above estab-
lished. Thus the spectrum of the bright star ft Aurigse
shows a continuous spectrum crossed by a few heavy ab-
sorption lines which are known from laboratory experi-
ments to be produced only by hydrogen. There must
therefore be an atmosphere of relatively cool hydrogen
surrounding this star. The spectrum of Pollux is quite
similar to that of the sun and is to be interpreted as show-
ing a physical condition similar to that of the sun, while
the spectrum of a Herculis is quite different from either of
the others. In subsequent chapters we shall have occasion
to consider more fully these different types of spectrum.

89. The Doppler principle. — This important principle of
the spectrum analysis is most readily appreciated through
the following experiment :

Listen to the whistle of a locomotive rapidly approach-
ing, and observe how the pitch changes and the note be-
comes more grave as the locomotive passes by and com-
mences to recede. During the approach of the whistle
each successive sound wave has a shorter distance to travel
in coming to the ear of the listener than had its predeces-
sor, and in consequence the waves appear to come in
quicker succession, producing a higher note with a corre-
spondingly shorter wave length than would be heard if the
same whistle were blown with the locomotive at rest. On
the other hand, the wave length is increased and the pitch
of the note lowered by the receding motion of the whistle.
A similar effect is produced upon the wave length of light
by a rapid change of distance between the source from
which it comes and the instrument which receives it, so
that a diminishing distance diminishes very slightly the
wave length of every line in the spectrum produced by the

148 ASTRONOMY

light, and an increasing distance increases these wave
lengths, and this holds true whether the change of dis-
tance is produced by motion of the source of light or by
motion of the instrument which receives it.

This change of wave length is sometimes described by
saying that when a body is rapidly approaching, the lines
of its spectrum are all displaced toward the violet end of
the spectrum, and are correspondingly displaced toward the
red end by a receding motion. The amount of this shift-
ing, when it can be measured, measures the velocity of the
body along the line of sight, but the observations are ex-
ceedingly delicate, and it is only in recent years that it has
been found possible to make them with precision. For this
purpose there is made to pass through the spectroscope
light from an artificial source which contains one or more
chemical elements known to be present in the star which
is to be observed, and the corresponding lines in the
spectrum of this light and in the spectrum of the star
are examined to determine whether they exactly match
in position, or show, as they sometimes do, a slight dis-
placement, as if one spectrum had been slipped past
the other. The difficulty of the observations lies in the
extremely small amount of this slipping, which rarely if
ever in the case of a moving star amounts to one sixth part
of the interval between the close parallel lines marked D
in Fig. 50. The spectral lines furnished by the headlight
of a locomotive running at the rate of a hundred miles
per hour would be displaced by this motion less than one
six-thousandth part of the space between the D lines,
an amount absolutely imperceptible in the most powerful
spectroscope yet constructed. But many of the celestial
bodies have velocities so much greater than a hundred
miles per hour that these may be detected and measured
by means of the Doppler principle.

90. Other instruments. — Other instruments of impor-
tance to the astronomer, but of which only casual mention

INSTRUMENTS USED AND PRINCIPLES INVOLVED 149

can here be made, are the meridian-circle ; the transit, one
form of which is shown in Fig. 52, and the zenith tele-
scope, which furnish refined methods for making observa-
tions similar in kind to those which the student has already
learned to make with plumb line and protractor ; the sex-
tant, which is pre-eminently the sailor's instrument for
finding the latitude and longitude at sea, by measuring the

FIG. 52. — A combined transit instrument and zenith telescope.

altitudes of sun and stars above the sea horizon ; the heli-
ometer, which serves for the very accurate measurement of
small angles, such as the angular distance between two stars
not more than one or two degrees apart ; and the photom-
eter, which is used for measuring the amount of light re-
ceived from the celestial bodies.

CHAPTEE IX

THE MOON

91. Results of observation with the unaided eye,— The
student who has made the observations of the moon which
are indicated in Chapter III has in hand data from which
much may be learned about the earth's satellite. Perhaps
the most striking feature brought out by them is the mo-
tion of the moon among the stars, always from west toward
east, accompanied by that endless series of changes in
shape and brightness — new moon, first quarter, full moon,
etc. — whose successive stages we represent by the words,
the phase of the moon. From his own observation the
student should be able to verify, at least approximately,
the following statements, although the degree of numer-
ical precision contained in some of them can be reached
only by more elaborate apparatus and longer study than he
has given to the subject :

A. The phase of the moon depends upon the distance
apart of sun and moon in the sky, new moon coming
when they are together, and full moon when they are as
far apart as possible.

B. The moon is essentially a round, dark body, giving
off no light of its own, but shining solely by reflected sun-
light. The proof of this is that whenever we see a part of
the moon which is turned away from the sun it looks dark
— e. g., at new moon, sun and moon are in nearly the same
direction from us and we see little or nothing of the moon,
since the side upon which the sun shines is turned away
from us. At full moon the earth is in line between sun

150 •

THE MOON, ONE DAY AFTER FIRST QUARTER.

From a photograph made at the Paris Observatory.

THE MOON 151

and moon, and we see, round and bright, the face upon
which the sun shines. At other phases, such as the quar-
ters, the moon turns toward the earth a part of its night
hemisphere and a part of its day hemisphere, but in gen-
eral only that part which belongs to the day side of the
moon is visible and the peculiar curved line which forms
the boundary— the " ragged edge," or terminator, as it is
called, is the dividing line between day and night upon
the moon.

A partial exception to what precedes is found for a few
days after new moon when the moon and sun are not very
far apart in the sky, for then the whole round disk of the
moon may often be seen, a small part of it brightly illu-
minated by the sun and the larger part feebly illuminated
by sunlight which fell first upon the earth and was by it
reflected back to the moon, giving the pleasing effect which
is sometimes called the old moon in the new moon's arms.
The new moon — i. e., the part illumined by the sun — usu-
ally appears to belong to a sphere of larger radius than the
old moon, but this is purely a trick played by the eyes of
the observer, and the effect disappears altogether in a tele-
scope. Is there any similar effect in the few days before
new moon ?

C. The moon makes the circuit of the sky from a given
star around to the same star again in a little more than
27 days (27.32166), but the interval between successive new
moons — i. e., from the sun around to the sun again — is
more than 29 days (29.53059). This last interval, which is
called a lunar month or synodical month, indicates what
we have learned before — that the sun has changed its place
among the stars during the month, so that it takes the
moon an extra two days to overtake him after having
made the circuit of the sky, just as it takes the minute
hand of a clock an extra 5 minutes to catch up with
the hour hand after having made a complete circuit of the
dial.

152 ASTRONOMY

D. Wherever the moon may be in the sky, it turns
always the same face toward the earth, as is shown by the
fact that the dark markings which appear on its surface
stand always upon (nearly) the same part of its disk. It
does not always turn the same face toward the sun, for
the boundary line between the illumined and unillumined
parts of the moon shifts from one side to the other as the
phase changes, dividing at each moment day from night
upon the moon and illustrating by its slow progress that
upon the moon the day and the month are of equal length
(29.5 terrestrial days), instead of being time units of differ-
ent lengths as with us.

92. The moon's motion, — The student should compare the
results of his own observations, as well as the preceding
section, with Fig. 53, in which the lines with dates printed
on them are all supposed to radiate from the sun and to
represent the direction from the sun of earth and moon
upon the given dates which are arbitrarily assumed for
the sake of illustration, any other set would do equally
well. The black dots, small and large, represent the
moon revolving about the earth, but having the circular
path shown in Fig. 34 (ellipse) transformed by the earth's
forward motion into the peculiar sinuous line here shown.
With respect to both earth and sun, the moon's orbit
deviates but little from a circle, since the sinuous curve
of Fig. 53 follows very closely the earth's orbit around
the sun and is almost identical with it. For clearness
of representation the distance between earth and moon
in the figure has been made ten times too great, and to
get a proper idea of the moon's orbit with reference to
the sun, we must suppose the moon moved up toward the
earth until its distance from the line of the earth's orbit is
only a tenth part of what it is in the figure. When this is
done, the moon's path becomes almost indistinguishable
from that of the earth, as may be seen in the figure, where
the attempt has been made to show both lines, and it

PIG. 53. — Motion of moon and earth relative to the sun.
11

154 ASTKONOMY

is to be especially noted that this real orbit of the moon is
everywhere concave toward the sun.

The phase presented by the moon at different parts of
its path is indicated by the row of circles at the right, and
the student should show why a new moon is associated
with June 30th and a full moon with July 15th, etc. What
was the date of first quarter ? Third quarter ?

We may find in Fig. 53 another effect of the same
kind as that noted above in C. Between noon, June 30th,
and noon, July 3d, the earth makes upon its axis three com-
plete revolutions with respect to the sun, but the meridian
which points toward the moon at noon on June 30th will
not point toward it at noon on July 3d, since the moon has
moved into a new position and is now 37° away from the
meridian. Verify this statement by measuring, in Fig. 53,
with the protractor, the moon's angular distance from the
meridian at noon on July 3d. When will the meridian
overtake the moon ?

93. Harvest moon. — The interval between two successive
transits of the meridian past the moon is called a lunar
day, and the student should show from the figure that on
the average a lunar day is 51 minutes longer than a solar
day — i. e., upon the average each day the moon comes to
the meridian 51 minutes of solar time later than on the
day before. It is also true that on the average the moon
rises and sets 51 minutes later each day than on the day
before. But there is a good deal of irregularity in the
retardation of the time of moonrise and moonset, since
the time of rising depends largely upon the particular
point of the horizon at which the moon appears, and be-
tween two days this point may change so much on account
of the moon's orbital motion as to make the retardation
considerably greater or less than its average value. In
northern latitudes this effect is particularly marked in the
month of September, when the eastern horizon is nearly
parallel with the moon's apparent path in the sky, and near

THE MOON 155

the time of full moon in that month the moon rises on
several successive nights at nearly the same hour, and in
less degree the same is true for October. This highly
convenient arrangement of moonlight has caused the full
moons of these two months to be christened respectively
the Harvest Moon and the Hunter's Moon.

94. Size and mass of the moon. — It has been shown in
Chapter I how the distance of the moon from the earth
may be measured and its diameter determined by means of
angles, and without enlarging upon the details of these ob-
servations, we note as their result that the moon is a globe
2,163 miles in diameter, and distant from the earth on the
average about 240,000 miles. But, as we have seen in
Chapter VII, this distance changes to the extent of a few
thousand miles, sometimes less, sometimes greater, mainly
on account of the elliptic shape of the moon's orbit about
the earth, but also in part from the disturbing influence of
other bodies, such as the sun, which pull the moon to and
fro, backward and forward, to quite an appreciable extent.

From the known diameter of the moon it is a matter of
elementary geometry to derive in miles the area of its sur-
face and its volume or solid contents. Leaving this as an
exercise for the student, we adopt the earth as the standard
of comparison and find that the diameter of the moon is
rather more than a quarter, u/g," that of the earth, the area
of its surface is a trifle more than -^ that of the earth,
and its volume a little more than ¥V of the earth's. So
much is pure geometry, but we may combine with it some
mechanical principles which enable us to go a step farther
and to " weigh " the moon — i. e., determine its mass and
the average density of the material of which it is made.

We have seen that the moon moves around the sun in a
path differing but little from the smooth curve shown in
Fig. 53, with arrows indicating the direction of motion,
and it would follow absolutely such a smooth path were
it not for the attraction of the earth, and in less degree

156 ASTRONOMY

of some of the other planets, which swing it about first
to one side then to the other. But action and reaction
are equal ; the moon pulls as strongly upon the earth
as does the earth upon the moon, and if earth and moon
were of equal mass, the deviation of the earth from the
smooth curve in the figure would be just as large as that
of the moon. It is shown in the figure that the moon does
displace the earth from this curve, and we have only to
measure the amount of this displacement of the earth and
compare it with the displacement suffered by the moon to
find how much the mass of the one exceeds that of the
other. It may be seen from the figure that at first quarter,
about July 7th, the earth is thrust ahead in the direction
of its orbital motion, while at the third quarter, July 22d, it
is pulled back by the action of the moon, and at all times
it is more or less displaced by this action, so that, in order
to be strictly correct, we must amend our former statement
about the moon moving around the earth and make it read,
Both earth and moon revolve around a point on line be-
tween their centers. This point is called their center of
gravity, and the earth and the moon both move in ellipses
having this center of gravity at their common focus.
Compare this with Kepler's First Law. These ellipses are
similarly shaped, but of very different size, corresponding
to Newton's third law of motion (Chapter IV), so that the
action of the earth in causing the small moon to move
around a large orbit is just equal to the reaction of the
moon in causing the larger earth to move in the smaller
orbit. This is equivalent to saying that the dimensions of
the two orbits are inversely proportional to the masses of
the earth and the moon.

By observing throughout the month the direction from
the earth to the sun or to a near planet, such as Mars or
Venus, astronomers have determined that the diameter of
the ellipse in which the earth moves is about 5,850 miles,
so that the distance of the earth from the center of gravity

THE MOON 157

is 2,925 miles, and the distance of the moon from it is
240,000 — 2,925 = 237,075. We may now write in the form
of a proportion —

Mass of earth : Mass of moon : : 237,075 : 2,925,

and find from it that the mass of the earth is 81 times
as great as the mass of the moon — i. e., leaving kind and
quality out of account, there is enough material in the
earth to make 81 rnoons. We may note in this con-
nection that the diameter of the earth, 7,926 miles, is
greater than the diameter of the monthly orbit in which
the moon causes it to move, and therefore the center of
gravity of earth and moon always lies inside the body of
the earth, about 1,000 miles below the surface.

95. Density of the moon. — It is believed that in a general
way the moon is made of much the same kind of material
which goes to make up the earth — metals, minerals, rocks,
etc.— and a part of the evidence upon which this belief is
based lies in the density of the moon. By density of a
substance we mean the amount of it which is contained in
a given volume — i. e., the weight of a bushel or a cubic
centimeter of the stuff. The density of chalk is twice as
great as the density of water, because a cubic centimeter
of chalk weighs twice as much as an equal volume of
water, and similarly in other cases the density is found by
dividing the mass or weight of the body by the mass or
weight of an equal volume of water.

We know the mass of the earth (§ 40), and knowing
the mass of a cubic foot of water, it is easy, although a
trifle tedious, to compute what would be the mass of a vol-
ume of water equal in size to the earth. The quotient
obtained by dividing one of these masses by the other (mass
of earth -5- mass of water) is the average density of the ma-
terial composing the earth, and we find numerically that
this is 5.6— i. e., it would take 5.6 water earths to attract as
strongly as does the real one. From direct experiment we

158 ASTRONOMY

know that the average density of the principal rocks which
make up the crust of the earth is only about half of this,
showing that the deep-lying central parts of the earth are
denser than the surface parts, as we should expect them to
be, because they have to bear the weight of all that lies
above them and are compressed by it.

Turning now to the moon, we find in the same way as
for the earth that its average density is 3.4 as great as that
of water.

96. Force of gravity upon the moon. — This number, 3.4,
compared with the 5.6 which we found for the earth, shows
that on the whole the moon is made of lighter stuff than is
the body of the earth, and this again is much what we should
expect to find, for weight, the force which tends to com-
press the substance of the moon, is less there than here.
The weight of a cubic yard of rock at the surface of either
earth or moon is the force with which the earth or moon
attracts it, and this by the law of gravitation is for the
earth —

mm'
'•

and for the moon —

m'

™ si

w = k. _?L;
(1081)2

from which we find by division—

TF/3963X2
W = 81 -

The cubic yard of rock, which upon the earth weighs two
tons, would, if transported to the moon, weigh only one
third of a ton, and would have only one sixth as much
influence in compressing the rocks below it as it had upon
the earth. Xote that this rock when transported to the
moon would be still attracted by the earth and would have
weight toward the earth, but it is not this of which we are

THE MOON 159

speaking ; by its weight in the moon we mean the force
with which the moon attracts it. Making due allowance
for the difference in compression produced by weight, we
may say that in general, so far as density goes, the moon is
very like a piece of the earth of equal mass set off by itself
alone.

97. Albedo. — In another respect the lunar stuff is like
that of which the earth is made : it reflects the sunlight in
much the same way and to the same amount. The con-
trast of light and dark areas on the moon's surface shows,
as we shall see in another section, the presence of different
substances upon the moon which reflect the sunlight in
different degrees. This capacity for reflecting a greater or
less percentage of the incident sunlight is called albedo
(Latin, whiteness), and the brilliancy of the full moon might
lead one to suppose that its albedo is very great, like that
of snow or those masses of summer cloud which we call
thunderheads. But this is only an effect of contrast with
the dark background of the sky. The same moon by day
looks pale, and its albedo is, in fact, not very different
from that of our common rocks — weather-beaten sandstone
according to Sir John Herschel — so that it would be pos-
sible to build an artificial moon of rock or brick which
would shine in the sunlight much as does the real moon.

The effect produced by the differences of albedo upon
the moon's face is commonly called the " man in the moon,"
but, like the images presented by glowing coals, the face in
the moon is anything which we choose to make it. Among
the Chinese it is said to be a monkey pounding rice ; in
India, a rabbit ; in Persia, the earth reflected as in a mir-
ror, etc.

98. Librations. — We have already learned that the moon
turns always the same face toward the earth, and we have
now to modify this statement and to find that here, as in
so many other cases, the thing we learn first is only ap-
proximately true and needs to be limited or added to or

160 ASTRONOMY

modified in some way. In general, Nature is too complex
to be completely understood at first sight or to be per-
fectly represented by a simple statement. In Fig. 55 we
have two photographs of the moon, taken nearly three years
apart, the right-hand one a little after first quarter and the
left-hand one a little before third quarter. They there-
fore represent different parts of the moon's surface, but
along the ragged edge the same region is shown on both
photographs, and features common to both pictures may
readily be found — e. g., the three rings which form a right-
angled triangle about one third of the way down from the
top of the cut, and the curved mountain chain just below
these. If the moon turned exactly the same face toward
us in the two pictures, the distance of any one of these
markings from any part of the moon's edge must be the
same in both pictures ; but careful measurement will show
that this is not the case, and that in the left-hand pic-
ture the upper edge of the moon is tipped toward us and
the lower edge away from us, as if the whole moon had
been rotated slightly about a horizontal line and must be
turned back a little (about 7°) in order to match perfectly
the other part of the picture.

This turning is called a libration, and it should be borne
in mind that the moon librates not only in the direction
above measured, north and south, but also at right angles
to this, east and west, so that we are able to see a little
farther around every part of the moon's edge than would
be possible if it turned toward us at all times exactly the
same face. But in spite of the librations there remains on
the farther side of the moon an area of 6,000,000 square
miles which is forever hidden from us, and of whose char-
acter we have no direct knowledge, although there is no
reason to suppose it very different from that which is visi-
ble, despite the fact that some of the books contain quaint
speculations to the contrary. The continent of South
America is just about equal in extent to this unknown re-

THE MOON

161

gion, while North America is a fair equivalent for all the
rest of the moon's surface, both those central parts which
are constantly visible, and the zone around the edge whose
parts sometimes come into sight and are sometimes hidden.

An interesting consequence of the peculiar rotation of
the moon is that from our side of it the earth is always
visible. Sun, stars, and planets rise and set there as well
as here, but to an observer on the moon the earth swings
always overhead, shifting its position a few degrees one
way or the other on account of the libration but running
through its succession of phases, new earth, first quarter,
etc., without ever going below the horizon, provided the
observer is anywhere near the center of the moon's disk.

99. Cause of librations. — That the moon should librate
is by no means so remarkable a fact as that it should at all
times turn very nearly the
same face toward the earth.
This latter fact can have but
one meaning : the moon re-
volves about an axis as does
the earth, but the time re-
quired for this revolution is
just equal to the time re-
quired to make a revolution
in its orbit. Place two coins
upon a table with their heads
turned toward the north, as
in Fig. 54, and move the
smaller one around the larger

in such a way that its face shall always look away from the
larger one. In making one revolution in its orbit the head
on this small coin will be successively directed toward every
point of the compass, and when it returns to its initial
position the small coin will have made just one revolu-
tion about an axis perpendicular to the plane of its or-
bit. In no other way can it be made to face always away

FIG. 54. — Illustrating the moon's
rotation.

162 ASTRONOMY

from the figure at the center of its orbit while moving
around it.

We are now in a position to understand the moon's
librations, for, if the small coin at any time moves faster or
slower in its orbit than it turns about its axis, a new side
will be turned toward the center, and the same may happen
if the central coin itself shifts into a new position. This is
what happens to the moon, for its orbital motion, like that
of Mercury (Fig. 16), is alternately fast and slow, and in
addition to this there are present other minor influences,
such as the fact that its rotation axis is not exactly per-
pendicular to the plane of its orbit ; in addition to this the
observer upon the earth is daily carried by its rotation from
one point of view to another, etc., so that it is only in a gen-
eral way that the rotation upon the axis and motion in the
orbit keep pace with each other. In a general way a cable
keeps a ship anchored in the same place, although wind and
waves may cause it to " librate " about the anchor.

How the moon came to have this exact equality be-
tween its times of revolution and rotation constitutes a
chapter of its history upon which we shall not now enter ;
but the equality having once been established, the mechan-
ism by which it is preserved is simple enough.

The attraction of the earth for the moon has very
slightly pulled the latter out of shape (§ 42), so that the
particular diameter, which points toward the earth, is a lit-
tle longer than any other, and thus serves as a handle which
the earth lays hold of and pulls down into its lowest possible
position — i. e., the position in which it points toward the
center of the earth. Just how long this handle is, remains
unknown, but it may be shown from the law of gravitation
that less than a hundred yards of elongation would suffice
for the work it has to do.

100. The moon as a world. — Thus far we have considered
the moon as a satellite of the earth, dependent upon the
earth, and interesting chiefly because of its relation to it.

THE MOON 163

But the moon is something more than this ; it is a world in
itself, very different from the earth, although not wholly
unlike it. The most characteristic feature of the earth's
surface is its division into land and water, and 'nothing of
this kind can be found upon the moon. It is true that the
first generation of astronomers who studied the moon with
telescopes fancied that the large dark patches shown in
Fig. 55 were bodies of water, and named them oceans,
seas, lakes, and ponds, and to the present day we keep
those names, although it is long since recognized that these
parts of the moon's surface are as dry as any other. Their
dark appearance indicates a different kind of material from
that composing the lighter parts of the moon, material
with a different albedo, just as upon the earth we have
light-colored and dark-colored rocks, marble and slate,
which seen from the moon must present similar contrasts
of brightness. Although these dark patches are almost
the only features distinguishable with the unaided eye, it
is far otherwise in the telescope or the photograph, espe-
cially along the ragged edge where great numbers of rings
can be seen, which are apparently depressions in the moon
and are called craters. These we find in great number
all over the moon, but, as the figure shows, they are seen
to the best advantage near the terminator — i. e., the divid-
ing line between day and night, since the long shadows
cast here by the rising or setting sun bring out the details
of the surface better than elsewhere. Carefully examine
Fig. 55 with reference to these features.

Another feature which exists upon both earth and
moon, although far less common there than here, is illus-
trated in the chain of mountains visible near the termina-
tor, a little above the center of the moon in both parts of
Fig. 55. This particular range of mountains, which is
called the Lunar Apennines, is by far the most prominent
one upon the moon, although others, the Alps and Cauca-
sus, exist. But for the most part the lunar mountains

THE MOON 165

stand alone, each by itself, instead of being grouped into
ranges, as on the earth. Note in the figure that some of
the lunar mountains stretch out into the night side of the
moon, their peaks projecting up into the sunlight, and
thus becoming visible, while the lowlands are buried in the
shadow.

A subordinate feature of the moon's surface is the sys-
tem of rays which seem to radiate like spokes from some
of the larger craters, extending over hill and valley some-
times for hundreds of miles. A suggestion of these rays
may be seen in Fig. 55, extending from the great crater
Copernicus a little southwest of the end of the Apennines,
but their most perfect development is to be seen at the
time of full moon around the crater Tycho, which lies near
the south pole of the moon. Look for them with an opera
glass.

Another and even less conspicuous feature is furnished
by the rills, which, under favorable conditions of illumina-
tion, appear like long cracks on the moon's surface, per-
haps analogous to the canons of our Western country.

101. The map of the moon. — Fig. 55 furnishes a fairly
good map of a limited portion of the moon near the termi-
nator, but at the edges little or no detail can be seen. This
is always true ; the whole of the moon can not be seen to
advantage at any one time, and to remedy this we need to
construct from many photographs or drawings a map which
shall represent the several parts of the moon as they appear
at their best. Fig. 56 shows such a map photographed from
a relief model of the moon, and representing the principal
features of the lunar surface in a way they can never be
seen simultaneously. Perhaps its most striking feature is
the shape of the craters, which are shown round in the cen-
tral parts of the map and oval at the edges, with their long
diameters parallel to the moon's edge. This is, of course,
an eif ect of the curvature of the moon's surface, for we look
very obliquely at the edge portions, and thus see their for-

166

ASTKONOMY

mations much foreshortened in the direction of the moon's
radius.

The north and south poles of the moon are at the top
and bottom of the map respectively, and a mere inspection

FIG. 56.— Eelief map of the moon's surface.— After NASMTTH and CARPENTER.

of the regions around them will show how much more
rugged is the southern hemisphere of the moon than the
northern. It furnishes, too, some indication of how numer-
ous are the lunar craters, and how in crowded regions they
overlap one another.

The student should pick out upon the map those features
which he has learned to know in the photograph (Fig. 55)
— the Apennines, Copernicus, and the continuation of the
Apennines, extending into the dark part of the moon.

THE MOON 167

102. Size of the lunar features. — We may measure dis-
tances here in the same way as upon a terrestrial map, re-
membering that near the edges the scale of the map is very
much distorted parallel to the moon's diameter, and meas-
urements must not be taken in this direction, but may be
taken parallel to the edge. Measuring with a millimeter
scale, we find on the map for the diameter of the crater
Copernicus, 2.1 millimeters. To turn this into the diam-
eter of the real Copernicus in miles, we measure upon the
same map the diameter of the moon, 79.7 millimeters, and
then have the proportion —

Diameter of Copernicus in miles : 2,163 : : 2.1 : 79.7,

which when solved gives 57 miles. The real diameter of
Copernicus is a trifle over 56 miles. At the eastern edge

FIG. 57.— Mare Imbrium. Photographed at Goodsell Observatory.

of the moon, opposite the Apennines, is a large oval spot
called the Mare Crisium (Latin, ma-re = sea). Measure its

168

ASTRONOMY

length. The large crater to the northwest of the Apen-
nines is called Archimedes. Measure its diameter both in
the map and in the photograph (Fig. 55), and see how the
two results agree. The true diameter of this crater, east
and west, is very approximately 50 miles. The great smooth
surface to the west of Archimedes is the Mare Imbrium. Is

it larger or smaller than
Lake Superior ? Fig.
57 is from a photo-
graph of the Mare Im-
brium, and the amount
of detail here shown at
the bottom of the sea
is a sufficient indica-
tion that, in this case
at least, the water has
been drawn off, if in-
deed any was ever pres-
ent.

Fig. 58 is a repre-
sentation of the Mare
Crisium at a time when
night was beginning to
encroach upon its east-
ern border, and it
serves well to show the
rugged character of the ring-shaped wall which incloses
this area.

With these pictures of the smoother parts of the moon's
surface we may compare Fig. 59, which shows a region
near the north pole of the moon, and Fig. 60, giving an
early morning view of Archimedes and the Apennines.
Note how long and sharp are the shadows.

103. The moon's atmosphere. — Upon the earth the sun
casts no shadows so sharp and black as those of Fig. 60,
because his rays are here scattered and reflected in all direc-

FIG. 58. — Mare Crisium.
Lick Observatory photographs.

THE MOON

169

tions by the dust and vapors of the atmosphere (§ 51),
so that the place from which direct sunlight is cut off
is at least partially illumined by this reflected light. The
shadows of Fig. 60 show that upon the moon it must be
otherwise, and suggest that if the moon has any atmosphere
whatever, its density must be utterly insignificant in com-
parison with that of the earth. In its motion around the
earth the moon fre-
quently eclipses stars
(occults is the tech-
nical word), and if the
moon had an atmos-
phere such as is shown
in Fig. 61, the light
from the star A must
shine through this at-
mosphere just before
the moon's advancing
body cuts it off, and it
must be refracted by
the atmosphere so that
the star would appear
in a slightly different
direction (nearer to
B) than before. The
earth's atmosphere re-
fracts the starlight

under such circumstances by more than a degree, but no
one has been able to find in the case of the moon any effect
of this kind amounting to even a fraction of a second of
arc. While this hardly justifies the statement sometimes
made that the moon has no atmosphere, we shall be entire-
ly safe in saying that if it has one at all its density is less
than a thousandth part of that of the earth's atmosphere.
Quite in keeping with this absence of an atmosphere is the
fact that clouds never float over the surface of the moon.
12

FIG. 59. — Illustrating the rugged character of the
moon's surface. — NASMYTH and CARPENTER.

170

ASTRONOMY

Its features always stand out hard and clear, without any
of that haze and softness of outline which our atmosphere
introduces into all terrestrial landscapes.

104. Height of the lunar mountains. — Attention has al-
ready been called to the detached mountain peaks, which

in Fig. 55 pro-
long the range of
Apennines into
the lunar night.
These are the be-
ginnings of the
Caucasus moun-
tains, and from
the photograph
we may measure
as follows the
height to which
they rise above
the surrounding
level of the moon :
Fig. 62 repre-
sents a part of

the lunar surface along the boundary line between night
and day, the horizontal line at the top of the figure repre-
senting a level ray of sunlight which just touches the moon
at T and barely illuminates the top of the mountain, M,
whose height, /i, is to be determined. If we let R stand for
the radius of the moon and s for the distance, T M, we shall
have in the right-angled triangle M T C,

FIG. 60.— Archimedes and Apennines.
NASMYTH and CARPENTER.

and we need only to measure s — that is, the distance from
the terminator to the detached mountain peak — to make
this equation determine ^, since R is already known, being
half the diameter of the moon — 1,081 miles. Practically it
is more convenient to use instead of this equation another

THE MOON

171

form, which the student who is expert in algebra may show
to be very nearly equivalent to it :

s2
h (miles) = ^-77^, or h (feet) = 2.44 s2.

FIG. 61. — Occultations and the moon's
atmosphere.

The distance s must be expressed in miles in all of these
equations. In Fig. 55 the distance from the terminator
to the first detached peak
of the Caucasus moun-
tains is 1.7 millimeters =
52 miles, from which we
find the height of the
mountain to be 1.25
miles, or 6,600 feet.

Two things, however,
need to be borne in mind
in this connection. On
the earth we measure the

heights of mountains above sea level, while on the moon
there is no sea, and our 6,600 feet is simply the height of

the mountain top above
the level of that par-
ticular point in the
terminator, from which
we measure its distance.
So too it is evident
from the appearance of
things, that the sun-
light, instead of just
touching the top of the
particular mountain
whose height we have
measured, really extends
some little distance down from its summit, and the 6,600
feet is therefore the elevation of the lowest point on the
mountains to which the sunlight reaches. The peak itself

Night

FIG. 62. — Determining the height of a lunar
mountain.

172 ASTRONOMY

may be several hundred feet higher, and our photograph
must be taken at the exact moment when this peak appears
in the lunar morning or disappears in the evening if we are
to measure the altitude of the mountain's summit. Meas-
ure the height of the most northern visible mountain of
the Caucasus range. This is one of the outlying spurs of
the great mountain Calippus, whose principal peak, 19,000
feet high, is shown in Fig. 55 as the brightest part of the
Caucasus range.

The highest peak of the lunar Apennines, Huyghens,
has an altitude of 18,000 feet, and the Leibnitz and Doerfel
Mountains, near the south pole of the moon, reach an alti-
tude 50 per cent greater than this, and are probably the
highest peaks on the moon. This falls very little short of
the highest mountain on the earth, although the moon is
much smaller than the earth, and these mountains are con-
siderably higher than anything on the western continent of
the earth.

The vagueness of outline of the terminator makes it
difficult to measure from it with precision, and somewhat
more accurate determinations of the heights of lunar
mountains can be obtained by measuring the length of
the shadows which they cast, and the depths of craters
may also be measured by means of the shadows which fall
into them.

105. Craters. — Fig. 63 shows a typical lunar crater, and
conveys a good idea of the ruggedness of the lunar land-
scape. Compare the appearance of this crater with the
following generalizations, which are based upon the accurate
measurement of many such :

A. A crater is a real depression in the surface of the
moon, surrounded usually by an elevated ring which rises
above the general level of the region outside, while the bot-
tom of the crater is about an equal distance below that
level.

B. Craters are shallow, their diameters ranging from

THE MOON 173

five times to more than fifty times their depth. Archi-
medes, whose diameter we found to be 50 miles, has an
average depth of about 4,000 feet below the crest of its
surrounding wall, and is relatively a shallow crater. .

FIG. 63.— A typical lunar crater.— NASMYTH and CARPENTER.

C. Craters frequently have one or more hills rising
within them which, however, rarely, if ever, reach up to the
level of the surrounding wall.

D. Whatever may have been the mode of their forma-
tion, the craters can not have been produced by scooping
out material from the center and piling it up to make the
wall, for in three cases out of four the volume of the exca-
vation is greater than the volume of material contained in
the wall.

106. Moon and earth. — We have gone far enough now
to appreciate both the likeness and the unlikeness of the
moon and earth. They may fairly enough be likened to
offspring of the same parent who have followed very differ-
ent careers, and in the fullness of time find themselves in
very different circumstances. The most serious point of
difference in these circumstances is the atmosphere, which
gives to the earth a wealth of phenomena altogether lack-

174 ASTRONOMY

ing in the moon. Clouds, wind, rain, snow, dew, frost, and
hail are all dependent upon the atmosphere and can not be
found where it is not. There can be nothing upon the
moon at all like that great group of changes which we
call weather, and the unruffled aspect of the moon's face
contrasts sharply with the succession of cloud and sunshine
which the earth would present if seen from the moon.

The atmosphere is the chief agent in the propagation
of sound, and without it the moon must be wrapped in
silence more absolute than can be found upon the surface
of the earth. So, too, the absence of an atmosphere shows
that there can be no water or other liquid upon the moon,
for if so it would immediately evaporate and produce a
gaseous envelope which we have seen does not exist. With
air and water absent there can be of course no vegetation
or life of any kind upon the moon, and we are compelled
to regard it as an arid desert, utterly waste.

107. Temperature of the moon. — A characteristic feature
of terrestrial deserts, which is possessed in exaggerated de-
gree by the moon, is the great extremes of temperature to
which they and it are subject. Owing to its slow rotation
about its axis, a point on the moon receives the solar radia-
tion uninterruptedly for more than a fortnight, and that
too unmitigated by any cloud or vaporous covering. Then
for a like period it is turned away from the sun and allowed
to cool off, radiating into interplanetary space without hin-
drance its accumulated store of heat. It is easy to see that
the range of temperature between day and night must be
much greater under these circumstances than it is with us
where shorter days and clouded skies render day and night
more nearly alike, to say nothing of the ocean whose waters
serve as a great balance wheel for equalizing temperatures.
Just how hot or how cold the moon becomes is hard to
determine, and very different estimates are to be found in
the books. Perhaps the most reliable of these are fur-
nished by the recent researches of Professor Very, whose

THE MOON 175

experiments lead him to conclude that " its rocky surface at
midday, in latitudes where the sun is high, is probably hotter
than boiling water and only the most terrible of earth's des-
erts, where the burning sands blister the skin, and men,
beasts, and birds drop dead, can approach a noontide on
the cloudless surface of our satellite. Only the extreme
polar latitudes of the moon can have an endurable tem-
perature by day, to say nothing of the night, when we
should have to become troglodytes to preserve ourselves
from such intense cold."

While the night temperature of the moon, even very
soon after sunset, sinks to something like 200° below zero
on the centigrade scale, or 320° below zero on the Fahren-
heit scale, the lowest known temperature upon the earth,
according to General Greely, is 90° Fahr. below zero, re-
corded in Siberia in January, 1885.

Winter and summer are not markedly different upon
the moon, since its rotation axis is nearly perpendicular to
the plane of the earth's orbit about the sun, and the sun
never goes far north or south of the moon's equator. The
month is the one cycle within which all seasonal changes in
its physical condition appear to run their complete course.

108. Changes in the moon. — It is evidently idle to look
for any such changes in the condition of the moon's sur-
face as with us mark the progress of the seasons or
the spread of civilization over the wilderness. But minor
changes there may be, and it would seem that the violent
oscillations of temperature from day to night ought to have
some effect in breaking down and crumbling the sharp
peaks and crags which are there so common and so pro-
nounced. For a century past astronomers have searched
carefully for changes of this kind — the filling up of some
crater or the fall of a mountain peak; but while some
things of this kind have been reported from time to time,
the evidence in their behalf has not been altogether conclu-
sive. At the present time it is an open question whether

176

ASTRONOMY

changes of this sort large enough to be seen from the
earth are in progress. A crater much less than a mile
wide can be seen in the telescope, but it is not easy to
tell whether so minute an object has changed in size or
shape during a year or a decade, and even if changes are
seen they may be apparent rather than real. Fig. 64 con-
tains two views of the crater Archimedes, taken under a

f

FIG. 64.— Archimedes in the lunar morning and afternoon.— WEINEK.

morning and an afternoon sun respectively, and shows a
very pronounced difference between the two which pro-
ceeds solely from a difference of illumination. In the pres-
ence of such large fictitious changes astronomers are slow
to accept smaller ones as real.

r— ' "^ It is this absence of change that is responsible for the

\ rugged and sharp-cut features of the moon which continue

\ substantially as they were made, while upon the earth rain

I and frost are continually wearing down the mountains and

\ spreading their substance upon the lowland in an unending

\ process of smoothing off the roughnesses of its surface.

\ Upon the moon this process is almost if not wholly want-

} ing, and the moon abides to-day much more like its primi-

; tive condition than is the earth.

109. The moon's influence upon the earth. — There is a
"widespread popular belief that in many ways the moon exer-

THE MOON 177

cises a considerable influence upon terrestrial affairs : that
it affects the weather for good or ill, that crops must be
planted and harvested, pigs must be killed, and timber cut
at the right time of the moon, etc. Our common word
lunatic means moonstruck — i. e., one upon whom the moon
has shone while sleeping. There is not the slightest scien-
tific basis for any of these beliefs, and astronomers every-
where class them with tales of witchcraft, magic, and pop-
ular delusion. For the most part the moon's influence
upon the earth is limited to the light which it sends and
the effect of its gravitation, chiefly exhibited in the ocean
tides. We receive from the moon a very small amount of
second-hand solar heat and there is also a trifling magnetic
influence, but neither of these last effects comes within the
range of ordinary observation, and we shall not go far wrong
in saying that, save the moonlight and the tides, every sup-
posed lunar influence upon the earth is either fictitious or
too small to be readily detected.

CHAPTEE X

THE SUN

110. Dependence of the earth upon the sun. — There is no
better introduction to the study of the sun than Byron's
Ode to Darkness, beginning with the lines —

" I dreamed a dream
That was not all a dream.
The bright sun was extinguished,"

and proceeding to depict in vivid words the consequences
of this extinction. The most matter-of-fact language of
science agrees with the words of the poet in declaring the
earth's dependence upon the sun for all those varied forms
of energy which make it a fit abode for living beings. The
winds blow and the rivers run ; the crops grow, are gathered
and consumed, by virtue of the solar energy. Factory,
locomotive, beast, bird, and the human body furnish types
of machines run by energy derived from the sun ; and the
student will find it an instructive exercise to search for
kinds of terrestrial energy which are not derived either
directly or indirectly from the sun. There are a few such,
but they are neither numerous nor important.

111. The sun's distance from the earth.— To the astron-
omer the sun presents problems of the highest consequence
and apparently of very diverse character, but all tending
toward the same goal : the framing of a mechanical explana-
tion of the sun considered as a machine, what it is, and
how it does its work. In the forefront of these problems
stand those numerical determinations of distance, size,

178

THE SUN 179

mass, density, etc., which we have already encountered in
connection with the moon, but which must here be dealt
with in a different manner, because the immensely greater
distance of the sun makes impossible the resort to any such
simple method as the triangle used for determining the
moon's distance. It would be like determining the distance'
of a steeple a mile away by observing its 'direction first
from one eye, then from the other ; too short a base for the
triangle. In one respect, however, we stand upon a better
footing than in the case of the moon, for the mass of the
earth has already been found (Chapter IV) as a fractional
part of the sun's mass, and we have only to invert the
fraction in order to find that the sun's mass is 329,000
times that of the earth and moon combined, or 333,000
times that of the earth alone.

If we could rely implicitly upon this number we might
make it determine for us the distance of the sun through
the law of gravitation as follows : It was suggested in § 38
that Newton proved Kepler's three laws to be imperfect
corollaries from the law of gravitation, requiring a little
amendment to make them strictly correct, and below we
give in the form of an equation Kepler's statement of the
Third Law together with Newton's amendment of it. In
these equations —

T = Periodic time of any planet ;

a = One half the major axis of its orbit ;

m = Its mass ;

M = The mass of the sun ;

Tc — The gravitation constant corresponding to the par-
ticular set of units in which J7, #, m, and M are expressed.

(Kepler) ~ = h ; (Newton) ^-= k (M+ m).

Kepler's idea was : For every planet which moves
around the sun, a3 divided by T2 always gives the same
quotient, h ; and he did not concern himself with the sig-

180 ASTRONOMY

nificance of this quotient further than to note that if the
particular a and T which belong to any planet — e. g., the
earth — be taken as the units of length and time, then the
quotient will be 1. Newton, on the other hand, attached
a meaning to the quotient, and showed that it is equal to
the product obtained by multiplying the sum of the two
masses, planet and sun, by a number which is always the
same when we are dealing with the action of gravitation,
whether it be between the sun and planet, or between
moon and earth, or between the earth and a roast of beef
in the butcher's scales, provided only that we use always
the same units with which to measure times, distances,
and masses.

Numerically, Newton's correction to Kepler's Third
Law does not amount to much in the motion of the
planets. Jupiter, which shows the greatest effect, makes
the circuit of his orbit in 4,333 days instead of 4,335, which
it would require if Kepler's law were strictly true. But in
another respect the change is of the utmost importance,
since it enables us to extend Kepler's law, which relates
solely to the sun and its planets, to other attracting bodies,
such as the earth, moon, and stars. Thus for the moon's
motion around the earth we write —

from which we may find that, with the units here employed,
the earth's mass as the unit of mass, the mean solar day as
the unit of time, and the mile as the unit of distance —

k = 1830 X 1010.

If we introduce this value of Jc into the corresponding
equation, which represents the motion of the earth around
the sun, we shall have —

= 1830 X 1010 (333,000 + 1),

(365:25)*

THE SUN 181

where the large number in the parenthesis represents the
number of times the mass of the sun is greater than the
mass of the earth. We shall find by solving this equation
that «, the mean distance of the sun from the earth, is
very approximately 93,000,000 miles.

113. Another method of determining the sun's distance, — N
This will be best appreciated by a reference to Fig. 16. It
appears here that the earth makes its nearest approach to the
orbit of Mars in the month of August, and if in any August
Mars happens to be in opposition, its distance from the earth
will be very much less than the distance of the sun from
the earth, and may be measured by methods not unlike
those which served for the moon. If now the orbits of
Mars and the earth were circles having their centers at the
sun this distance between them, which we may represent by
Z>, would be the difference of the radii of these orbits —

D = a" - «', i(ff '

where the accents " ' represent Mars and the earth respec-
tively. Kepler's Third Law furnishes the relation —

and since the periodic times of the earth and Mars, T', T",
are known to a high degree of accuracy, these two equa-
tions are sufficient to determine the two unknown quanti-
ties, 0', a" — i. e., the distance of the sun from Mars as well
as from the earth. The first of these equations is, of
course, not strictly true, on account of the elliptical shape
of the orbits, but this can be allowed for easily enough.

In practice it is found better to apply this method of
determining the sun's distance through observations of an
asteroid rather than observations of Mars, and great inter-
est has been aroused among astronomers by the discovery,
in 1898, of an asteroid, or planet, Eros, which at times comes
much closer to the earth than does Mars or any other heav-

182 ASTRONOMY

enly body except the moon, and which will at future oppo-
sitions furnish a more accurate determination of the sun's
distance than any hitherto available. Observations for this
purpose are being made at the present time (October, 1900).

Many other methods of measuring the sun's distance
have been devised by astronomers, some of them extremely
ingenious and interesting, but every one of them has its
weak point — e. g., the determination of the mass of the
earth in the first method given above and the measurement
of D in the second method, so that even the best results at
present are uncertain to the extent of 200,000 miles or more,
and astronomers, instead of relying upon any one method,
must use all of them, and take an average of their results,
According to Professor Harkness, this average value is 92,-
796,950 miles, and it seems certain that a line of this length
drawn from the earth toward the sun would end somewhere
within the body of the sun, but whether on the nearer or
the farther side of the center, or exactly at it, no man
knows.

114. Parallax and distance. — It is quite customary among
astronomers to speak of the sun's parallax, instead of its
distance from the earth, meaning by parallax its difference
of direction as seen from the center and surface of the
earth — i. e., the angle subtended at the sun by a radius of
the earth placed at right angles to the line of sight. The
greater the sun's distance the smaller will this angle be,
and it therefore makes a substitute for the distance which
has the advantage of being represented by a small number,
8".8, instead of a large one.

The books abound with illustrations intended to help
the reader comprehend how great is a distance of 93,000,000
miles, but a single one of these must suffice here. To ride
100 miles a day 365 days in the year would be counted a
good bicycling record, but the rider who started at the be-
ginning of the Christian era and rode at that rate toward
the sun from the year 1 A. D. down to the present moment

THE SUN

183

would not yet have reached his destination, although his
journey would be about three quarters done. He would
have crossed the orbit of Venus about the time of Charle-
magne, and that of
Mercury soon after
the discovery of
America.

115. Size and
density of the sun,
— Knowing the dis-
tance of the sun,
it is easy to find
from the angle sub-
tended by its di-
ameter (32 minutes
of arc) that the
length of that di-
ameter is 865,000
miles. We recall
in this connection
that the diameter
of the moon's or-
bit is only 480,000
miles, but little
more than half the
diameter of the
sun, thus affording
abundant room in-
side the sun, and

to spare, for the moon to perform the monthly revolution
about its orbit, as shown in Fig. 65.

In the same manner in which the density of the moon
was found from its mass and diameter, the student may
find from the mass and diameter of the sun given above
that its mean density is 1.4 times that of water. This is
about the same as the density of gravel or soft coal, and

FIG. 65. — The sun's size. — YOUNG.

184 ASTRONOMY

is just about one quarter of the average density of the
earth.

We recall that the small density of the moon was ac-
counted for by the diminished weight of objects upon it,
but this explanation can not hold in the case of the sun,
for not only is the density less but the force of gravity
(weight) is there 28 times as great as upon the earth. The
athlete who here weighs 175 pounds, if transported to the
surface of the sun would weigh more than an elephant does
here, and would find his bones break under his own weight
if his muscles were strong enough to hold him upright.
The tremendous pressure exerted by gravity at the surface
of the sun must be surpassed below the surface, and as it
does not pack the material together and make it dense, we
are driven to one of two conclusions : Either the stuff of
which the sun is made is altogether unlike that of the
earth, not so readily compressed by pressure, or there is
some opposing influence at work which more than balances
the effect of gravity and makes the solar stuff much lighter
than the terrestrial.

116. Material of which the sun is made. — As to the first
of these alternatives, the spectroscope comes to our aid and
shows in the sun's spectrum (Fig. 50) the characteristic
line marked D, which we know always indicates the pres-
ence of sodium and identifies at least one terrestrial sub-
stance as present in the sun in considerable quantity. The
lines marked C and F are produced by hydrogen, which is
one of the constituents of water, E shows calcium to be
present in the sun, b magnesium, etc. In this way it has
been shown that about one half of our terrestrial elements,
mainly the metallic ones, are present as gases on or near the
sun's surface, but it must not be inferred that elements not
found in this way are absent from the sun. They may be
there, probably are there, but the spectroscopic proof of
their presence is more difficult to obtain. Professor Row-
land, who has been prominent in the study of the solar

THE SUN 185

spectrum, says : " Were the whole earth heated to the tem-
perature of the sun, its spectrum would probably resemble
that of the sun very closely."

Some of the common terrestrial elements found in the
sun are :

Aluminium. Nickel.

Calcium. Potassium.

Carbon. Silicon.

Copper. Silver.

Hydrogen. Sodium.

Iron. Tin.

Lead. Zinc.
Oxygen (?)

Whatever differences of chemical structure may exist
between the sun and the earth, it seems that we must re-
gard these bodies as more like than unlike to each other in
substance, and we are brought back to the second of our
alternatives : there must be some influence opposing the
force of gravity and making the substance of the sun light
instead of heavy, and we need not seek far to find it in —

117. The heat of the sun. — That the sun is hot is too
evident to require proof, and it is a familiar fact that heat
expands most substances and makes them less dense. The
sun's heat falling upon the earth expands it and diminishes
its density in some small degree, and we have only to im-
agine this process of expansion continued until the earth's
diameter becomes 58 per cent larger than it now is, to find
the earth's density reduced to a level with that of the sun.
Just how much the temperature of the earth must be raised
to produce this amount of expansion we do not know,
neither do we know accurately the temperature of the sun,
but there can be no doubt that heat is the cause of the
sun's low density and that the corresponding temperature
is very high.

Before we inquire more closely into the sun's tempera-
13

186 ASTRONOMY

ture, it will be well to draw a sharp distinction between the
two terms heat and temperature, which are often used as if
they meant the same thing. Heat is a form of energy
which may be found in varying degree in every substance,
whether warm or cold — a block of ice contains a consider-
able amount of heat — while temperature corresponds to our
sensations of warm and cold, and measures the extent to
which heat is concentrated in the body. It is the amount
of heat per molecule of the body. A barrel of warm water
contains more heat than the flame of a match, but its tem-
perature is not so high. Bearing in mind this distinction,
we seek to determine not the amount of heat contained in
the sun but the sun's temperature, and this involves the
same difficulty as does the question, What is the tempera-
ture of a locomotive ? It is one thing in the fire box and
another thing in the driving wheels, and still another at
the headlight ; and so with the sun, its temperature is cer-
tainly different in different parts— one thing at the center
and another at the surface. Even those parts which we
see are covered by a veil of gases which produce by absorp-
tion the dark lines of the solar spectrum, and seriously
interfere both with the emission of energy from the sun
and with our attempts at measuring the temperature of
those parts of the surface from which that energy streams.

In view of these and other difficulties we need not be
surprised that the wildest discordance has been found in
estimates of the solar temperature made by different investi-
gators, who have assigned to it values ranging from 1,400° C.
to more than 5,000,000° C. Quite recently, however, im-
proved methods and a better understanding of the problem
have brought about a better agreement of results, and it
now seems probable that the temperature of the visible
surface of the sun lies somewhere between 5,000° and
10,000° C., say 15,000° of the Fahrenheit scale.

118. Determining the sun's temperature.— One ingenious
method which has been used for determining this tempera-

THE SUN 187

ture is based upon the principle stated above, that every
object, whether warm or cold, contains heat and gives it
off in the form of radiant energy. The radiation from a
body whose temperature is lower than 500° C. is made up
exclusively of energy whose wave length, is greater than
7,600 tenth meters, and is therefore invisible to the eye, al-
though a thermometer or even the human hand can often
detect it as radiant heat. A brick wall in the summer sun-
shine gives oif energy which can be felt as heat but can
not be seen. When such a body is further heated it con-
tinues to send off the same kinds (wave lengths) of energy
as before, but new and shorter waves are added to its radia-
tion, and when it begins to emit energy of wave length 7,500
or 7,600 tenth meters, it also begins to shine with a dull-
red light, which presently becomes brighter and less ruddy
and changes to white as the temperature rises, and waves
of still shorter length are thereby added to the radiation.
We say, in common speech, the body becomes first red hot
and then white hot, and we thus recognize in a general
way that the kind or color of the radiation which a body
gives off is an index to its temperature. The greater the
proportion of energy of short wave lengths the higher is
the temperature of the radiating body. In sunlight the
maximum of brilliancy to the eye lies at or near the wave
length, 5,600 tenth meters, but the greatest intensity of
radiation of all kinds (light included) is estimated to fall
somewhere between green and blue in the spectrum at or
near the wave length 5,000 tenth meters, and if we can ap-
ply to this wave length Paschen's law— temperature reck-
oned in degrees centigrade from the absolute zero is always
equal to the quotient obtained by dividing the number
27,000,000 by the wave length corresponding to maximum
radiation— we shall find at once for the absolute tempera-
ture of the sun's surface 5,400° C.

Paschen's law has been shown to hold true, at least
approximately, for lower temperatures and longer wave

188 ASTRONOMY

lengths than are here involved, but as it is not yet certain
that it is strictly true and holds for all temperatures, too
great reliance must not be attached to the numerical result
furnished by it.

119. The sun's surface. — A marked contrast exists be-
tween the faces of sun and moon in respect of the amount

s

FIG. 66.— The sun, August 11, 1894. Photographed at the Goodsell Observatory.

of detail to be seen upon them, the sun showing nothing
whatever to correspond with the mountains, craters, and
seas of the moon. The unaided eye in general finds in the
sun only a blank bright circle as smooth and unmarked as
the surface of still water, and even the telescope at first
sight seems to show but little more. There may usually be
found upon the sun's face a certain number of black patches
called sun spots, such as are shown in Figs. 66 to 69, and

THE SUN 189

occasionally these are large enough to be seen through a
smoked glass without the aid of a telescope. When seen
near the edge of the sun they are quite frequently accom-
panied, as in Fig. 69, by vague patches called faculce (Latin,
facula = a little torch), which look a little brighter than
the surrounding parts of the sun. So, too, a good photo-

8

FIG. 67.— The sun, August 14, 1894. Photographed at the Goodsell Observatory.

graph of the sun usually shows that the central parts of
the disk are rather brighter than the edge, as indeed we
should expect them to be, since the absorption lines in the
sun's spectrum have already taught us that the visible sur-
face of the sun is enveloped by invisible vapors which in
some measure absorb the emitted light and render it feebler
at the edge where it passes through a greater thickness of
this envelope than at the center (see Fig. 70), where it is

190

ASTRONOMY

shown that the energy coming from the edge of the sun to
the earth has to traverse a much longer path inside the
vapors than does that coming from the center.

Examine the sun spots in the four photographs, Figs.
66 to 69, and note that the two spots which appear at the
extreme left of the first photograph, very much distorted

FIG. 68.— The sun, August 18, 1894. Photographed at the Goodsell Observatory.

and foreshortened by the curvature of the sun's surface, are
seen in a different part of the second picture, and are not
only more conspicuous but show better their true shape.

120. The sun's rotation. — The changed position of these
spots shows that the sun rotates about an axis at right
angles to the direction of the spot's motion, and the posi-
tion of this axis is shown in the figure by a faint line ruled
obliquely across the face of the sun nearly north and south

THE EQUA1!

LIAL CONSTELLATIONS

THE SLTN 191

in each of the four photographs. This rotation in the
space of three days has carried the spots from the edge
halfway to the center of the disk, and the student should
note the progress of the spots in the two later photographs,
that of August 21st showing them just ready to disappear
around the farther edge of the sun.

S
FIG. 69.— The sun, August 21, 1894. Photographed at the Goodsell Observatory.

Plot accurately in one of these figures the positions of
the spots as shown in the other three, and observe whether
the path of the spots across the sun's face is a straight line.
Is there any reason why it should not be straight ?

These four pictures may be made to illustrate many
things about the sun. Thus the sun's axis is not parallel
to that of the earth, for the letters N S mark the direction
of a north and south line across the face of the sun, and

192 ASTRONOMY

this line, of course, is parallel to the earth's axis, while it is
evidently not parallel to the sun's axis. The group of

spots took more than
ten days to move
across the sun's face,
and as at least an
equal time must be
required to move
around the opposite
side of the sun, it is
evident that the pe-

FIG. 70.— Absorption at the sun's edge.

nod of the sun s ro-
tation is something more than 20 days. It is, in fact, a
little more than 25 days, for this same group of spots reap-
peared again on the left-hand edge of the sun on Septem-
ber 5th.

121. Sun spots. — Another significant fact comes out
plainly from the photographs. The spots are not perma-
nent features of the sun's face, since they changed their
size and shape very appreciably in the few days covered by
the pictures. Compare particularly the photographs of
August 14th and August 18th, where the spots are least
distorted by the curvature of the sun's surface. By Sep-
tember 16th this group of spots had disappeared absolutely
from the sun's face, although when at its largest the group
extended more than 80,000 miles in length, and several of
the individual spots were large enough to contain the
earth if it had been dropped upon them. From Fig. 67
determine in miles the length of the group on August
14th. Fig. 71 shows an enlarged view of these spots as
they appeared on August 17th, and in this we find some
details not so well shown in the preceding pictures. The
larger spots consist of a black part called the nucleus or
umbra (Latin, shadow), which is surrounded by an irregu-
lar border called the penumbra (partial shadow), which is
intermediate in brightness between the nucleus and the

THE SUN

193

surrounding parts of the sun. It should not be inferred
from the picture that the nucleus is really black or even
dark. It shines, in
fact, with a brilliancy
greater than that of
an electric lamp, but
the background fur-
nished by the sun's
surface is so much
brighter that by con-
trast with it the nu-
cleus and penumbra
appear relatively dark.
The bright shining
surface of the sun, the
background for the
spots, is called the
photosphere (Greek,
light sphere), and, as Fig. 71 shows, it assumes under a
suitable magnifying power a mottled aspect quite different

FIG. 71. — Sun spots, August 17, 1894.
Goodsell Observatory.

FIG. 72.— Sun spot of March 5, 1873.— From LANGLKY, The New Astronomy.
By permission of the publishers.

from the featureless expanse shown in the earlier pictures.
The photosphere is, in fact, a layer of little clouds with

194

ASTRONOMY

darker spaces between them, and the fine detail of these
clouds, their complicated structure, and the way in which,
when projected against the background of a sun spot, they
produce its penumbra, are all brought out in Fig. 72.
Note that the little patch in one corner of this picture
represents North and South America drawn to the same
scale as the sun spots.

122. Faculse.— We have seen in Fig. 69 a few of the
bright spots called faculae. At the telescope or in the
ordinary photograph these can be seen only at the edge of

the sun, because else-
where the background
furnished by the pho-
tosphere is so bright
that they are lost in it.
It is possible, however,
by an ingenious appli-
cation of the spectro-
scope to break up the
sunlight into a spec-
trum in such a way as
to diminish the bright-
ness of this back-
ground, much more
than the brightness of
the faculae is dimin-
ished, and in this way to obtain a photograph of the sun's
surface which shall show them wherever they occur, and
such a photograph, showing faintly the spectral lines, is
reproduced in Fig. 73. The faculae are the bright patches
which stretch inconspicuously across the face of the sun,
in two rather irregular belts with a comparatively empty
lane between them. This lane lies along the sun's equa-
tor, and it is upon either side of it between latitudes 5°
and 40° that faculae seem to be produced. It is significant
of their connection with sun spots that the spots occur

FIG. 73. — Spectroheliograph, showing distribu-
tion of faculae upon the sun. — HALE.

196 ASTRONOMY

in these particular zones and are rarely found outside
them.

123. Invisible parts of the sun. The Corona. — Thus far
we have been dealing with parts of the sun that may be
seen and photographed under all ordinary conditions.

FIG. 75.— Eclipse of April 16, 1893.— SCHAEBERLE.

But outside of and surrounding these parts is an envelope,
or rather several envelopes, of much greater extent than
the visible sun. These envelopes are for the most part
invisible save at those times when the brighter central
portions of the sun are hidden in a total eclipse.

Fig. 74 is from a drawing, and Figs. 75 and 76 are from
eclipse photographs showing this region, in which the most

THE SUN

197

conspicuous object is the halo of soft light called the corona,
that completely surrounds the sun but is seen to be of dif-

FIG. 76.— Eclipse of January 21, 1898.— CAMPBELL.

fering shapes and differing extent at the several eclipses
here shown, although a large part of these apparent differ-
ences is due to technical difficulties in photographing, and
reproducing an object with outlines so vague as those of
the corona. The outline of the corona is so indefinite and
its outer portions so faint that it is impossible to assign to
it precise dimensions, but at its greatest extent it reaches
out for several millions of miles and fills a space more than
twenty times as large as the visible part of the sun. De-
spite its huge bulk, it is of most unsubstantial character,

198

ASTRONOMY

FIG. 77.— Solar prominence of March 25,
1895.— HALE.

an airy nothing through which comets have been known
to force their way around the sun from one side to the
other, literally for millions of miles, without having their

course influenced or their
velocity checked to any
appreciable extent. This
would hardly be possible
if the density even at the
bottom of the corona were
greater than that of the
best vacuum which we
are able to produce in lab-
oratory experiments. It
seems odd that a vacuum
should give off so bright
a light as the coronal pic-
tures show, and the exact character of that light and the
nature of the corona are still subjects of dispute among
astronomers, although it is generally agreed that, in part
at least, its light is ordinary sunlight faintly reflected
from the widely scattered molecules composing the sub-
stance of the corona. It is also probable that in part the
light has its origin in the corona itself. A curious and at
present unconfirmed result announced by one of the ob-
servers of the eclipse of May 28, 1900, is that the corona is
not hot, its effective temperature being lower than that of
the instrument used for the observation.

124. The chromosphere.— Between the corona and the
photosphere there is a thin separating layer called the
chromosphere (Greek, color sphere), because when seen at
an eclipse it shines with a brilliant red light quite unlike
anything else upon the sun save the prominences which are
themselves only parts of the chromosphere temporarily
thrown above its surface, as in a fountain a jet of water is
thrown up from the basin and remains for a few moments
suspended in mid-air. Not infrequently in such a foun-

THE SUN

199

tain foreign matter is swept up by the rush of the water —
dirt, twigs, small fish, etc.^-and in like manner the promi-
nences often carry along with them parts of the under-
lying layers of the sun, photosphere, faculae, etc., which
reveal their presence in the prominence by adding their
characteristic lines to the spectrum, like that of the chro-
mosphere, which the prominence presents when they are
absent. None of the eclipse photographs (Figs. 74 to 76)
show the chromosphere, because the color effect is lacking
in them, but a great curving prominence may be seen near
the bottom of Fig. 75, and smaller ones at other parts of
the sun's edge.

125. Prominences. — Fig. 77 shows upon a larger scale one
of these prominences rising to a height of 160,000 miles
above the photo-
sphere ; and an-
other photograph,
taken 18 minutes
later, but not re-
produced here,
showed the same
prominence grown
in this brief inter-
val to a stature
of 280,000 miles.
These pictures
were not taken
during an eclipse,
but in full sun-
light, using the
same spectroscop-
ic apparatus which
was employed in
connection with

the faculae to diminish the brightness of the background
without much enfeebling the brilliancy of the prominence

FIG. 78.— A solar prominence.— HALE.

200 ASTRONOMY

itself. The dark base from which the prominence seems
to spring is not the sun's edge, but a part of the appara-
tus used to cut off the direct sunlight.

Fig. 78 contains a series of photographs of another
prominence taken within an interval of 1 hour 47 minutes
and showing changes in size and shape which are much
more nearly typical of the ordinary prominence than was
the very unusual change in the case of Fig. 77.

The preceding pictures are from photographs, and with
them the student may compare Fig. 79, which is con-

FIG. 79.— Contrasted forms of solar prominences.— ZOELLNEB.

structed from drawings made at the spectroscope by the
German astronomer Zoellner. The changes here shown
are most marked in the prominence at the left, which is
shaped like a broken tree trunk, and which appears to be
vibrating from one side to the other like a reed shaken
in the wind. Such a prominence is frequently called an
eruptive one, a name suggested by its appearance of hav-
ing been blown out from the sun by something like an
explosion, while the prominence at the right in this series
of drawings, which appears much less agitated, is called by
contrast with the other a quiescent prominence. These
quiescent prominences are, as a rule, much longer-lived

THE SUN 201

than the eruptive ones. One more picture of prominences
(Fig. 80) is introduced to show the continuous stretch of
chromosphere out of which they spring.

Prominences are seen only at the edge of the sun, be-
cause it is there alone that the necessary background can
be obtained, but they must occur at the center of the sun
and elsewhere quite as well as at the edge, and it is prob-
able that quiescent prominences are distributed over all

FIG. 80.— Prominences and chromosphere. HALE.

parts of the sun's surface, but eruptive prominences show
a strong tendency toward the regions of sun spots and
faculae as if all three were intimately related phenomena.

126. The sun as a machine. — Thus far we have consid-
ered the anatomy of the sun, dissecting it into its several
parts, and our next step should be a consideration of its
physiology, the relation of the parts to each other, and
their function in carrying on the work of the solar organ-
ism, but this step, unfortunately, must be a lame one.
The science of astronomy to-day possesses no comprehen-
sive and well-established theory of this kind, but looks to
the future for the solution of this the greatest pending
14

202 ASTRONOMY

problem of solar physics. Progress has been made toward
its solution, and among the steps of this progress that we
shall have to consider, the first and most important is the
conception of the sun as a kind of heat engine.

In a steam engine coal is burned under the boiler, and
its chemical energy, transformed into heat, is taken up by
the water and delivered, through steam as a medium, to
the engine, which again transforms and gives it out as
mechanical work in the turning of shafts, the driving of
machinery, etc. Now, the function of the sun is exactly
opposite to that of the engine and boiler : it gives out,
instead of receiving, radiant energy ; but, like the engine,
it must be fed from some source ; it can not be run upon
nothing at all any more than the engine can run day after
day without fresh supplies of fuel under its boiler. We
know that for some thousands of years the sun has been
furnishing light and heat to the earth in practically un-
varying amount, and not to the earth alone, but it has
been pouring forth these forms of energy in every direc-
tion, without apparent regard to either use or economy.
Of all the radiant energy given off by the sun, only two
parts out of every thousand million fall upon any planet
of the solar system, and of this small fraction the earth
takes about one tenth for the maintenance of its varied
forms of life and action. Astronomers and physicists have
sought on every hand for an explanation of the means by
which this tremendous output of energy is maintained
century after century without sensible diminution, and
have come with almost one mind to the conclusion that
the gravitative forces which reside in the sun's own mass
furnish the only adequate explanation for it, although
they may be in some small measure re-enforced by minor
influences, such as the fall of meteoric dust and stones
into the sun.

Every boy who has inflated a bicycle tire with a hand
pump knows that the pump grows warm during the opera-

THE SUN 203

tion, on account of the compression of the air within the
cylinder. A part of the muscular force (energy) expended
in working the pump reappears in the heat which warms
both air and pump, and a similar process is forever going on
in the sun, only in place of muscular force we must there sub-
stitute the tremendous attraction of gravitation, 23 times
as great as upon the earth. " The matter in the interior
of the sun must be as a shuttlecock between the stupen-
dous pressure and the enormously high temperature," the
one tending to compress and the other to expand it, but
with this important difference between them : the tem-
perature steadily tends to fall as the heat energy is wasted
away, while the gravitative force suffers no corresponding
diminution, and in the long run must gain the upper
hand, causing the sun to shrink and become more dense.
It is this progressive shrinking and compression of its
molecules into a smaller space which supplies the energy
contained in the sun's output of light and heat. Accord-
ing to Lord Kelvin, each centimeter of shrinkage in the
sun's diameter furnishes the energy required to keep up
its radiation for something more than an hour, and,, on
account of the sun's great distance, the shrinkage might
go on at this rate for many centuries without producing
any measurable effect in the sun's appearance.

127. Gaseous constitution of the sun. — But Helmholtz's dy-
namical theory of the maintenance of the sun's heat, which
we are here considering, includes one essential feature
that is not sufficiently stated above. In order that the
explanation may hold true, it is necessary that the sun
should be in the main a gaseous body, composed from cen-
ter to circumference of gases instead of solid or liquid
parts. Pumping air warms the bicycle pump in a way
that pumping water or oil will not.

The high temperature of the sun itself furnishes suffi-
cient reason for supposing the solar material to be in the
gaseous state, but the gas composing those parts of the

204: ASTRONOMY

sun below the photosphere must be very different in some
of its characteristics from the air or other gases with which
we are familiar at the earth, since its average density is
1,000 times as great as that of air, and its consistence and
mechanical behavior must be more like that of honey or tar
than that of any gas with which we are familiar. It is
worth noting, however, that if a hole were dug into the
crust of the earth to a depth of 15 or 20 miles the air at
the bottom of the hole would be compressed by that above
it to a density comparable with that of the solar gases.

128. The sun's circulation. — It is plain that under the
conditions which exist in the sun the outer portions, which
can radiate their heat freely into space, must be cooler than
the inner central parts, and this difference of temperature
must set up currents of hot matter drifting upward and out-
ward from within the sun and counter currents of cooler
matter settling down to take its place. So, too, there must
be some level at which the free radiation into outer space
chills the hot matter sufficiently to condense its less refrac-
tory gases into clouds made up of liquid drops, just as on a
cloudy day there is a level in our own atmosphere at which
the vapor of water condenses into liquid drops which form
the thin shell of clouds that hovers above the earth's surface,
while above and below is the gaseous atmosphere. In the
case of the sun this cloud layer is always present and is that
part which we have learned to call the photosphere. Above
the photosphere lies the chromosphere, composed of gases
less easily liquefied, hydrogen is the chief one, while be-
tween photosphere and chromosphere is a thin layer of me-
tallic vapors, perhaps indistinguishable from the top crust
of the photosphere itself, which by absorbing the light
given off from the liquid photosphere produces the greater
part of the Fraunhofer lines in the solar spectrum.

From time to time the hot matter struggling up from
below breaks through the photosphere and, carrying with
it a certain amount of the metallic vapors, is launched into

THE SUN 205

the upper and cooler regions of the snn, where, parting
with its heat, it falls back again upon the photosphere and
is absorbed into it. It is altogether probable that the
corona is chiefly composed of fine particles ejected from
the sun with velocities sufficient to carry them to a height
of millions of miles, or even sufficient to carry them off
never to return. The matter of the corona must certainly
be in a state of the most lively agitation, its particles being
alternately hurled up from the photosphere and falling
back again like fireworks, the particles which make up the
corona of to-day being quite a different set from those of
yesterday or last week. It seems beyond question that
the prominences and faculae too are produced in some
way by this up-and-down circulation of the sun's matter,
and that any mechanical explanation of the sun must be
worked out along these lines ; but the problem is an exceed-
ingly difficult one, and must include and explain many other
features of the sun's activity of which only a few can be con-
sidered here.

129. The sun-spot period.— Sun spots come and go, and
at best any particular spot is but short-lived, rarely lasting
more than a month or two, and more often its duration is
a matter of only a few days. They are not equally numer-
ous at all times, but, like swarms of locusts, they seem to
come and abound for a season and then almost to disap-
pear, as if the forces which produced them were of a peri-
odic character alternately active and quiet. The effect of
this periodic activity since 1870 is shown in Fig. 81, where
the horizontal line is a scale of times, and the distance of
the curve above this line for any year shows the relative
number of spots which appeared upon the sun in that
year. This indicates very plainly that 1870, 1883, and
1893 were years of great sun-spot activity, while 1879 and
1889 were years in which few spots appeared. The older
records, covering a period of two centuries, show the same
fluctuations in the frequency of sun spots and from these

206

ASTRONOMY

records curves (which may be found in Young's, The Sun)
have been plotted, showing a succession of waves extend-
ing back for many years.

The sun-spot period is the interval of time from the
crest or hollow of one wave to the corresponding part of
the next one, and on the average this appears to be a little
more than eleven years, but is subject to considerable varia-
tion. In accordance with this period there is drawn in

1870 1SSO 1890 4900 19iO

FIG. 81. — The curve of sun-spot frequency.

broken lines at the right of Fig. 81 a predicted continua-
tion of the sun-spot curve for the first decade of the twen-
tieth century. The irregularity shown by the three pre-
ceding waves is such that we must not expect the actual
course of future sun spots to correspond very closely to
the prediction here made ; but in a general way 1901 and
1911 will probably be years of few sun spots, while they
will be numerous in 1905, but whether more or less numer-
ous than at preceding epochs of greatest frequency can not
be foretold with any approach to certainty so long as we
remain in our present ignorance of the causes which make
the sun-spot period.

Determine from Fig. 81 as accurately as possible the
length of the sun-spot period. It is hard to tell the ex-
act position of a crest or hollow of the curve. Would it
do to draw a horizontal line midway between top and bot-
tom of the curve and determine the length of the period

THE SUN

207

from its intersections with the curve — e. g., in 1874 and
1885?

130. The sun-spot zones. — It has been already noted that
sun spots are found only in certain zones of latitude upon
the sun, and that faculse and eruptive prominences abound

FIG. 82.— Illustrating change of the sun-spot zones.

in these zones more than elsewhere, although not strictly
confined to them. We have now to note a peculiarity of
these zones which ought to furnish a clew to the sun's
mechanism, although up to the present time it has not
been successfully traced out. Just before a sun-spot mini-
mum the few spots which appear are for the most part
clustered near the sun's equator. As these spots die out

208 ASTRONOMY

two new groups appear, one north the other south of the
sun's equator and about 25° or 30° distant from it, and as
the period advances toward a maximum these groups shift
their positions more and more toward the equator, thus ap-
proaching each other but leaving between them a vacant
lane, which becomes steadily narrower until at the close
of the period, when the next minimum is at hand, it
reaches its narrowest dimensions, but does not altogether
close up even then. In Fig. 82 these relations are shown
for the period falling between 1879 and 1890, by means of
the horizontal lines ; for each year one line in the north-
ern and one in the southern hemisphere of the sun, their
lengths being proportional to the number of spots which
appeared in the corresponding hemisphere during the year,
and their positions on the sun's disk showing the average
latitude of the spots in question. It is very apparent from
the figure that during this decade the sun's southern hemi-
sphere was much more active than the northern one in the
production of spots, and this appears to be generally the
case, although the difference is not usually as great as in
this particular decade.

131. Influence of the sun-spot period. — Sun spots are cer-
tainly less hot than the surrounding parts of the sun's sur-
face, and, in view of the intimate dependence of the earth
upon the solar radiation, it would be in no way surprising
if their presence or absence from the sun's face should
make itself felt in some degree upon the earth, raising and
lowering its temperature and quite possibly affecting it in
other ways. Ingenious men have suggested many such
kinds of influence, which, according to their investigations,
appear to run in cycles of eleven years. Abundant and
scanty harvests, cyclones, tornadoes, epidemics, rainfall,
etc., are among these alleged effects, and it is possible that
there may be a real connection between any or all of them
and the sun-spot period, but for the most part astronomers
are inclined to hold that there is only one case in which

THE SUN

the evidence is strong enough to really establish a connec-
tion of this kind. The magnetic condition of the earth
and its disturbances, which are called magnetic storms, do
certainly follow in a very marked manner the course of
sun-spot activity, and perhaps there should be added to
this the statement that auroras (northern lights) stand in
close relation to these magnetic disturbances and are most
frequent at the times of sun-spot maxima.

Upon the sun, however, the influence of the spot period
is not limited to things in and near the photosphere, but
extends to the outermost limits of the corona. Determine
from Fig. 81 the particular part of the sun-spot period
corresponding to the date of each picture of the corona
and note how the pictures which were taken near times of
sun-spot minima present a general agreement in the shape
and extent of the corona, while the pictures taken at a time
of maximum activity of the sun spots show a very differ-
ently shaped and much smaller corona.

132. The law of the sun's rotation. — We have seen in a
previous part of the chapter how the time required by the
sun to make a complete rotation upon its axis may be de-
termined from photographs showing the progress of a spot
or group of spots across its disk, and we have now to add
that when this is done systematically by means of many
spots situated in different solar latitudes it leads to a
very peculiar and extraordinary result. Each particular
parallel of latitude has its own period of rotation different
from that of its neighbors on either side, so that there can
be no such thing as a fixed geography of the sun's surface.
Every part of it is constantly taking up a new position
with respect to every other part, much as if the Gulf of
Mexico should be south of the United States this year,
southeast of it next year, and at the end of a decade should
have shifted around to the opposite side of the earth from
us. A meridian of longitude drawn down the Mississippi
Valley remains always a straight line, or, rather, great

210 ASTRONOMY

circle, upon the surface of the earth, while Fig. 83 shows
what would become of such a meridian drawn through
the equatorial parts of the sun's disk. In the first dia-
gram it appears as a straight line running down the mid-
dle of the sun's disk. Twenty-five days later, when the
same face of the sun comes back into view again, after
making a complete revolution about the axis, the equa-
torial parts will have moved so much faster and far-
ther than those in higher latitudes that the meridian

FIG. 83. — Effect of the sun's peculiar rotation in warping a meridian, originally

straight.

will be warped as in the second diagram, and still more
warped after another and another revolution, as shown in
the figure.

At least such is the case if the spots truly represent the
way in which the sun turns round. There is, however, a
possibility that the spots themselves drift with varying
speeds across the face of the sun, and that the differences
which we find in their rates of motion belong to them
rather than to the photosphere. Just what happens in the
regions near the poles is hard to say, for the sun spots only
extend about halfway from the equator to the poles, and
the spectroscope, which may be made to furnish a certain
amount of information bearing upon the case, is not as yet
altogether conclusive, nor are the faculae which have also
been observed for this purpose.

The simple theory that the solar phenomena are caused
by an interchange of hotter and cooler matter between the
photosphere and the lower strata of the sun furnishes in

THE SUN 211

its present shape little or no explanation of such features
as the sun-spot period, the variations in the corona, the
peculiar character of the sun's rotation, etc., and we have
still unsolved in the mechanical theory of the sun one of
the noblest problems of astronomy, and one upon which
both observers and theoretical astronomers are assiduously
working at the present time. A close watch is kept upon
sun spots and prominences, the corona is observed at every
total eclipse, and numerous are the ingenious methods
which are being suggested and tried for observing it with-
out an eclipse in ordinary daylight. Attempts, more or
less plausible, have been made and are now pending to
explain photosphere, spots and the reversing layer by means
of the refraction of light within the sun's outer envelope
of gases, and it seems altogether probable, in view of these
combined activities, that a considerable addition to our
store of knowledge concerning the sun may be expected in
the not distant future.

CHAPTEE XI

THE PLANETS

133. Planets. — Circling about the sun, under the influ-
ence of his attraction, is a family of planets each member
of which is, like the moon, a dark body shining by reflected
sunlight, and therefore presenting phases ; although only
two of them, Mercury and Venus, run through the com-
plete series — new, first quarter, full, last quarter — which
the moon presents. The way in which their orbits are
grouped about the sun has been considered in Chapter
III, and Figs. 16 and 17 of that chapter may be completed
so as to represent all of the planets by drawing in Fig. 16
two circles with radii of 7.9 and 12.4 centimeters respec-
tively, to represent the orbits of the planets Uranus and
Neptune, which are more remote from the sun than Sat-
urn, and by introducing a little inside the orbit of Jupiter
about 500 ellipses of different sizes, shapes, and positions to
represent a group of minor planets or asteroids as they are
often called. It is convenient to regard these asteroids as
composing by themselves a class of very small planets, while
the remaining 8 larger planets fall naturally into two other
classes, a group of medium-sized ones — Mercury, Venus,
Earth, and Mars — called inner planets by reason of their
nearness to the sun ; and the outer planets — Jupiter, Sat-
urn, Uranus, Neptune — each of which is much larger and
more massive than any planet of the inner group. Com-
pare in Figs. 84 and 85 their relative sizes. The earth, E, is
introduced into Fig. 85 as a connecting link between the
two figures.

Some of these planets, like the earth, are attended by
212

THE PLANETS

213

one or more moons, technically called satellites, which also
shine by reflected sunlight and which move about their
respective planets in accordance with the law of gravitation,
much as the moon moves around the earth.

Force of Gravity 0.43
Diameter .3030

0.88
7700

o.n

2/63

J.OO
7927

"Density 6.3

Mass

FIG. 84. — The inner planets and the moon.

134. Distances of the planets from the sun. — It is a com-
paratively simple matter to observe these planets year after
year as they move among the stars, and to find from these
observations how long each one of them requires to make
its circuit around the sun — that is, its periodic time, T7,
which figures in Kepler's Third Law, and when these peri-
odic times have been ascertained, to use them in connection
with that law to determine the mean distance of each

force of Gravity
Mean Diameter

0.9 0.9

32000 35000

Density
Mass

i.3

ste

FIG. 85.— The outer planets.

planet from the sun. Thus, Jupiter requires 4,333 days to
move completely around its orbit ; and comparing this with
the periodic time and mean distance of the earth we find—

fl3 _ (93?000,000)3;
(4333)2 ~ (365.S5)2

214 ASTRONOMY

which when solved gives as the mean distance of Jupiter
from the sun, 483,730,000 miles, or 5.20 times as distant as
the earth. If we make a similar computation for each
planet, we shall find that their distances from the sun show
a remarkable agreement with an artificial series of numbers
called Bode's law. We write down the numbers contained
in the first line of figures below, each of which, after the
second, is obtained by doubling the preceding one, add 4
to each number and point off one place of decimals; the
resulting number is (approximately) the distance of the
corresponding planet from the sun.

1

3

a
1

@

1

3

j&
'3.

3

3

d

I

0

3

6

12

24

48

96

192

384

4

4

4

4

4

4

4

4

4

0.4

0.7

1.0

1.6

2.8

5.2

10.0

19.6

38.8

0.4

0.7

1.0

1.5

2.8

5.2

9.5

19.2

30.1

The last line of figures shows the real distance of the
planet as determined from Kepler's law, the earth's mean
distance from the sun being taken as the unit for this pur-
pose. With exception of Neptune, the agreement between
Bode's law and the true distances is very striking, but most
remarkable is the presence in the series of a number, 2.8,
with no planet corresponding to it. This led astronomers
at the time Bode published the law, something more than
a century ago, to give new heed to a suggestion made long
before by Kepler, that there might be an unknown planet
moving between the orbits of Mars and Jupiter, and a num-
ber of them agreed to search for such a planet, each in a
part of the sky assigned him for that purpose. But they
were anticipated by Piazzi, an Italian, who found the new
planet, by accident, on the first day of the nineteenth cen-
tury, moving at a distance from the sun represented by the
number 2.77.

THE PLANETS 215

This planet was the first of the asteroids, and in the
century that has elapsed hundreds of them have been dis-
covered, while at the present time no year passes by with-
out several more being added to the number. While some
of these are nearer to the sun than is the first one discov?
ered, and others are farther from it, their average distance
is fairly represented by the number 2.8.

Why Bode's law should hold true, or even so nearly
true as it does, is an unexplained riddle, and many astron-
omers are inclined to call it no law at all, but only a chance
coincidence— an illustration of the " inherent capacity of
figures to be juggled with " ; but if so, it is passing strange
that it should represent the distance of the asteroids and
of Uranus, which was also an undiscovered planet at the
time the law was published.

135. The planets compared with each other. — When we
pass from general considerations to a study of the indi-
vidual peculiarities of the planets, we find great differences
in the extent of knowledge concerning them, and the reason
for this is not far to seek. Neptune and Uranus, at the
outskirts of the solar system, are so remote from us and so
feebly illumined by the sun that any detailed study of them
can go but little beyond determining the numbers which
represent their size, mass, density, the character of their
orbits, etc. The asteroids are so small that in the telescope
they look like mere points of light, absolutely indistinguish-
able in appearance from the fainter stars. Mercury, al-
though closer at hand and presenting a disk of considerable
size, always stands so near the sun that its observation is
difficult on this account. Something of the same kind is
true for Venus, although in much less degree ; while Mars,
Jupiter, and Saturn are comparatively easy objects for tele-
scopic study, and our knowledge of them, while far from
complete, is considerably greater than for the other planets.

Figs. 84 and 85 show the relative sizes of the planets
composing the inner and outer groups respectively, and fur-

216 ASTRONOMY

nish the numerical data concerning their diameters, masses,
densities, etc., which are of most importance in judging of
their physical condition. Each planet, save Saturn, is
represented by two circles, of which the outer is drawn
proportional to the size of the planet, and the inner shows
the amount of material that must be subtracted from the
interior in order that the remaining shell shall just float in
water. Note the great difference in thickness of shell
between the two groups. Saturn, having a mean density
less than that of water, must have something loaded upon
it, instead of removed, in order that it should float just
submerged.

JUPITER

136. Appearance, — Commencing our consideration of the
individual planets with Jupiter, which is by far the largest
of them, exceeding both in bulk and mass all the others
combined, we have in Fig. 86 four representations of
Jupiter and his family of satellites as they may be seen in
a very small telescope — e. g., an opera glass — save that the
little dots which here represent the satellites are numbered
j?, #, $, 4-> in order to preserve their identity in the succes-
sive pictures.

The chief interest of these pictures lies in the satellites,
but, reserving them for future consideration, we note that
the planet itself resembles in shape the full moon, although
in respect of brightness it sends to us less than ^Vo Par^
as much light as the moon. From a consideration of the
motion of Jupiter and the earth in Fig. 16, show that
Jupiter can not present any such phases as does the moon,
but that its disk must be at all times nearly full. As seen
from Saturn, what kind of phases would Jupiter present ?

137. The belts. — Even upon the small scale of Fig. 86
we detect the most characteristic feature of Jupiter's ap-
pearance in the telescope, the two bands extending across
his face parallel to the line of the satellites, and in Fig. 87
these same dark bands may be recognized amid the abun-

THE PLANETS 217

dance of detail which is here brought out by a large tele-
scope. Photography does not succeed as a means of repro-
ducing this detail, and for it we have to rely upon the skill
of the artist astronomer. The lettering shows the Pacific

FIG. 86. — Jupiter and his satellites.

Standard time at which the sketches were made, and also
the longitude of the meridian of Jupiter passing down the
center of the planet's disk.

The dark bands are called technically the belts of Jupi-
ter ; and a comparison of these belts in the second and third
pictures of the group, in which nearly the same face of the
planet is turned toward us, will show that they are subject
to considerable changes of form and position even within
the space of a few days. So, too, by a comparison of such
markings as the round white spots in the upper parts of
the disks, and the indentations in the edges of the belts,
we may recognize that the planet is in the act of turning
round, and must therefore have an axis about which it
turns, and poles, an equator, etc. The belts are in fact
parallel to the planet's equator ; and generalizing from what
appears in the pictures, we may say that there is always a
strongly marked belt on each side of the equator with a
15

FIG. 87.— Drawings of Jupiter made at the 36-inch telescope of the Lick
Observatory. — KEELER.

THE PLANETS 219

lighter colored streak between them, and that farther from
the equator are other belts variable in number, less con-
spicuous, and less permanent than the two first seen. Com-
pare the position of the principal belts with the position of
the zones of sun-spot activity in the sun. A feature of
the planet's surface, which can not be here reproduced, is
the rich color effect to be found upon it. The principal
belts are a brick-red or salmon color, the intervening spaces
in general white but richly mottled, and streaked with
purples, browns, and greens.

The drawings show the planet as it appeared in the
telescope, inverted, and they must be turned upside down
if we wish the points of the compass to appear as upon a
terrestrial map. Bearing this in mind, note in the last
picture the great oval spot in the southern hemisphere of
Jupiter. This is a famous marking, known from its color
as the great red spot, which appeared first in 1878 and has
persisted to the present day (1900), sometimes the most
conspicuous marking on the planet, at others reduced to a
mere ghost of itself, almost invisible save for the inden-
tation which it makes in the southern edge of the belt
near it.

138. Rotation and flattening at the poles, — One further
significant fact with respect to Jupiter may be obtained
from a careful measurement of the drawings ; the planet is
flattened at the poles, so that its polar diameter is about
one sixteenth part shorter than the equatorial diameter.
The flattening of the earth amounts to only one three-
hundredth part, and the marked difference between these
two numbers finds its explanation in the greater swiftness
of Jupiter's rotation about its axis, since in both cases it is
this rotation which makes the flattening.

It is not easy to determine the precise dimensions of the
planet, since this involves a knowledge both of its distance
from us and of the angle subtended by its diameter, but
the most recent determinations of this kind assign as the

220 ASTRONOMY

equatorial diameter 90,200 miles, and for the polar diam-
eter 84,400 miles. Determine from either of these num-
bers the size of the great red spot.

The earth turns on its axis once in 24 hours but no
such definite time can be assigned to Jupiter, which, like
the sun, seems to have different rotation periods in differ-
ent latitudes — 9h. 50m. in the equatorial belt and 9h. 56m.
in the dark belts and higher latitudes. There is some indi-
cation that the larger part of the visible surface rotates in
9h. 55.6m., while a broad stream along the equator flows
eastward some 270 miles per hour, and thus comes back to
the center of the planet, as seen from the earth, five or six
minutes earlier than the parts which do not share in this
motion. Judged by terrestrial standards, 270 miles per
hour is a great velocity, but Jupiter is constructed on a
colossal scale, and, too, we have to compare this movement,
not to a current flowing in the ocean, but to a wind blow-
ing in the upper regions of the earth's atmosphere. The
visible surface of Jupiter is only the top of a cloud forma-
tion, and contains nothing solid or permanent, if indeed
there is anything solid even at the core of the planet. The
great red spot during the first dozen years of its existence,
instead of remaining fixed relative to the surrounding for-
mations, drifted two thirds of the way around the planet,
and having come to a standstill about 1891, it is now slowly
retracing its path.

139. Physical condition. — For a better understanding of
the physical condition of Jupiter, we have now to consider
some independent lines of evidence which agree in point-
ing to the conclusion that Jupiter, although classed with
the earth as a planet, is in its essential character much
more like the sun.

Appearance. — The formations which we see in Fig. 87
look like clouds. They gather and disappear, and the only
element of permanence about them is their tendency to
group themselves along zones of latitude. If we measure

THE PLANETS 221

the light reflected from the planet we find that its albedo
is very high, like that of snow or our own cumulus clouds,
and it is of course greater from the light parts of the disk
than from the darker bands. The spectroscope shows that
the sunlight reflected from these darker belts is like that
reflected from the lighter parts, save that a larger portion of
the blue and violet rays has been absorbed out of it, thus
producing the ruddy tint of the belts, as sunset colors are
produced on the earth, and showing that here the light has
penetrated farther into the planet's atmosphere before
being thrown back by reflection from lower-lying cloud sur-
faces. The dark bands are therefore to be regarded as rifts
in the clouds, reaching down to some considerable distance
and indicating an atmosphere of great depth. The great
red spot, 28,000 miles long, and obviously thrusting back
the white clouds on every side of it, year after year, can
hardly be a mere patch on the face of the planet, but indi-
cate? aome considerable depth of atmosphere.

Density. — So, too, the small mean density of the planet,
only 1.3 times that of water and actually less than the den-
sity of the sun, suggests that the larger part of the planet's
bulk may be made of gases and clouds, with very little solid
matter even at the center ; but here we get into a difficulty
from which there seems but one escape. The force of
gravity at the visible surface of Jupiter may be found
from its mass and dimensions to be 2.6 times as great as
at the surface of the earth, and the pressure exerted upon
iis atmosphere by this force ought to compress the lower
strata into something more dense than we find in the
)lanet. Some idea of this compression may be obtained
from Fig. 88, where the line marked E shows approximately
low the density of the air increases as we move from its
ipper strata down toward the surface of the earth through
distance of 16 miles, the density at any level being pro-
>rtional to the distance of the curved line from the straight
oiae near it. The line marked J in the same figure shows

222 ASTRONOMY

how the density would increase if the force of gravity were
as great here as it is in Jupiter, and indicates a much
greater rate of increase. Starting from the upper surface
of the cloud in Jupiter's atmosphere, if we descend,
not 16 miles, but 1,600 or 16,000, what must the den-
sity of the atmosphere become and how is this to be
reconciled with what we know to be the very small
mean density of the planet ?

We are here in a dilemma between density on the
one hand and the effects of gravity on the other, and
the only escape from it lies in the assumption that
the interior of Jupiter is tremendously hot, and that
this heat expands the substance of the planet in spite
of the pressure to which it is subject, making a large
planet with a low density, possibly gaseous at
the very center, but in its outer part surrounded
by a shell of clouds con-
densed from the gases by
radiating their heat into

FIG. 88-Increase of density in the atmos- the Cold of Outer space.

pheres of Jupiter and the earth. This is essentially the

same physical condition

that we found for the sun, and we may add, as further
points of resemblance between it and Jupiter, that there
seems to be a circulation of matter from the hot interior of
the planet to its cooler surface that is more pronounced in
the southern hemisphere than in the northern, and that has
its periods of maximum and minimum activity, which, cu-
riously enough, seem to coincide with periods of maximum
and minimum sun-spot development. Of this, however, we
can not be entirely sure, since it is only in recent years that
it has been studied with sufficient care, and further obser-
vations are required to show whether the agreement is
something more than an accidental and short-lived coin-
cidence.

Temperature. — The temperature of Jupiter must, of

THE PLANETS 223

course, be much lower than that of the sun, since the sur-
face which we see is not luminous like the sun's ; but below
the clouds it is not improbable that Jupiter may be incan-
descent, white hot, and it is surmised with some show of
probability that a little of its light escapes through the
clouds from time to time, and helps to produce the striking
brilliancy with which this planet shines.

140. The satellites of Jupiter. — The satellites bear much
the same relation to Jupiter that the moon bears to the
earth, revolving about the planet in accordance with the
law of gravitation, and conforming to Kepler's three laws,
as do the planets in their courses about the sun. Observe in
Fig. 86 the position of satellite No. 1 on the four dates, and
note how it oscillates back and forth from left to right of
Jupiter, apparently making a complete revolution in about
two days, while No. 4 moves steadily from left to right dur-
ing the entire period, and has evidently made only a frac-
tion, of a revolution in the time covered by the pictures.
This quicker motion, of course, means that No. 1 is nearer
to Jupiter than No. 4, and the numbers given to the satel-
lites show the order of their distances from the planet.
The peculiar way in which the satellites are grouped, always
standing nearly in a straight line, shows that their orbits
must lie nearly in the same plane, and that this plane, which
is also the plane of the planets' equator, is turned edgewise
toward the earth.

These satellites enjoy the distinction of being the first
objects ever discovered with the telescope, having been
found by Galileo almost immediately after its invention,
A. D. 1610. It is quite possible that before this time they
may have been seen with the naked eye, for in more recent
years reports are current that they have been seen under
favorable circumstances by sharp-eyed persons, and very
little telescopic aid is required to show them. Look for
them with an opera or field glass. They bear the names
lo, Europa, Ganymede, Callisto, which, however, are rarely

224

ASTRONOMY

used, and, following the custom of astronomers, we shall
designate them by the Eoman numerals I, II, III, IV.

For nearly three centuries (1610 to 1892) astronomers
spoke of the four satellites of Jupiter ; but in September,
1892, a fifth one was added to the number by Professor Bar-
nard, who, observing with the largest telescope then extant,
found very close to Jupiter a tiny object only ^ part as

/C.754 days

FIG. 89.— Orbits of Jupiter's satellites.

bright as the other satellites, but, like them, revolving around
Jupiter, a permanent member of his system. This is called
the fifth satellite, and Fig. 89 shows the orbits of these satel-
lites around Jupiter, which is here represented on the same
scale as the orbits themselves. The broken line just inside
the orbit of I represents the size of the moon's orbit. The
cut shows also the periodic times of the satellites expressed
in days, and furnishes in this respect a striking illustra-
tion of the great mass of Jupiter. Satellite I is a little

THE PLANETS 225

farther from Jupiter than is the moon from the earth, but
under the influence of a greater attraction it makes the cir-
cuit of its orbit in 1.77 days, instead of taking 29.53 days,
as does the moon. Determine from the figure by the method
employed in § 111 how much more massive is Jupiter than
the earth.

Small as these satellites seem in Fig. 86, they are really
bodies of considerable size, as appears from Fig. 90, where
their dimensions are compared with those of the earth
and moon, save that the fifth satellite is not included.
This one is so small as to escape all attempts at measuring
its diameter, but, judging from the amount of light it re-
flects, the period printed with the legend of the figure
represents a gross exaggeration of this satellite's size.

FIG. 90.— Jupiter's satellites compared with the earth and moon.

Like the moon, each of these satellites may fairly be
considered a world in itself, and as such a fitting object of
detailed study, but, unfortunately, their great distance from
us makes it impossible, even with the most powerful tele-
scope, to see more upon their surfaces than occasional vague
markings, which hardly suffice to show the rotations of the
satellites upon their axes.

One striking feature, however, comes out from a study
of their influence in disturbing each other's motion about
Jupiter. Their masses and the resulting densities of the
satellites are smaller than we should have expected to find,
the density being less than that of the moon, and aver-
aging only a little greater than the density of Jupiter

226 ASTRONOMY

itself. At the surface of the third satellite the force of
gravity is but little less than on the moon, although the
moon's density is nearly twice as great as that of III, and
there can be no question here of accounting for the low
density through expansion by great heat, as in the case of
the sun and Jupiter. It has been surmised that these satel-
lites are not solid bodies, like the earth and moon, but only
shoals of rock and stone, loosely piled together and kept
from packing into a solid mass by the action of Jupiter in
raising tides within them. But the explanation can hardly
be regarded as an accepted article of astronomical belief,
although it is supported by some observations which tend
to show that the apparent shapes of the satellites change un-
der the influence of the tidal forces impressed upon them.
141. Eclipses of the satellites, — It may be seen from Fig.
89 that in their motion around the planet Jupiter's satellites
must from time to time pass through his shadow and be
eclipsed, and that the shadows of the satellites will occasion-
ally fall upon the planet, producing to an observer upon
Jupiter an eclipse of the sun, but to an observer on the earth
presenting only the appearance of a round black spot mov-
ing slowly across the face of the planet. Occasionally also
a satellite will pass exactly between the earth and Jupiter,
and may be seen projected against the planet as a back-
ground. All of these phenomena are duly predicted and
observed by astronomers, but the eclipses are the only ones
we need consider here. The importance of these eclipses
was early recognized, and astronomers endeavored to con-
struct a theory of their recurrence which would permit
accurate predictions of them to be made. But in this they
met with no great success, for while it was easy enoug.h
to foretell on what night an eclipse of a given satellite
would occur, and even to assign the hour of the night, it
was not possible to make the predicted minute agree with
the actual time of eclipse until after Roemer, a Danish
astronomer of the seventeenth century, found where lay the

THE PLANETS 227

trouble. His discovery was, that whenever the earth was
on the side of its orbit toward Jupiter the eclipses really
occurred before the predicted time, and when the earth
was on the far side of its orbit they came a few minutes
later than the predicted time. He correctly inferred thatx
this was to be explained, not by any influence which the
earth exerted upon Jupiter and his satellites, but through
the fact that the light by which we see the satellite and its
eclipse requires an appreciable time to cross the interven-
ing space, and a longer time when the earth is far from
Jupiter than when it is near.

For half a century Roemer's views found little credence,
but we know now that he was right, and that on the
average the eclipses come 8m. 18s. early when the earth is
nearest to Jupiter, and 8m. 18s. late when it is on the op-
posite side of its orbit. This is equivalent to saying that
light takes 8m. 18s. to cover the distance from the sun to
the earth, so that at any moment we see the sun not as it
then is, but as it was 8 minutes earlier. It has been found
possible in recent years to measure by direct experiment
the velocity with which light travels — 186,337 miles per
second — and multiplying this number by the 498s. (= 8m.
18s.) we obtain a new determination of the sun's distance
from the earth. The product of the two numbers is
92,795,826, in very fair agreement with the 93,000,000
miles found in Chapter X ; but, as noted there, this method,
like every other, has its weak side, and the result may be a
good many thousands of miles in error.

It is worthy of note in this connection that both meth-
ods of obtaining the sun's distance which were given in
Chapter X involve Kepler's Third Law, while the result
obtained from Jupiter's satellites is entirely independent
of this law, and the agreement of the several results is
therefore good evidence both for the truth of Kepler's laws
and for the soundness of Eoemer's explanation of the
eclipses. This mode of proof, by comparing the numerical

228

ASTRONOMY

results furnished by two or more different principles, and
showing that they agree or disagree, is of wide application
and great importance in physical science.

SATUEI*

142. The ring of Saturn, — In respect of size and mass
Saturn stands next to Jupiter, and although far inferior to
him in these respects, it contains more material than all
the remaining planets combined. But the unique feature
of Saturn which distinguishes it from every other known

body in the heavens is
its ring, which was long
a puzzle to the astrono-
mers who first studied
the planet with a tele-
scope (one of them called
Saturn a planet with
ears), but, was after
nearly half a century
correctly understood and
described by Huyghens,
whose Latin text we
translate into — " It is
surrounded by a ring,
thin, flat, nowhere touch-
ing it, and making quite
an angle with the eclip-
tic."

Compare with this
description Fig. 91, which shows some of the appearances
presented by the ring at different positions of Saturn in
its orbit. It was their varying aspects that led Huyghens
to insert the last words of his description, for, if the plane
of the ring coincided with the plane of the earth's orbit,
then at all times the ring must be turned edgewise toward
the earth, as shown in the middle picture of the group.

FIG. 91. — Aspects of Saturn's rings.

THE PLANETS

229

Fig. 92 shows the sun and the orbit of the earth placed
near the center of Saturn's orbit, across whose circumfer-
ence are ruled some oblique lines representing the plane
of the ring, the right end always tilted up, no matter where

FIG. 92.— Aspects of the ring in their relation to Saturn's orbital motion.

the planet is in its orbit. It is evident that an observer
upon the earth will see the N side of the ring when the
planet is at N and the 8 side when it is at $, as is shown
in the first and third pictures of Fig. 91, while midway be-
tween these positions the edge of the ring will be presented
to the earth.

The last occasion of this kind was in October, 1891, and
with the large telescope of the Washburn Observatory the

230 ASTRONOMY

writer at that time saw Saturn without a trace of a ring
surrounding it. The ring is so thin that it disappears
altogether when turned edgewise. The names of the zo-
diacal constellations are inserted in Fig. 92 in their proper
direction from the sun, and from these we learn that the
ring will disappear, or be exceedingly narrow, whenever
Saturn is in the constellation Pisces or near the boundary
line between Leo and Virgo. It will be broad and show its
northern side when Saturn is in Scorpius or Sagittarius, and
its southern face when the planet is in Gemini. What will
be its appearance in 1907 at the date marked in the figure?

143. Nature of the ring. — It is apparent from Figs. 91
and 93 that Saturn's ring is really made up of two or more
rings lying one inside of the other and completely sepa-
rated by a dark space which, though narrow, is as clean and
sharp as if cut with a knife. Also, the inner edge of the
ring fades off into an obscure border called the dusky ring
or crape ring. This requires a pretty good telescope to
show it, as may be inferred from the fact that it escaped
notice for more than two centuries during which the planet
was assiduously studied with telescopes, and was discovered
at the Harvard College Observatory as recently as 1850.

Although the rings appear oval in all of the pictures,
this is mainly an effect of perspective, and they are in fact
nearly circular with the planet at their center. The ex-
treme diameter of the ring is 172,000 miles, and from this
number, by methods already explained (Chapter IX), the
student should obtain the width of the rings, their distance
from the ball of the planet, and the diameter of the ball.
As to thickness, it is evident, from the disappearance of the
ring when its edge is turned toward the earth, that it is
very thin in comparison with its diameter, probably not
more than 100 miles thick, although no exact measurement
of this can be made.

From theoretical reasons based upon the law of gravita-
tion astronomers have held that the rings of Saturn could

FIG. 93.— Saturn.

232 ASTRONOMY

not possibly be solid or liquid bodies. The strains im-
pressed upon them by the planet's attraction would tear
into fragments steel rings made after their size and shape.
Quite recently Professor Keeler has shown, by applying the
spectroscope (Doppler's principle) to determine the velocity
of the ring's rotation about Saturn, that the inner parts of
the ring move, as Kepler's Third Law requires, more rapidly
than do the outer parts, thus furnishing a direct proof that
they are not solid, and leaving no doubt that they are made
up of separate fragments, each moving about the planet in
its own orbit, like an independent satellite, but standing so
close to its neighbors that the whole space reflects the sun-
light as completely as if it were solid. With this under-
standing of the rings it is easy to see why they are so thin.
Like Jupiter, Saturn is greatly flattened at the poles, and
this flattening, or rather the protuberant mass about the
equator, lays hold of every satellite near the planet and
exerts upon it a direct force tending to thrust it down
into the plane of the planet's equator and hold it there.
The ring lies in the plane of Saturn's equator because each
particle is constrained to move there.

The division of the ring into two parts, an outer and an
inner ring, is usually explained as follows : Saturn is sur-
rounded by a numerous brood of satellites, which by their
attractions produce perturbations in the material compos-
ing the rings, and the dividing line between the outer and
inner rings falls at the place where by the law of gravita-
tion the perturbations would have their greatest effect.
The dividing line between the rings is therefore a narrow
lane, 2,400 miles wide, from which the fragments have been
swept clean away by the perturbing action of the satellites.
Less conspicuous divisions are seen from time to time in
other parts of the ring, where the perturbations, though
less, are still appreciable. But it is open to some question
whether this explanation is sufficient.

The curious darkness of the inner or crape ring is easily

THE PLANETS 233

explained. The particles composing it are not packed to-
gether so closely as in the outer ring, and therefore reflect
less sunlight. Indeed, so sparsely strewn are the particles
in this ring that it is in great measure transparent to the
sunlight, as is shown by a recorded observation of one of the*
satellites which was distinctly although faintly seen while
moving through the shadow of the dark ring, but disap-
peared in total eclipse when it entered the shadow cast by
the bright ring.

144. The ball of Saturn.— The ball of the planet is in
most respects a smaller copy of Jupiter. With an equa-
torial diameter of 76,000 miles, a polar diameter of 69,000
miles, and a mass 95 times that of the earth, its density
is found to be the least of any planet in the solar system,
only 0.70 of the density of water, and about one half as
great as is the density of Jupiter. The force of gravity at
its surface is only a little greater (1.18) than on the earth ;
and this, in connection with the low density, leads, as in the
case of Jupiter, to the conclusion that the planet must be
mainly composed of gases and vapors, very hot within, but
inclosed by a shell of clouds which cuts off their glow from
our eyes.

Like Jupiter in another respect, the planet turns very
swiftly upon its axis, making a revolution in 10 hours 14
minutes, but up to the present it remains unknown whether
different parts of the surface have different rotation times.

145. The satellites. — Saturn is attended by a family of
nine satellites, a larger number than belongs to any other
planet, but with one exception they are exceedingly small
and difficult to observe save with a very large telescope.
Indeed, the latest one to be discovered was found in 1898 by
means of the image which it impressed upon a photographic
plate, and it has never been seen.

Titan, the largest of them, is distant 771,000 miles from
the planet and bears much the same relation to Saturn that
Satellite III bears to Jupiter, the similarity in distance, size,
16

234 ASTRONOMY

and mass being rather striking, although, of course, the
smaller mass of Saturn as compared with Jupiter makes the
periodic time of Titan — 15 days 23 hours — much greater
than that of III. Can you apply Kepler's Third Law to
the motion of Titan so as to determine from the data given
above, the time required for a particle at the outer or inner
edge of the ring to revolve once around Saturn ?

Japetus, the second satellite in point of size, whose dis-
tance from Saturn is about ten times as great as the moon's
distance from the earth, presents the remarkable peculiar-
ity of being always brighter in one part of its orbit than
in another, three or four times as bright when west of
Saturn as when east of it. This probably indicates that,
like our own moon, the satellite turns always the same face
toward its planet, and further, that one side of the satellite
reflects the sunlight much better than the other side — i. e.,
has a higher albedo. With these two assumptions it
is easily seen that the satellite will always turn toward
the earth one face when west, and the other face when
east of Saturn, and thus give the observed difference of
brightness.

UKANUS AND NEPTUNE

146. Chief characteristics. — The two remaining large
planets are interesting chiefly as modern additions to the
known members of the sun's family. The circumstances
leading to the discovery of Neptune have been touched
upon in Chapter IV, and for Uranus we need only note
that it was found by accident in the year 1781 by William
Herschel, who for some time after the discovery considered
it to be only a comet. It was the first planet ever discov-
ered, all of its predecessors having been known from pre-
historic times.

Uranus has four satellites, all of them very faint, which
present only one feature of special importance. Instead of
moving in orbits which are approximately parallel to the

WILLIAM HEESCHEL (1738-1822).

THE PLANETS 235

plane of the ecliptic, as do the satellites of the other planets,
their orbit planes are tipped up nearly perpendicular to the
planes of the orbits of both Uranus and the earth. The
one satellite which Neptune possesses has the same pecul-
iarity in even greater degree, for its motion around the
planet takes place in the direction opposite to that in
which all the planets move around the sun, much as if the
orbit of the satellite had been tipped over through an angle
of 150°. Turn a watch face down and note how the hands
go round in the direction opposite to that in which they
moved before the face was turned through 180°.

Both Uranus and Neptune are too distant to allow
much detail to be seen upon their surfaces, but the pres-
ence of broad absorption bands in their spectra shows that
they must possess dense atmospheres quite different in con-
stitution from the atmosphere of the earth. In respect of
density and the force of gravity at their surfaces, they are
not very unlike Saturn, although their density is greater
and gravity less than his, leading to the supposition that
they are for the most part gaseous bodies, but cooler and
probably more nearly solid than either Jupiter or Saturn.

Under favorable circumstances Uranus may be seen
with the naked eye by one who knows just where to look
for it. Neptune is never visible save in a telescope.

147. The inner planets. — In sharp contrast with the giant
planets which we have been considering stands the group
of four inner planets, or five if we count the moon as an
independent body, which resemble each other in being all
small, dense, and solid bodies, which by comparison with
the great distances separating the outer planets may fairly
be described as huddled together close to the sun. Their
relative sizes are shown in Fig. 84, together with the nu-
merical data concerning size, mass, density, etc., which we
have already found important for the understanding of a
planet's physical condition.

236

ASTRONOMY

VENUS

148. Appearance,— Omitting the earth, Venus is by far
the most conspicuous member of this group, and when at its
brightest is, with exception of the sun and moon, the most
brilliant object in the sky, and may be seen with the naked
eye in broad daylight if the observer knows just where to
look for it. But its brilliancy is subject to considerable
variations on account of its changing distance from the

FIG. 94. — The phases of Venus. — ANTONIADI.

earth, and the apparent size of its disk varies for the same
reason, as may be seen from Fig. 94. These drawings bring
out well the phases of the planet, and the student should
determine from Fig. 17 what are the relative positions in
their orbits of the earth and Venus at which the planet
would present each of these phases. As a guide to this,
observe that the dark part of Venus's earthward side is
always proportional in area to the angle at Venus between
the earth and sun. In the first picture of Fig. 94 about

THE PLANETS 237

two thirds of the surface corresponding to the full hemi-
sphere of the planet is dark, and the angle at Venus
between earth and sun is therefore two thirds of 180° — i. e.,
120°. In Fig. 17 find a place on the orbit of Venus from
which if lines be drawn to the sun and earth, as there
shown, the angle between them will be 120°. Make a simi-
lar construction for the fourth picture in Fig. 94. Which
of these two positions is farther from the earth ? How do
the distances compare with the apparent size of Venus in
the two pictures ? What is the phase of Venus to-day ?

The irregularities in the shading of the illuminated
parts of the disk are too conspicuous in Fig. 94, on account
of difficulties of reproduction; these shadings are at the
best hard to see in the telescope, and distinct permanent
markings upon the planet are wholly lacking. This absence
of markings makes almost impossible a determination of
the planet's time of rotation about its axis, and -astrono-
mers are divided in this respect into two parties, one of
which maintains that Venus, like the earth, turns upon its
axis in some period not very different from 24 hours, while
the other contends that, like the moon, it turns always the
same face toward the center of its orbit, making a rotation
upon its axis in the same period in which it makes a revo-
lution about the sun. The reason why no permanent mark-
ings are to be seen on this planet is easily found. Like
Jupiter and Saturn, its atmosphere is at all times heavily
cloud-laden, so that we seldom, if ever, see down to the
level of its solid parts. There is, however, no reason here
to suppose the interior parts hot and gaseous. It is much
more probable that Venus, like the earth, possesses a solid
crust whose temperature we should expect to be consider-
ably higher than that of the earth, because Venus is nearer
the sun. But the cloud layer in its atmosphere must modify
the temperature in some degree, and we have practically
no knowledge of the real temperature conditions at the
surface of the planet.

238 ASTRONOMY

It is the clouds of Venus which in great measure are
responsible for its marked brilliancy, since they are an ex-
cellent medium for reflecting the sunlight, and give to its
surface an albedo greater than that of any other planet,
although Saturn is nearly equal to it.

Of course, the presence of such cloud formations indi-
cates that Venus is surrounded by a dense atmosphere, and
we have independent evidence of this in the shape of its
disk when the planet is very nearly between the earth and
sun. The illuminated part, from tip to tip of the horns?
then stretches more than halfway around the planet's cir-
cumference, and shows that a certain amount of light must
have been refracted through its atmosphere, thus making
the horns of the crescent appear unduly prolonged. This
atmosphere is shown by the spectroscope to be not unlike
that of the earth, although probably more dense.

MERCURY

149. Chief characteristics. — Mercury, on account of its
nearness to the sun, is at all times a difficult object to ob-
serve, and Copernicus, who spent most of his life in Poland,
is said, despite all his efforts, to have gone to his grave with-
out ever seeing it. In our more southern latitude it can
usually be seen for about a fortnight at the time of each
elongation — i. e., when at its greatest angular distance from
the sun — and the student should find from Fig. 16 the time
at which the next elongation occurs and look for the planet,
shining like a star of the first magnitude, low down in the
sky just after sunset or before sunrise, according as the
elongation is to the east or west of the sun. When seen in
the morning sky the planet grows brighter day after day
until it disappears in the sun's rays, while in the evening
sky its brilliancy as steadily diminishes until the planet is
lost. It should therefore be looked for in the evening as
soon as possible after it emerges from the sun's rays.

Mercury, as the smallest of the planets, is best compared

THE PLANETS 239

with the moon, which it does not greatly surpass in size
and which it strongly resembles in other respects. Careful
comparisons of the amount of light reflected by the planet
in different parts of its orbit show not only that its albedo
agrees very closely with that of the moon, but also that its
light changes with the varying phase of the planet in al-
most exactly the same way as the amount of moonlight
changes. We may therefore infer that its surface is like
that of the moon, a rough and solid one, with few or no
clouds hanging over it, and most probably covered with
very little or no atmosphere. Like Venus, its rotation pe-
riod is uncertain, with the balance of probability favoring
the view that it rotates upon its axis once in 88 days, and
therefore always turns the same face toward the sun.

If such is the case, its climate must be very peculiar :
one side roasted in a perpetual day, where the direct heat-
ing power of the sun's rays, when the planet is at perihelion,
is ten times as great as on the moon, and which six weeks
later, when the planet is at its farthest from the sun, has
fallen off to less than half of this. On the opposite side of
the planet there must reign perpetual night and perpetual
cold, mitigated by some slight access of warmth from the
day side, and perhaps feebly imitating the rapid change of
season which takes place on the day side of the planet.
This view, however, takes no account of a possible devia-
tion of the planet's axis from being perpendicular to the
plane of its orbit, or of the librations which must be pro-
duced by the great eccentricity of the orbit, either of which
would complicate without entirely destroying the ideal
conditions outlined above.

MAKS

150. Appearance. — The one remaining member of the
inner group, Mars, has in recent years received more atten-
tion than any other planet, and the newspapers and maga-
zines have announced marvelous things concerning it : that

240

ASTRONOMY

it is inhabited by a race of beings superior in intelligence
to men ; that the work of their hands may be seen upon
the face of the planet ; that we should endeavor to com-
municate with them, if indeed they are not already sending
messages to us, etc. — all of which is certainly important,
if true, but it rests upon a very slender foundation of evi-
dence, a part of which we shall have to consider.

Beginning with facts of which there is no doubt, this
ruddy-colored planet, which usually shines about as brightly

as a star of the first mag-
nitude, sometimes dis-
plays more than tenfold
this brilliancy, surpass-
ing every other planet
save Venus and present-
ing at these times espe-
cially favorable opportu-
nities for the study of
its surface. The expla-
nation of this increase
of brilliancy is, of course,
that the planet approach-
es unusually near to the
earth, and we have al-
ready seen from a con-
sideration of Fig. 17
that this can only hap-
pen in the months of August and September. The last
favorable epoch of this kind was in 1894. From Fig. 17
the student should determine when the next one will
come.

Fig. 95 presents nine drawings of the planet made at
one of the epochs of close approach to the earth, and shows
that its face bears certain faint markings which, though
inconspicuous, are fixed and permanent features of the
planet. The dark triangular projection in the lower half

FIG. 95.— Mars.— SCHAEBERLE.

THE PLANETS

241

of the second drawing was seen and sketched by Huyghens.
1659 A. D. In Fig. 96 some of these markings are shown
much more plainly, but Fig. 95 gives a better idea of their
usual appearance in the telescope.

151. Rotation. — It may be seen readily enough, from a
comparison of the first two sketches of Fig. 95, that the
planet rotates about an
axis, and from a more
extensive study it is
found to be very like
the earth in this re-
spect, turning once in
24h. 37m. around an
axis tipped from being
perpendicular to the
plane of its orbit about
a degree and a half
more than is the earth's
axis. Since it is this
inclination of the axis
which is the cause of
changing seasons upon
the earth, there must
be similar changes,

winter and summer, as well as day and night, upon Mars,
only each season is longer there than here in the same pro-
portion that its year is longer than ours — i. e., nearly two
to one. It is summer in the northern hemisphere of Mars
whenever the sun, as seen from Mars, stands in that con-
stellation which is nearest the point of the sky toward
which the planet's axis points. But this axis points toward
the constellation Cygnus, and Alpha Cygni is the bright
star nearest the north pole of Mars. As Pisces is the
zodiacal constellation nearest to Cygnus, it must be sum-
mer in the northern hemisphere of Mars when the sun is in
Pisces, or, turning the proposition about, it must be summer

FIG. 96.— Four views of Mars differing 90° in
longitude. — BARNARD.

242

ASTRONOMY

in the southern hemisphere of Mars when the planet, as
seen from the sun, lies in the direction of Pisces.

152. The polar caps. — One effect of the changing seasons
upon Mars is shown in Fig. 97, where we have a series of
drawings of the region about its south pole made in 1894,
on dates between May 21st and December 10th. Show
from Fig. 16 that during this time it was summer in the
region here shown. Mars crossed the prime radius in 1894
on September 5th. The striking thing in these pictures is
the white spot surrounding the pole, which shrinks in size

from the beginning to
near the end of the se-
ries, and then disappears
altogether. The spot
came back again a year
later, and like a similar
spot at the north pole of
the planet it waxes in the
winter and wanes during
the summer of Mars in
endless succession.

Sir W. Herschel, who
studied these appear-
ances a century ago, com-
pared them with the snow
fields which every winter

FIG. 97.— The south polar cap of Mars in .. . ,

1894.-BABNARD. spread out from the re-

gion around the terres-
trial pole, and in the summer melt and shrink, although
with us they do not entirely disappear. This explanation of
the polar caps of Mars has been generally accepted among
astronomers, and from it we may draw one interesting con-
clusion : the temperature upon Mars between summer and
winter oscillates above and below the freezing point of
water, as it does in the temperate zones of the earth. But
this conclusion plunges us into a serious difficulty. The

THE PLANETS 243

temperature of the earth is made by the sun, and at the
distance of Mars from the sun the heating effect of the
latter is reduced to less than half what it is at the earth,
so that, if Mars is to be kept at the same temperature as
the earth, there must be some peculiar means for storing
the solar heat and using it more economically than is done
here. Possibly there is some such mechanism, although
no one has yet found it, and some astronomers are very
confident that it does not exist, and assert that the com-
parison of the polar caps with snow fields is misleading,
and that the temperature upon Mars must be at least 100°,
and perhaps 200° or more, below zero.

153. Atmosphere and climate. — In this connection one
feature of Mars is of importance. The markings upon its
surface are always visible when turned toward the earth,
thus showing that the atmosphere contains no such amount
of cloud as does our own, but on the whole is decidedly
clear and sunny, and presumably much less dense than
ours. AVe have seen in comparing the earth and the moon
how important is the service which the earth's atmosphere
renders in storing the sun's heat and checking those great
vicissitudes of temperature to which the moon is subject ;
and with this in mind we must regard the smaller density
and cloudless character of the atmosphere of Mars as un-
favorable to the maintenance there of a temperature like
that of the earth. Indeed, this cloudlessness must mean
one of two things : either the temperature is so low that
vapors can not exist in any considerable quantity, or the
surface of Mars is so dry that there is little water or other
liquid to be evaporated. The latter alternative is adopted
by those astronomers who look upon the polar caps as true
snow fields, which serve as the chief reservoir of the planet's
water supply, and who find in Fig. 98 evidence that as the
snow melts and the water flows away over the flat, dry sur-
face of the planet, vegetation springs up, as shown by the
dark markings on the disk, and gradually dies out with

244

ASTRONOMY

the advancing season. Note that in the first of these pic-
tures the season upon Mars corresponds to the end of May
with us, and in the last picture to the beginning of August,
a period during which in much of our western country the
luxuriant vegetation of spring is burned out by the scorch-
ing sun. From this point of view the permanent dark
spots are the low-lying parts of the planet's surface, in
which at all times there is a sufficient accumulation of
water to support vegetable life.

154. The canals.— In Fig. 98 the lower part of the disk
of Mars shows certain faint dark lines which are generally
called canals, and in Plate III there is given a map of Mars

FIG. 98.— The same face of Mars at three different seasons.— LOWELL.

showing many of these canals running in narrow, dusky
streaks across the face of the planet according to a pattern
almost as geometrical as that of a spider's web. This must
not be taken for a picture of the planet's appearance in a
telescope. No man ever saw Mars look like this, but the
map is useful as a plain representation of things dimly
seen. Some of the regions of this map are marked Mare
(sea), in accordance with the older view which regarded
the darker parts of the planet — and of themotm— as bodies
of water, but this is now known to be an error in both
cases. The curved surface of a planet can not be accurately
reproduced upon the flat surface of paper, but ifi always
more or less distorted by the various methods of/" project-
ing " it which are in use. Compare the map/of Mars in

THE PLANETS 245

Plate III with Fig. 99, in which the projection represents
very well the equatorial parts of the planet, but enormously
exaggerates the region arou nd the poles.

It is a remarkable feature of the canals that they all
begin and end in one of these dark parts of the planetV
surface ; they show no loose ends lying on the bright parts
of the planet. Another even more remarkable feature is
that while the larger canals are permanent features of the
planet's surface, they at times appear " doubled " — i. e., in
place of one canal two parallel ones side by side, lasting
for a time and then giving place again to a single canal.

It is exceedingly difficult to frame any reasonable ex-
planation of these canals and the varied appearances which
they present. The source of the wild speculations about
Mars, to which reference is made above, is to be found in
the suggestion frequently made, half in jest and half in
earnest, that the canals are artificial water courses con-
structed upon a scale vastly exceeding any public works
upon the earth, and testifying to the presence in Mars of
an advanced civilization. The distinguished Italian as-
tronomer, Schiaparelli, who has studied these formations
longer than any one else, seems inclined to regard them as
water courses lined on either side by vegetation, which
flourishes as far back from the central channel as water
can be supplied from it — a plausible enough explanation if
the fundamental difficulty about temperature can be over-
come.

155. Satellites. — In 1877, one of the times of near ap-
proach, Professor Hall, of Washington, discovered two tiny
satellites revolving about Mars in orbits so small that the
nearer one, Phobos, presents the remarkable anomaly of
completing the circuit of its orbit in less time than the
planet takes for a rotation about its axis. This satellite, in
fact, makes three revolutions in its orbit while the planet
turns once upon its axis, and it therefore rises in the west
and sets in the east, as seen from Mars, going from one

3 S SS?g2o2SS?3S?

THE PLANETS 247

horizon to the other in a little less than 6 hours. The
other satellite, Deimos, takes a few hours more than a day
to make the circuit of its orhit, but the difference is so
small that it remains continuously above the horizon of
any given place upon Mars for more than 60 hours at a
time, and during this period runs twice through its com-
plete set of phases — new, first quarter, full, etc. In ordi-
nary telescopes these satellites can be seen only under espe-
cially favorable circumstances, and are far too small to
permit of any direct measurement of their size. The
amount of light which they reflect has been compared
with that of Mars and found to be as much inferior to it
as is Polaris to two full moons, and, judging from this com-
parison, their diameters can not much exceed a half dozen
miles, unless their albedo is far less than that of Mars,
which does not seem probable.

THE ASTEKOIDS

156. Minor planets. — These may be dismissed with few
words. There are about 500 of them known, all discovered
since the beginning of the nineteenth century, and new
ones are still found every year. No one pretends to
remember the names which have been assigned them, and
they are commonly represented by a number inclosed in a
circle, showing the order in which they were discovered —
e. g., Q = Ceres, @ — Eros, etc. For the most part they
are little more than chips, world fragments, adrift in space,
and naturally it was the larger and brighter of them that
were first discovered. The size of the first four of them —
Ceres, Pallas, Juno, and Vesta — compared with the size of
the moon, according to Professor Barnard, is shown in Fig.
100. The great majority of them must be much smaller
than the smallest of these, perhaps not more than a score
of miles in diameter.

A few of the asteroids present problems of special in-
terest, such as Eros, on account of its close approach to the

248

ASTRONOMY

earth ; Polyhymnia, whose very eccentric orbit makes it a
valuable means for determining the mass of Jupiter, etc.;
but these are special cases and the average asteroid now
receives scant attention, although half a century ago, when
only a few of them were known, they were regarded with
much interest, and the discovery of a new one was an event
of some consequence.

It was then a favorite speculation that they were in fact
fragments of an ill-fated planet which once filled the gap

between the orbits of Mars
and Jupiter, but which, by
some mischance, had been
blown into pieces. This is
now known to be well-nigh
impossible, for every frag-
ment which after the explo-
sion moved in an elliptical
orbit, as all the asteroids do
move, would be brought
back once in every revolu-
tion to the place of the ex-
plosion, and all the asteroid
orbits must therefore inter-
sect at this place. But there is no such common point of
intersection.

157. Life on the planets. — There is a belief firmly
grounded in the popular mind, and not without its ad-
vocates among professional astronomers, that the planets
are inhabited by living and intelligent beings, and it seems
proper at the close of this chapter to inquire briefly how
far the facts and principles here developed are consistent
with this belief, and what support, if any, they lend to it.

At the outset we must observe that the word life is an
elastic term, hard to define in any satisfactory way, and yet
standing for something which we know here upon the
earth. It is this idea, our familiar though crude knowl-

FIG. 100.— The size of the first four
asteroids. — BARNARD.

THE PLANETS 249

edge of life, which lies at the root of the matter. Life, if
it exists in another planet, must be in its essential char-
acter like life upon the earth, and must at least possess
those features which are common to all forms of terrestrial
life. It is an abuse of language to say that life in Mars-
may be utterly unlike life in the earth ; if it is absolutely
unlike, it is not life, whatever else it may be. Now, every
form of life found upon the earth has for its physical basis
a certain chemical compound, called protoplasm, which
can exist and perpetuate itself only within a narrow range
of temperature, roughly speaking, between 0° and 100°
centigrade, although these limits can be considerably over-
stepped for short periods of time. Moreover, this proto-
plasm can be active only in the presence of water, or water
vapor, and we may therefore establish as the necessary con-
ditions for the continued existence and reproduction of
life in any place that its temperature must not be perma-
nently above 100° or below 0°, C., and water must be pres-
ent in that place in some form.

With these conditions before us it is plain that life can
not exist in the sun on account of its high temperature.
It is conceivable that active and intelligent beings, salaman-
ders, might exist there, but they could not properly be said
to live. In Jupiter and Saturn the same condition of high
temperature prevails, and probably also in Uranus and
Xeptune, so that it seems highly improbable that any of
these planets should be the home of life.

Of the inner planets, Mercury and the moon seem desti-
tute of any considerable atmospheres, and are therefore
lacking in the supply of water necessary for life, and the
same is almost certainly true of all the asteroids. There
remain Venus, Mars, and the satellites of the outer planets,
which latter, however, we must drop from consideration as
being too little known. On Venus there is an atmosphere
probably containing vapor of water, and it is well within
the range of possibility that liquid water should exist upon
17

250 ASTRONOMY

the surface of this planet and that its temperature should
fall within the prescribed limits. It would, however, be
straining our actual knowledge to affirm that such is the
case, or to insist that if such were the case, life would ne-
cessarily exist upon the planet.

On Mars we encounter the fundamental difficulty of
temperature already noted in § 152. If in some unknown
way the temperature is maintained sufficiently high for the
polar caps to be real snow, thawing and forming again with
the progress of the seasons, the necessary conditions of life
would seem to be fulfilled here and life if once introduced
upon the planet might abide and flourish. But of positive
proof that such is the case we have none.

On the whole, our survey lends little encouragement to
the belief in planetary life, for aside from the earth, of all
the hundreds of bodies in the solar system, not one is found
in which the necessary conditions of life are certainly ful-
filled, and only two exist in which there is a reasonable
probability that these conditions may be satisfied.

CHAPTEE XII

COMETS AND METEORS

158. Visitors in the solar system.— All of the objects —
sun, moon, planets, stars — which we have thus far had to
consider, are permanent citizens of the sky, and we have no
reason to suppose that their present appearance differs ap-
preciably from what it was 1,000 years or 10,000 years ago.
But there is another class of objects — comets, meteors —
which appear unexpectedly, are visible for a time, and then
vanish and are seen no more. On account of this temporary
character the astronomers of ancient and mediaeval times
for the most part refused to regard them as celestial bodies
but classed them along with clouds, fogs, Jack-o'-lanterns,
and fireflies, as exhalations from the swamps or the vol-
cano ; admitting them to be indeed important as harbingers
of evil to mankind, but having no especial significance for
the astronomer.

The comet of 1018 A. D. inspired the lines —

" Eight things there be a Comet brings,
When it on high doth horrid range :
Wind, Famine, Plague, and Death to Kings,

War, Earthquakes, Floods, and Direful Change,"

which, according to White (History of the Doctrine of
Comets), were to be taught in all seriousness to peasants
and school children.

It was by slow degrees, and only after direct measure-
ments of parallax had shown some of them to be more dis-
tant than the moon, that the tide of old opinion was turned
and comets were transferred from the sublunary to the

251

252

ASTRONOMY

celestial sphere, and in more recent times meteors also
have been recognized as coming to us from outside the
earth. A meteor, or shooting star as it is often called, is
one of the commonest of phenomena, and one can hardly
watch the sky for an hour on any clear and moonless night
without seeing several of those quick flashes of light which
look as if some star had suddenly left its place, dashed
swiftly across a portion of the sky and then vanished. It
is this misleading appearance that prohably is responsible
for the name shooting star.

159. Comets, — Comets are less common and much longer-
lived than meteors, lasting usually for several weeks, and
may be visible night after night for many months, but
never for many years, at a time. During the last decade

FIG. 101.— Douati's comet.— BOND.

there is no year in which less than three comets have
appeared, and 1898 is distinguished by the discovery of
ten of these bodies, the largest number ever found in
one year. On the average, we may expect a new comet to

COMETS AND METEORS

253

be found about once in every ten weeks, but for the most
part they are small affairs, visible only in the telescope, and
a fine large one, like Donati's comet of 1858 (Fig. 101), or
the Great Comet of Septem-
ber, 1882, which was visible in
broad daylight close beside the
sun, is a rare spectacle, and as
striking and impressive as it
is rare.

Note in Fig. 102 the great
variety of aspect presented
by some of the more famous
comets, which are here repre-
sented upon a very small scale.

Fig. 103 is from a photo-
graph of one of the faint
comets of the year 1893, which
appears here as a rather feeble
streak of light amid the stars
which are scattered over the
background of the picture.

An apparently detached portion of this comet is shown at
the extreme left of the picture, looking almost like another
independent comet. The clean, straight line running diag-
onally across the picture is the flash of a bright meteor
that chanced to pass within the range of the camera while
the comet was being photographed.

A more striking representation of a moderately bright
telescopic comet is contained in Figs. 104 and 105, which
present two different views of the same comet, showing a
considerable change in its appearance. A striking feature
of Fig. 105 is the star images, which are here drawn out into
short lines all parallel with each other. During the expos-
ure of 2h. 20m. required to imprint this picture upon the
photographic plate, the comet was continually changing its
position among the stars on account of its orbital motion,

FIG. 102. — Some famous comets.

254

ASTRONOMY

and the plate was therefore moved from time to time, so as
to follow the comet and make its image always fall at the
same place. Hence the plate was continually shifted rela-
tive to the stars whose images, drawn out into lines, show
the direction in which the plate was moved — i. e., the direc-
tion in which the comet was moving across the sky. The
same effect is shown in the other photographs, but less
conspicuously than here on account of their shorter expos-
ure times.

These pictures all show that one end of the comet is
brighter and apparently more dense than the other, and it

is customary to call
this bright part the
head of the comet,
while the brushlike
appendage that
streams away from
it is called the
comet's tail.

160. The parts
of a comet. — It is
not every comet
that has a tail,
though all the
large ones do, and
in Fig. 103 the de-
tached piece of
cometary matter at
the left of the
picture represents

very well the appearance of a tailless comet, a rather large
but not very bright star of a fuzzy or hairy appearance.
The word comet means long-haired or hairy star. Some-
thing of this vagueness of outline is found in all comets,
whose exact boundaries are hard to define, instead of being
sharp and clean-cut like those of a planet or satellite.

FIG. 103.— Brooke's comet, November 13, 1893.
BARNARD.

COMETS AND METEORS 255

Often, however, there is found in the head of a comet a
much more solid appearing part, like the round white ball
at the center of Fig. 106, which is called the nucleus of

FIG. 104.— Swift's comet, April 17, 1892.— BAKNARD.

the comet, and appears to be in some sort the center from
which its activities radiate. As shown in Figs. 106 and
107, the nucleus is sometimes surrounded by what are
called envelopes, which have the appearance of successive
wrappings or halos placed about it, and odd, spurlike pro-
jections, called jets, are sometimes found in connection
with the envelopes or in place of them. These figures also
show what is quite a common characteristic of large
comets, a dark streak running down the axis of the tail,
showing that the tail is hollow, a mere shell surrounding
empty space.

The amount of detail shown in Figs. 106 and 107 is,
however, quite exceptional, and the ordinary comet is much
more like Fig. 103 or 104. Even a great comet when it

256 ASTRONOMY

first appears is not unlike the detached fragment in Fig.
103, a faint and roundish patch of foggy light which grows
through successive stages to its maximum estate, develop-
ing a tail, nucleus, envelopes, etc., only to lose them again
as it shrinks and finally disappears.

161. The orbits of comets,— It will be remembered that
Newton found, as a theoretical consequence of the law of
gravitation, that a body moving under the influence of the
sun's attraction might have as its orbit any one of the
conic sections, ellipse, parabola, or hyperbola, and among
the 400 and more comet orbits which have been deter-
mined every one of these orbit forms appear, but curiously
enough there is not a hyperbola among them which, if
drawn upon paper, could be distinguished by the unaided

FIG. 105.— Swift's comet, April 24, 1892.— BARNARD.

eye from a parabola, and the ellipses are all so long and
narrow, not one of them being so nearly round as is the
most eccentric planet orbit, that astronomers are accus-
tomed to look upon the parabola as being the normal type

COMETS AND METEORS

257

of comet orbit, and to regard a comet whose motion differs
much from a parabola as being abnormal and calling for
some special explanation.

The fact that comet orbits are parabolas, or differ but
little from them, explains at once the temporary character
and speedy disappearance
of these bodies. They
are visitors to the solar
system and visible for
only a short time, because
the parabola in which
they travel is not a closed
curve, and the comet, hav-
ing passed once along
that portion of it near the
earth and the sun, moves
off along a path which
ever thereafter takes it
farther and farther away,
beyond the limit of visi-
bility. The development
of the comet during the
time it is visible, the
growth and disappearance

of tail, nucleus, etc., depend upon its changing distance
from the sun, the highest development and most complex
structure being presented when it is nearest to the sun.

Fig. 108 shows the path of the Great Comet of 1882
during the period in which it was seen, from September 3,
1882, to May 26, 1883. These dates— IX, 3, and V, 26— are
marked in the figure opposite the parts of the orbit in
which the comet stood at those times. Similarly, the posi-
tions of the earth in its orbit at the beginning of Septem-
ber, October, Xovember, etc., are marked by the Roman
numerals IX, X, XI, etc. The line S V shows the direction
from the sun to the vernal equinox, and S& is the line

FIG. 106.— Head of Coggia's comet,
July 13, 1874.— BOND.

258

ASTRONOMY

along which the plane of the comet's orbit intersects the
plane of the earth's orbit — i. e., it is the line of nodes of the
comet orbit. Since the comet approached the sun from
the south side of the ecliptic, all of its orbit, save the little
segment which falls to the left of $Q, lies below (south) of
the plane of the earth's orbit, and the part which would
be hidden if this plane were opaque is represented by a
broken line.

162. Elements of a comet's orbit,— There is a theorem of
geometry to the effect that through any three points not
in the same straight line one circle, and only one, can be
drawn. Corresponding to this there is a theorem of celes-
tial mechanics, that through any three positions of a comet

one conic section, and
only one, can be passed
along which the comet
can move in accordance
with the law of gravita-
tion. This conic section
is, of course, its orbit, and
at the discovery of a com-
et astronomers always
hasten to observe its po-
sition in the sky on dif-
ferent nights in order to
obtain the three positions
(right ascensions and de-
clinations) necessary for
determining the particu-
lar orbit in which it
moves. The circle, to
which reference was made
above, is completely as-
certained and defined when we know its radius and the
position of its center. A parabola is not so simply defined,
and five numbers, called the elements of its orbit, are

FIG. 107.— Head of Donati's comet, Septem-
ber 30, October 2, 1858.— BOND.

COMETS AND METEORS

259

required to fix accurately a comet's path around the sun.
Two of these relate to the position of the line of nodes and
the angle which the orbit plane makes with the plane of the
ecliptic ; a third fixes the direction of the axis of the orbit

FIG. 108.— Orbits of the earth and the
Great Comet of 1882.

in its plane, and the remaining two, which are of more
interest to us, are the date at which the comet makes its
nearest approach to the sun (perihelion passage) and its
distance from the sun at that date (perihelion distance).
The date, September 17th, placed near the center of Fig.
108, is the former of these elements, while the latter, which
is too small to be accurately measured here, may be found
from Fig. 109 to be 0.82 of the sun's diameter, or, in terms
of the earth's distance from the sun, C.008.

Fig. 109 shows on a large scale the shape of that part of
the orbit near the sun and gives the successive positions of
the comet, at intervals of T2¥ of a day, on September 16th
and 17th, showing that in less than 10 hours — 17.0 to 17.4
— the comet swung around the sun through an angle of

260

ASTRONOMY

more than 240°. When at its perihelion it was moving
with a velocity of 300 miles per second ! This very unusual
velocity was due to the comet's extraordinarily close ap-
proach to the sun. The earth's velocity in its orbit is only
19 miles per second, and the velocity of any comet at any
distance from the sun, provided its orbit is a parabola, may
be found by dividing this number by the square root of
half the comet's distance — e. g., 300 miles per second equals
19-^0.004.

Most of the visible comets have their perihelion dis-
tances included between ^ and f of the earth's distance
from the sun, but occasionally one is found, like the
second comet of 1885, whose nearest approach to the sun

FIG. 109.— Motion of the Great Comet of 1882 in passing around the sun.

lies far outside the earth's orbit, in this case half-way
out to the orbit of Jupiter; but such a comet must be a
very large one in order to be seen at all from the earth.

COMETS AND METEORS

261

FIG. 110.— The Great Comet of 1843.

There is, however, some reason for believing that the num-
ber of comets which move around the sun without ever
coming inside the orbit of Jupiter, or even that of Saturn,
is much larger than the number of those which come close
enough to be discovered from the earth. In any case we
are reminded of Kepler's saying, that comets in the sky are
as plentiful as fishes in the sea, which seems to be very little
exaggerated when we consider that, according to Kleiber,
out of all the comets which enter the solar system probably
not more than 2 or 3 per cent are ever discovered.

163. Dimensions of comets, — The comet whose orbit is
shown in Figs. 108 and 109 is the finest and largest that
has appeared in recent years. Its tail, which at its maxi-
mum extent would have more than bridged the space be-
tween sun and earth (100,000,000 miles), is made very much
too short in Fig. 109, but when at its best was probably not
inferior to that of the Great Comet in 1843, shown in Fig.

262 ASTRONOMY

110. As we shall see later, there is a peculiar and special
relationship between these two comets.

The head of the comet of 1882 was not especially large
— about twice the diameter of the ball of Saturn — but its
nucleus, according to an estimate made by Dr. Elkin when
it was very near perihelion, was as large as the moon. The
head of the comet shown in Fig. 107 was too large to be
put in the space between the earth and the moon, and the
Great Comet of 1811 had a head considerably larger than
the sun itself. From these colossal sizes down to the
smallest shred just visible in the telescope, comets of all
dimensions may be found, but the smaller the comet the
less the chance of its being discovered, and a comet as small
as the earth would probably go unobserved unless it ap-
proached very close to us.

164. The mass of a comet, — There is no known case in
which the mass of a comet has ever been measured, yet
nothing about them is more sure than that they are bodies
with mass which is attracted by the sun and the planets,
and which in its turn attracts both sun and planets and
produces perturbations in their motion. These perturba-
tions are, however, too small to be measured, although the
corresponding perturbations in the comet's motion are
sometimes enormous, and since these mutual perturbations
are proportional to the masses of comet and planet, we are
forced to say that, by comparison with even such small
bodies as the moon or Mercury, the mass of a comet is
utterly insignificant, certainly not as great as a ten-thou-
'"salrdth part of the mass of the earth. In the case of the
Great Comet of 1882, if we leave its hundred million miles
of tail out^pf account and suppose the entire mass condensed
into its head, we find by a little computation that the aver-
age density of^ the head under these circumstances must
have been less\ than T^Vo- Part of tne density of air. In
ordinary laboratory practice this would be called a pretty
good vacuum.

COMETS AND METEORS 263

A striking observation made on September 17, 1882,
goes to confirm the very small density of this comet. It
is shown in Fig. 109 that early on that day the comet
crossed the line joining earth and sun, and therefore passed
in transit over the sun's disk. Two observers at the Cape
of Good Hope saw the comet approach the sun, and fol-
lowed it with their telescopes until the nucleus actually
reached the edge of the sun and disappeared, behind it as
they supposed, for no trace of the comet, not even its
nucleus, could be seen against the sun, although it was care-
fully looked for. Now, the figure shows that the comet
passed between the earth and sun, and its densest parts
were therefore too attenuated to cut off any perceptible
fraction of the sun's rays. In other cases stars have been
seen through the head of a comet, shining apparently with
undimmed luster, although in some cases they seem to
have been slightly refracted out of their true positions.

165. Meteors. — Before proceeding further with the study
of comets it is well to turn aside and consider their hum-
bler relatives, the shooting stars. On some clear evening,
when the moon is absent from the sky, watch the heavens
for an hour and count the meteors visible during that time.
Note their paths, the part of the sky where they appear
and where they disappear, their brightness, and whether
they all move with equal swiftness. Out of such simple
observations with the unaided eye there has grown a large
and important branch of astronomical science, some parts
of which we shall briefly summarize here.

A particular meteor is a local phenomenon seen over
only a small part of the earth's surface, although occasion-
ally a very big and bright one may travel and be visible
over a considerable territory. Such a one in December,
1876, swept over the United States from Kansas to Penn-
sylvania, and was seen from eleven different States. But the
ordinary shooting star is much less conspicuous, and, as we
know from simultaneous observations made at neighboring

264: ASTRONOMY

places, it makes its appearance at a height of some 75 miles
above the earth's surface, occupies something like a second
in moving over its path, and then disappears at a height
of ahout 50 miles or more, although occasionally a big one
comes down to the very surface of the earth with force
sufficient to bury itself in the ground, from which it may
be dug up, handled, weighed, and turned over to the chem-
ist to be analyzed. The pieces thus found show that the
big meteors, at least, are masses of stone or mineral ; iron
is quite commonly found in them, as are a considerable
number of other terrestrial substances combined in rather
peculiar ways. But no chemical element not found on the
earth has ever been discovered in a meteor.

166. Nature of meteors. — The swiftness with which the
meteors sweep down shows that they must come from out-
side the earth, for even half their velocity, if given to them
by some terrestrial volcano or other explosive agent, would
send them completely away from the earth never to return.
We must therefore look upon them as so many projectiles,
bullets, fired against the earth from some outside source
and arrested in their motion by the earth's atmosphere,
which serves as a cushion to protect the ground from the
bombardment which would otherwise prove in the highest
degree dangerous to both property and life. The speed of
the meteor is checked by the resistance which the atmos-
phere offers to its motion, and the energy represented by
that speed is transformed into heat, which in less than a
second raises the meteor and the surrounding air to incan-
descence, melts the meteor either wholly or in part, and
usually destroys its identity, leaving only an impalpable
dust, which cools off as it settles slowly through the lower
atmosphere to the ground. The heating effect of the air's
resistance is proportional to the square of the meteor's
velocity, and even at such a moderate speed as 1 mile per
second the effect upon the meteor is the same as if it stood
still in a bath of red-hot air. Now, the actual velocity of

COMETS AND METEORS 265

meteors through the air is often 30 or 40 times as great as
this, and the corresponding effect of the air in raising its
temperature is more than 1,000 times that of red heat.
Small wonder that the meteor is brought to lively incan-
descence and consumed even in a fraction of a second.

167. The number of meteors. — A single observer may
expect to see in the evening hours about one meteor every
10 minutes on the average, although, of course, in this
respect much irregularity may occur. Later in the night
they become more frequent, and after 2 A. M. there are
about three times as many to be seen as in the evening
hours. But no one person can keep a watch upon the
whole sky, high and low, in front and behind, and experi-
ence shows that by increasing the number of observers and
assigning to each a particular part of the sky, the total
number of meteors counted may be increased about five-
fold. So, too, the observers at any one place can keep an
effective watch upon only those meteors which come into the
earth's atmosphere within some moderate distance of their
station, say 50 or 100 miles, and to watch every part of that
atmosphere would require a large number of stations, esti-
mated at something more than 10,000, scattered systemat-
ically over the whole face of the earth. If we piece to-
gether the several numbers above considered, taking 14 as
a fair average of the hourly number of meteors to be seen
by a single observer at all hours of the night, we shall find
for the total number of meteors encountered by the earth
in 24 hours, 14 X 5 X 10,000 x 24 = 16,800,000. Without
laying too much stress upon this particular number, we
may fairly say that the meteors picked up by the earth
every day are to be reckoned by millions, and since they
come at all seasons of the year, we shall have to admit that
the region through which the earth moves, instead of being
empty space, is really a dust cloud, each individual particle
of dust being a prospective meteor.

On the average these individual particles are very small
18

266 ASTRONOMY

and very far apart ; a cloud of silver dimes each about 250
miles from its nearest neighbor is perhaps a fair representa-
tion of their average mass and distance from each other,
but, of course, great variations are to be expected both in the
size and in the frequency of the particles. There must be
great numbers of them that are too small to make shooting
stars visible to the naked eye, and such are occasionally
seen darting by chance across the field of view of a tele-
scope.

168. The zodiacal light is an effect probably due to the
reflection of sunlight from the myriads of these tiny meteors
which occupy the space inside the earth's orbit. It is a
faint and diffuse stream of light, something like the Milky
Way, which may be seen in the early evening or morning
stretching up from the sunrise or sunset point of the
horizon along the ecliptic and following its course for
many degrees, possibly around the entire circumference of
the sky. It may be seen at any season of the year, although
it shows to the best advantage in spring evenings and
autumn mornings. Look for it.

169. Great meteors. — But there are other meteors, veri-
table fireballs in appearance, far more conspicuous and im-
posing than the ordinary shooting star. Such a one ex-
ploded over the city of Madrid, Spain, on the morning of
February 10, 1896, giving in broad sunlight " a brilliant
flash which was followed ninety seconds later by a succes-
sion of terrific noises like the discharge of a battery of
artillery." Fig. 110 shows a large meteor which was seen
in California in the early evening of July 27, 1894, and
which left behind it a luminous trail or cloud visible for
more than half an hour.

Not infrequently large meteors are found traveling
together, two or three or more in company, making their
appearance simultaneously as did the California meteor of
October 22, 1896, which is described as triple, the trio fol-
lowing one another like a train of cars, and Arago cites an

COMETS AND METEORS

26T

instance, from the year 1830, where within a short space of
time some forty brilliant meteors crossed the sky, all mov-
ing in the same direction with a whistling noise and dis-
playing in their flight all the colors of the rainbow.

The mass of great meteors such as these must be meas-
ured in hundreds if not thousands of pounds, and stories
are current, although not
very well authenticated, of
even larger ones, many tons
in weight, having been found
partially buried in the ground.
Of meteors which have been
actually seen to fall from the
sky, the largest single frag-
ment recovered weighs about
500 pounds, but it is only a
fragment of the original me-
teor, which must have been
much more massive before it
was broken up by collision
with the atmosphere.

170. The velocity of me-
teors.— Every meteor, big or
little, is subject to the law of
gravitation, and before it en-
counters the earth must be
moving in some kind of orbit
having the sun at its focus,
the particular species of orbit — ellipse, parabola, hyperbola
— depending upon the velocity and direction of its motion.
Xow, the direction in which a meteor is moving can be
determined without serious difficulty from observations of
its apparent path across the sky made by two or more ob-
servers, but the velocity can not be so readily found, since
the meteors go too fast for any ordinary process of timing.
But by photographing one of them two or three times on

FIG. 111.— The California meteor of
July 27, 1894.

268 ASTRONOMY

the same plate, with an interval of only a tenth of a second
between exposures, Dr. Elkin has succeeded in showing, in
a few cases, that their velocities varied from 20 to 25 miles
per second, and must have been considerably greater than
this before the meteors encountered the earth's atmosphere.
This is a greater velocity than that of the earth in its orbit,
19 miles per second, as might have been anticipated, since
the mere fact that meteors can be seen at all in the evening
hours shows that some of them at least must travel consid-
erably faster than the earth, for, counting in the direction
of the earth's motion, the region of sunset and evening is
always on the rear side of the earth, and meteors in order
to strike this region must overtake it by their swifter
motion. We have here, in fact, the reason why meteors
are especially abundant in the morning hours ; at this time
the observer is on the front side of the earth which catches
swift and slow meteors alike, while the rear is pelted only
by the swifter ones which follow it.

A comparison of the relative number of morning and
evening meteors makes it probable that the average meteor
moves, relative to the sun, with a velocity of about 26 miles
per second, which is very approximately the average velocity
of comets when they are at the earth's distance from the
sun. Astronomers, therefore, consider meteors as well as
comets to have the parabola and the elongated ellipse as
their characteristic orbits.

171. Meteor showers— The radiant. — There is evident
among meteors a distinct tendency for individuals, to the
number of hundreds or even hundreds of millions, to
travel together in flocks or swarms, all going the same way
in orbits almost exactly alike. This gregarious tendency is
made manifest not only by the fact that from time to time
there are unusually abundant meteoric displays, but also
by a striking peculiarity of their behavior at such times.
The meteors all seem to come from a particular part of the
heavens, as if here were a hole in the sky through which

COMETS AND METEORS 269

they were introduced, and from which they flow away in
every direction, even those which do not visibly start from
this place having paths among the stars which, if prolong-
ing backward, would pass through it. The cause of this
appearance may be understood from Fig. 112, which repre-^

FIG. 112. — Explanation of the radiant of a meteoric shower. — DENNING.

sents a group of meteors moving together along parallel
paths toward an observer at D. Traveling unseen above
the earth until they encounter the upper strata of its at-
mosphere, they here become incandescent and speed on in
parallel paths, -?, #, 3, ^, 5, 0, which, as seen by the observer,
are projected back against the sky into luminous streaks
that, as is shown by the arrowheads, #, c, d, all seem to
radiate from the point a — i. e., from the point in the sky
whose direction from the observer is parallel to the paths
of the meteors.

Such a display is called a meteor shower, and the point
a is called its radiant. Note how those meteors which
appear near the radiant all have short paths, while those
remote from it in the sky have longer ones. Query : As
the night wears on and the stars shift toward the west, will

270

ASTKONOMY

the radiant share in their motion or will it be left behind ?
Would the luminous part of the path of any of these me-
teors pass across the radiant from one side to the other ?
Is such a crossing of the radiant possible under any circum-
stances ? Fig. 113 shows how the meteor paths are grouped
around the radiant of a strongly marked shower. Select
from it the meteors which do not belong to this shower.

FIG. 113. — The radiant of a meteoric shower, showing also the paths of three meteors
which do not belong to this shower.— DENNING.

Many hundreds of these radiants have been observed in
the sky, each of which represents an orbit along which a
group of meteors moves, and the relation of one of these

COMETS AND METEOBS 271

orbits to that of the earth is shown in Fig. 114. The orbit
of the meteors is an ellipse extending out beyond the orbit
of Uranus, but so eccentric that a part of it comes inside
the orbit of the earth, and the figure shows only that part
of it which lies nearest the sun. The Eoman numerals

Fia. 114.— The orbits of the earth and the November meteors.

which are placed along the earth's orbit show the position
of the earth at the beginning of the tenth month, eleventh
month, etc. The meteors flow along their orbit in a long
procession, whose direction of motion is indicated by the
arrow heads, and the earth, coming in the opposite direc-
tion, plunges into this stream and receives the meteor
shower when it reaches the intersection of the two orbits.
The long arrow at the left of the figure represents the
direction of motion of another meteor shower which
encounters the earth at this point.

Can you determine from the figure answers to the fol-
lowing questions ? On what day of the year will the earth
meet each of these showers? Will the radiant points of
the showers lie above or below the plane of the earth's

272 ASTRONOMY

orbit ? Will these meteors strike the front or the rear of
the earth ? Can they be seen in the evening hours ?

From many of the radiants year after year, upon the
same day or week in each year, there comes a swarm of
shooting stars, showing that there must be a continuous
procession of meteors moving along this orbit, so that some
are always ready to strike the earth whenever it reaches
the intersection of its orbit with theirs. Such is the expla-
nation of the shower which appears each year in the first
half of August, and whose meteors are sometimes called
Perseids, because their radiant lies in the constellation
Perseus, and a similar explanation holds for all the star
showers which are repeated year after year.

172. The Leonids. — There is, however, a kind of star
shower, of which the Leonids (radiant in Leo) is the most
conspicuous type, in which the shower, although repeated
from year to year, is much more striking in some years
than in others. Thus, to quote from the historian : " In
1833 the shower was well observed along the whole eastern
coast of North America from the Gulf of Mexico to Hali-
fax. The meteors were most numerous at about 5 A. M. on
November 13th, and the rising sun could not blot out all
traces of the phenomena, for large meteors were seen now and
then in full daylight. Within the scope that the eye could
contain, more than twenty could be seen at a time shooting
in every direction. Not a cloud obscured the broad expanse,
and millions of meteors sped their way across in every
point of the compass. Their coruscations were bright,
gleaming, and incessant, and they fell thick as the flakes in
the early snows of December." But, so far as is known, none
of them reached the ground. An illiterate man on the fol-
lowing day remarked : " The stars continued to fall until
none were left. I am anxious to see how the heavens will
appear this evening, for I believe we shall see no more stars."

An eyewitness in the Southern States thus describes
the effect of this shower upon the plantation negroes :

COMETS AND METEORS 2Y3

" Upward of a hundred lay prostrate upon the ground,
some speechless and some with the bitterest cries, but with
their hands upraised, imploring God to save the world and
them. The scene was truly awful, for never did rain fall
much thicker than the meteors fell toward the earth — east,
west, north, and south it was the same." In the preceding
year a similar but feebler shower from the same radiant
created much alarm in France, and through the old historic
records its repetitions may be traced back at intervals of 33
or 34 years, although with many interruptions, to October
12, 902, 0. S., when " an immense number of falling stars
were seen to spread themselves over the face of the sky
like rain."

Such a star shower differs from the one repeated every
year chiefly in the fact that its meteors, instead of being
drawn out into a long procession, are mainly clustered in a
single flock which may be long enough to require two or
three or four years to pass a given point of its orbit, but
which is far from extending entirely around it, so that me-
teors from this source are abundant only in those years in
which the flock is at or near the intersection of its orbit
with that of the earth. The fact that the Leonid shower is
repeated at intervals of 33 or 34 years (it appeared in 1799,
1832-'33, 1866-'67) shows that this is the " periodic time "
in its orbit, which latter must of course be an ellipse, and
presumably a long and narrow one. It is this orbit which
is shown in Fig. 114, and the student should note in this
figure that if the meteor stream at the point where it cuts
through the plane of the earth's orbit were either nearer to
or farther from the sun than is the earth there could be no
shower ; the earth and the meteors would pass by without a
collision. Now, the meteors in their motion are subject to
perturbations, particularly by the large planets Jupiter,
Saturn, and Uranus, which slightly change the meteor orbit,
and it seems certain that the changes thus produced will
sometimes thrust the swarm inside or outside the orbit of

274 ASTRONOMY

the earth, and thus cause a failure of the shower at times
when it is expected. The meteors were due at the crossing
of the orbits in November, 1899 and 1900, and, although a
few were then seen, the shower was far from being a bril-
liant one, and its failure was doubtless caused by the outer
planets, which switched the meteors aside from the path in
which they had been moving for a century. Whether they
will be again switched back so as to produce future showers
is at the present time uncertain.

173. Capture of the Leonids.— But a far more striking
effect of perturbations is to be found in Fig. 115, which
shows the relation of the Leonid orbit to those of the prin-
cipal planets, and illustrates a curious chapter in the his-
tory of the meteor swarm that has been worked out by
mathematical analysis, and is probably a pretty good ac-
count of what actually befell them. Early in the second
century of the Christian era this flock of meteors came
down toward the sun from outer space, moving along a
parabolic orbit which would have carried it just inside the
orbit of Jupiter, and then have sent it off to return no
more. But such was not to be its fate. As it approached
the orbit of Uranus, in the year 126 A. D., that planet
chanced to be very near at hand and perturbed the motion
of the meteors to such an extent that the character of their
orbit was completely changed into the ellipse shown in the
figure, and in this new orbit they have moved from that
time to this, permanent instead of transient members of
the solar system. The perturbations, however, did not end
with the year in which the meteors were captured and an-
nexed to the solar system, but ever since that time Jupiter,
Saturn, and Uranus have been pulling together upon the
orbit, and have gradually turned it around into its present
position as shown in the figure, and it is chiefly this shift-
ing of the orbit's position in the thousand years that have
elapsed since 902 A. D. that makes the meteor shower now
come in November instead of in October as it did then.

276 ASTRONOMY

174. Breaking up a meteor swarm,— How closely packed
together these meteors were at the time of their annexation
to the solar system is unknown, but it is certain that ever
since that time the sun has been exerting upon them a
tidal influence tending to break up the swarm and distribute
its particles around the orbit, as the Perseids are distrib-
uted, and, given sufficient time, it will accomplish this, but
up to the present the work is only partly done. A certain
number of the meteors have gained so much over the slower
moving ones as to have made an extra circuit of the orbit
and overtaken the rear of the procession, so that there is a
thin stream of them extending entirely around the orbit
and furnishing in every November a Leonid shower; but by
far the larger part of the meteors still cling together, al-
though drawn out into a stream or ribbon, which, though
very thin, is so long that it takes some three years to pass
through the perihelion of its orbit. It is only when the
earth plunges through this ribbon, as it should in 1899,
1900, 1901, that brilliant Leonid showers can be expected.

175. Relation of comets and meteors. — It appears from
the foregoing that meteors and comets move in similar or-
bits, and we have now to push the analogy a little further
and note that in some, instances at least they move in iden-
tically the same orbit, or at least in orbits so like that an
appreciable difference between them is hardly to be found.
Thus a comet which was discovered and observed early in
the year 1866, moves in the same orbit with the Leonid
meteors, passing its perihelion about ten months ahead of
the main body of the meteors. If it were set back in its
orbit by ten months' motion, it would be a part of the meteor
swarm. Similarly, the Perseid meteors have a comet moving
in their orbit actually immersed in the stream of meteor
particles, and several other of the more conspicuous star
showers have comets attending them.

Perhaps the most remarkable case of this character is
that of a shower which comes in the latter part of Govern-

COMETS AND METEORS 27Y

ber from the constellation Andromeda, and which from its
association with the comet called Biela (after the name of
its discoverer) is frequently referred to as the Bielid shower.
This comet, an inconspicuous one moving in an unusually
small elliptical orbit, had been observed at various times
from 1772 down to 1846 without presenting anything re-
markable in its appearance; but about the beginning of the
latter year, with very little warning, it broke in two, and
for three months the pieces were watched by astronomers
moving off, side by side, something more than half as far
apart as are the earth and moon. It disappeared, made the
circuit of its orbit, and six years later came back, with the
fragments nearly ten times as far apart as before, and after
a short stay near the earth once more disappeared in the dis-
tance, never to be seen again, although the fragments should
have returned to perihelion at least half a dozen times since
then. In one respect the orbit of the comet was remark-
able : it passed through the place in which the earth stands
on November 27th of each year, so that if the comet were at
that particular part of its orbit on any November 27th, a
collision between it and the earth would be inevitable. So
far as is known, no such collision with the comet has ever
occurred, but the Bielid meteors which are strung along
its orbit do encounter the earth on that date, in greater or
less abundance in different years, and are watched with
much interest by the astronomers who look upon them as
the final appearance of the debris of a worn-out comet.

176. Periodic comets, — The Biela comet is a specimen of
the type which astronomers call periodic comets — i. e.,
those which move in small ellipses and have correspond-
ingly short periodic times, so that they return frequently
and regularly to perihelion. The comets which accompany
the other meteor swarms — Leonids, Perseids, etc. — also be-
long to this class as do some 30 or 40 others which have
periodic times less than a century. As has been already
indicated, these deviations from the normal parabolic orbit

2Y8 ASTRONOMY

call for some special explanation, and the substance of that
explanation is contained in the account of the Leonid
meteors and their capture by Uranus. Any comet may be
thus captured by the attraction of a planet near which it
passes. It is only necessary that the perturbing action
of the planet should result in a diminution of the comet's
velocity, for we have already learned that it is this velocity
which determines the character of the orbit, and anything
less than the velocity appropriate to a parabola must pro-
duce an ellipse — i. e., a closed orbit around which the body
will revolve time after time in endless succession. We
note in Fig. 115 that when the Leonid swarm encountered
Uranus it passed in front of the planet and had its velocity
diminished and its orbit changed into an ellipse thereby.
It might have passed behind Uranus, it would have passed
behind had it come a little later, and the effect would then
have been just the opposite. Its velocity would have been
increased, its orbit changed to a hyperbola, and it would
have left the solar system more rapidly than it came into
it, thrust out instead of held in by the disturbing planet.
Of such cases we can expect no record to remain, but the
captured comet is its own witness to what has happened,
and bears imprinted upon its orbit the brand of the planet
which slowed down its motion. Thus in Fig. 115 the changed
orbit of the meteors has its aphelion (part remotest from
the sun) quite close to the orbit of Uranus, and one of its
nodes, y, the point in which it cuts through the plane of
the ecliptic from north to south side, is also very near to
the same orbit. It is these two marks, aphelion and node,
which by their position identify Uranus as the planet in-
strumental in capturing the meteor swarm, and the date of
the capture is found by working back with their respective
periodic times to an epoch at which planet and comet were
simultaneously near this node.

Jupiter, by reason of his great mass, is an especially effi-
cient capturer of comets, and Fig. 116 shows his group of

COMETS AND METEORS 279

captives, his family of comets as they are sometimes called.
The several orbits are marked with the names commonly
given to the comets. Frequently this is the name of their
discoverer, but often a different system is followed — e. g.,

FIG. 116.— Jupiter's family of comets.

the name 1886, IV, means the fourth comet to pass through
perihelion in the year 1886. The other great planets —
Saturn, Uranus, Neptune — have also their families of cap-
tured comets, and according to Schulhof, who does not
entirely agree with the common opinion about captured
comets, the earth has caught no less than nine of these
bodies.

1 77. Comet groups. — But there is another kind of comet
family, or comet group as it is called, which deserves some
notice, and which is best exemplified by the Great Comet of
1882 and its relatives. No less than four other comets are
known to be traveling in substantially the same orbit with

280 ASTRONOMY

this one, the group consisting of comets 1668, I ; 1843, I ;
1880, I ; 1882, II ; 1887, I. The orbit itself is not quite a
parabola, but a very elongated ellipse, whose major axis
and corresponding periodic time can not be very accu-
rately determined from the available data, but it certainly
extends far beyond the orbit of Neptune, and requires not
less than 500 years for the comet to complete a revolution
in it. It was for a time supposed that some one of the
recent comets of this group of five might be a return of
the comet of 1668 brought back ahead of time by unknown
perturbations. There is still a possibility of this, but it is
quite out of the question to suppose that the last four
members of the group are anything other than separate
and distinct comets moving in practically the same orbit.
This common orbit suggests a common origin for the
comets, but leaves us to conjecture how they became sep-
arated.

The observed orbits of these five comets present some
slight discordances among themselves, but if we suppose
each comet to move in the average of the observed paths it
is a simple matter to fix their several positions at the pres-
ent time. They have all receded from the sun nearly on
line toward the bright star Sirius, and were all of them, at
the beginning of the year 1900, standing nearly motionless
inside of a space not bigger than the sun and distant from
the sun about 150 radii of the earth's orbit. The great
rapidity with which they swept through that part of their
orbit near the sun (see § 162) is being compensated by
the present extreme slowness of their motions, so that
the comets of 1668 and 1882, whose passages through the
solar system were separated by an interval of more than
two centuries, now stand together near the aphelion of their
orbits, separated by a distance only 50 per cent greater than
the diameter of the moon's orbit, and they will continue
substantially in this position for some two or three centu-
ries to come.

COMETS AND METEORS 281

The slowness with which these bodies move when far
from the sun is strikingly illustrated by an equation of
celestial mechanics which for parabolic orbits takes the
place of Kepler's Third Law — viz. :

where T is the time, in years, required for the comet to
move from its perihelion to any remote part of the orbit,
whose distance from the sun is represented, in radii of the
earth's orbit, by r. If the comet of 1668 had moved in a
parabola instead of the ellipse supposed above, how many
years would have been required to reach its present dis-
tance from the sun ?

178. Relation of comets to the solar system. — The orbits
of these comets illustrate a tendency which is becoming
ever more strongly marked. Because comet orbits are
nearly parabolas, it used to be assumed that they were
exactly parabolic, and this carried with it the conclusion
that comets have their origin outside the solar system. It
may be so, and this view is in some degree supported by
the fact that these nearly parabolic orbits of both comets
and meteors are tipped at all possible angles to the plane
of the ecliptic instead of lying near it as do the orbits of
the planets ; and by the further fact that, unlike the planets,
the comets show no marked tendency to move around their
orbits in the direction in which the sun rotates upon his
axis. There is, in fact, the utmost confusion among them
in this respect, some going one way and some another.
The law of bhe solar system (gravitation) is impressed upon
their movements, but its order is not.

But as observations grow more numerous and more
precise, and comet orbits are determined with increasing
accuracy, there is a steady gain in the number of elliptic
orbits at the expense of the parabolic ones, and if comets
are of extraneous origin we must admit that a very con-
19

282 ASTRONOMY

siderable percentage of them have their velocities slowed
down within the solar system, perhaps not so much by the
attraction of the planets as by the resistance offered to their
motion by meteor particles and swarms along their paths.
A striking instance of what may befall a comet in this way
is shown in Fig. 117, where the tail of a comet appears

FIG. 117.— Brooks's comet, October 21, 1893.— BARNARD.

sadly distorted and broken by what is presumed to have
been a collision with a meteor swarm. A more famous case
of impeded motion is oifered by the comet which bears the
name of Encke. This has a periodic time less than that of
any other known comet, and at intervals of forty months
comes back to perihelion, each time moving in a little
smaller orbit than before, unquestionably on account of
some resistance which it has suffered.

179. The development of a comet, — "We saw in § 174
that the sun's action upon a meteor swarm tends to
break it up into a long stream, and the same tendency to

COMETS AND METEORS 283

break up is true of comets whose attenuated substance pre-
sents scant resistance to this force. According to the
mathematical analysis of Eoche, if the comet stood still
the sun's tidal force would tend first to draw it out on line
with the sun, just as the earth's tidal force pulled the-
moon out of shape (§ 42), and then it would cause the
lighter part of the comet's substance to flow away from
both ends of this long diameter. This destructive action
of the sun is not limited to comets and meteor streams,
for it tends to tear the earth and moon to pieces as well ;
but the densities and the resulting mutual attractions of
their parts are far too great to permit this to be accom-
plished.

As a curiosity of mathematical analysis we may note
that a spherical cloud of meteors, or dust particles weigh-
ing a gramme each, and placed at the earth's distance from
the sun, will be broken up and dissipated by the sun's tidal
action if the average distance between the particles exceeds
two yards. Now, the earth is far more dense than such a
cloud, whose extreme tenuity, however, suggests what we
have already learned of the small density of comets, and
prepares us in their case for an outflow of particles at both
ends of the diameter directed toward the sun. Some-
thing of this kind actually occurs, for the tail of a comet
streams out on the side opposite to the sun, and in general
points away from the sun, as is shown in Fig. 109, and the
envelopes and jets rise up toward the sun ; but an inspec-
tion of Fig. 106 will show that the tail and the envelope
are too unlike to be produced by one and the same set of
forces.

It was long ago suggested that the sun possibly exerts
upon a comet's substance a repelling force in addition to
the attracting force which we call gravity. We think nat-
urally in this connection of the repelling force which a
charge of electricity exerts upon a similar charge placed
on a neighboring body, and we note that if both sun and

284 ASTRONOMY

comet carried a considerable store of electricity upon their
surfaces this would furnish just such a repelling force as
seems indicated by the phenomena of comets' tails ; for the
force of gravity would operate between the substance of
sun and comet, and on the whole would be the controlling
force, while the electric charges would produce a repulsion,
relatively feeble for the big particles and strong for the
little ones, since an electric charge lies wholly on the sur-
face, while gravity permeates the whole mass of a body,
and the ratio of volume (gravity) to surface (electric
charge) increases rapidly with increasing size. The repel-
ling force would thrust back toward the comet those parti-
cles which flowed out toward the sun, while it would urge
forward those which flowed away from it, thus producing
the difference in appearance between tail and envelopes,
the latter being regarded from this standpoint as stunted
tails strongly curved backward. In recent years the Eus-
sian astronomer Bredichin has made a careful study of the
shape and positions of comets' tails and finds that they fit
with mathematical precision to the theories of electric
repulsion.

180. Comet tails. — According to Bredichin, a comet's
tail is formed by something like the following process : In
the head of the comet itself a certain part of its matter is
broken up into fine bits, single molecules perhaps, which,
as they no longer cling together, may be described as in
the condition of vapor. By the repellent action of both
sun and comet these molecules are cast out from the head
of the comet and stream away in the direction opposite to
the sun with different velocities, the heavy ones slowly and
the light ones faster, much as particles of smoke stream
away from a smokestack, making for the comet a tail
which like a trail of smoke is composed of constantly
changing particles. The result of this process is shown
in Fig. 118, where the positions of the comet in its orbit
on successive days are marked by the Roman numerals, and

COMETS AND METEORS

285

the broken lines represent the paths of molecules m1, m11,
mm, etc., expelled from it on their several dates and travel-
ing thereafter in
orbits determined
by the combined
effect of the sun's
attraction, the
sun's repulsion,
and the comet's
repulsion. The
comet's attrac-
tion (gravity) is
too small to be
taken into ac-
count. The line
drawn upward
from VI repre-
sents the posi-
tions of these
molecules on the
sixth day, and
shows that all of
them are arranged
in a tail pointing

nearly away from the sun. A similar construction for the
other dates gives the corresponding positions of the tail,
always pointing away from the sun.

Only the lightest kind of molecules — e. g., hydrogen —
could drift away from the comet so rapidly as is here shown.
The heavier ones, such as carbon and iron, would be re-
pelled as strongly by the electric forces, but they would be
more strongly pulled back by the gravitative forces, thus
producing a much slower separation between them and the
head of the comet. Construct a figure such as the above,
in which the molecules shall recede from the comet only
one eighth as fast as in Fig. 118, and note what a different

FIG. 118.— Formation of a comet's tail.

286 ASTRONOMY

position it gives to the comet's tail. Instead of pointing
directly away from the sun, it will be bent strongly to one
side, as is the large plume-shaped tail of the Donati comet
shown in Fig. 101. But observe that this comet has also a
nearly straight tail, like the theoretical one of Fig. 118.
We have here two distinct types of comet tails, and accord-
ing to Bredichin there is still another but unusual type,
even more strongly bent to one side of the line joining
comet and sun, and appearing quite short and stubby.
The existence of these three types, and their peculiarities
of shape and position, are all satisfactorily accounted for
by the supposition that they are made of different mate-
rials. The relative molecular weights of hydrogen, some of
the hydrocarbons, and iron, are such that tails composed
of these molecules would behave just as do the actual tails
observed and classified . into these three types. The spec-
troscope shows that these materials — hydrogen, hydrocar-
bons, and iron — are present in comets, and leaves little
room for doubt of the essential soundness of Bredichin's
theory.

181. Disintegration of comets. — We must regard the tail
as waste matter cast off from the comet's head, and although
the amount of this matter is very small, it must in some
measure diminish the comet's mass. This process is, of
course, most active at the time of perihelion passage, and
if the comet returns to perihelion time after time, as the
periodic ones which move in elliptic orbits must do, this
waste of material may become a serious matter, leading
ultimately to the comet's destruction. It is significant in
this connection that the periodic comets are all small and
inconspicuous, not one of them showing a tail of any con-
siderable dimensions, and it appears probable that they are
far advanced along the road which, in the case of Biela's
comet, led to its disintegration. Their fragments are in
part strewn through the solar system, making some small
fraction of its cloud of cosmic dust, and in part they have

COMETS AND METEORS 287

been carried away from the sun and scattered throughout
the universe along hyperbolic orbits impressed upon them
at the time they left the comet.

But it is not through the tail only that the disinte-
grating process is worked out. While Biela's comet is per-
haps the most striking instance in which the head has
broken up, it is by no means the only one. The Great
Comet of 1882 cast off a considerable number of fragments
which moved away as independent though small comets
and other more recent comets have been seen to do the
same. An even more striking phenomenon was the grad-
ual breaking up of the nucleus of the same comet, 1882,
II, into a half dozen nuclei arranged in line like beads
upon a string, and pointing along the axis of the tail. See
Fig. 119, which shows the series of changes observed in
the head of this comet.

182. Comets and the spectroscope. — The spectrum pre-
sented by comets was long a puzzle, and still retains some-
thing of that character, although much progress has been
made toward an understanding of it. In general it con-
sists of two quite distinct parts — first, a faint background
of continuous spectrum due to ordinary sunlight reflected
from the comet ; and, second, superposed upon this, three
bright bands like the carbon band shown at the middle of
Fig. 48, only not so sharply defined. These bands make a
discontinuous spectrum quite similar to that given off by
compounds of hydrogen and carbon, and of course indicate
that a part of the comet's light originates in the body
itself, which must therefore be incandescent, or at least
must contain some incandescent portions.

By heating hydrocarbons in our laboratories until they
become incandescent, something like the comet spectrum
may be artificially produced, but the best approximation
to it is obtained by passing a disruptive electrical dis-
charge through a tube in which fragments of meteors
have been placed. A flash of lightning is a disruptive

October 9, 1882.

November 21, 1882.

February 1, 1883. March 3, 1883.

FIG. 119.— The head of the Great Comet of 1882.— WINLOCK.

COMETS AND METEORS 289

electrical discharge upon a grand scale. Now, meteors
and electric phenomena have been independently brought
to our notice in connection with comets, and with this
suggestion it is easy to frame a general idea of the phys-
ical condition of these objects — for example, a cloud of
meteors of different sizes so loosely clustered that the
average density of the swarm is very low indeed ; the sev-
eral particles in motion relative to each other, as well as to
the sun, and disturbed in that motion by the sun's tidal
action. Each particle carries its own electric charge,
which may be of higher or lower tension than that of its
neighbor, and is ready to leap across the intervening gap
whenever two particles approach each other. To these
conditions add the inductive effect of the sun's electric
charge, which tends to produce a particular and artificial
distribution of electricity among the comet's particles, and
we may expect to find an endless succession of sparks, tiny
lightning flashes, springing from one particle to another,
most frequent and most vivid when the comet is near the
sun, but never strong enough to be separately visible.
Their number is, however, great enough to make the comet
in part self-luminous with three kinds of light — i. e., the three
bright bands of its spectrum, whose wave lengths show in
the comet the same elements and compounds of the ele-
ments— carbon, hydrogen, and oxygen — which chemical
analysis finds in the fallen meteor. It is not to be sup-
posed that these are the only chemical elements in the
comet, as they certainly are not the only ones in the me-
teor. They are the easy ones to detect under ordinary cir-
cumstances, but in special cases, like that of the Great
Comet of 1882, whose near approach to the sun rendered
its whole substance incandescent, the spectrum glows with
additional bright lines of sodium, iron, etc.

183. Collisions. — A question sometimes asked, What
would be the effect of a collision between the earth and a
comet ? finds its answer in the results reached in the pre-

290 ASTRONOMY

ceding sections. There would be a star shower, more or
less brilliant according to the number and size of the pieces
which made up the comet's head. If these were like the
remains of the Biela comet, the shower might even be a
very tame one ; but a collision with a great comet would
certainly produce a brilliant meteoric display if its head
came in contact with the earth. If the comet were built of
small pieces whose individual weights did not exceed a few
ounces or pounds, the earth's atmosphere would prove a
perfect shield against their attacks, reducing the pieces to
harmless dust before they could reach the ground, and
leaving the earth uninjured by the encounter, although the
comet might suffer sadly from it. But big stones in the
comet, meteors too massive to be consumed in their flight
through the air, might work a very different effect, and by
their bombardment play sad havoc with parts of the earth's
surface, although any such result as the wrecking of the
earth, or the destruction of all life upon it, does not seem
probable. The 40 meteors of § 169 may stand for a colli-
sion with a small comet. Consult the Bible (Joshua x, 11)
for an example of what might happen with a larger one.

CHAPTEE XIII

THE FIXED STARS

184. The constellations. — In the earlier chapters the stu-
dent has learned to distinguish between wandering stars
(planets) and those fixed luminaries which remain year after
year in the same constellation, shining for the most part
with unvarying brilliancy, and presenting the most perfect
known image of immutability. Homer and Job and pre-
historic man saw Orion and the Pleiades much as we see
them to-day, although the precession, by changing their
relation to the pole of the heavens, has altered their risings
and settings, and it may be that their luster has changed
in some degree as they grew old with the passing centuries.

The division of the sky into constellations dates back to
the most primitive times, long before the Christian era,
and the crooked and irregular boundaries of these con-
stellations as shown by the dotted lines in Fig. 120, such
as no modern astronomer would devise, are an inher-
itance from antiquity, confounded and made worse in its
descent to our day. The boundaries assigned to constella-
tions near the south pole are much more smooth and regu-
lar, since this part of the sky, invisible to the peoples from
whom we inherit, was not studied and mapped until more
modern times. The old traditions associated with each
constellation a figure, often drawn from classical mythol-
ogy, which was supposed to be suggested by the grouping
of the stars : thus Ursa Major is a great bear, stalking across
the sky, with the handle of the Dipper for his tail ; Leo is a
lion ; Cassiopeia, a lady in a chair ; Andromeda, a maiden

291

THE FIXED STARS 293

chained to a rock, etc. ; but for the most part the resem-
blances are far-fetched and quite too fanciful to be followed
by the ordinary eye.

185. The number of stars. — " As numerous as the stars
of heaven " is a familiar figure of speech for expressing the
idea of countless number, but as applied to the visible
stars of the sky the words convey quite a wrong impression,
for, under ordinary circumstances, in a clear sky every star
to be seen may be counted in the course of a few hours,
since they do not exceed 3,000 or 4,000, the exact number
depending upon atmospheric conditions and the keenness
of the individual eye. Test your own vision by counting
the stars of the Pleiades. Six are easily seen, and you may
possibly find as many as ten or twelve ; but however many
are seen, there will be a vague impression of more just be-
yond the limit of visibility, and doubtless this impression is
partly responsible for the popular exaggeration of the num-
ber of the stars. In fact, much more than half of what we
call starlight comes from stars which are separately too
small to be seen, but whose number is so great as to more
than make up for their individual faintness.

The Milky Way is just such a cloud of faint stars, and
the student who can obtain access to a small telescope, or
even an opera glass, should not fail to turn it toward the
Milky Way and see for himself how that vague stream of
light breaks up into shining points, each an independent
star. These faint stars, which are found in every part of
the sky as well as in the Milky Way, are usually called
telescopic, in recognition of the fact that they can be seen
only in the telescope, while the other brighter ones are
known as lucid stars.

186. Magnitudes, — The telescopic stars show among them-
selves an even greater range of brightness than do the lucid
ones, and the system of magnitudes (§ 9) has accordingly
been extended to include them, the faintest star visible in
the greatest telescope of the present time being of the six-

294 ASTRONOMY

teenth or seventeenth magnitude, while, as we have already
learned, stars on the dividing line between the telescopic and
the lucid ones are of the sixth magnitude. To compare the
amount of light received from the stars with that from the
planets, and particularly from the sun and moon, it has
been found necessary to prolong the scale of magnitudes
backward into the negative numbers, and we speak of the
sun as having a stellar magnitude represented by the num-
ber —26.5. The full moon's stellar magnitude is — 12, and
the planets range from — 3 (Venus) to -f- 8 (Neptune).
Even a very few of the stars are so bright that negative
magnitudes must be used to represent their true relation
to the fainter ones. Sirius, for example, the brightest of
the fixed stars, is of the — 1 magnitude, and such stars as
Arcturus and Vega are of the 0 magnitude.

The relation of these magnitudes to each other has been
so chosen that a star of any one magnitude is very approxi-
mately 2.5 times as bright as one of the next fainter mag-
nitude, and this ratio furnishes a convenient method of
comparing the amount of light received from different stars.
Thus the brightness of Venus is 2.5 X 2-5 times that of
Sirius. The full moon is (2.5)9 times as bright as Venus,
etc. ; only it should be observed that the number 2.5 is not
exactly the value of the light ratio between two consecutive
magnitudes. Strictly this ratio is the \/ 100 = 2.5119-f-,
so that to be entirely accurate we must say that a difference
of five magnitudes gives a hundredfold difference of bright-
ness. In mathematical symbols, if B represents the ratio of
brightness (quantity of light) of two stars whose magni-
tudes are m and n, then

B = (100) '"?L

How much brighter is an ordinary first-magnitude star,
such as Aldebaran or Spica, than a star just visible to the
naked eye ? How many of the faintest stars visible in a
great telescope would be required to make one star just

THE FIXED STARS 295

visible to the unaided eye ? How many full moons must
be put in the sky in order to give an illumination as bright
as daylight ? How large a part of the visible hemisphere
would they occupy ?

187. Classification by magnitudes. — The brightness of all
the lucid stars has been carefully measured with an instru-
ment (photometer) designed for that special purpose, and
the following table shows, according to the Harvard Pho-
tometry, the number of stars in the whole sky, from pole to
pole, which are brighter than the several magnitudes
named in the table :

The number of stars brighter than magnitude 1.0 is 11

2.0 " 39

" " " " 3.0 " 142

" " " «« " 4.0 " 463

" " " " " 5.0 " 1,483

6.0 " 4,326

It must not be inferred from this table that there are
in the whole sky only 4,326 stars visible to the naked eye.
The actual number is probably 50 or 60 per cent greater
than this, and the normal human eye sees stars as faint as
the magnitude 6.4 or 6.5, the discordance between this num-
ber and the previous statement, that the sixth magnitude is
the limit of the naked-eye vision, having been introduced
in the attempt to make precise and accurate a classification
into magnitudes which was at first only rough and approxi-
mate. This same striving after accuracy leads to the intro-
duction of fractional numbers to represent gradations of
brightness intermediate between whole magnitudes. Thus
of the 2,843 stars included between the fifth and sixth
magnitudes a certain proportion are said to be of the 5.1
magnitude, 5.2 magnitude, and so on to the 5.9 magnitude,
even hundredths of a magnitude being sometimes employed.

We have found the number of stars included between
the fifth and sixth magnitudes by subtracting from the
last number of the preceding table the number immedi-

296 ASTRONOMY

ately preceding it, and similarly we may find the number
included between each other pair of consecutive magni-
tudes, as follows :

Magnitude 01234 5 6

Number of stars. ... 11 28 103 321 1,020 2,843
4 x 3m 12 36 108 324 972 2,916

In the last line each number after the first is found by
multiplying the preceding one by 3, and the approximate
agreement of each such number with that printed above it
shows that on the whole, as far as the table goes, the fainter
stars are approximately three times as numerous as those
a magnitude brighter.

The magnitudes of the telescopic stars have not yet
been measured completely, and their exact number is un-
known ; but if we apply our principle of a threefold increase
for each successive magnitude, we shall find for the fainter
stars — those of the tenth and twelfth magnitudes — prodi-
gious numbers which run up into the millions, and even these
are probably too small, since down to the ninth or tenth
magnitude it is certain that the number of the telescopic
stars increases from magnitude to magnitude in more than
a threefold ratio. This is balanced in some degree by the
less rapid increase which is known to exist in magnitudes
still fainter ; and applying our formula without regard to
these variations in the rate of increase, we obtain as a rude
approximation to the total number of stars down to the
fifteenth magnitude, 86,000,000. The Herschels, father
and son, actually counted the number of stars visible in
nearly 8,000 sample regions of the sky, and, inferring the
character of the whole sky from these samples, we find it
to contain 58,500,000 stars ; but the magnitude of the faint-
est star visible in their telescope, and included in their
count, is rather uncertain.

How many first-magnitude stars would be needed to
give as much light as do the 2,843 stars of magnitude 5.0

THE FIXED STARS 297

to 6.0 ? How many tenth-magnitude stars are required to
give the same amount of light ?

To the modern man it seems natural to ascribe the dif-
ferent brilliancies of the stars to their different distances
from us ; but such was not the case 2,000 years ago, when
each fixed star was commonly thought to be fastened to
a " crystal sphere," which carried them with it, all at the
same distance from us, as it turned about the earth. In
breaking away from this erroneous idea and learning to
think of the sky itself as only an atmospheric illusion
through which we look to stars at very different distances
beyond, it was easy to fall into the opposite error and to
think of the stars as being much alike one with another,
and, like pebbles on the beach, scattered throughout space
with some rough degree of uniformity, so that in every
direction there should be found in equal measure stars
near at hand and stars far off, each shining with a luster
proportioned to its remoteness.

188. Distances of the stars, — Now, in order to separate
the true from the false in this last mode of thinking about
the stars, we need some knowledge of their real distances
from the earth, and in seeking it we encounter what is
perhaps the most delicate and difficult problem in the
whole range of observational astronomy. As shown in
Fig. 121, the principles involved in determining these dis-
tances are not fundamentally different from those em-
ployed in determining the moon's distance from the earth.
Thus, the ellipse at the left of the figure represents the
earth's orbit and the position of the earth at different
times of the year. The direction of the star A at these
several times is shown by lines drawn through A and pro-
longed to the background apparently furnished by the sky.
A similar construction is made for the star B, and it is
readily seen that owing to the changing position of the
observer as he moves around the earth's orbit, both A and
B will appear to move upon the background in orbits
20

298 ASTRONOMY

shaped like that of the earth as seen from the star, but
having their size dependent upon the star's distance, the
apparent orbit of A being larger than that of B, because A
is nearer the earth. By measuring the angular distance

July

FIG. 121.— Determining a star's parallax.

between A and B at opposite seasons of the year (e. g., the
angles A — Jan. — B, and A — July — B) the astronomer
determines from the change in this angle how much larger
is the one path than the other, and thus concludes how
much nearer is A than B. Strictly, the difference between
the January and July angles is equal to the difference be-
tween the angles subtended at A and B by the diameter of
the earth's orbit, and if B were so far away that the angle
Jan. — B — July were nothing at all we should get imme-
diately from the observations the angle Jan. — A — July,
which would suffice to determine the stars' distance. Sup-
posing the diameter of the earth's orbit and the angle at A
to be known, can you make a graphical construction that
will determine the distance of A from the earth ?

The angle subtended at A by the radius of the earth's
orbit — i. e., -J- (Jan. — A — July) — is called the star's paral-
lax, and this is commonly used by astronomers as a meas-
ure of the star's distance instead of expressing it in linear
units such as miles or radii of the earth's orbit. The dis-

THE FIXED STARS 299

tance of a star is equal to the radius of the earth's orbit
divided by the parallax, in seconds of arc, and multiplied
by the number 206265.

A weak point of this method of measuring stellar dis-
tances is that it always gives what is called a relative paral-
lax— i. e., the difference between the parallaxes of A and
B ; and while it is customary to select for B a star or stars
supposed to be much farther off than A, it may happen,
and sometimes does happen, that these comparison stars
as they are called are as near or nearer than A, and give
a negative parallax — i. e., the difference between the angles
at A and B proves to be negative, as it must whenever the
star B is nearer than A.

The first really successful determinations of stellar
parallax were made by Struve and Bessel a little prior to
1840, and since that time the distances of perhaps 100 stars
have been measured with some degree of reliability, al-
though the parallaxes themselves are so small — never as
great as 1" — that it is extremely difficult to avoid falling
into error, since even for the nearest star the problem of
its distance is equivalent to finding the distance of an ob-
ject more than 5 miles away by looking at it first with one
eye and then with the other. Too short a base line.

189. The sun and his neighbors. — The distances of the
sun's nearer neighbors among the stars are shown in Fig.
123, where the two circles having the sun at their center
represent distances from it equal respectively to 1,000,000
and 2,000,000 times the distance between earth and sun.
In the figure the direction of each star from the sun cor-
responds to its right ascension, as shown by the Eoman
numerals about the outer circle ; the true direction of the
star from the sun can not, of course, be shown upon the
flat surface of the paper, but it may be found by elevat-
ing or depressing the star from the surface of the paper
through an angle, as seen from the sun, equal to its declina-
tion, as shown in the fifth column of the following table,

300

ASTRONOMY

The Surfs Nearest Neighbors

No.

STAR.

Magni-
tude.

R. A.

Dec.

Parallax.

Distance.

1

a Centauri .

0.7

14. 5h.

—60°

0 75"-

0.27

9

LI. 21,185

6.8

11.0

+ 37

0.45

0 46

8

61 Cve-ni

5 0

21 0

+ 38

0 40

0 51

4

ft Herculis . .

3.6

16.7

+ 39

0.40

0.51

5

Sirius

—1.4

6.7

— 17

0.37

0.56

6

2 2 398

8.2

18.7

+ 59

0.35

0 58

7

Procyon

—0.5

7.6

+ 5

0.34

0.60

8

•y Draconis

4.8

17 5

+ 55

0.30

0.68

q

Gr 34

7.9

0.2

+43

0 29

0 71

10

Lac 9 352 ....

7.5

23.0

—36

0 28

0.74

11
12
18

ff Draconis
A. 0. 17,415-6 ....
i\ Cassiopeias

4.8
9.0
3.4

19.5
17.6
0.7

+ 69

+ 68

+ 57

0.25
0.25
0.25

0.82
0.82
0.82

14

Altair

1 0

19 8

+ 9

0 21

0.97

15

€ Indi

5.2

21.9

—57

0.20

1.03

16

Gr. 1,618

6.7

10.1

+ 50

0.20

1.03

17
18

10 Ursae Majoris. .
Castor

4.2

1.5

8.9

7.5

+ 42
+ 32

0.20
0.20

1.03
1.03

19

LI. 21,258

8.5

11.0

+ 44

0.20

1.03

90

o^ Eridani

4.5

4.2

— 8

0.19

1.08

21

A 0 11 677

9 0

11 2

+ 66

0.19

1.08

22
23
94

LI. 18,115
B. D. 36°, 3,883 . . .
Gr. 1,618

8.0
7.1
6.5

9.1
20.0
10.1

+ 53
+ 36
+ 50

0.18
0.18
0.17

1.14
1.14
1.21

9,5

ft Cassiopeias

2.3

0.1

+ 59

0.16

1.28

96

70 Ophiuchi

4.4

18.0

+ 2

0.16

1.28

27
98

21,516
Gr 1 830

6.5
6.6

11.2
11.8

+ 74
+ 39

0.15
0.15

1.38
1.38

99

fi Cassiopeia)

5.4

1.0

+ 54

0.14

1.47

30

e Eridani

4.4

3.5

-10

0.14

1.47

31
32

t Qrsae Majoris
ft Hydri

3.2
2.9

8.9
0.3

+ 48

-78

0.13
0.13

1.58
1.58

33

Fomalhaut

1.0

22.9

-30

0.13

1.58

34
35

Br. 3,077
e Cvffni . .

6.0
2.5

23.1

20.8

+ 57
+ 33

0.13
0.12

1.58
1.71

36

ft Comae

4.5

13.1

+ 28

0.11

1.87

37

dp AurigaB

8.8

6.6

+ 44

0.11

1.87

38

if Herculis

3.3

17.2

+ 37

0.11

1.87

39

Aldebaran

1.1

4.5

+ 16

0.10

2.06

40

Capella

0.1

5.1

+ 46

0.10

2.06

41
49

B. D. 35°, 4,003 . . .
Gr. 1 646

9.2
6.3

20.1
10.3

+ 35

+ 49

0.10
0.10

2.06
2.06

43

y Cysrni. .

2.3

20.3

+ 40

0.10

2.06

44

Regulus

1.2

10.0

+ 12

0.10

2.06

45

Vega

0.2

18.6

+ 39

0.10

2.06

THE FIXED STARS

301

in which the numbers in the first column are those placed
adjacent to the stars in the diagram to identify them.

190. Light years.— The radius of the inner circle in Fig.
122, 1,000,000 times the earth's distance from the sun, is a
convenient unit in which to express the stellar distances,

XII

XIII

XVIII

XIX

FIG. 122.— Stellar neighbors of the sun.

and in the preceding table the distances of the stars from
the sun are expressed in terms of this unit. To express
them in miles the numbers in the table must be multi-
plied by 93,000,000,000,000. The nearest star, a Centauri,
is 25,000,000,000,000 miles away. But there is another
unit in more common use — i. e., the distance traveled over

302 ASTRONOMY

by light in the period of one year. We have already found
(§ 141) that it requires light 8m. 18s. to come from the sun
to the earth, and it is a simple matter to find from this
datum that in a year light moves over a space equal to
63,368 radii of the earth's orbit. This distance is called a
light year, and the distance of the same star, a Centauri,
expressed in terms of this unit, is 4.26 years — i. e., it takes
light that long to come from the star to the earth.

In Fig. 122 the stellar magnitudes of the stars are indi-
cated by the size of the dots — the bigger the dot the brighter
the star — and a mere inspection of the figure will serve to
show that within a radius of 30 light years from the sun
bright stars and faint ones are mixed up together, and that,
so far as distance is concerned, the sun is only a member
of this swarm of stars, whose distances apart, each from its
nearest neighbor, are of the same order of magnitude as
those which separate the sun from the three or four stars
nearest it.

Fig. 122 is not to be supposed complete. Doubtless
other stars will be found whose distance from the sun is less
than 2,000,000 radii of the earth's orbit, but it is not prob-
able that they will ever suffice to more than double or per-
haps treble the number here shown. The vast majority of
the stars lie far beyond the limits of the figure.

191. Proper motions. — It is evident that these stars are too
far apart for their mutual attractions to have much influ-
ence one upon another, and that we have here a case in which,
according to § 34, each star is free to keep unchanged its
state of rest or motion with unvarying velocity along a
straight line. Their very name, fixed stars, implies that
they are at rest, and so astronomers long believed. Hippar-
chus (125 B. c.) and Ptolemy (130 A. D.) observed and re-
corded many allineations among the stars, in order to give
to future generations a means of settling this very question
of a possible motion of the stars and a resulting change in
their relative positions upon the sky. For example, they

THE FIXED STARS 303

found at the beginning of the Christian era that the four
stars, Capella, e Persei, a and (3 Arietis, stood in a straight
line — i. e., upon a great circle of the sky. Verify this by
direct reference to the sky, and see how nearly these stars
have kept the same position for nearly twenty centuries.
Three of them may be identified from the star maps, and the
fourth, e Persei, is a third-magnitude star between Capella
and the other two.

Other allineations given by Ptolemy are : Spica, Arc-
turus and ft Bootis ; Spica, 8 Corvi and y Corvi ; a Librse,
Arcturus and £ Ursas Majoris. Arcturus does not now fit
very well to these alignments, and nearly two centuries
ago it, together with Aldebaran and Sirius, was on other
grounds suspected to have changed its place in the sky
since the days of Ptolemy. This discovery, long since
fully confirmed, gave a great impetus to observing with all
possible accuracy the right ascensions and declinations of the
stars, with a view to finding other cases of what was called
proper motion — i. e., a motion peculiar to the individual
star as contrasted with the change of right ascension and
declination produced for all stars by the precession.

Since the middle of the eighteenth century there have
been made many thousands of observations of this kind,
whose results have gone into star charts and star cata-
logues, and which are now being supplemented by a photo-
graphic survey of the sky that is intended to record per-
manently upon photographic plates the position and mag-
nitude of every star in the heavens down to the fourteenth
magnitude, with a view to ultimately determining all their
proper motions.

The complete achievement of this result is, of course, a
thing of the remote future, but sufficient progress in deter-
mining these motions has been made during the past cen-
tury and a half to show that nearly every lucid star pos-
sesses some proper motion, although in most cases it is very
small, there being less than 100 known stars in which it

304 ASTRONOMY

amounts to so much as 1" per annum — i. e., a rate of mo-
tion across the sky which would require nearly the whole
Christian era to alter a star's direction from us by so much
as the moon's angular diameter. The most rapid known
proper motion is that of a telescopic star midway between
the equator and the south pole, which changes its position
at the rate of nearly 9" per annum, and the next greatest is
that of another telescopic star, in the northern sky, No. 28
of Fig. 122. It is not until we reach the tenth place in a
list of large proper motions that we find a bright lucid
star, No. 1 of Fig. 122. It is a significant fact that for the
most part the stars with large proper motions are precisely
the ones shown in Fig. 122, which is designed to show stars
near the earth. This connection between nearness and
rapidity of proper motions is indeed what we should expect
to find, since a given amount of real motion of the star
along its orbit will produce a larger angular displacement,
proper motion, the nearer the star is to the earth, and this
fact has guided astronomers in selecting the stars to be
observed for parallax, the proper motion being determined
first and the parallax afterward.

192. The paths of the stars. — We have already seen rea-
son for thinking that the orbit along which a star moves is
practically a straight line, and from a study of proper mo-
tions, particularly their directions across the sky, it appears
that these orbits point in all possible ways— north, south,
east, and west — so that some of them are doubtless directed
nearly toward or from the sun ; others are square to the
line joining sun and star; while the vast majority occupy
some position intermediate between these two. Now, our
relation to these real motions of the stars is well illus-
trated in Fig. 112, where the observer finds in some of the
shooting stars a tremendous proper motion across the sky,
but sees nothing of their rapid approach to him, while
others appear to stand motionless, although, in fact, they
are moving quite as rapidly as are their fellows. The fixed

THE FIXED STARS 305

star resembles the shooting star in this respect, that its
proper motion is only that part of its real motion which
lies at right angles to the line of sight, and this needs to
he supplemented by that other part of the motion which
lies parallel to the line of sight, in order to give us any
knowledge of the star's real orbit.

193. Motion in the line of sight. — It is only within the
last 25 years that anything whatever has been accomplished
in determining these stellar motions of approach or reces-
sion, but within that time much progress has been made by
applying the Doppler principle (§ 89) to the study of stel-
lar spectra, and at the present time nearly every great tele-
scope in the world is engaged upon work of this kind. The
shifting of the lines of the spectrum toward the violet or

4450 4500 4550

FIG. 123.— Motion of Polaris in the line of sight as determined by the spectroscope.

FBOST.

toward the red end of the spectrum indicates with cer-
tainty the approach or recession of the star, but this shift-
ing, which must be determined by comparing the star's
spectrum with that of some artificial light showing corre-
sponding lines, is so small in amount that its accurate meas-
urement is a matter or extreme difficulty, as may be seen
from Fig. 123. This cut shows along its central line a part
of the spectrum of Polaris, between wave lengths 4,450 and
4,600 tenth meters, while above and below are the corre-
sponding parts of the spectrum of an electric spark whose
light passed through the same spectroscope and was photo-
graphed upon the same plate with that of Polaris. This
comparison spectrum is, as it should be, a discontinuous or
bright-line one, while the spectrum of the star is a con-

306 ASTRONOMY

tinuous one, broken only by dark gaps or lines, many of
which have no corresponding lines in the comparison spec-
trum. But a certain number of lines in the two spectra
do correspond, save that the dark line is always pushed a
very little toward the direction of shorter wave lengths,

111 I I

FIG. 124.— Spectrum of /3 Aurigae.— PICKERING.

showing that this star is approaching the earth. This spec-
trum was photographed for the express purpose of deter-
mining the star's motion in the line of sight, and with it
there should be compared Figs. 124 and 125, which show
in the upper part of each a photograph obtained without
comparison spectra by allowing the star's light to pass
through some prisms placed just in front of the telescope.
The lower section of each figure shows an enlargement of
the original photograph, bringing out its details in a way
not visible to the unaided eye. In the enlarged spectrum
of /? Aurigas a rate of motion equal to that of the earth in
its orbit would be represented by a shifting of 0.03 of a
millimeter in the position of the broad, hazy lines.

Despite the difficulty of dealing with such small quanti-
ties as the above, very satisfactory results are now obtained,
and from them it is known that the velocities of stars in
the line of sight are of the same order of magnitude as the
velocities of the planets in their orbits, ranging all the way
from 0 to 60 miles per second — more than 200,000 miles per
hour — which latter velocity, according to Campbell, is the
rate at which ^ Cassiopeise is approaching the sun.

THE FIXED STARS 307

The student should not fail to note one important
difference between proper motions and the motions deter-
mined spectroscopically : the latter are given directly in
miles per second, or per hour, while the former are ex-
pressed in angular measure, seconds of arc, and there can
be no direct comparison between the two until by means
of the known distances of the stars their proper motions
are converted from angular into linear measure. We are
brought thus to the very heart of the matter ; parallax,
proper motion, and motion in the line of sight are inti-

; t lii 1 i i.HitllHil! Ill I 11 i II '

HI III I i i

:.

FIG. 125.— Spectrum of Pollux.— PICKERING.

mately related quantities, all of which are essential to a
knowledge of the real motions of the stars.

194. Star drift. — An illustration of how they may be
made to work together is furnished by some of the stars
—which make up the Great Dipper — /3, y, €, and £ Ursae Ma-
joris, whose proper motions have long been known to point
in nearly the same direction across the sky and to be nearly
equal in amount. More recently it has been found that
these stars are all moving toward the sun with approxi-
mately the same velocity — 18 miles per second. One other
star of the Dipper, 8 Ursae Majoris, shares in the common
proper motion, but its velocity in the line of sight has not
yet been determined with the spectroscope. These similar
motions make it probable that the stars are really traveling
together through space along parallel lines; and on the

308

ASTRONOMY

supposition that such is the case it is quite possible to
write out a set of equations which shall involve their
known proper motions and motions in the line of sight,
together with their unknown distances and the unknown
direction and velocity of their real motion along their
orbits. Solving these equations for the values of the un-
known quantities, it is found that the five stars probably
lie in a plane which is turned nearly edgewise toward us,
and that in this plane they are moving about twice as fast
as the earth moves around the sun, and are at a distance
from us represented by a parallax of less than 0.02" — i. e.,
six times as great as the outermost circle in Fig. 122. A
most extraordinary system of stars which, although sepa-
rated from each oth-
er by distances as
great as the whole
breadth of Fig. 122,
yet move along in
parallel paths which
it is difficult to re-
gard as the result
of chance, and for
which it is equally
difficult to frame an
explanation.

The stars a and
rj of the Great Dip-
per do not share
in this motion, and
must ultimately part
company with the
other five, to the
complete destruction

of the Dipper's shape. Fig. 126 illustrates this change of
shape, the upper part of the figure (a) showing these seven
stars as they were grouped at a remote epoch in the past,

FIG. 126.— The Great Dipper, past, present, and
future.

THE FIXED STARS 309

while the lower section (c) shows their position for an
equally remote epoch in the future. There is no resem-
blance to a dipper in either of these configurations, but it
should be observed that in each of them the stars a and 17
keep their relative position unaltered, and the other five
stars also keep /together, the entire change of appearance
being due to/the changing positions of these two groups
with respect to each other.

This phenomenon of groups of stars moving together is
called star drift, and quite a number of cases of it are
found in different parts of the sky. The Pleiades are per-
haps the most conspicuous one, for here some sixty or
more stars are found traveling together along similar paths.
Eepeated careful measurements of the relative positions of
stars in this cluster show that one of the lucid stars and
four or five of the telescopic ones do not share in this
motion, and therefore are not to be considered as members
of the group, but rather as isolated stars which, for a time,
chance to be nearly on line with the Pleiades, and prob-
ably farther off, since their proper motions are smaller.

To rightly appreciate the extreme slowness with which
proper motions alter the constellations, the student should
bear in mind that the changes shown in passing from one
section of Fig. 126 to the next represent the effect of the
present proper motions of the stars accumulated for a pe-
riod of 200,000 years. Will the stars continue to move in
straight paths for so long a time ?

195. The sun's way. — Another and even more interest-
ing application of proper motions and motions in the line
of sight is the determination from them of the sun's orbit
among the stars. The principle involved is simple enough.
If the sun moves with respect to the stars and carries the
earth and the other planets year after year into new regions
of space, our changing point of view must displace in some
measure every star in the sky save those which happen to
be exactly on the line of the sun's motion, and even these

310 ASTRONOMY

will show its effect by their apparent motion of approach
or recession along the line of sight. So far as their own
orbital motions are concerned, there is no reason to sup-
pose that more stars move north than south, or that more
go east than west ; and when we find in their proper mo-
tions a distinct tendency to radiate from a point some-
where near the bright star Vega and to converge toward
a point on the opposite side of the sky, we infer that this
does not come from any general drift of the stars in that
direction, but that it marks the course of the sun among
them. That it is moving along a straight line pointing
toward Vega, and that at least a part of the velocities
which the spectroscope shows in the line of sight, comes
from the motion of the sun and earth. Working along
these lines, Kapteyn finds that the sun is moving through
space with a velocity of 11 miles per second, which is de-
cidedly below the average rate of stellar motion — 19 miles
per second.

196. Distance of Sirian and solar stars, — By combining
this rate of motion of the sun with the average proper mo-
tions of the stars of different magnitudes, it is possible to
obtain some idea of the average distance from us of a first-
magnitude star or a sixth-magnitude star, which, while it
gives no information about the actual distance of any par-
ticular star, does show that on the whole the fainter stars
are more remote. But here a broad distinction must be
drawn. By far the larger part of the stars belong to one of
two well-marked classes, called respectively Sirian and solar
stars, which are readily distinguished from each other by
the kind of -spectrum they furnish. Thus ft Aurigse belongs
to the Sirian class, as does every other star which has a spec-
trum like that of Fig. 124, while Pollux is a solar star pre-
senting in Fig. 125 a spectrum like that of the sun, as do
the other stars of this class.

Two thirds of the sun's near neighbors, shown in Fig.
122, have spectra of the solar type, and in general stars of

THE FIXED STARS 311

this class are nearer to us than are the stars with spectra
unlike that of the sun. The average distance of a solar
star of the first magnitude is very approximately repre-
sented hy the outer circle in Fig. 122, 2,000,000 times the
distance of the sun from the earth ; while the correspond-
ing distance for a Sirian star of the first magnitude is rep-
resented by the number 4,600,000.

A third-magnitude star is on the average twice as far
away as one of the first magnitude, a fifth-magnitude star
four times as far off, etc., each additional two magnitudes
doubling the average distance of the stars, at least down to
the eighth magnitude and possibly farther, although be-
yond this limit we have no certain knowledge. Put in
another way, the naked eye sees many Sirian stars which
may have " gone out " and ceased to shine centuries ago,
for the light by which we now see them left those stars
before the discovery of America by Columbus. For the
student of mathematical tastes we note that the results of
Kapteyn's investigation of the mean distances (D) of the
stars of magnitude (m) may be put into two equations :

m

For Solar Stars, D = 23 X 2¥

m

For Sirian Stars, D = 52 X 2*

where the coefficients 23 and 52 are expressed in light
years. How long a time is required for light to come from
an average solar star of the sixth magnitude ?

197. Consequences of stellar distance. — The amount of
light which comes to us from any luminous body varies
inversely as the square of its distance, and since many of
the stars are changing their distance from us quite rapidly,
it must be that with the lapse of time they will grow
brighter or fainter by reason of this altered distance.
But the distances themselves are so great that the most
rapid known motion in the line of sight would require
more than 1,000 years (probably several thousand) to pro-
duce any perceptible change in brilliancy.

312 ASTRONOMY

The law in accordance with which this change of bril-
liancy takes place is that the distance must be increased or
diminished tenfold in order to produce a change of five
magnitudes in the brightness of the object, and we may
apply this law to determine the sun's rank among the stars.
If it were removed to the distance of an average first-, or
second-, or third-magnitude star, how would its light com-
pare with that of the stars ? The average distance of a
third-magnitude star of the solar type is, as we have seen
above, 4,000,000 times the sun's distance from the earth,
and since 4,000,000 = 106-6, we find that at this distance the
sun's stellar magnitude would be altered by 6.6 X 5 magni-
tudes, and would therefore be —26.5 + 33.0 = 6.5 — i. e., the
sun if removed to the average distance of the third-magni-
tude stars of its type would be reduced to the very limit
of naked-eye visibility. It must therefore be relatively
small and feeble as compared with the brightness of the
average star. It is only its close proximity to us which
makes the sun look brighter than the stars.

The fixed stars may have planets circling around them,
but an application of the same principles will show how
hopeless is the prospect of ever seeing them in a telescope.
If the sun's nearest neighbor, a Centauri, were attended by
a planet like Jupiter, this planet would furnish to us no
more light than does a star of the twenty-second magni-
tude— i. e., it would be absolutely invisible, and would re-
main invisible in the most powerful telescope yet built,
even though its bulk were increased to equal that of the
sun. Let the student make the computation leading to
this result, assuming the stellar magnitude of Jupiter to
be -1.7.

198. Double stars, — In the constellation Taurus, not far
from Aldebaran, is the fourth-magnitude star 6 Tauri,
which can readily be seen to consist of two stars close
together. The star a Capricorni is plainly double, and a
sharp eye can detect that one of the faint stars which with

THE FIXED STARS 313

Vega make a small equilateral triangle, is also a double
star. Look for them in the sky.

In the strict language of astronomy the term double
star would not be applied to the first two of these objects,
since it is usually restricted to those stars whose angular
distance from each other is so small that in the telescope
they appear much as do the stars named above to the naked
eye — i. e., their angular separation is measured by a few
seconds or fractions of a single second, instead of the six
minutes which separate the component stars of 0 Tauri or
a Capricorni. There are found in the sky many thousands
of these close double stars, of which some are only optic-
ally double — i. e., two stars nearly on line with the earth
but at very different distances from it— while more of them
are really what they seem, stars near each other, and in
many cases near enough to influence each other's motion.
These are called binary systems, and in cases of this kind
the principles of celestial mechanics set forth in Chapter
IV hold true, and we may expect to find each component
of a double star moving in a conic section of some kind,
having its focus at the common center of gravity of the
two stars. We are thus presented with problems of orbital
motion quite similar to those which occur in the solar sys-
tem, and careful telescopic observations are required year
after year to fix the relative positions of the two stars — i. e.,
their angular separation, which it is customary to call their
distance, and their direction one from the other, which is
called position angle.

199. Orbits of double stars. — The sun's nearest neighbor,
a Centauri, is such a double star, whose position angle and
distance have been measured by successive generations of
astronomers for more than a century, and Fig. 127 shows
the result of plotting their observations. Each black dot
that lies on or near the circumference of the long ellipse
stands for an observed direction and distance of the fainter
of the two stars from the brighter one, which is represented
21

314

ASTRONOMY

by the small circle at the intersection of the lines inside
the ellipse. It appears from the figure that during this

time the one star has
gone completely around
the other, as a planet
goes around the sun,
and the true orbit must
therefore be an ellipse
having one of its foci
at the center of gravity
of the two stars. The
other star moves in an
ellipse of precisely simi-
lar shape, but probably
smaller size, since the
dimensions of the two
FIG. is?.— The orbit of a Centauri.— SEE. orbits are inversely pro-

portional to the masses

of the two bodies, but it is customary to neglect this motion
of the larger star and to give to the smaller one an orbit
whose diameter is equal to the sum of the diameters of the
two real orbits. This practice, which has been followed in
Fig. 127, gives correctly the relative positions of the two
stars, and makes one orbit do the work of two.

In Fig. 127 the bright star does not fall anywhere near
the focus of the ellipse marked out by the smaller one, and
from this we infer that the figure does not show the true
shape of the orbit, which is certainly distorted, foreshort-
ened, by the fact that we look obliquely down upon its
plane. It is possible, however, by mathematical analysis,
to find just how much and in what direction that plane
should be turned in order to bring the focus of the
ellipse up to the position of the principal star, and thus
give the true shape and size of the orbit. See Fig. 128
for a case in which the true orbit is turned exactly edge-
wise toward the earth, and the small star, which really

THE FIXED STABS

315

moves in an ellipse like that shown in the figure, appears
to oscillate to and fro along a straight line drawn through
the principal star, as shown at the left of the figure.

In the case of a
Centauri the true orbit
proves to have a major
axis 47 times, and a
minor axis 40 times,
as great as the distance
of the earth from the
sun. The orbit, in
fact, is intermediate
in size between the
orbits of Uranus and
Xeptune, and the pe-
riodic time of the star
in this orbit is 81
years, a little less than
the period of Uranus.

200. Masses of double stars. — If we apply to this orbit
Kepler's Third Law in the form given it at page 179, we
shall find—

FIG. 128. — Apparent orbit and real orbit of the
double star 42 Comse Berenicis. — SEE.

where M and m represent the masses of the two stars. We
have already seen that &, the gravitation constant, is equal
to 1 when the masses are measured in terms of the sun's
mass taken as unity, and when T and a are expressed in
years and radii of the earth's orbit respectively, and with
this value of Ic we may readily find from the above equa-
tion, M-\-m = 2.5 — i. e., the combined mass of the two com-
ponents of a Centauri is equal to rather more than twice
the mass of the sun. It is not every double star to which
this process of weighing can be applied. The major axis
of the orbit, #, is found from the observations in angular
measure, 35" in this case, and it is only when the parallax

316

ASTRONOMY

of the star is known that this can be converted into the
required linear units, radii of the earth's orbit, by dividing
the angular major axis by the parallax ; 47 = 35" -j- 0.75".
Our list of distances (§ 189) contains six double stars
whose periodic times and major axes have been fairly well
determined, and we find in the accompanying table the in-
formation which they give about the masses of double stars
and the size of the orbits in which they move :

STAR.

Major axis.

Minor axis.

Periodic
time.

Mass.

t\ CassiopGisB

66

56

196

1

o'2 Eridani . ...

i 63

62

139

2

a Centauri

47

40

81

2

70 Ophiuchi

.... 56

48

88

3

Procyon

... 34

31

40

3

Sirius . . .

I 43

34

52

4

The orbit of Uranus, diameter = 38, and Neptune, diam-
eter = 60, are of much the same size as these double-star
orbits ; but the planetary orbits are nearly circular, while
in every case the double stars show a substantial difference
between the long and short diameters of their orbits. This
is a characteristic feature of most double-star orbits, and
seems to stand in some relation to their periodic times, for,
on the average, the longer the time required by a star to
make its orbital revolution the more eccentric is its orbit
likely to prove.

Another element of the orbits of double stars, which
stands in even closer relation to the periodic time, is the
major axis ; the smaller the long diameter of the orbit the
more rapid is the motion and the shorter the periodic time,
so that astronomers in search of interesting double-star
orbits devote themselves by preference to those stars whose
distance apart is so small that they can barely be distin-
guished one from the other in the telescope.

Although the half-dozen stars contained in the table
all have orbits of much the same size and with much the

THE FIXED STARS 31Y

same periodic time as those in which Uranus and Neptune
move, this is by no means true of all the double stars, many
of which have periods running up into the hundreds if not
thousands of years, while a few complete their orbital revo-
lutions in periods comparable with, or even shorter than,
that of Jupiter.

201. Dark stars. — Procyon, the next to the last star of
the preceding table, calls for some special mention, as the
determination of its mass and orbit stands upon a rather
different basis from that of the other stars. More than
half a century ago it was discovered that its proper motion
was not straight and uniform after the fashion of ordinary
stars, but presented a series of loops like those marked out
by a bright point on the rim of a swiftly running bicycle
wheel. The hub may move straight forward with uniform
velocity, but the point near the tire goes up and down, and,
while sharing in the forward motion of the hub, runs some-
times ahead of it, sometimes behind, and such seemed to
be the motion of Procyon and of Sirius as well. Bessel,
who discovered it, did not hesitate to apply the laws of mo-
tion, and to affirm that this visible change of the star's
motion pointed to the presence of an unseen companion,
which produced upon the motions of Sirius and Procyon
just such effects as the visible companions produce in the
motions of double stars. A new kind of star, dark instead
of bright, was added to the astronomer's domain, and its
discoverer boldly suggested the possible existence of many
more. " That countless stars are visible is clearly no argu-
ment againsu the existence of as many more invisible ones."
" There is no reason to think radiance a necessary property
of celestial bodies." But most astronomers were incredu-
lous, and it was not until 1862 that, in the testing of a new
and powerful telescope just built, a dark star was brought
to light and the companion of Sirius actually seen. The
visual discovery of the dark companion of Procyon is
of still more recent date (November, 1896), when it was

318 ASTRONOMY

detected with the great telescope of the Lick Observatory.
This discovery is so recent that the orbit is still very uncer-
tain, being based almost wholly upon the variations in the
proper motion of the star, and while the periodic time must
be very nearly correct, the mass of the stars and dimensions
of the orbit may require considerable correction.

The companion of Sirius is about ten magnitudes and
that of Procyon about twelve magnitudes fainter than the
star itself. How much more light does the bright star give
than its faint companion ? Despite the tremendous differ-
ence of brightness represented by the answer to this ques-
tion, the mass of Sirius is only about twice as great as
that of its companion, and for Procyon the ratio does not
exceed five or six. /

The visual discovery of the companions to Sirius and
Procyon removes them from the list of dark stars, but
others still remain unseen, although their/existence is in-
dicated by variable proper motions oi^Jtfy variable orbital
motion, as in the case of £ Cancri, where one of the compo-
nents of a triple star moves around the other two in a series
of loops whose presence indicates a disturbing body which
has never yet been seen.

202. Multiple stars. — Combinations of three, four, or
more stars close to each other, like £ Cancri, are called mul-
tiple stars, and while they are far from being as common as
are double stars, there is a considerable number of them in
the sky, 100 or more as against the more than 10,000 dou-
ble stars that are known. That their relative motions are
subject to the law of gravitation admits of no serious doubt,
but mathematical analysis breaks down in face of the diffi-
culties here presented, and no astronomer has ever been
able to determine what will be the general character of
the motions in such a system.

203. Spectroscopic binaries. — In the year 1890 Professor
Pickering, of the Harvard Observatory, announced the dis-
covery of a new class of double stars, invisible as such in

THE FIXED STARS 319

even the most powerful telescope, and producing no per-
turbations such as have been considered above, but show-
ing in their spectrum that two or more bodies must be
present in the source of light which to the eye is indistin-
guishable from a single star. In Fig. 129 we suppose A
and B to be the two components of a double star, each
moving in its own orbit about their common center of

To the Earth

A
FIG. 129.— Illustrating the motion of a spectroscopic binary.

gravity, C\ whose distance from the earth is several million
times greater than the distance between the stars them-
selves. Under such circumstances no telescope could dis-
tinguish between the two stars, which would appear fused
into one ; but the smaller the orbit the more rapid would
be their motion in it, and if this orbit were turned edgewise
toward the earth, as is supposed in the figure, whenever
the stars were in the relative position there shown, A would
be rapidly approaching the earth by reason of its orbital
motion, while B would move away from it, so that in
accordance with the Doppler principle the lines composing
their respective spectra would be shifted in opposite direc-
tions, thus producing a doubling of the lines, each single
line breaking up into two, like the double-sodium line Z>,
only not spaced so far apart. When the stars have moved
a quarter way round their orbit to the points A1, B', their
velocities are turned at right angles to the line of sight

320 ASTRONOMY

and the spectrum returns to the normal type with single
lines, only to break up again when after another quarter
revolution their velocities are again parallel with the line
of sight. The interval of time between consecutive dou-
blings of the lines in the spectrum thus furnishes half
the time of a revolution in the orbit. The distance be-
tween the components of a double line shows by means of
the Doppler principle how fast the stars are traveling, and
this in connection with the periodic times fixes the size
of the orbit, provided we assume that it is turned exactly
edgewise to the earth. This assumption may not be quite
true, but even though the orbit should deviate consider-
ably from this position, it will still present the phenomenon
of the double lines whose displacement will now show some-
thing less than the true velocities of the stars in their or-
bits, since the spectroscope measures only that component
of the whole velocity which is directed toward the earth,
and it is important to note that the real orbits and masses
of these spectroscopic binaries, as they are called, will usu-
ally be somewhat larger than those indicated by the spec-
troscope, since it is only in exceptional cases that the orbit
will be turned exactly edgewise to us.

The bright star Capella is an excellent illustration of
these spectroscopic binaries. At intervals of a little less
than a month the lines of its spectrum are alternately
single and double, their maximum separation correspond-
ing to a velocity in the line of sight amounting to 37 miles
per second. Each component of a doubled line appears to
be shifted an equal amount from the position occupied by
the line when it is single, thus indicating equal velocities
and equal masses for the two component stars whose peri-
odic time in their orbit is 104 days. From this periodic
time, together with the velocity of the star's motion, let the
student show that the diameter of the orbit — i. e., the dis-
tance of the stars from each other — is approximately 53,000,-
000 miles, and that their combined mass is a little less than

THE FIXED STARS 321

that of a Centauri, provided that their orbit plane is turned
exactly edgewise toward the earth.

There are at the present time (1901) 34 spectroscopic
binaries known, including among them such stars as Pola-
ris, Capella, Algol, Spica, (3 Aurigae, £ Ursae Majoris, etc.,
and their number is rapidly increasing, about one star out of
every nine whose motion in the line of sight is determined
proving to be a binary or, as in the case of Polaris, possibly
triple. On account of smaller distance apart their periodic
times are much shorter than those of the ordinary double
stars, and range from a few days up to several months —
more than two years in the case of y Pegasi, which has the
longest known period of any star of this class.

Spectroscopic binaries agree with ordinary double stars
in having masses rather greater than that of the sun, but
there is as yet no assured case of a mass ten times as great
as that of the sun.

204. Variable stars. — Attention has already been drawn
(§23) to the fact that some stars shine with a changing
brightness — e. g., Algol, the most famous of these variable
stars, at its maximum of brightness furnishes three times
as much light as when at its minimum, and other variable
stars show an even greater range. The star o Ceti has been
named Mira (Latin, the wonderful), from its extraordinary
range of brightness, more than six-hundred-fold. For the
greater part of the time this star is invisible to the naked
eye, but during some three months in every year it bright-
ens up sufficiently to be seen, rising quite rapidly to its
maximum brilliancy, which is sometimes that of a second-
magnitude star, but more frequently only third or even
fourth magnitude, and, after shining for a few weeks with
nearly maximum brilliancy, falling off to become invisi-
ble for a time and then return to its maximum bright-
ness after an interval of eleven months from the preceding
maximum. In 1901 it should reach its greatest brilliancy
about midsummer, and a month earlier than this for each

322 ASTRONOMY

succeeding year. Find it by means of the star map, and
by comparing its brightness from night to night with
neighboring stars of about the same magnitude see how it
changes with respect to them.

The interval of time from maximum to maximum of
brightness — 331.6 days for Mira — is called the star's pe-
riod, and within its period a star regularly variable runs
through all its changes of brilliancy, much as the weather
runs through its cycle of changes in the period of a year.
But, as there are wet years and dry ones, hot years and cold,
so also with variable stars, many of them show differences
more or less pronounced between different periods, and
one such difference has already been noted in the case of
Mira ; its maximum brilliancy is different in different years.
So, too, the length of the period fluctuates in many cases,
as does every other circumstance connected with it, and
predictions of what such a variable star will do are notori-
ously unreliable.

205. The Algol variables. — On the other hand, some vari-
able stars present an almost perfect regularity, repeating
their changes time after time with a precision like that of
clockwork. Algol is one type of these regular variables,
having a period of 68.8154 hours, during six sevenths of
which time it shines with unchanging luster as a star of
the 2.3 magnitude, but during the remaining 9 hours of
each period it runs down to the 3.5 magnitude, and comes
back again, as is shown by a curve in Fig. 130. The horizon-
tal scale here represents hours, reckoned from the time of
the star's minimum brightness, and the vertical scale shows
stellar magnitudes. Such a diagram is called the star's
light curve, and we may read from it that at any time be-
tween 5h. and 32h. after the time of minimum the star's
magnitude is 2.32; at 2h. after a minimum the magni-
tude is 2.88, etc. What is the magnitude an hour and a
half before the time of minimum ? What is the magnitude
43 days after a minimum ?

THE FIXED STARS

323

The arrows shown in Fig. 130 are a feature not usually
found with light curves, but in this case each one repre-
sents a spectroscopic determination of the motion of Algol
in the line of sight. These observations extended over a

FIG. 130.— The light curve of Algol.

period of more than two years, but they are plotted in the
figure with reference to the number of hours each one pre-
ceded or followed a minimum of the star's light, and each
arrow shows not only the direction of the star's motion
along the line of sight, the arrows pointing down denoting
approach of the star toward the earth, but also its velocity,
each square of the ruling corresponding to 10 kilometers
(6.2 miles per second). The differences of velocity shown
by adjacent arrows come mainly from errors of observation
and furnish some idea of how consistent among themselves
such observations are, but there can be no doubt that before
minimum the star is moving away from the earth, and after
minimum is approaching it. It is evident from these ob-
servations that in Algol we have to do with a spectroscopic
binary, one of whose components is a dark star which, once
in each revolution, partially eclipses the bright star and
produces thus the variations in its light. By combining
the spectroscopic observations with the variations in the
star's light, Vogel finds that the bright star, Algol, itself
has a diameter somewhat greater than that of the sun, but

324:

ASTRONOMY

is of low density, so that its mass is less than half that of
the sun, while the dark star is a very little smaller than the
sun and has about a quarter of its mass. The distance be-
tween the two stars, dark and bright, is 3,200,000 miles.
Fig. 129, which is drawn to scale, shows the relative posi-
tions and sizes of these stars as well as the orbits in which
they move.

The mere fact already noted that close binary systems
exist in considerable numbers is sufficient to make it
probable that a certain proportion of these stars would
have their orbit planes turned so nearly edgewise toward
the earth as to produce eclipses, and corresponding to this
probability there are already known no less than 15 stars of
the Algol type of eclipse variables, and only a beginning
has been made in the search for them.

206. Variables of the (3 Lyrse type. — In addition to these
there is a certain further number of binary variables in
which both components are bright and where the varia-
tion of brightness follows a very different course. Capella

Days

FIG. 131.— The light curve of 0 Lyrse.

would be such a variable if its orbit plane were directed
exactly toward the earth, and the fact that its light is not
variable shows conclusively that such is not the position of
the orbit. Fig. 131 represents the light curve of one of the

THE FIXED STARS 325

best-known variable systems of this second type, that of
/? Lyrse, whose period is 12 days 21.8 hours, and the student
should read from the curve the magnitude of the star for
different times during this interval. According to Myers,
this light curve and the spectroscopic observations of the
star point to the existence of a binary star of very remark-
able character, such as is shown, together with its orbit and
a scale of miles, in Fig. 132. Note the tide which each of

To the Earth

10,000,000 miles

FIG. 132.— The system of /3 Lyrae.— MYERS.

these stars raises in the other, thus changing their shapes
from spheres into ellipsoids. The astonishing dimensions
of these stars are in part compensated by their very low
density, which is less than that of air, so that their masses
are respectively only 10 times and 21 times that of the
sun ! But these dimensions and masses perhaps require
confirmation, since they depend upon spectroscopic obser-
vations of doubtful interpretation. In Fig. 132 what rela-
tive positions must the stars occupy in their orbit in order
that their combined light should give ft Lyrae its maxi-
mum brightness ? What position will furnish a minimum
brightness ?

207. Variables of long and short periods, — It must not be
supposed that all variable stars are binaries which eclipse
each other. By far the larger part of them, like Mira, are
not to be accounted for in this way, and a distinction which

326 ASTRONOMY

is pretty well marked in the length of their periods is sig-
nificant in this connection. There is a considerable num-
ber of variable stars with periods shorter than a month, and
there are many having periods longer than 6 months, but
there are very few having periods longer than 18 months,
or intermediate between 1 month and 6 months, so that it
is quite customary to divide variable stars into two classes
— those of long period, 6 months or more, and those of
short period less than 6 months, and that this distinction
corresponds to some real difference in the stars themselves
is further marked by the fact that the long-period variables
are prevailingly red in color, while the short-period stars
are almost without exception white or very pale yellow.
In fact, the longer the period the redder the star, although
it is not to be inferred that all red stars are variable ; a
considerable percentage of them shine with constant light.
The eclipse explanation of variability holds good only for
short-period variables, and possibly not for all of them,
while for the long-period variables there is no explanation
which commands the general assent of astronomers, al-
though unverified hypotheses are plenty.

The number of stars known to be variable is about 400,
while a considerable number of others are "suspected,"
and it would not be surprising if a large fraction of all the
stars should be found to fluctuate a little in brightness.
The sun's spots may suffice to make it a variable star with
a period of 11 years.

The discovery of new variables is of frequent occur-
rence, and may be expected to become more frequent when
the sky is systematically explored for them by the ingen-
ious device suggested by Pickering and illustrated in Fig.
133. A given region of the sky— e. g., the Northern Crown
— is photographed repeatedly upon the same plate, which is
shifted a little at each new exposure, so that the stars shall
fall at new places upon it. The finally developed plate
shows a row of images corresponding to each star, and if

THE FIXED STARS

327

the star's light is constant the images in any given row will
all be of the same size, as are most of those in Fig. 133 ;
but a variable star such as is shown by the arrowhead
reveals its presence by the broken aspect of its row of

..•*

FIG. 133. — Discovery of a variable star by means of photography. — PICKERING.

dots, a minimum brilliancy being shown by smaller and a
maximum by larger ones. In this particular case, at two
exposures the star was too faint to print its image upon
the plate.

208. New stars. — Next to the variable stars of very long
or very irregular period stand the so-called new or tempo-
rary stars, which appear for the most part suddenly, and
after a brief time either vanish altogether or sink to com-
parative insignificance. These were formerly thought to
be very remarkable and unusual occurrences — " the birth
of a new world " — and it is noteworthy that no new star
is recorded to have been seen from 1670 to 1848 A. D., for
since that time there have been no less than four of them

328 ASTRONOMY

visible to the naked eye and others telescopic. In so far
as these new stars are not ordinary variables (Mira, first
seen in 1596, was long counted as a new star), they are com-
monly supposed due to chance encounters between stars
or other cosmic bodies moving with considerable velocities
along orbits which approach very close to each other. The
actual collision of two dark bodies moving with high ve-
locities is clearly sufficient to produce a luminous star —
e. g., meteors — and even the close approach of two cooled-
off stars, might result in tidal actions which would rend
open their crusts and pour out the glowing matter from
within so as to produce temporarily a very great accession
of brightness.

The most famous of all new stars is that which, accord-
ing to Tycho Brahe's report, appeared in the year 1572, and
was so bright when at its best as to be seen with the naked
eye in broad daylight. It continued visible, though with
fading light, for about 16 months, and finally disappeared
to the naked eye, although there is some reason to suppose
that it can be identified with a ruddy star of the eleventh
magnitude in the constellation Cassiopeia, whose light still
shows traces of variability.

No modern temporary star approaches that of Tycho
in splendor, but in some respects the recent ones surpass
it in interest, since it has been possible to apply the spec-
troscope to the analysis of their light and to find thereby
a much more complex set of conditions in the star than
would have been suspected from its light changes alone.
The temporary star which appeared in the constellation
Auriga in December, 1891, disappeared in April, 1892, and
three months later reappeared for another season, is the
most remarkable of recent temporary stars, and presents
many anomalies for which no entirely satisfactory expla-
nation has yet been found. Its spectrum contained both
dark and bright lines, apparently due to the same chemical
substances, but displaced toward opposite ends of the spec-

THE FIXED STARS 329

trum, as if they came from different bodies moving past
each other with velocities to be measured in hundreds of
miles per second. In character the lines, chiefly those of
hydrogen and iron, suggested at one time the sun's chro-
mosphere, at another the conditions which obtain in neb-
ulas (Chapter XI V), and the only conclusion regarding it
upon which there seems to be a substantial agreement is
that in producing and reviving the temporary brightness
of this star at least two and possibly several independent
bodies were involved, although even this is not altogether
certain.

CHAPTER XIV

STARS AND NEBULJB

209. Stellar colors,— We have already seen that one star
differs from another in respect of color as well as bright-
ness, and the diligent student of the sky will not fail to
observe for himself how the luster of Sirius and Rigel is
more nearly a pure white than is that of any other stars in
the heavens, while at the other end of the scale a Orionis
and Aldebaran are strongly ruddy, and Antares presents an
even deeper tone of red. Between these extremes the
light of every star shows a mixture of the rainbow hues, in
which a very pale yellow is the predominant color, shading
off, as we have seen, to white at one end of the scale and
red at the other. There are no green stars, or blue stars,
or violet stars, save in one exceptional class of cases — viz.,
where the two components of a double star are of very dif-
ferent brightness, it is quite the usual thing for them to
have different colors, and then, almost without exception,
the color of the fainter star lies nearer to the violet end
of the spectrum than does the color of the bright one,
and sometimes shows a distinctly blue or green hue. A
fine type of such double star is ft Cygni, in which the
components are respectively yellow and blue, and the yel-
low star furnishes eight times as much light as the blue
one.

The exception which double stars thus make to the gen-
eral rule of stellar colors, yellow and red, but no color of
shorter wave length, has never been satisfactorily explained,
330

STARS AND NEBULA 331

but the rule itself presents no difficulties. Each star is an
incandescent body, giving off radiant energy of every wave
length within the limits of the visible spectrum, and, in-
deed, far beyond these limits. If this radiant energy could
come unhindered to our eyes every star would appear white,
but they are all surrounded by atmospheres — analogous to
the chromosphere and reversing layer of the sun — which
absorb a portion of their radiant energy and, like the earth's
atmosphere, take a heavier toll from the violet than from
the red end of the spectrum. The greater the absorption
in the star's atmosphere, therefore, the feebler and the rud-
dier will be its light, and corresponding to this the red stars
are as a class fainter than the white ones.

210. Chemistry of the stars,— The spectroscope is pre-em-
inently the instrument to deal with this absorption of light
in the stellar atmospheres, just as it deals with that absorp-
tion in the sun's atmosphere to which are due the dark lines
of the solar spectrum, although the faiiitness of starlight,
compared with that of the sun, presents a serious obstacle
to its use. Despite this difficulty most of the lucid stars
and many of the telescopic ones have been studied with
the spectroscope and found to be similar to the sun and
the earth as respects the material of which they are made.
Such familiar chemical elements as hydrogen and iron, car-
bon, sodium, and calcium are scattered broadcast through-
out the visible universe, and while it would be unwarranted
by the present state of knowledge to say that the stars con-
tain nothing not found in the earth and the sun, it is evi-
dent that in a broad way their substance is like rather than
unlike that composing the solar system, and is subject to
the same physical and chemical laws which obtain here.
Galileo and Kewton extended to the heavens the terrestrial
sciences of mathematics and mechanics, but it remained to
the nineteenth century to show that the physics and chem-
istry of the sky are like the physics and chemistry of the
earth.

332 ASTRONOMY

211. Stellar spectra, — When the spectra of great numbers
of stars are compared one with another, it is found that
they bear some relation to the colors of the stars, as, indeed,
we should expect, since spectrum and color are both pro-
duced by the stellar atmospheres, and it is found useful to
classify these spectra into three types, as follows :

Type I. Sirian stars. — Speaking generally, the stars
which are white or very faintly tinged with yellow, furnish
spectra like that of Sirius, from which they take their
name, or that of (3 Aurigse (Fig. 124), which is a continuous
spectrum, especially rich in energy of short wave length —
i. e., violet and ultra-violet light, and is crossed by a rela-
tively small number of heavy dark lines corresponding to
the spectrum of hydrogen. Sometimes, however, these lines
are much fainter than is here shown, and we find associated
with them still other faint ones pointing to the presence of
other metallic substances in the star's atmosphere. These
metallic lines are not always present, and sometimes even
the hydrogen lines themselves are lacking, but the spectrum
is always rich in violet and ultra-violet light.

Since with increasing temperature a body emits a con-
tinually increasing proportion of energy of short wave
length (§ 118), the richness of these spectra in such energy
points to a very high temperature in these stars, probably
surpassing in some considerable measure that of the sun.
Stars with this type of spectrum are more numerous than
all others combined, but next to them in point of numbers
stands —

Type II. Solar stars. — To this type of spectrum belong
the yellow stars, which show spectra like that of the sun,
or of Pollux (Fig. 125). These are not so rich in violet
light as are those of Type I, but in complexity of spectrum
and in the number of their absorption lines they far sur-
pass the Sirian stars. They are supposed to be at a lower
temperature than the Sirian stars, and a much larger num-
ber of chemical elements seems present and active in the

STARS AND NEBULAE 333

reversing layer of their atmospheres. The strong resem-
blance which these spectra bear to that of the sun, together
with the fact that most of the sun's stellar neighbors have
spectra of this type, justify us in ranking both them and it
as members of one class, called solar stars.

Type III. Red stars. — A small number of stars show
spectra comparable with that of a Herculis (Fig. 134), in
which the blue and the violet part of the spectrum is al-
most obliterated, and the remaining yellow and red parts

FIG. 134.— The spectrum of a Herculis.— ESPIN.

show not only dark lines, but also numerous broad dark
bands, sharp at one edge, and gradually fading out at the
other. It is this selective absorption, extinguishing the blue
and leaving the red end of the spectrum, which produces
the ruddy color of these stars, while the bands in their
spectra " are characteristic of chemical combinations, and
their presence . . . proves that at certain elevations in the
atmospheres of these stars the temperature has sunk so low
that chemical combinations can be formed and maintained "
(Scheiner-Frost). One of the chemical compounds here in-
dicated is a hydrocarbon similar to that found in comets.
In the white and yellow stars the temperatures are so high
that the same chemical elements, although present, can not
unite one with another to form compound substances.

Most of the variable stars are red and have spectra of
the third type ; but this does not hold true for the eclipse
variables like Algol, all of which are white stars with spec-
tra of the first type. The ordinary variable star is there-
fore one with a dense atmosphere of relatively low tempera-
ture and complex structure, which produces the prevailing
red color of these stars by absorbing the major part of

334 ASTRONOMY

their radiant energy of short wave length while allowing
the longer, red waves to escape. Although their exact
nature is not understood, there can be little doubt that the
fluctuation in the light of these stars is due to processes
taking place within the star itself, but whether above or
below its photosphere is still uncertain.

212. Classes of stars, — There is no hard-and-fast dividing
line between these types of stellar spectra, but the change
from one to another is by insensible gradations, like the
transition from youth to manhood and from manhood to
old age, and along the line of transition are to be found
numberless peculiarities and varieties of spectra not enu-
merated above — e. g., a few stars show not only dark absorp-
tion lines in their spectra but bright lines as well, which,
like those in Fig. 48, point to the presence of incandescent
vapors, even in the outer parts of their atmospheres. Among
the lucid stars about 75 per cent have spectra of the first
type, 23 per cent are of the second type, 1 per cent of the
third type, and the remaining 1 per cent are peculiar or of
doubtful classification. Among the telescopic stars it is
probable that much the same distribution holds, but in the
present state of knowledge it is not prudent to speak with
entire confidence upon this point.

That the great number of stars whose spectra have been
studied should admit of a classification so simple as the
above, is an impressive fact which, when supplemented by
the further fact of a gradual transition from one type of
spectrum to the next, leaves little room for doubt that in
the stars we have an innumerable throng of individuals be-
longing to the same species but in different stages of devel-
opment, and that the sun is only one of these individuals,
of something less than medium size and in a stage of de-
velopment which is not at all peculiar, since it is shared by
nearly a fourth of all the stars.

213. Star clusters. — In previous chapters we have noted
the Pleiades and Prsesepe as star clusters visible to the

STARS AND NEBULAE

335

FIG. 135.— Star cluster in Hercules.

naked eye, and to them we may add the Hyades, near Aldeb-
aran, and the little constellation Coma Berenices. But
more impressive than any of these, although visible only
in a telescope, is the splendid cluster in Hercules, whose
appearance in a tele-
scope of moderate size
is shown in Fig. 135,
while Fig. 136 is a pho-
tograph of the same
cluster taken with a
very large reflecting
telescope. This is only
a type of many tele-
scopic clusters which
are scattered over the
sky, and which are made
up of stars packed so
closely together as to become indistinguishable, one from
another, at the center of the cluster. Within an area
which could be covered by a third of the full moon's face
are crowded in this cluster more than five thousand stars
which are unquestionably close neighbors, but whose ap-
parent nearness to each other is doubtless due to their
great distance from us. It is quite probable that even at
the center of this cluster, where more than a thousand stars
are included within a radius of 160", the actual distances
separating adjoining stars are much greater than that sepa-
rating earth and sun, but far less than that separating the
sun from its nearest stellar neighbor.

An interesting discovery of recent date, made by Pro-
fessor Bailey in photographing star clusters, is that some
few of them, which are especially rich in stars, contain an
extraordinary number of variable stars, mostly very faint
and of short period. Two clusters, one in the northern and
one in the southern hemisphere, contain each more than a
hundred variables, and an even more extraordinary case is

336 ASTRONOMY

presented by a cluster, called Messier 5, not far from the
star a Serpentis, which contains no less than sixty-three
variables, all about of the fourteenth magnitude, all having
light periods which differ, but little from half a day, all

FIG. 136. — Star cluster in Hercules. — KEELER.

having light curves of about the same shape, and all having
a range of brightness from maximum to minimum of about
one magnitude. An extraordinary set of coincidences
which "points unmistakably to a common origin and cause
of variability."

STARS AND NEBULAE 337

214. Nebulae, — Returning to Fig. 136, we note that its
background has a hazy appearance, and that at its center

FIG. 137.— The Andromeda nebula as seen in a very small telescope.

the stars can no longer be distinguished, but blend one
with another so as to appear like a bright cloud. The

FIG. 138.— The Andromeda nebula and Holmes's comet.
Photographed by BARNARD.

338 ASTRONOMY

outer part of the cluster is resolved into stars, while in the
picture the inner portion is not so resolved, although in

FIG. 139.— A drawing of the Andromeda nebula.

the original photographic plate the individual stars can be
distinguished to the very center of the cluster. In many

FIG. 140.— A photograph of the Andromeda nebula.— ROBERTS.

STARS AND NEBULA

339

cases, however, this is not possible, and we have an irre-
solvable duster which it is customary to call a nebula
(Latin, little cloud).

The most conspicuous example of this in the northern
heavens is the great nebula in Andromeda (R. A. Oh 37m,
Dec. + 41°), which may be seen with the naked eye as a
faint patch of foggy light. Look for it. This appears in
an opera glass or very small telescope not unlike Fig. 137,
which is reproduced from a sketch. Fig. 138 is from a
photograph of the same object showing essentially the same
shape as in the preceding figure, but bringing out more
detail. Note the two small nebulae adjoining the large
one, and at the bottom of the picture an object which might
easily be taken for another nebula but which is in fact
a tailless comet that chanced to be passing that part of
the sky when the picture was taken. Fig. 139 is from an-
other drawing of this nebula,
although it is hardly to be
recognized as a representa-
tion of the same thing; but
its characteristic feature, the
two dark streaks near the cen-
ter of the picture, is justified
in part by Fig. 140, which is
from a photograph made with
a large reflecting telescope.

A comparison of these sev-
eral representations of the
same thing will serve to illus-
trate the vagueness of its out-
lines, and how much the im-
pressions to be derived from
nebulae depend upon the tele-
scopes employed and upon the

observer's own prepossessions. The differences among the
pictures can not be due to any change in the nebula itself,

FIG. 141.— Types of nebulae.

34:0 ASTRONOMY

for half a century ago it was sketched much as shown in
the latest of them (Fig. 140).

215. Typical nebulae. — Some of the fantastic forms which
nebulae present in the telescope are shown on a small scale
in Fig. 141, but in recent years astronomers have learned to

FIG. 142.— The Trifld nebula.— KEELER.

place little reliance upon drawings such as these, which are
now almost entirely supplanted by photographs made with
long exposures in powerful telescopes. One of the most
exquisite of these modern photographs is that of the Trifid

STARS AND NEBULA

341

nebula in Sagittarius (Fig. 142). Note especially the dark
lanes that give to this nebula its name, Trifid, and which run
through its brightest parts, breaking it into seemingly inde-
pendent sections. The area of the sky shown in this cut is
about 15 per cent less than that covered by the full moon.

FIG. 143.— A nebula in Cygnus.— KEELER.

Fig. 143 shows a very different type of nebula, found in
the constellation Cygnus, which appears made up of fila-
ments closely intertwined, and stretches across the sky for
a distance considerably greater than the moon's diameter.

342

ASTRONOMY

A much smaller but equally striking nebula is that in
the constellation Canes Venatici (Fig. 144), which shows a
most extraordinary spiral structure, as if the stars compos-
ing it were flowing in along curved lines toward a center of
condensation. The diameter of the circular part of this

FIG. 144.— Spiral nebula in Canes Venatici.— KEELER.

nebula, omitting the "projection toward the bottom of the
picture, is about five minutes of arc, a sixth part of the
diameter of the moon, and its thickness is probably very
small compared with its breadth, perhaps not much exceed-

STARS AND NEBULA 343

ing the width of the spiral streams which compose it. Note
how the bright stars that appear within the area of this
nebula fall on the streams of nebulous matter as if they
were part of them. This characteristic grouping of the
stars, which is followed in many other nebulas, shows that

FIG. 145.— Great nebula about the e tar p Ophiuchi.— BARNARD.

they are really part and parcel of the nebula and not merely
on line with it. Fig. 145 shows how a great nebula is asso-
ciated with the star p Ophiuchi.

Probably the most impressive of all nebulae is the great
one in Orion (Fig. 146), whose position is shown on the
star map between Eigel and £ Orionis. Look for it with
an opera glass or even with the unaided eye. This is some-
times called an amorphous — i. e., shapeless — nebula, because
it presents no definite form which the eye can grasp and
little trace of structure or organization. It is "without
form and void " at least in its central portions, although on
its edges curved filaments may be traced streaming away

344 ASTRONOMY

from the brighter parts of the central region. This nebula,
as shown in Fig. 146, covers an area about equal to that of
the full moon, without counting as any part of this the
companion nebula shown at one side, but photographs
made with suitable exposures show that faint outlying parts
of the nebula extend in curved lines over the larger part of

FIG. 146.— The Orion nebula.

the constellation Orion. Indeed, over a large part of the
entire sky the background is faintly covered with nebulous
light whose brighter portions, if each were counted as a
separate nebula, would carry the total number of such ob-
jects well into the hundreds of thousands.

The Pleiades (Plate IV) present a case of a resolvable
star cluster projected against such a nebulous background
whose varying intensity should be noted in the figure. A
part of this nebulous matter is shown in wisps extending
from one star to the next, after the fashion of a bridge, and
leaving little doubt that the nebula is actually a part of the
cluster and not merely a background for it.

Fig. 147 shows a series of so-called double nebulae per-
haps comparable with double stars, although the most
recent photographic work seems to indicate that they are

•

STARS AND NEBULA

345

really faint spiral nebulae in which only the brightest parts
are shown by the telescope.

According to Keeler, the spiral is the prevailing type
of nebulae, and while Fig. 144 presents the most perfect ex-
ample of such a nebula, the
student should not fail to
note that the Andromeda neb-
ula (Fig. 140) shows distinct
traces of a spiral structure,
only here we do not see its
true shape, the nebula being
turned nearly edgewise toward
us so that its presumably cir-
cular outline is foreshortened
into a narrow ellipse.

Another type of nebula of
some consequence presents in
the telescope round disks like
those of Uranus or Xeptune,
and this appearance has given
them the name planetary neb-

iilce. The comet in Fig. 138, if smaller, would represent
fairly well the nebulae of this type. Sometimes a planetary
nebula has a star at its center, arid sometimes it appears
hollow, like a smoke ring, and is then called a ring nebula.
The most famous of these is in the constellation Lyra, not
far from Vega.

216. Spectra of nebulae.— A star cluster, like the one in
Hercules, shows, of course, stellar spectra, and even when
irresolvable the spectrum is a continuous one, testifying to
the presence of stars, although they stand too close to-
gether to be separately seen. But in a certain, number of
nebulae the spectrum is altogether different, a discontinu-
ous one containing only a few bright lines, showing that
here the nebular light comes from glowing gases which
are subject to no considerable pressure. The planetary

FIG. 147.— Double nebulae.
HERSCHEL.

346 ASTRONOMY

nebulae all have spectra of this kind and make up about
half of all the known gaseous nebulae. It is worthy of
note that a century ago Sir William Herschel had observed
a green shimmer in the light of certain nebulae which led
him to believe that they were " not of a starry nature," a
conclusion which has been abundantly confirmed by the
spectroscope. The green shimmer is, in fact, caused by a
line in the green part of the spectrum that is always pres-
ent and is always the brightest part of the spectrum of
gaseous nebulae.

In faint nebulae this line constitutes the whole of their
visible spectrum, but in brighter ones two or three other
and fainter lines are usually associated with it, and a very
bright nebula, like that in Orion, may show a considerable
number of extra lines, but for the most part they can not
be identified in the spectrum of any terrestrial substances.
An exception to this is found in the hydrogen lines, which
are well marked in most spectra of gaseous nebulae, and
there are indications of one or two other known sub-
stances.

217. Density of nebulae. — It is known from laboratory
experiments that diminishing the pressure to which an in-
candescent gas is subject, diminishes the number of lines
contained in its spectrum, and we may surmise from the
very simple character and few lines of these nebular spec-
tra that the gas which produces them has a very small
density. But this is far from showing that the nebula
itself is correspondingly attenuated, for we must not as-
sume that this shining gas is all that exists in the nebula ;
so far as telescope or camera are concerned, there may be
associated with it any amount of dark matter which can
not be seen because it sends to us no light. It is easy
to think in this connection of meteoric dust or the stuff of
which comets are made, for these seem to be scattered
broadcast on every side of the solar system and may, per-
chance, extend out to the region of the nebulae.

STARS AND NEBULAE 347

But, whatever may be associated in the nebula with the
glowing gas which we see, the total amount of matter, in-
visible as well as visible, must be very small, or rather its
average density must be very small, for the space occupied
by such a nebula as that of Orion is so great that if the
average density of its matter were equal to that of air the
resulting mass by its attraction would exert a sensible effect
upon the motion of the sun through space. The brighter
parts of this nebula as seen from the earth subtend an angle
of about half a degree, and while we know nothing of its
distance from us, it is easy to see that the farther it is away
the greater must be its real dimensions, and that this in-
crease of bulk and mass with increasing distance will just
compensate the diminishing intensity of gravity at great
distances, so that for a given angular diameter — e. g., half
a degree — the force with which this nebula attracts the sun
depends upon its density but not at all upon its distance.
Now, the nebula must attract the sun in some degree, and
must tend to move it and the planets in an orbit about
the attracting center so that year after year we should see
the nebula from slightly different points of view, and this
changed point of view should produce a change in the ap-
parent direction of the nebula from us — i. e., a proper mo-
tion, whose amount would depend upon the attracting force,
and therefore upon the density of the attracting matter.
Observations of the Orion nebula show that its proper
motion is wholly inappreciable, certainly far less than half
a second of arc per year, and corresponding to this amount
of proper motion the mean density of the nebula must be
some millions of times (1010 according to Eanyard) less than
that of air at sea level— i. e., the average density throughout
the nebula is comparable with that of those upper parts
of the earth's atmosphere in which meteors first become
visible.

218. Motion of nebulae. — The extreme minuteness of
their proper motions is a characteristic feature of all

348 ASTRONOMY

nebulae. Indeed, there is hardly a known case of sensible
proper motion of one of these bodies, although a dozen or
more of them show velocities in the line of sight ranging
in amount from -f-30 to —40 miles per second, the plus
sign indicating an increasing distance. While a part of
these velocities may be only apparent and due to the mo-
tion of earth and sun through space, a part at least is real
motion of the nebulas themselves. These seem to move
through the celestial spaces in much the same way and

FIG. 148.— A part of the Milky Way.

with the same velocities as do the stars, and their smaller
proper motions across the line of sight (angular motions)
are an index of their great distance from us. No one has
ever succeeded in measuring the parallax of a nebula or
star cluster.

The law of gravitation presumably holds sway within
these bodies, and the fact that their several parts and the
stars which are involved within them, although attracted
by each other, have shown little or no change of position

STARS AND NEBULA

349

during the past century, is further evidence of their low
density and feeble attraction. In a few cases, however,
there seem to be in progress within a nebula changes of
brightness, so that what was formerly a faint part has be-
come a brighter one, or vice versa ; but, on the whole, even
these changes are very small.

219. The Milky Way.— Closely related to nebulae and
star clusters is another feature of the sky, the galaxy or
Milky Way, with whose appearance to the unaided eye the

FIG. 149.— The Milky Way near 6 Ophiuchi.— BAUNARD.

student should become familiar by direct study of the thing
itself. Figs. 148 and 149 are from photographs of two
small parts of it, and serve to bring out the small stars of
which it is composed. Every star shown in these pictures
is invisible to the naked eye, although their combined light
is easily seen. The general course of the galaxy across the
heavens is shown in the star maps, but these contain no
indication of the wealth of detail which even the naked eye
may detect in it. Bright and faint parts, dark rifts which

350

ASTRONOMY

cut it into segments, here and there a hole as if the ribbon
of light had been shot away — such are some of the features
to be found by attentive examination.

Speaking generally, the course of the Milky Way is a
great circle completely girdling the sky and having its
north pole in the constellation Coma Berenices. The
width of this stream of light is very different in different
parts of the heavens, amounting where it is widest, in Lyra
and Cygnus, to something more than 30°, although its
boundaries are too vague and ill denned to permit much
accuracy of measurement. Observe the very bright part
between ft and y Cygni, nearly opposite Vega, and note

FIG. 150.— The Milky Way near /3 Cygni.— BARNAKD.

how even an opera glass will partially resolve the nebulous
light into a great number of stars, which are here rather
brighter than in other parts of its course. But the resolu-
tion into stars is only partial, and there still remains a
background of unresolved shimmer. Fig. 150 is a photo-

STARS AND NEBULAE 351

graph of a small part of this region in which, although
each fleck of light represents a separate star, the galaxy is
not completely resolved. Compare with this region, rich
in stars, the nearly empty space between the branches of
the galaxy a little west of Altair. Another hole in the
Milky Way may be found a little north and east of a Cygni,
and between the extremes of abundance and poverty here
noted there may be found every gradation of nebulous
light.

The Milky Way is not so simple in its structure as might
at first be thought, but a clear and moonless night is
required to bring out its details. The nature of these
details, the structure of the galaxy, its shape and extent,
the arrangement of its parts, and their relation to stars
and nebulae in general, have been subjects of much specu-
lation by astronomers and others who have sought to trace
out in this way what is called the construction of the
heavens.

220. Distribution of the stars. — How far out into space
do the stars extend ? Are they limited or infinite in num-
ber ? Do they form a system of mutually related parts, or
are they bunched promiscuously, each for itself, without
reference to the others ? Here is what has been well called
"the most important problem of stellar astronomy, the
acquisition of well-founded ideas about the distribution of
the stars." While many of the ideas upon this subject
which have been advanced by eminent astronomers and
which are still current in the books are certainly wrong,
and few of their speculations along this line are demon-
strably true, the theme itself is of such grandeur and per-
manent interest as to demand at least a brief considera-
tion. But before proceeding to its speculative side we
need to collect facts upon which to build, and these, how-
ever inadequate, are in the main simple and not far to seek.

Parallaxes, proper motions, motions in the line of sight,
while pertinent to the problem of stellar distribution, are

352 ASTRONOMY

of small avail, since they are far too scanty in number and
relate only to limited classes of stars, usually the very
bright ones or those nearest to the sun. Almost the sole
available data are contained in the brightness of the stars
and the way in which they seem scattered in the sky. The
most casual survey of the heavens is enough to show that
the stars are not evenly sprinkled upon it. The lucid stars
are abundant in some regions, few in others, and the labori-
ous star gauges, actual counting of the stars in sample
regions of the sky, which have been made by the Herschels,
Celoria, and others, suffice to show that this lack of uni-
formity in distribution is even more markedly true of the
telescopic stars.

The rate of increase in the number of stars from one
magnitude to the next, as shown in § 187, is proof of
another kind of irregularity in their distribution. It is not
difficult to show, mathematically, that if in distant regions
of space the stars were on the average as numerous and as
bright as they are in the regions nearer to the sun, then
the stars of any particular magnitude ought to be four
times as numerous as those of the next brighter magnitude
— e. g., four times as many sixth-magnitude stars as there
are fifth-magnitude ones. But, as we have already seen in
§ 187, by actual count there are only three times as many,
and from the discrepancy between these numbers, an actual
threefold increase instead of a fourfold one, we must con-
clude that on the whole the stars near the sun are either
bigger or brighter or more numerous than in the remoter
depths of space.

221. The stellar system, — But the arrangement of the
stars is not altogether lawless and chaotic ; there are traces
of order and system, and among these the Milky Way is the
dominant feature. Telescope and photographic plate alike
show that it is made up of stars which, although quite ir-
regularly scattered along its course, are on the average
some twenty times as numerous in the galaxy as at its

STARS AND NEBULAE 353

poles, and which thin out as we recede from it on either
side, at first rapidly and then more slowly. This tendency
to cluster along the Milky Way is much more pronounced
among the very faint telescopic stars than among the
brighter ones, for the lucid stars and the telescopic ones
down to the tenth or eleventh magnitude, while very
plainly showing the clustering tendency, are not more than
three times as numerous in the galaxy as in the constella-
tions most remote from it. It is remarkable as showing
the condensation of the brightest stars that one half of all
the stars in the sky which are brighter than the second
magnitude are included within a belt extending 12° on
either side of the center line of the galaxy.

In addition to this general condensation of stars toward
the Milky Way, there are peculiarities in the distribution of
certain classes of stars which are worth attention. Planet-
ary nebulae and new stars are seldom, if ever, found far
from the Milky Way, and stars with bright lines in their
spectra especially affect this region of the sky. Stars with
spectra of the first type — Sirian stars — are much more
strongly condensed toward the Milky Way than are stars
of the solar type, and in consequence of this the Milky
Way is peculiarly rich in light of short wave lengths. Ee-
solvable star clusters are so much more numerous in the
galaxy than elsewhere, that its course across the sky would
be plainly indicated by their grouping upon a map showing
nothing but clusters of this kind.

On the other hand, nebulae as a class show a distinct
aversion for the galaxy, and are found most abundantly in
those parts of the sky farthest from it, much as if they
represented raw material which was lacking along the
Milky Way, because already worked up to make the stars
which are there so numerous.

222. Relation of the sun to the Milky Way.— The fact
that the galaxy is a great circle of the sky, but only of mod-
erate width, shows that it is a widely extended and com-

354 ASTRONOMY

paratively thin stratum of stars within which the solar sys-
tem lies, a member of the galactic system, and probably not
very far from its center. This position, however, is not to
be looked upon as a permanent one, since the sun's motion,
which lies nearly in the plane of the Milky Way, is cease-
lessly altering its relation to the center of that system, and
may ultimately carry us outside its limits.

The Milky Way itself is commonly thought to be a
ring, or series of rings, like the coils of the great spiral
nebula in Andromeda, and separated from us by a space far
greater than the thickness of the ring itself. Note in Figs.
149 and 150 how the background is made up of bright and
dark parts curiously interlaced, and presenting much the
appearance of a thin sheet of cloud through which we look
to barren space beyond. While, mathematically, this ap-
pearance can not be considered as proof that the galaxy
is in fact a distant ring, rather than a sheet of starry
matter stretching continuously from the nearer stellar
neighbors of the sun into the remotest depths of space,
nevertheless, most students of the question hold it to be
such a ring of stars, which are relatively close together
while its center is comparativeljjyag^i. although even
here are 1^01116 liuiiTIreds'ol1 Ln'ousanos of stars which on the
whole have a tendency to cluster near its plane and to
crowd together a little more densely than elsewhere in the
region where the sun is placed.

223. Dimensions of the galaxy, — The dimensions of this
stellar system are wholly unknown, but there can be no
doubt that it extends farther in the plane of the Milky
Way than at right angles to that plane, for stars of the fif-
teenth and sixteenth magnitudes are common in the galaxy,
and testify by their feeble light to their great distance
from the earth, while near the poles of the Milky Way there
seem to be few stars fainter than the twelfth magnitude.
Herschel, with his telescope of 18 inches aperture, could
count in the Milky Way more than a dozen times as many

STARS AND NEBULA 355

stars per square degree as could Celoria with a telescope of
4 inches aperture ; but around the poles of the galaxy the
two telescopes showed practically the same number of stars,
indicating that here even the smaller telescope reached to
the limits of the stellar system. Very recently, indeed, the .
telescope with which Fig. 140 was photographed seems to
have reached the farthest limit of the Milky Way, for on a
photographic plate of one of its richest regions Roberts
finds it completely resolved into stars which stand out upon
a black background with no trace of nebulous light between
them.

224,. Beyond the Milky Way.— Each additional step into
the depths of space brings us into a region of which less is
known, and what lies beyond the Milky Way is largely a
matter of conjecture. We shrink from thinking it an in-
finite void, endless emptiness, and our intellectual sympa-
thies go out to Lambert's speculation of a universe filled
with stellar systems, of which ours, bounded by the galaxy,
is only one. There is, indeed, little direct evidence that
other such systems exist, but the Andromeda nebula is not
altogether unlike a galaxy with a central cloud of stars,
and in the southern hemisphere, invisible in our latitudes,
are two remarkable stellar bodies like the Milky Way in
appearance, but cut off from all apparent connection with
it, much as we might expect to find independent stellar
systems, if such there be.

These two bodies are known as the Magellanic clouds,
and individually bear the names of Major and Minor Xubec-
ula. According to Sir John Herschel, " the Xubecula
Major, like the Minor, consists partly of large tracts and
ill-defined patches of irresolvable nebula, and of nebulosity
in every stage of resolution up to perfectly resolved stars
like the Milky Way, as also of regular and irregular nebulae
... of globular clusters in every stage of resolvability, and
of clustering groups sufficiently insulated and condensed to
come under the designation of clusters of stars." Its out-

356 ASTRONOMY

lines are vague and somewhat uncertain, but surely include
an area of more than 40 square degrees — i. e., as much as
the bowl of the Big Dipper — and within this area Herschel
counted several hundred nebulse and clusters " which far
exceeds anything that is to be met with in any other region
of the heavens." Although its excessive complexity of de-
tail baffled Herschel's attempts at artistic delineation, it
has yielded to the modern photographic processes, which
show the Nubecula Major to be an enormous spiral nebula
made up of subordinate stars, nebula?, and clusters, as is
the Milky Way.

Compared with the Andromeda nebula, its greater angu-
lar extent suggests a smaller distance, although for the
present all efforts at determining the parallax of either
seem hopeless. But the spiral form which is common to
both suggests that the Milky Way itself may be a gigantic
spiral nebula near whose center lies the sun, a humble
member of a great cluster of stars which is roughly globu-
lar in shape, but flattened at the poles of the galaxy
and completely encircled by its coils. However plausible
such a view may appear, it is for the present, at least, pure
hypothesis, although vigorously advocated by Easton, who
bases his argument upon the appearance of the galaxy
itself.

225. Absorption of starlight. — We have had abundant
occasion to learn that at least within the confines of the
solar system meteoric matter, cosmic dust, is profusely scat-
tered, and it appears not improbable that the same is true,
although in smaller degree, in even the remoter parts of
space. In this case the light which comes from the farther
stars over a path requiring many centuries to travel, must
be in some measure absorbed and enfeebled by the obstacles
which it encounters on the way. Unless celestial space is
transparent to an improbable degree the remoter stars do
not show their true brightness ; there is a certain limit
beyond which no star is able to send its light, and beyond

STARS AND NEBULA 357

which the universe must be to us a blank. A lighthouse
throws into the fog its beams only to have them extin-
guished before a single mile is passed, and though the
celestial lights shine farther, a limit to their reach is none
the less certain if meteoric dust exists outside the solar
system. If there is such an absorption of light in space,
as seems plausible, the universe may well be limitless and
the number of stellar systems infinite, although the most
attenuated of dust clouds suffices to conceal from us and
to shut off from our investigation all save a minor fraction
of it and them.

CHAPTEE XV

GROWTH AND DECAY

226. Nature of the problem. — To use a common figure of
speech, the universe is alive. We have found it filled with
an activity that manifests itself not only in the motions of
the heavenly bodies along their orbits, but which extends
to their minutest parts, the molecules and atoms, whose
vibrations furnish the radiant energy given off by sun and
stars. Some of these activities, such as the motions of the
heavenly bodies in their orbits, seem fitted to be of endless
duration ; while others, like the radiation of light and heat,
are surely temporary, and sooner or later must come to an
end and be replaced by something different. The study of
things as they are thus leads inevitably to questions of
what has been and what is to be. A sound science should
furnish some account of the universe of yesterday and
to-morrow as well as of to-day, and we need not shrink
from such questions, although answers to them must be
vague and in great measure speculative.

The historian of America finds little difficulty with events
of the nineteenth century or even the eighteenth, but the
sources of information about America in the fifteenth cen-
tury are much less definite ; the tenth century presents
almost a blank, and the history of American mankind in
the first century of the Christian era is wholly unknown.
So, as we attempt to look into the past or the future of the
heavens, we must expect to find the mists of obscurity grow
denser with remoter periods until even the vaguest outlines
of its development are lost, and we are compelled to say,
358

GROWTH AND DECAY 359

beyond this lies the unknown. Our account of growth and
decay in the universe, therefore, can not aspire to cover the
whole duration of things, but must be limited in its scope
to certain chapters whose epochs lie near to the time in
which we live, and even for these we need to bear con-
stantly in mind the logical bases of such an inquiry and
the limitations which they impose upon us.

227. Logical bases and limitations. — The first of these
bases is : An adequate knowledge of the present universe.
Our only hope of reading the past and future lies in an
understanding of the present; not necessarily a complete
knowledge of it, but one which is sound so far as it goes.
Our position is like that of a detective who is called upon
to unravel a mystery or crime, and who must commence
with the traces that have been left behind in its commis-
sion. The foot print, the blood stain, the broken glass must
be examined and compared, and fashioned into a theory of
how they came to be ; and as a wrong understanding of
these elements is sure to vitiate the theories based upon
them, so a false science of the universe as it now is, will
surely give a false account of what it has been; while a
correct but incomplete knowledge of the present does not
wholly bar an understanding of the past, but only puts us
in the position of the detective who correctly understands
what he sees but fails to take note of other facts which
might greatly aid him.

The second basis of our inquiry is : The assumed per-
manence of natural laws. The law of gravitation certainly
held true a century ago as well as a year ago, and for aught
we know to the contrary it may have been a law of the uni-
verse for untold millions of years ; but that it has prevailed
for so long a time is a pure assumption, although a neces-
sary one for our purpose. So with those other laws of
mathematics and mechanics and physics and chemistry to
which we must appeal ; if there was ever a time or place
in which they did not hold true, that time and place lie

360 ASTRONOMY

beyond the scope of our inquiry, and are in the domain
inaccessible to scientific research. It is for this reason
that science knows nothing and can know nothing of a
creation or an end of the universe, but considers only its
orderly development within limited periods of time. What
kind of a past universe would, under the operation of
known laws, develop into the present one, is the question
with which we have to deal, and of it we may say with
Helmholtz : " From the standpoint of science this is no
idle speculation but an inquiry concerning the limitations
of its methods and the scope of its known laws."

To ferret out the processes by which the heavenly bodies
have been brought to their present condition we seek first
of all for lines of development now in progress which tend
to change the existing order of things into something dif-
ferent, and, having found these, to trace their effects into
both past and future. Any force, however small, or any
process, however slow, may produce great results if it works
always and ceaselessly in the same direction, and it is in
these processes, whose trend is never reversed, that we find
a partial clew to both past and future.

228. The sun's development.— The first of these to claim
our attention is the shrinking of the sun's diameter which,
as we have seen in Chapter X, is the means by which the
solar output of radiant energy is maintained from year to
year. Its amount, only a few feet per annum, is far too
small to be measured with any telescope ; but it is cumula-
tive, working century after century in the same direction,
and, given time enough, it will produce in the future, and
must have produced in the past, enormous transformations
in the sun's bulk and equally significant changes in its
physical condition.

Thus, as we attempt to trace the sun's history into the
past, the farther back we go the greater shall we expect to
find its diameter and the greater the space (volume)
through which its molecules are spread. By reason of this

GROWTH AND DECAY 361

expansion its density must have been less then than now,
and by going far enough back we may even reach a time at
which the density was comparable with what we find in the
nebulae of to-day. If our ideas of the sun's present mechan-
ism are sound, then, as a necessary consequence of these,,
its past career must have been a process of condensation in
which its component particles were year by year packed
closer together by their own attraction for each other. As
we have seen in § 126, this condensation necessarily devel-
oped heat, a part of which was radiated away as fast as pro-
duced, while the remainder was stored up, and served to
raise the temperature of the sun to what we find it now.
At the present time this temperature is a chief obstacle to
further shrinkage, and so powerfully opposes the gravita-
tive forces as to maintain nearly an equilibrium with them,
thus causing a very slow rate of further condensation. But
it is not probable that this was always so. In the early
stages of the sun's history, when the temperature was low,
contraction of its bulk must have been more rapid, and
attempts have been made by the mathematicians to measure
its rate of progress and to determine how long a time has
been consumed in the development of the present sun from
a primitive nebulous condition in which it filled a space of
greater diameter than Xeptune's orbit. Of course, numer-
ical precision is not to be expected in results of this kind,
but, from a consideration of the greatest amount of heat
that could be furnished by the shrinkage of a mass equal to
that of the sun, it seems that the period of this develop-
ment is to be measured in tens of millions or possibly hun-
dreds of millions of years, but almost certainly does not
reach a thousand millions.

229. The sun's future,— The future duration of the sun
as a source of radiant energy is surely to be measured in
far smaller numbers than these. Its career as a dispenser
of light and heat is much more than half spent, for the
shrinkage results in an ever-increasing density, which
24

362 ASTRONOMY

makes its gaseous substance approximate more and more
toward the behavior of a liquid or solid, and we recall that
these forms of matter can not by any further condensation
restore the heat whose loss through radiation caused them
to contract. They may continue to shrink, but their tem-
perature must fall, and when the sun's substance becomes
too dense to obey the laws of gaseous matter its surface
must cool rapidly as a consequence of the radiation into
surrounding space, and must congeal into a crust which,
although at first incandescent, will speedily become dark
and opaque, cutting off the light of the central portions,
save as it may be rent from time to time by volcanic
outbursts of the still incandescent mass beneath. But
such outbursts can be of short duration only, and its final
.condition must be that of a dark body, like the earth or
moon, no longer available as a source of radiant energy.
Even before the formation of a solid crust it is quite pos-
sible that the output of light and heat may be seriously
diminished by the formation of dense vapors completely
enshrouding it, as is now the case with Jupiter and Saturn.
It is believed that these planets were formerly incandescent,
and at the present time are in a state of development
through which the earth has passed and toward which the
sun is moving. According to Kewcomb, the future during
which the sun can continue to furnish light and heat at its
present rate is not likely to exceed 10,000,000 years.

This idea of the sun as a developing body whose pres-
ent state is only temporary, furnishes a clew to some of the
vexing problems of solar physics. Thus the sun-spot period,
the distribution of the spots in latitude, and the peculiar
law of rotation of the sun in different latitudes, may be,
and very probably are, results not of anything now operat-
ing beneath its photosphere, but of something which hap-
pened to it in the remote past — e. g., an unsymmetrical
shrinkage or possibly a collision with some other body. At
sea the waves continue to toss long after the storm which

GROWTH AND DECAY 363

produced them has disappeared, and, according to the
mathematical researches of Wilsing, a profound agitation
of the sun's mass might well require tens of thousands, or
even hundreds of thousands of years to subside, and during
this time its effects would be visible, like the waves, as phe-
nomena for which the actual condition of things furnishes
no apparent cause.

230. The nebular hypothesis. — The theory of the sun's
progressive contraction as a necessary result of its radiation
of energy is comparatively modern, but more than a cen-
tury ago philosophic students of Nature had been led in
quite a different way to the belief that in the earlier stages
of its career the sun must have been an enormously ex-
tended body whose outer portions reached even beyond the
orbit of the remotest planet. Laplace, whose speculations
upon this subject have had a dominant influence during
the nineteenth century, has left, in a popular treatise upon
astronomy, an admirable statement of the phenomena of
planetary motion, which suggest and lead up to the nebular
theory of the sun's development, and in presenting this
theory we shall follow substantially his line of thought,
but with some freedom of translation and many omissions.

He says : " To trace out the primitive source of the plan-
etary movements, we have the following five phenomena :
(1) These movements all take place in the same direction
and nearly in the same plane. (2) The movements of the
satellites are in the same direction as those of the planets.
(3) The rotations of the planets and the sun are in the
same direction as the orbital motions and nearly in the same
plane. (4) Planets and satellites alike have nearly circular
orbits. (5) The orbits of comets are wholly unlike these by
reason of their great eccentricities and inclinations to the
ecliptic." That these coincidences should be purely the
result of chance seemed to Laplace incredible, and, seeking
a cause for them, he continues : " Whatever its nature may
be, since it has produced or controlled the motions of the

364 ASTRONOMY

planets, it must have reached out to all these bodies, and, in
view of the prodigious distances which separate them, the
cause can have been nothing else than a fluid of great ex-
tent which must have enveloped the sun like an atmosphere.
A consideration of the planetary motions leads us to think
that . . . the sun's atmosphere formerly extended far be-
yond the orbits of all the planets and has shrunk by degrees
to its present dimensions." This is not very different from
the idea developed in § 228 from a consideration of the
sun's radiant energy ; but in Laplace's day the possibility
of generating the sun's heat by contraction of its bulk was
unknown, and he was compelled to assume a very high tem-
perature for the primitive nebulous sun, while we now know
that this is unnecessary. Whether the primitive nebula
was hot or cold the shrinkage would take place in much
the same way, and would finally result in a star or sun of
very high temperature, but its development would be slower
if it were hot in the beginning than if it were cold.

But again Laplace : " How did the sun's atmosphere
determine the rotations and revolutions of planets and
satellites ? If these bodies had been deeply immersed in
this atmosphere its resistance to their motion would have
made them fall into the sun, and we may therefore conjec-
ture that the planets were formed, one by one, at the outer
limits of the solar atmosphere by the condensation of zones
of vapor which were cast off in the plane of the sun's equa-
tor." Here he proceeds to show by an appeal to dynamical
principles that something of this kind must happen, and
that the matter sloughed off by the nebula in the form of a
ring, perhaps comparable to the rings of Saturn or the
asteroid zone, would ultimately condense into a planet,
which in its turn might shrink and cast off rings to pro-
duce satellites.

Planets and satellites would then all have similar mo-
tions, as noted at the beginning of this section, since in
every case this motion is an inheritance from a common

PIERRE SIMON LAPLACE (1749-1827).

GROWTH AND DECAY 365

source, the rotation of the primitive nebula about its own
axis. " All the bodies which circle around a planet having
been thus formed from rings which its atmosphere succes-
sively abandoned as rotation became more and more rapid,
this rotation should take place in less time than is required
for the orbital revolution of any of the bodies which have
been cast off, and this holds true for the sun as compared
with the planets."

231. Objections to the nebular hypothesis. — In Laplace's
time this slower rate of motion was also supposed to hold
true for Saturn's rings as compared with the rotation of
Saturn itself, but, as we have seen in Chapter XI, this ring is
made up of a great number of independent particles which
move at different rates of speed, and comparing, through
Kepler's Third Law, the motion of the inner edge of the
ring with the known periodic time of the satellites, we may
find that these particles must rotate about Saturn more
rapidly than the planet turns upon its axis. Similarly the
inner satellite of Mars completes its revolution in about
one third of a Martian day, and we find in cases like this
grounds for objection to the nebular theory. Compare also
Laplace's argument with the peculiar rotations of Uranus,
Neptune; and their satellites (Chapter XI). Do these for-
tify or weaken his case ?

Despite these objections and others equally serious that
have been raised, the nebular theory agrees with the facts
of Nature at so many points that astronomers upon the
whole are strongly inclined to accept its major outlines as
being at least an approximation to the course of develop-
ment actually followed by the solar system ; but at some
points — e. g., the formation of planets and satellites through
the casting off of nebulous rings — the objections are so
many and strong as to call for revision and possibly serious
modification of the theory.

One proposed modification, much discussed in recent
years, consists in substituting for the primitive gaseous

366 ASTRONOMY

nebula imagined by Laplace, a very diffuse cloud of mete-
oric matter which in the course of its development would
become transformed into the gaseous state by rising tem-
perature. From this point of view much of the meteoric
dust still scattered throughout the solar system may be
only the fragments left over in fashioning the sun and
planets. Chamberlin and Moulton, who have recently
given much attention to this subject, in dissenting from
some of Laplace's views, consider that the primitive nebu-
lous condition must have been one in which the matter of
the system was " so brought together as to give low mass,
high momentum, and irregular distribution to the outer
part, and high mass, low momentum, and sphericity to the
central part," and they suggest a possible oblique collision
of a small nebula with the outer parts of a large one.

232. Bode's law. — We should not leave the theory of
Laplace without noting the light it casts upon one point
otherwise obscure — the meaning of Bode's law (§ 134).
This law, stated in mathematical form, makes a geomet-
rical series, and similar geometrical series apply to the
distances of the satellites of Jupiter and Saturn from
these planets. Now, Eoche has shown by the application
of physical laws to the shrinkage of a gaseous body that
its radius at any time may be expressed by means of a
certain mathematical formula very similar to Bode's law,
save that it involves the amount of time that has elapsed
since the beginning of the shrinking process. By compar-
ing this formula with the one corresponding to Bode's law
he reaches the conclusion that the peculiar spacing of the
planets expressed by that law means that they were formed
at successive equal intervals of time — i. e., that Mars is as
much older than the earth as the earth is older than
Venus, etc. The failure of Bode's law in the case of
Neptune would then imply that the interval of time be-
tween the formation of Neptune and Uranus was shorter
than that which has prevailed for the other planets. But

GROWTH AND DECAY 367

too much stress should not be placed upon this conclusion.
So long as the manner in which the planets came into being
continues an open question, conclusions about their time
of birth must remain of doubtful validity.

233. Tidal friction between earth and moon. — An impor-
tant addition to theories of development within the solar
system has been worked out by Prof. G. H. Darwin, who,
starting with certain very simple assumptions as to the
present condition of things in earth and moon, derives
from these, by a strict process of mathematical reasoning,
far-reaching conclusions of great interest and importance.
The key to these conclusions lies in recognition of the fact
that through the influence of the tides (§ 42) there is now
in progress and has been in progress for a very long time, a
gradual transfer of motion (moment of momentum) from
the earth to the moon. The earth's motion of rotation is
being slowly destroyed by the friction of the tides, as the
motion of a bicycle is destroyed by the friction of a brake,
and, in consequence of this slowing down, the moon is
pushed farther and farther away from the earth, so that
it now moves in a larger orbit than it had some millions
of years ago.

Fig. 24 has been used to illustrate the action of the
moon in raising tides upon the earth, but in accordance
with the third law of motion (§ 36) this action must be
accompanied by an equal and contrary reaction whose
nature may readily be seen from the same figure. The
moon moves about its orbit from west to east and the
earth rotates about its axis in the same direction, as
shown by the curved arrow in the figure. The tidal wave,
/, therefore points a little in advance of the moon's posi-
tion in its orbit and by its attraction must tend to pull the
moon ahead in its orbital motion a little faster than it
would move if the whole substance of the earth were
placed inside the sphere represented by the broken circle
in the figure. It is true that the tidal wave at I" pulls

368 ASTRONOMY

back and tends to neutralize the effect of the wave at /,
but on the whole the tidal wave nearer the moon has the
stronger influence, and the moon on the whole moves a
very little faster, and by virtue of this added impetus
draws continually a little farther away from the earth
than it would if there were no tides.

234. Consequences of tidal friction upon the earth. — This
process of moving the moon away from the earth is a
cumulative one, going on century after century, and with
reference to it the moon's orbit must be described not as
a circle or ellipse, or any other curve which returns into
itself, but as a spiral, like the balance spring of a watch,
each of whose coils is a little larger than the preceding
one, although this excess is, to be sure, very small, be-
cause the tides themselves are small and the tidal in-
fluence feeble when compared with the whole attrac-
tion of the earth for the moon. But^ given time enough,
even this small force may accomplish great results, and
something like 100,000,000 years of past opportunity
would have sufficed for the tidal forces to move the moon
from close proximity with the earth out to its present po-
sition.

For millions of years to come, if moon and earth endure
so long, the distance between them must go on increasing,
although at an ever slower rate, since the farther away the
moon goes the smaller will be the tides and the slower the
working out of their results. On the other hand, when
the moon was nearer the earth than now, tidal influences
must have been greater and their effects more rapidly
produced than at the present time, particularly if, as
seems probable, at some past epoch the earth was hot and
plastic like Jupiter and Saturn. Then, instead of tides in
the water of the sea, such as we now have, the whole sub-
stance of the earth would respond to the moon's attraction
in bodily tides of semi-fluid matter not only higher, but with
greater internal friction of their molecules one upon an-

GROWTH AND DECAY 369

other, and correspondingly greater effect in checking the
earth's rotation.

But, whether the tide be a bodily one or confined to the
waters of the sea, so long as the moon causes it to flow
there will be a certain amount of friction which will affect
the earth much as a brake affects a revolving wheel, slow-
ing down its motion, and producing thus a longer day as
well as a longer month on account of the moon's increased
distance. Slowing down the earth's rotation is the direct
action of the moon upon the earth. Pushing the moon
away is the form in which the earth's equal and contrary
reaction manifests itself.

235. Consequences of tidal friction upon the moon. — When
the moon was plastic the earth must have raised in it a
bodily tide manifold greater than the lunar tides upon the
earth, and, as we have seen in Chapter IX, this tide has
long since worn out the greater part of the moon's rotation
and brought our satellite to the condition in which it pre-
sents always the same face toward the earth.

These two processes, slowing down the rotation and
pushing away the disturbing body, are inseparable — one
requires the other ; and it is worth noting in this connec-
tion that when for any reason the tide ceases to flow, and
the tidal wave takes up a permanent position, as it has in
the moon (§ 99), its work is ended, for when there is no
motion of the wave there can be no friction to further
reduce the rate of rotation of the one body, and no reaction
to that friction to push away the other. But this perma-
nent and stationary tidal wave in the moon, or elsewhere,
means that the satellite presents always the same face
toward its planet, moving once about its orbit in the time
required for one revolution upon its axis, and the tide
raised by the moon upon the earth tends to produce here
the result long since achieved in our satellite, to make our
day and month of equal length, and to make the earth
turn always the same side toward the moon. But the

370 ASTRONOMY

moon's tidal force is small compared with that of the earth,
and has a vastly greater momentum to overcome, so that
its work upon the earth is not yet complete. According
to Thomson and Tait, the moon must be pushed off an-
other hundred thousand miles, and the day lengthened out
by tidal influence to seven of our present weeks before the
day and the lunar month are made of equal length, and
the moon thereby permanently hidden from one hemisphere
of the earth.

236. The earth-moon system, — Eetracing into the past
the course of development of the earth and moon, it is pos-
sible to reach back by means of the mathematical theory
of tidal friction to a time at which these bodies were much
nearer to each other than now, but it has not been found
possible to trace out the mode of their separation from one
body into two, as is supposed in the nebular theory. In
the earliest part of their history accessible to mathematical
analysis they are distinct bodies at some considerable dis-
tance from each other, with the earth rotating about an
axis more nearly perpendicular to the moon's orbit and to
the ecliptic than is now the case. Starting from such a
condition, the lunar tides, according to Darwin, have been
instrumental in tipping the earth's rotation axis into its
present oblique position, and in determining the eccen-
tricity of the moon's orbit and its position with respect to
the ecliptic as well as the present length of day and month.

337. Tidal friction upon the planets. — The satellites of the
outer planets are equally subject to influences of this kind,
and there appears to be independent evidence that some of
them, at least, turn always the same face toward their
respective planets, indicating that the work of tidal friction
has here been accomplished. We saw in Chapter XI that
it is at present an open question whether the inner planets,
Venus and Mercury, do not always turn the same face
toward the sun, their day and year being of equal length.
In addition to the direct observational evidence upon this

GKOWTH AND DECAY 371

point, Schiaparelli has sought to show by an appeal to tidal
theory that such is probably the case, at least for Mercury,
since the tidal forces which tend to bring about this result
in that planet are about as great as the forces which have
certainly produced it in the case of the moon and Saturn's
satellite, Japetus. The same line of reasoning would show
that every satellite in the solar system, save possibly the
newly discovered ninth satellite of Saturn, must, as a con-
sequence of tidal friction, turn always the same face toward
its planet.

238. The solar tide, — The sun also raises tides in the
earth, and their influence must be similar in character to
that of the lunar tides, checking the rotation of the earth
and thrusting earth and sun apart, although quantitatively
these effects are small compared with those of the moon.
They must, however, continue so long as the solar tide
lasts, possibly until the day and year are made of equal
length — i. e., they may continue long after the lunar tidal
influence has ceased to push earth and moon apart. Should
this be the case, a curious inverse effect will be produced.
The day being then longer than the month, the moon will
again raise a tide in the earth which will run around it
from west to east, opposite to the course of the present tide,
thus tending to accelerate the earth's rotation, and by its
reaction to bring the moon back toward the earth again,
and ultimately to fall upon it.

We may note that an effect of this kind must be in
progress now between Mars and its inner satellite, Phobos,
whose time of orbital revolution is only one third of a Mar-
tian day. It seems probable that this satellite is in the last
stages of its existence as an independent body, and must
ultimately fall into Mars.

239. Roche's limit— In looking forward to such a catas-
trophe, however, due regard must be paid to a dynamical
principle of a different character. The moon can never be
precipitated upon the earth entire, since before it reaches

372 ASTRONOMY

us it will have been torn asunder by the excess of the
earth's attraction for the near side of its satellite over that
which it exerts upon the far side. As the result of Eoche's
mathematical analysis we are able to assign a limiting dis-
tance between any planet and its satellite within which the
satellite, if it turns always the same face toward the planet,
can not come without being broken into fragments. If we
represent the radius of the planet by r, and the quotient
obtained by dividing the density of the 'planet by the den-
sity of the satellite by <?, then

Eoche's limit = 2.44 r l/q.

Thus in the case of earth and moon we find from the den-
sities given in § 95, q = 1.65, and with r = 3,963 miles we
obtain 11,400 miles as the nearest approach which the moon
could make to the earth without being broken up by the
difference of the earth's attractions for its opposite sides.

We must observe, however, that Eoche's limit takes no
account of molecular forces, the adhesion of one molecule
to another, by virtue of which a stick or stone resists frac-
ture, but is concerned only with the gravitative forces by
which the molecules are attracted toward the moon's center
and toward the earth. Within a stone or rock of moderate
size these gravitative forces are insignificant, and cohesion
is the chief factor in preserving its integrity, but in a large
body like the moon, the case is just reversed, cohesion plays
a small part and gravitation a large one in holding the
body together. We may conclude, therefore, that at a
proper distance these forces are capable of breaking up the
moon, or any other large body, into fragments of a size
such that molecular cohesion instead of gravitation is the
chief agent in preserving them from further disintegration.

240. Saturn's rings. — Saturn's rings are of peculiar in-
terest in this connection. The outer edge of the ring sys-
tem lies just inside of Eoche's limit for this planet, and we
have already seen that the rings are composed of small frag-

GROWTH AND DECAY 3Y3

ments independent of each other. Whatever may have
been the process by which the nine satellites of Saturn
came into existence, we have in Eoche's limit the explana-
tion why the material of the ring was not worked up into
satellites ; the forces exerted by Saturn would tear into
pieces any considerable satellite thus formed and equally
would prevent the formation of one from raw material.

Saturn's rings present the only case within the solar
system where matter is known to be revolving about a
planet at a distance less than Roche's limit, and it is an
interesting question whether these rings can remain as a
permanent part of the planet's system or are only a tempo-
rary feature. The drawings of Saturn made two centuries
ago agree among themselves in representing the rings as
larger than they now appear, and there is some reason to
suppose that as a consequence of mutual disturbances — col-
lisions— their momentum is being slowly wasted so that
ultimately they must be precipitated into the planet. But
the direct evidence of such a progress that can be drawn
from present data is too scanty to justify positive conclu-
sions in the matter. On the other hand, Xolan suggests
that in the outer parts of the ring small satellites might be
formed whose tidal influence upon Saturn would suffice to
push them away from the ring beyond Roche's limit, and
that the very small inner satellites of Saturn may have
been thus formed at the expense of the ring.

The inner satellite of Mars is very close to Roche's limit
for that planet, and, as we have seen above, must be approach-
ing still nearer to the danger line.

241. The moon's development— The fine series of photo-
graphs of the moon obtained within the last few years at
Paris, have been used by the astronomers of that observa-
tory for a minute study of the lunar formations, much as
geologists study the surface of the earth to determine some-
thing about the manner in which it was formed. Their
conclusions are, in general, that at some past time the moon

374: ASTRONOMY

was a hot and fluid body which, as it cooled and condensed,
formed a solid crust whose further shrinkage compressed
the liquid nucleus and led to a long series of fractures in
the crust and outbursts of liquid matter, whose latest and
feeblest stages produced the lunar craters, while traces of
the earlier ones, connected with a general settling of the
crust, although nearly obliterated, are still preserved in cer-
tain large but vague features of the lunar topography, such
as the distribution of the seas, etc. They find also in cer-
tain markings of the surface what they consider convincing
evidence of the existence in past times of a lunar atmos-
phere. But this seems doubtful, since the force of gravity
at the moon's surface is so small that an atmosphere similar
to that of the earth, even though placed upon the moon,
could not permanently endure, but would be lost by the
gradual escape of its molecules into the surrounding space.
The molecules of a gas are quite independent one of
another, and are in a state of ceaseless agitation, each one
darting to and fro, colliding with its neighbors or with
whatever else opposes its forward motion, and traveling
with velocities which, on the average, amount to a good
many hundreds of feet per second, although in the case of
any individual molecule they may be much less or much
greater than the average value, an occasional molecule hav-
ing possibly a velocity several times as great as the average.
In the upper regions of our own atmosphere, if one of these
swiftly moving particles of oxygen or nitrogen were headed
away from the earth with a velocity of seven miles per sec-
ond, the whole attractive power of the earth would be
insufficient to check its motion, and it would therefore,
unless stopped by some collision, escape from the earth and
return no more. But, since this velocity of seven miles per
second is more than thirty times as great as the average
velocity of the molecules of air, it must be very seldom in-
deed that one is found to move so swiftly, and the loss of
the earth's atmosphere by leakage of this sort is insignifi-

GROWTH AND DECAY 375

cant. But upon the moon, or any other body where the
force of gravity is small, conditions are quite different, and
in our satellite a velocity of little more than one mile per
second would suffice to carry a molecule away from the
outer limits of its atmosphere. This velocity, only five times
the average, would be frequently attained, particularly in
former times when the moon's temperature was high, for
then the average velocity of all the molecules would be con-
siderably increased, and the amount of leakage might be-
come, and probably would become, a serious matter, steadi-
ly depleting the moon's atmosphere and leading finally to
its present state of exhaustion. It is possible that the
moon may at one time have had an atmosphere, but if so it
could have been only a temporary possession, and the same
line of reasoning may be applied to the asteroids and to
most of the satellites of the solar system, and also, though
in less degree, to the smaller planets, Mercury and Mars.

242. Stellar development. — We have already considered
in this chapter the line of development followed by one
star, the sun, and treating this as a typical case, it is com-
monly believed that the life history of a star, in so far as it
lies within our reach, begins with a condition in which its
matter is widely diffused, and presumably at a low tempera-
ture. Contracting in bulk under the influence of its own
gravitative forces, the star's temperature rises to a maxi-
mum, and then falls off in later stages until the body ceases
to shine and passes over to the list of dark stars whose
existence can only be detected in exceptional cases, such
as are noted in Chapter XIII. The most systematic devel-
opment of this idea is due to Lockyer, who looks upon all
the celestial bodies — sun, moon and planets, stars, nebulae,
and comets — as being only collections of meteoric matter in
different stages of development, and who has sought by
means of their spectra to classify these bodies and to deter-
mine their stage of advancement. While the fundamental
ideas involved in this " meteoritic hypothesis " are not seri-

376 ASTRONOMY

ously controverted, the detailed application of its principles
is open to more question, and for the most part those
astronomers who hold that in the present state of knowl-
edge stellar spectra furnish a key to a star's age or degree
of advancement do not venture beyond broad general state-
ments.

24:3. Stellar spectra.— Thus the types of stellar spectra
shown in Fig. 151 are supposed to illustrate successive
stages in the development of an average star. Type I cor-

FIG. 151. — Types of stellar spectra substantially according to SECCHT.

responds to the period in which its temperature is near the
maximum ; Type II belongs to a later stage in which the
temperature has commenced to fall ; and Type III to the
period immediately preceding extinction.

While human life, or even the duration of the human
race, is too short to permit a single star to be followed
through all the stages of its career, an adequate picture of
that development might be obtained by examining many
stars, each at a different stage of progress, and, following

GROWTH AND DECAY 377

this idea, numerous subdivisions of the types of stellar
spectra shown in Fig. 151 have been proposed in order to
represent with more detail the process of stellar growth
and decay ; but for the most part these subdivisions and
their interpretation are accepted by astronomers with much
reserve.

It is significant that there are comparatively few stars
with spectra of Type III, for this is what we should expect
to find if the development of a star through the last stages
of its visible career occupied but a small fraction of its
total life. From the same point of view the great number
of stars with spectra of the first type would point to a long
duration of this stage of life. The period in which the
sun belongs, represented by TjTpe II, probably has a dura-
tion intermediate between the others. Since most of the
variable stars, save those of the Algol class, have spectra of
the third type, we conclude that variability, with its associ-
ated ruddy color and great atmospheric absorption of light,
is a sign of old age and approaching extinction. The Algol
or eclipse variables, on the other hand, having spectra of the
first type, are comparatively young stars, and, as we shall
see a little later, the shortness of their light periods in some
measure confirms this conclusion drawn from their spectra.

We have noted in § 196 that the sun's near neighbors
are prevailingly stars with spectra of the second type,
while the Milky Way is mainly composed of first-type stars,
and from this we may now conclude that in our particular
part of the entire celestial space the stars are, as a rule,
somewhat further developed than is the case elsewhere.

244. Double stars. — The double stars present special
problems of development growing out of the effects of tidal
friction, which must operate in them much as it does be-
tween earth and moon, tending steadily to increase the dis-
tance between the components of such a star. So, too,
in such a system as is shown in Fig. 133, gravity must
tend to make each component of the double star shrink to
25

378 ASTRONOMY

smaller dimensions, and this shrinkage must result in
faster rotation and increased tidal friction, which in turn
must push the components apart, so that in view of the
small density and close proximity of those particular stars
we may fairly regard a star like {3 Lyrae as in the early stages
of its career and destined with increasing age to lose its
variability of light, since the eclipses which now take place
must cease with increasing distance between the compo-
nents unless the orbit is turned exactly edgewise toward the
earth. Close proximity and the resulting shortness of pe-
riodic time in a double star seem, therefore, to be evidence
of its youth, and since this shortness of periodic time is
characteristic of both Algol variables and spectroscopic
binaries as a class, we may set them down as being, upon
the whole, stars in the early stages of their career. On
the other hand, it is generally true that the larger the or-
bit, and the greater the periodic time in the orbit, the
farther is the star advanced in its development.

In his theory of tidal friction, Darwin has pointed out
that whenever the periodic time in the orbit is more than
twice as long as the time required for rotation about the
axis, the effect of the tides is to increase the eccentricity of
the orbit, and, following this indication, See has urged that
with increasing distance between the components of a
double star their orbits about the common center of grav-
ity must grow more and more eccentric, so that we have in
the shape of such orbits a new index of stellar develop-
ment ; the more eccentric the orbit, the farther advanced
are the stars. It is important to note in this connection
that among the double stars whose orbits have been com-
puted there seems to run a general rule — the larger the
orbit the greater is its eccentricity— a relation which must
hold true if tidal friction operates as above supposed, and
which, being found to hold true, confirms in some degree
the criteria of stellar age which are furnished by the theory
of tidal friction.

GROWTH AND DECAY 379

245. Nebulae, — The nebular hypothesis of Laplace has
inclined astronomers to look upon nebulae in general as
material destined to be worked up into stars, but which is
now in a very crude and undeveloped stage. Their great
bulk and small density seem also to indicate that gravitation
has not yet produced in them results at all comparable with
what we see in sun and stars. But even among nebulae
there are to be found very different stages of development.
The irregular nebula, shapeless and void like that of
Orion ; the spiral, ring, and planetary nebulas and the star
cluster, clearly differ in amount of progress toward their
final goal. But it is by no means sure that these several
types are different stages in one line of development ; for
example, the primitive nebula which grows into a spiral
may never become a ring or planetary nebula, and vice
versa. So too there is no reason to suppose that a star
cluster will ever break up into isolated stars such as those
whose relation to each other is shown in Fig. 122.

246. Classification. — Considering the heavenly bodies
with respect to their stage of development, and arranging
them in due order, we should probably find lowest down in
the scale of progress the irregular nebula of chaotic ap-
pearance such as that represented in Fig. 146. Above
these in point of development stand the spiral, ring, and
planetary nebulae, although the exact sequence in which
they should be arranged remains a matter of doubt. Still
higher, up in the scale are star clusters whose individual
members, as well as isolated stars, are to be classified by
means of their spectra, as shown in Fig. 151, where the
order of development of each star is probably from Type I,
through II, into III and beyond, to extinction of its light
and the cutting off of most of its radiant energy. Jupiter
and Saturn are to be regarded as stars which have recently
entered this dark stage. The earth is further developed
than these, but it is not so far along as are Mars and Mer-
cury ; while the moon is to be looked upon as the most

380 ASTRONOMY

advanced heavenly body accessible to our research, having
reached a state of decrepitude which may almost be called
death— a stage typical of that toward which all the others
are moving.

Meteors and comets are to be regarded as fragments of
celestial matter, chips, too small to achieve by themselves
much progress along the normal lines of development, but
destined sooner or later, by collision with some larger body,
to share thenceforth in its fortunes.

247. Stability of the universe, — It was considered a great
achievement in the mathematical astronomy of a century
ago when Laplace showed that the mutual attractions of
sun and planets might indeed produce endless perturba-
tions in the motions and positions of these bodies, but
could never bring about collisions among them or greatly
alter their existing orbits. But in the proof of this great
theorem two influences were neglected, either of which is
fatal to its validity. One of these — tidal friction — as we
have already seen, tends to wreck the systems of satellites,
and the same effect must be produced upon the planets by
any other influence which tends to impede their orbital
motion. It is the inertia of the planet in its forward move-
ment that balances the sun's attraction, and any diminu-
tion of the planet's velocity will give this attraction the
upper hand and must ultimately precipitate the planet
into the sun. The meteoric matter with which the earth
comes ceaselessly into collision must have just this influ-
ence, although its effects are very small, and some-
thing of the same kind may come from the medium
which transmits radiant energy through the interstellar
spaces.

It seems incredible that the luminiferous ether, which
is supposed to pervade all space, should present absolutely
no resistance to the motion of stars and planets rushing
through it with velocities which in many cases exceed
50,000 miles per hour. If there is a resistance to this mo-

GROWTH AND DECAY 381

tion, however small, we may extend to the whole visible
universe the words of Thomson and Tait, who say in their
great Treatise on Katural Philosophy, " We have no data in
the present state of science for estimating the relative im-
portance of tidal friction and of the resistance of the resist-
ing medium through which the earth and moon move ;
but, whatever it may be, there can be but one ultimate
result for such a system as that of the sun and planets,
if continuing long enough under existing laws and not
disturbed by meeting with other moving masses in
space. That result is the falling together of all into
one mass, which, although rotating for a time, must in
the end come to rest relatively to the surrounding me-
dium."

Compare with this the words of a great poet who in
The Tempest puts into the mouth of Prospero the lines :

" The cloud-capp'd towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve ;
And, like this insubstantial pageant faded,
Leave not a rack behind."

248. The future. — In spite of statements like these, it
lies beyond the scope of scientific research to affirm that
the visible order of things will ever come to naught, and
the outcome of present tendencies, as sketched above, may
be profoundly modified in ages to come, by influences of
which we are now ignorant. We have already noted that
the farther our speculation extends into either past or
future, the more insecure are its conclusions, and the re-
moter consequences of present laws are to be accepted with
a corresponding reserve. But the one great fact which
stands out clear in this connection is that of change. The
old concept of a universe created in finished form and des-
tined so to abide until its final dissolution, has passed away
from scientific thought and is replaced by the idea of slow

382 ASTRONOMY

development. A universe which is ever becoming some-
thing else and is never finished, as shadowed forth by
Goethe in the lines :

" Thus work I at the roaring loom of Time,
And weave for Deity a living robe sublime "

APPENDIX

THE GEEEK ALPHABET

THE Greek letters are so much used by astronomers in
connection with the names of the stars, and for other pur-
poses, that the Greek alphabet is printed below — not neces-
sarily to be learned, but for convenient reference :

Greek.
A a

B ft

r 7

A d

E e or e

Z f

H T,

e # or 6

1 i
K K
A X
M /A
N v
» I
O o

n TT

p p

2 a- or $•
T T

Y v

Name.

English.

Alpha

a

Beta

b

Gamma

g

Delta

d

Epsilon

6

Zeta

z

Eta

e

Theta

th

Iota

i

Kappa

k

Lambda

1

Mu

m

Nu

n

Xi

X

Omicron

6

Pi

P

Rho

r

Sigma

s

Tau

t

Upsilon

u

Phi

ph

Chi

ch

Psi

ps

Omega

6

383

384 ASTRONOMY

POPULAE LlTEEATUEE OF ASTEONOMY

THE following brief bibliography, while making no
pretense at completeness, may serve as a useful guide to
supplementary reading :

General Treatises

^ YOUNG. General Astronomy. An admirable general survey of the
entire field.

V NEWCOMB. Popular Astronomy. The second edition of a German
translation of this work by Engelmann and Vogel is especially valuable.

v BALL. Story of the Heavens. Somewhat easier reading than either
of the preceding.

v CHAMBERS. Descriptive Astronomy. An elaborate but elementary
work in three volumes.

vLANGLEY. The New Astronomy. Treats mainly of the physical
condition of the celestial bodies.

/PROCTOR and RANYARD. Old and New Astronomy.

Special Treatises

PROCTOR. The Noon. A general treatment of the subject.
NASMYTH and CARPENTER. The Moon. An admirably illustrated
but expensive work dealing mainly with the topography and physical
conditions of the moon. There is a cheaper and very good edition in
German.

v YOUNG. The Sun. International Scientific Series. The most recent
and authoritative treatise on this subject.

" PROCTOR. Other Worlds than Ours. An account of planets, com-
ets, etc.

NEWTON. Meteor. Encyclopaedia Britannica.
AIRY. Gravitation. A non-mathematical exposition of the laws
of planetary motion.

^ STOKES. On Light as a Means of Investigation. Burnett Lectures.
II. The basis of spectrum analysis.
^CHELLEN. Spectrum Analysis.

V/THOMSON (Sir W., Lord KELVIN), Popular Lectures, etc. Lectures
on the Tides, The Sun's Heat, etc.

APPENDIX 385

Time and Tide. An exposition of the researches of G. H.
Darwin upon tidal friction. ,

GORE. The Visible Universe. Deals with a class of problems inad-
equately treated in most popular astronomies.
y DARWIN. The Tides. An admirable elementary exposition.
^CLERKE. The System of the Stars. Stellar astronomy.

NEWCOMB. Chapters on the Stars, in Popular Science Monthly for
1900.

CLERKE. History of Astronomy during the Nineteenth Century.
An admirable work.

WOLF. Geschichte der Astronomic. Mlinchen, 1877. An excellent
German work.

386

ASTRONOMY

A LIST OF STARS FOR TIME OBSERVATIONS

See 8 20.

NAME.

Magnitude.

Right Ascension.

Declination.

0 Ceti

2

h. m.

0 38.6

0

— 18.5

77 Ceti

3

1 3.6

— 10.7

a Ceti

3

2 57.1

+ 3.7

y Eridani .

3

3 53.4

— 13 8

Aldebaran

1

4 30.2

4 16.3

Rig el

0

5 9.7

— 8.3

K Orioriis

2

5 43.0

— 9.7

2

6 18.3

—17.9

Siviiis

_1

6 40 7

—16.6

Procyon

0

7 34.1

+ 5.5

ct HvdrsB

2

9 22.7

— 8.2

Reoulus .

1

10 3.0

+ 12.5

v HydraB

3

10 44.7

-15.7

3

12 5.0

-22.1

y Corvi . . .

3

12 10.7

-17.0

Spica

1

13 19.9

-10.6

(* Virsrinis • ,

3

13 29.6

- 0.1

a Librae

3

14 45.3

-15.6

)8 LibraB

3

15 11.6

- 9.0

Antarcs . ...

1

16 23.3

-26.2

2

17 30.3

+ 12.6

e Sagittarii

2

18 17.5

-34.4

3

19 20.5

+ 2.9

Altair

1

19 45.9

+ 8.6

/8 Aquarii

3

21 26.3

- 6.0

3

22 0.6

- 0.8

FoTtmlhciut . .

1

22 52.1

-30.2

INDEX

The references are to section numbers.

Absorption of starlight, 225.
Absorption spectra, 87.
Accelerating force, 35.
Adjustment of observations, 2.
Albedo of moon, 97.

of Venus, 148.
Algol, 205.
Altitudes, 4, 21.
Andromeda nebula, 214.
Angles, measurement of, 2.
Angular diameter, 7.
Annular eclipse, 64.
Asteroids, 156.
Atmosphere of the earth, 49.

of the moon, 103.

of Jupiter, 139.

of Mars, 153.
Aurora, 51.
Azimuth, 5, 21.

Biela's comet, 181.
Bode's law, 134, 232.
Bredichin's theory of comet tails,
180.

Calendar, 0. S. and N. S., 61.
Capture of comets and meteors,

176.

Canals of Mars, 154.
Celestial mechanics, 32.
Changes upon the moon, 108.

Chemical constitution of sun, 116.

of stars, 210.

Chromosphere, the sun's, 124.
Chronology, 59.
Classification of stars, 212.
Clocks and watches, 74.

sidereal clock, 12.
Collisions with comets, 183.
Colors of stars, 209.
Comets, general characteristics,
158-164.

development of, 179, 181.

groups, 177.

orbits, 161.

periodic, 176.

spectra, 182.

tails, 180.
Comets and meteors, relation of,

175.

Conic sections, 38.
Constellations, 184.
Corona, the sun's, 123.
Craters, lunar, 105.

Dark stars, 201.
Day, 52, 62.
Declination, 21.
Development of comet, 179.

of moon, 241.

of nebulae, 245.

of stars, 242, 244.
387

388

ASTRONOMY

Development of sun, 228.

of universe, 226.
Distribution of stars and nebulae,

220.

Diurnal motion, 10, 15.
Doppler principle, 89.
Double nebulae, 215.
Double stars, 198.

development of, 244.
Driving clock, 80.

Earth, atmosphere, 48.

mass, 45.

size and shape, 44.

warming of the earth, 47.
Eclipses, nature of, 63.

annular eclipse, 64.

eclipse limits, 68.

eclipse maps, 70, 71.

number of, in a year, 69.

partial eclipse, 64.

prediction of, 70, 71.

recurrence of, 72.

shadow cone, 64, 66.

total eclipse, 64.

uses of, 73.

Eclipses of Jupiter's satellites, 141.
Eclipse theory of variable stars,

205.
Ecliptic, 26.

obliquity of, 25.
Ellipse, 33.

Epochs for planetary motion, 30.
Energy, radiant, 75.

condensation of, 76.
Epicycle, 32.
Equation of time, 53.
Equator, 16, 21.
Equatorial mounting, 80.
Equinoxes, 25.
Ether, 75.
Evening star, 31.

Faculae, 122.

Falling bodies, law of, 35.
Finding the stars, 14.
Fraunhofer lines, 87.

Galaxy, 219.

Geography of the sky, 16.
Graphical representation, 6.
Grating, diffraction, 84.
Gravitation, law of, 37.

Harvest moon, 93.

Heat of the sun, 118, 126.

Helmholtz, contraction theory of

the sun, 126, 228.
Horizon, 4, 21.
Hour angle, 21.
Hour circle, 21.
Hyperbola, 38.

Japetus, satellite of Saturn, 145.
Jupiter, 136.

atmosphere, 139.

belts, 137.

invisible from fixed stars, 197.

orbit of, 29.

physical condition, 139.

rotation and flattening, 138.

satellites, 140.

surface markings, 137.

Kepler's laws, 33, 111.

Latitude, determination of, 18.

Leap year, 61.

Lenses, 77.

Leonid meteor shower, 172.

perturbations of, 174.
Librations of moon, 98.
Life upon the planets, 157.
Light curves, 205.
Light, nature of, 75.

INDEX

389

Light year, 190.
Limits of eclipses, 68.
Longitude, 56.

determination of, 58.
Lunation, 60.

Magnifying power of telescope,

79.

Magnitude, stellar, 9, 186.
Mars, atmosphere, temperature,
150.

canals, 154.

orbit, 30.

polar caps, 152.

rotation, 151.

satellites, 155.

surface markings, 150.
Mass, determination of, 37.

of .comets, 164.

of double stars, 200.

of moon, 94.

of planets, 40, 133.
Measurements, accurate, 1.
Mercury, 149.

motion of its perihelion, 43.

orbit of, 30.
Meridian, 19, 21.
Meteors, nature of, 165, 169.

number of, 167.

velocity, 170.
Meteors and comets, relation of,

175.
Meteor showers, radiant, 171.

Leonids, capture of, 172, 173.

perturbations, 174.
Milky Way, 219.
Mira, o Ceti, 204.
Mirrors, 77.
Month, 60.
Moon, 91.

albedo, 97.

atmosphere, 103.

Moon, changes in, 108.

density, surface gravity, 95.

development of, 241.

harvest moon, 93.

influence upon the earth, 109,
233.

librations, 98.

map of, 101.

mass and size, 94.

motion, 24, 92.

mountains and craters, 104.

phases, 91, 92.

physical condition, 100, 107.
Month, 60.
Morning star, 31.
Motion in line of sight, 89, 193.
Multiple stars, 202.

Names of stars. 8.
Nebulae, 214.

density, 217.

development of, 245.

motion, 218.

spectra, 216.

types and classes of, 215.
Nebular hypothesis, 230.

objections to, 231.
Neptune, 146.

discovery of, 41.
Newton's laws of motion, 34.

law of gravitation, 37, 43.
Nodes, 39.

relation to eclipses, 67, 71.
Nucleus, of comet, 160.

Objective, of telescope, 78.
Obliquity of ecliptic, 25.
Observations, of stars, 10.
Occultation of stars, 103.
Orbits, of comets, 161.

of double stars, 199.

of moon, 92.

390

ASTRONOMY

Orbits, of planets, 38.
Orion nebula, 215.

Parabola, 35, 38, 161.
Parabolic velocity, 38.
Parallax, 114, 188.
Penumbra, 64, 121.
Perihelion, 38.
Periodic comets, 176.
Personal equation, 82.
Perturbations, 39.

of meteors, 174.
Phases, of the moon, 91, 92.
Photography, 81.

of stars, 13.

Photosphere, of sun, 121.
Planets, 26, 133.

distances from the sun, 134.

how to find, 29.

mass, density, size, 133.

motion of, 27, 38.

periodic times of, 30.
Planetary nebulas, 215.
Pleiades, 16, 215.
Plumb-line apparatus, 11, 18.
Poles, 21.
Precession, 46.
Prisms, 84.

Problem of three bodies, 39.
Prominences, solar, 125.
Proper motions, 191.
Protractor, 2.
Ptolemaic system, 32.

Radiant energy, 75.

Radiant, of meteor shower, 171.

Radius victor, 33.

Reference lines and circles, 17.

Refraction, 50.

Right ascension, 16, 20, 21.

Roche's limit, 239.

Rotation, of earth, 55.

Rotation, of Mars, 151.
of moon, 99.
of Jupiter, 138.
of Saturn, 144.
of sun, 120, 132.

Saros, 72.

Satellites, of Jupiter, 136, 140.

of Mars, 155.

of Saturn, 145.
Saturn, 142.

ball of, 144.

orbit, 29.

rings, 142.

rotation, 144.

satellites, 145.
Seasons, on the earth, 47.

on Mars, 151.
Shadow cone, 64, 66.
Sidereal time, 20, 54.
Shooting stars, 158. (See Meteor.)
Spectroscope, 84.
Spectroscopic binaries, 203.
Spectrum, 84, 87.

of comets, 182.

of nebulae, 216.

of stars, 211.

types of, 88.
Spectrum analysis, 85.
Spiral nebulae, 215.
Standard time, 57.
Stars, 8, 184.

classes of, 212.

clusters, 213.

colors, 209.

dark stars, 201.

development of, 242.

distances from the sun, 188, 196.

distribution of, 220.

double stars, 198, 203.

drift, 194.

magnitudes, 9, 196.

INDEX

391

Stars, number of, 185.

spectra, 211.

temporary, 208.

variable, 204.

Starlight, absorption of, 225.
Star maps, construction of, 23.
Stellar system, extent of, 223.
Sun's apparent motion, 25.

real motion, 195.
Sun, 110.

chemical composition, 116.

chromosphere, 124.

corona, 123.

distance from the earth, 111.

f acute, 119, 122.

gaseous constitution, 127.

heat of, 117.

mechanism of, 126.

physical properties, 115-120.

prominences, 125.

rotation, 120, 132.

surface of, 119.

temperature, 118.
Sun spots, 119, 121.

period, 129, 131.

zones, 130.

Telescopes, 78.

equatorial mounting for, 80.

magnifying power of, 79.
Temperature of Jupiter, 139.

of Mars, 152.

of Mercury, 149.

of moon, 107.

of sun, 118.
Temporary stars, 208.

Terminator, 91.
Tenth meter, 75.
Tidal friction, 233-238.
Tides, 42.
Time, sidereal, 20, 54.

solar, 52.

determination of, 20.

equation of, 53.

standard, 57.
Triangulation, 3.
Trifid nebula, 215.
Twilight, 51.
Twinkling, of stars, 48.

Universe, development of, 226.

stability of, 247.
Uranus, 146.

Variable stars, 204.

Velocity, its relation to orbital

motion, 38.
Venus, 148.

orbit of, 30.
Vernal equinox, 21, 25.
Vertical circle, 21.

Wave front, 76.
Wave lengths, 75, 86.

Year, 25.
leap year, 61.
sidereal year, 59.
tropical year, 60.

Zenith, 21.
Zodiac, 26.
Zodiacal light, 168.

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