ASTRONOMY
^
/o
A HANDY MANUAL FOR
STUDENTS AND OTHERS
BY
F. W. DYSON, F.R.S.
ASTRONOMER ROYAL FOR SCOTLAND ;
PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF EDINBURGH
WITH 95 DIAGRAMS AND ILLUSTRATIONS
LONDON
J. M. DENT & SONS, LTD.
29 & 30 BEDFORD STREET, W.C.
1910
All rights reserved
PREFACE
IN this little book I have attempted to give an
account of the methods employed by astronomers and
the reasons for some of the propositions they advance.
Astronomical investigations frequently seem compli-
cated owing to the amount of subsidiary detail, but
the principles underlying them are simple and usually
admit of a clear statement which can be followed by
a general reader. In the introduction to his lectures
delivered at Ipswich in 1848 Sir George Airy draws
attention to an attitude towards Astronomy which is
still prevalent. Such questions as the determination
of the distance of the Sun or Moon are considered as
beyond ordinary comprehension ; the instruments with
which astronomical measurements are made are sup-
posed to be based on obscure and difficult principles ;
therefore the best a layman can do is to accept state-
ments on the personal credit of the astronomer making
them. He points out that this is an exaggerated
view. The principles involved in measuring the dis-
tance of the Moon are no more abstruse than those
employed to find the distance of a tree on the other
side of a river. Astronomical instruments are as
simple in principle and far less complicated in detail
than a lathe or a steam-engine. It is quite true that
in both instruments and methods many subsidiary
details must be attended to when great accuracy is
required in order that disturbing causes may be
allowed for or eliminated. But an explanation of
the essential principles may be given which can be
readily understood with ordinary care and attention.
VI
PREFACE
As far as possible an historical order has been
followed. The reader's attention has been drawn to
the desirability of making for himself certain observa-
tions of the sky which do not require the use of a
telescope. Every educated person ought to see with
his own eyes how Sun, Moon, Stars and Planets move
in the sky, and be able to infer from his own observa-
tions the movement of the Earth about the Sun, the
comparative nearness of the Moon, and other common-
places of Astronomy.
It is difficult to acknowledge fully my obligations
to the authors of books and papers which I have con-
sulted. Mention should be specially made of Mr.
Arthur Berry's History of Astronomy, Prof. Young's
General Astronomy, and the articles by Prof. New-
comb on "Astronomy" and Prof. Hale on "Spec-
troscopy " in the Encyclopaedia Britannica.
I am indebted to the Astronomer Royal Sir
William Christie, Prof. Barnard, Prof. Ritchey and
other astronomers for permission to reproduce photo-
graphs published by them, and to Mr. W. B. Blaikie
for the map taken from his Monthly Star Maps
published by the Scottish Provident Association.
I wish to express my thanks to a number of friends
for help in various directions. Mr. Heath, first as-
sistant of the Royal Observatory, Edinburgh, copied
a number of photographs and supplied me with the
drawing on p. 172 ; Mr. Storey, assistant at the
Observatory, and Mr. MacGregor assisted with the
diagrams. I am much obliged to Mr. Storey and to
Dr. J. Reynolds Green, who read the book in proof,
for their valuable criticism and suggestions.
F. W. DYSON.
Royal Observatory, Edinburgh,
March 7, 79/0.
CONTENTS
CHAP. PAGE
I ANCIENT ASTRONOMY ..... i
II THE COPERNICAN SYSTEM . . . -3
III THE LAW OF GRAVITATION .... 45
IV ASTRONOMICAL INSTRUMENTS .... 63
V THE SUN'S DISTANCE 85
VI THE SUN .100
VII THE SOLAR SYSTEM . . . . . .129
VIII DISTANCES AND MOVEMENTS OF THE STARS . 164
IX STARS AND NEBULAE 193
X DOUBLE STARS AND CLUSTERS .... 208
XI VARIABLE STARS AND NEW STARS . . . 225
XII THE SIDEREAL UNIVERSE .... 239
CHAPTER I
ANCIENT ASTRONOMY
ASTRONOMY is the oldest of the sciences. The
orientation of the pyramids or of Stonehenge, the
mythology of the Greeks and the religious festivals of
the Jews are familiar evidences of astronomical know-
ledge in early civilizations. The constant repetition,
day by day, month by month, or year by year, of
similar phenomena both invited and aided study of
the heavenly bodies. Before the dawn of history men
wondered what caused the rising and setting of the
Sun and Moon each day, why the Moon went through
her phases each month, and why Orion reappeared
each year in the sky as surely as the seasons returned.
An out-of-door life was favourable to a knowledge of
the heavens, and the tribes of Chaldea and Arabia
two or three thousand years ago were, perhaps, better
acquainted with the appearance of the sky than we
are to-day. Modern conditions of life are not favour-
able to the general cultivation of practical astronomy.
Buildings circumscribe the view 7 of the sky, clocks and
watches save us the trouble of observing the Sun and
stars for time, and artificial illumination makes us
independent of moonlight. But the following phe-
2 ASTRONOMY
nomena of the skies ought not to be merely read of in
books, but should be verified by actual observation.
(1) The diurnal movement of the Sun; the different
positions of the Sun in the sky in summer and winter.
(2) The phases of the Moon ; the rapid movement of
the Moon among the stars.
(3) The diurnal movement of the stars ; the appear-
ance of different constellations at different times of the
year.
Observation of the Sun. In the latitude of London the
Sun rises on midsummer day at about 3 h. 45m.
at a point on the horizon considerably north of east.
At midday, when due south, it is high in the sky.
If we take a stick and point it horizontally and turn
it gradually towards the vertical, we shall not be
pointing to the Sun till the stick has been turned
through rather more than two-thirds of the right-
angle between the horizontal and vertical directions.
It sets in the evening about 8 h. 19 m. at a point on
the horizon considerably north of west. From mid-
summer to midwinter it rises later and sets earlier
each day ; the point of the horizon where it rises
gradually shifts from north of east to due east, and
then to south of east ; and the point where it sets shifts
in the other direction from north of west to due west,
and then to south of west. In midwinter the Sun
rises at 8 h. 7 m. and sets at 3 h. 51 m., and at noon,
instead of being high up in the sky, it is only 15,
or one-sixth of a right-angle, above the horizon.
ANCIENT ASTRONOMY 3
From midwinter to midsummer the days lengthen
and the Sun at noon is higher each day. Midway
between midsummer and midwinter, on March 22 and
Sep. 22, the Sun rises due east and sets due west,
and day and night are equal in length. This succes-
sion of phenomena repeats itself year by year, and is
more striking in the latitude of the British Isles than
in the more southern countries from which our
astronomical knowledge was derived.
Diagram I illustrates the path of the Sun across the
sky at different times of the year. The circle NES is
the horizon, and NPZS
the meridian or circle of
the sky cut by a vertical
plane in a direction due
north and south. The
diagram represents the
eastern half of the sky
the part above NES
being above the horizon
and visible, and the part Dj
below NES below the
horizon and invisible. On midsummer day the Sun
travels from A to C between midnight and midday,
crossing the horizon at B (i.e. rising) at 3 h. 45111.
All points of the circle ABC are 66J from P, i. e.
if we divide the arc of the sphere from the pole P to
the opposite one into 180 parts, all points of the
circle ABC are 66J parts from P. But on Septem-
B 2
ber 22 the Sun is 90 from P. At midnight on
that day it is at D, rises at E (due east) at 6h. om.,
and is at its highest point F (due south) at 12 h. om.
When we come to December 22 the Sun is 113^ from
P. At midnight it is at G, does not reach H, i. e.
does not rise till 8 h. 7 m., and is at K (due south) at
12 o'clock.
Solar Day. It is not quite correct to say that the Sun
is due south exactly at 12 o'clock, but this is suffi-
ciently true for the explanation given in the last
paragraph. The interval of time between the moment
when the Sun is due south one day to the moment
when it is due south the next is called the solar day,
and is the natural unit of time. The length of the solar
day is not quite constant, but varies to the extent of
one minute at different times of the year. Its average
length throughout the year is the mean solar day, and
is exactly the 24 hours of our clocks and watches.
Year. The exact time the Sun takes to go through
the cycle of changes described above is the year. The
length of the year can therefore be found approxi-
mately by counting the number of days from a par-
ticular day in any year to the day in the following
year when the Sun is the same height in the sky at
noon. When the Sun's height at noon, or, in tech-
nical language, its altitude, is measured accurately, it
is found that after 365 days have elapsed from March
22 the Sun is not quite so high, but after 366 days is
higher. Thus the year does not consist of an exact
number of days.
ANCIENT ASTRONOMY 5
The Greek astronomer, Hipparchus, made accurate
observations which showed that the year was rather
less than 365^ days a year of 365^ days giving,
according to his calculations, an error of only one
day in 300 years.
Calendar. It is hardly necessary to refer to the
difficulties different nations experienced with their
chronology till a civil year was devised, whose aver-
age length was equal to that of the actual solar or
tropical year. Our calendar is derived from the one
introduced by Julius Caesar with the advice and assist-
ance of Sosigenes. Every fourth year on this system
is a leap year, and consists of 366 days. The error,
according to this reckoning, is more than was sup-
posed by Hipparchus, and is very approximately 3
days in 400 years. In course of time this small error
accumulated, till in 1582, the equinoxes, midsummer
day, etc., all fell on dates 10 days different from those
on which they had fallen in A.D. 325, the year of the
Council of Nice. In the reformation of the calendar,
which was then introduced by Pope Gregory XIII, it
was ordained that the centurial years should not be
counted as leap years unless the number of centuries
is divisible by 4 without remainder. Thus 1700, 1800,
1900 are not leap years, but 2000 is a leap year. With
this correction the average length of the civil year
only differs from the solar year by one day in about
3300 years.
Observation of the Moon. Each month the Moon
changes from new to full and from full to new.
ASTRONOMY
These changes in the Moon's appearance are called
its phases, and observation shows that as the phase of
the Moon changes the angle between the directions of
the Sun and Moon changes also. The new Moon is
always seen in the west near the setting Sun ; when
half illuminated its direction makes a right-angle with
that of the Sun; and when full, its direction is
diametrically opposite to that of the Sun. The correct
interpretation of the Moon's phases was given by
Aristotle (384-322 B.C.), viz. that it is a spherical
body, illuminated by the very distant Sun. One half
of the sphere is bright and the other dark. The
appearance of the Moon from the Earth depends on
whether the Earth is in a position from which much
or little of the illuminated part is visible.
-
'-
J
CH
-
*
o C
1 .._,
C-
-sf
*
)-
Diag. II.
In the right half of Diagram II the appearance of
the Moon is shown : (i) a few days after it is new;
(2) shortly after first quarter; (3) full; (4) shortly be-
ANCIENT ASTRONOMY
fore third quarter; (5) a few days before it is new.
In the left half the illuminated and unilluminated
parts of the Moon are shown at corresponding times.
Another observation which the reader should make
consists in noting the position of the Moon with refer-
ence to the stars on two consecutive nights. In this way
its rapid movement across the sky will be duly appre-
ciated. The distance moved in 24 hours will be found
to be very considerable, approximately 12, or -^th
part of the whole circumference of the sky. Diagram
III illustrates this : if the Moon is at M x one night, it
will be at M 2 at the same time on the following night.
Further observa-
tions of the Moon
will show that it is
always to be found
in a certain narrow
belt of stars. This
belt is called the
zodiac, and its cen-
tral line is the
ecliptic. The eclip-
T7
nr
/Udeboron
Diag. III.
tic is an imaginary circle which divides the whole
sky into two equal portions, and is exactly like the
line formed on a globe by its intersection with a
plane passing through the centre.
Month. It is well worth while to verify for oneself
that when the Moon is new, it is in the same part of
the sky as the Sun, and that it travels round the sky
and reaches the Sun again in one month. The length
8 ASTRONOMY
of the month is approximately 29^ days, but varies a
little from month to month. The times of new and
full Moon were carefully investigated by the ancient
astronomers for purposes of chronology.
Melon's Cycle. As a lunar month consists of ap-
proximately 29^- days, twelve months will contain
approximately 354 days, and as this is iij days short
of the year, considerable difficulty was experienced in
harmonizing a system of chronology depending on the
Moon with one depending on the Sun. Meton, who
lived between 400 and 500 B.C., discovered (if, indeed,
the discovery is not older) that in 6940 days there
are almost exactly 19 years, and also 235 lunar months.
Consequently, if the dates of new and full Moon are
known for 19 years, the same dates will serve for the
next 19 years, and so on. A little complication arises
in practice from the way leap years happen to fall ;
but this cycle discovered by Meton is still the basis by
which Christian countries fix the festival of Easter.
As showing the accuracy attained by Meton in the
measure of the length of a month, it may be noted
that modern observations show that 235 months is
about 7|- hours less than 6940 days, or that Meton 's
rule makes the month only two minutes too short.
Observation of the Stars. We will now make a pre-
liminary observation of the stars. In the northern
hemisphere the Great Bear is one of the most striking
constellations. Its appearance is well described by
its American name, the Dipper. When it is once
recognized it can always be found without any diffi-
ANCIENT ASTRONOMY g
culty. Its position in the sky is different at different
times of the night and at different times of the year.
But it always preserves the same form ; the stars do
not change their relative positions, but the constella-
tion moves as a whole.
.Merit >
Diag. IV.
The character of this movement is easily seen.
If a line be drawn, as in Diagram IV, and produced,
it passes nearly through another star. This star, called
the Pole Star, is always to be found by looking due
north and (in the latitude of Great Britain) at an
altitude of about 53, or somewhat above the point
midway between the zenith and the northern horizon.
If the Great Bear be watched at intervals for a few
10
ASTRONOMY
hours it will be seen to be turning about the Pole
Star. In the diagram its position, marked A, B, C,
is shown at 6 p.m., midnight, and 6 a.m. on
January i . Not only the Great Bear, but all the stars
are seen to partake of this motion at the same rate.
The time they take to make a complete revolution is
evidently not very far from a day, for on consecutive
days at the same hour they are in nearly the same
positions.
If we take a constellation further from the North
VII
tf
10
-1C
-to
Sims
Ai,.l
Diag. V.
Pole, like Orion, we find that, unlike the Great Bear,
it cannot be seen at all times of the year. On January
ANCIENT ASTRONOMY
ii
i Orion is a little to the west of south at midnight ;
on April i it is nearly setting in the west at midnight ;
on July i it is not seen, and October i it is rising in
the east at midnight. But its appearance shows no
change, and its position is always midway between
Aldebaran and Sirius. At whatever part of the year
it is observed it describes the same journey in the
sky, rising at the same point of the horizon, reaching
the same altitude when due south and setting at the
same point of the horizon. The stars of this constel-
lation, like those of the Great Bear, keep at constant
distances from the pole.
The movement of the stars in the sky is exactly
what we should see if w r e were at the centre of a
Diagram of Circles (VI).
great globe on which they were fixed, and the globe
turned about an axis pointing to the pole. Thus,
in Diagram VI, which represents the eastern half of a
i 2 ASTRONOMY
globe, 1 1 1 is the path of a star which never sets ; 222 of
a star which is just at such a distance from the pole
that it rises at the north point of the horizon ; 333 is the
path of a star still farther from the pole, which rises
to the north of east and is above the horizon for the
greater part of its path but below it for a shorter
(dotted) part; 444 is the path of a star which is 90
from the pole, and for half of its path it is above the
horizon, for the other half below it and invisible; 555
shows the path of a star more than 90 from the pole,
the part of its path during which it is above the
horizon is less than half, and such a star rises at a
point south of east ; 666 is the limiting path of a star
which never rises in the latitude for which the diagram
is drawn.
This representation of the stars as fixed points on
a turning sphere agrees with the facts that the stars
do not change their relative positions, and that all
describe parallel circles in the sky in the same time.
This time is approximately 4 minutes less than 24
hours. Thus each star is at the same point of its daily
path 4 minutes earlier than it was on the preceding
day. In a month this makes the very perceptible
difference of two hours, and those stars which rise and
set, rise and set two hours earlier each month. Thus
the stars which are seen due south at midnight at
one time of year are due south at midday after six
months. They are not seen, owing to the glare of
the sunlight, but that is the only reason, and with a
13
telescope fairly bright stars may be seen in the middle
of the day.
The stars, then, do not change their positions in the
sky relatively to one another, but they all move
together like so many points pricked on a vast sphere
which turns uniformly about an axis pointing to the
pole. This very ancient discovery is important because
it states these everyday phenomena of the fixed stars
succinctly and accurately. It also furnishes us with a
new point of view with regard to the movements of
the other heavenly bodies, the Sun, Moon and planets.
Instead of considering their movement across the face
of the sky, we may consider their movements with
reference to the stars. That the five planets, Mercury,
Venus, Mars, Jupiter and Saturn do not remain in the
same position relatively to the fixed stars, but wander
among them, is very readily seen. Their motion is
not nearly so quick as that of the Moon, illustrated
in Diagram III, but is evident for some of them when
their positions are compared after an interval of a
few days, and for others after a few weeks. The
Sun, however, presents a difficulty. Its light obscures
the stars, and prevents a direct determination of its
position on the celestial sphere. By carefully observ-
ing the position of the Sun just before it sets relatively
to Venus or the Moon, and afterwards when the night
was dark enough for the stars to be seen, observing
the position of Venus or the Moon relatively to the
stars, early astronomers were able to mark the position
14 ASTRONOMY
of the Sun day by day on the celestial globe. This is
a very easy task in a modern observatory, thanks to
the instruments we now possess for measuring angles,
and clocks for accurately measuring time. But with
s
Di.ig. VII.
the simple apparatus possessed by the Chaldeans,
Egyptians and Greeks it was far from being an easy
task.
In the accompanying map, which represents two
ANCIENT ASTRONOMY 15
halves of a celestial globe on which all the brightest
stars are marked, the position of the Sun is marked
for the first day of each month. It will be seen that
these positions all lie on the dotted line called the
Diag. VII.
ecliptic. This line is an imaginary circle dividing
the sphere into two equal parts. It is a fixed line
among the stars and goes through the constellations
enumerated in the doggerel lines
16 ASTRONOMY
The Ram, the Bull, the Heavenly Twins,
And next the Crab, the Lion shines,
The Virgin and the Scales ;
The Scorpion, Archer, and He-Goat,
The Man that bears the watering-pot,
And Fish with glittering tails.
It is important to notice that the Sun makes this
same journey among the stars each year and that its
journey is intimately associated with the changes of its
position in the sky referred to on pp. 2, 3, and illus-
trated in Diagram I. For the circle of the ecliptic on
the globe is in some parts nearer to the north pole
than in others. It cuts the equinoctial or circle in the
sky midway between the poles in two points which
are 90 away from the poles, and half-way between
them is, as shown in the map, 23^ nearer to or farther
from the poles. On March 22 the Sun's position in
the ecliptic is at one of the points where the equinoctial
is cut. It is then 90 from the poles, and its path in
the sky on that day is the circle DEF of Diagram I.
The days and nights are equal, and the Sun rises due
east and sets due west. The Sun moves along the ecliptic
through Pisces, Aries and Taurus, and on June 22 it
has reached a point 66J distant from the north pole.
During this period the days have lengthened and the
nights shortened in the northern hemisphere.
The converse process goes on in the next three
months while the Sun passes through Gemini, Cancer
and Leo, till on September 22 the days and nights are
again equal. The Sun continues to move farther from
ANCIENT ASTRONOMY 17
the north for the next three months till December 22,
when the shortest day in the northern and longest in
the southern hemisphere occurs. It then moves north-
ward, and on March 22 completes its circle.
This annual movement of the Sun accounts for the
changing of the constellations visible at night at
different times of the year. For example, in June
at midday Orion is in the southern sky below the Sun,
and with a telescope the brighter stars may sometimes
be seen, but it is in December, when the Sun is at the
opposite part of the sky, that Orion is seen towards
the south at midnight.
The discovery of the movement of the Sun among
the stars is the first great landmark in the history of
astronomical science. The date of the discovery is
very uncertain, and has to be inferred from slender
evidence like the names of the constellations through
which the Sun passes. It is probably between 2000
and 3000 B.C.
Eclipses of the Sun and Moon. Eclipses of the Sun and
Moon, especially of the Sun, are very striking pheno-
mena. Excluding the Chinese accounts, the earliest
eclipse of which we have any record is referred to on
a Babylonian tablet and has been identified with one
which occurred in 1062 B.C. Some verses in the Book
of Amos, e.g. chapter viii., ver. 9, "to darken the
earth while it is yet day," may be taken as an indica-
tion that the writer had seen the total eclipse of the
Sun which passed across Samaria on June 19, 763 B.C.
i8 ASTRONOMY
From the fact that Thales is said to have predicted
an eclipse which occurred in 584 B.C., it is clear that
considerable knowledge of these phenomena was
possessed at that time in Ionia. But to the Baby-
lonians belongs the honour of having discovered a
law in these apparently very irregular occurrences. It
was doubtless perceived soon after records were kept
that eclipses of the Sun occurred at the time of new
Moon, and those of the Moon at the time of full Moon.
The correct explanation was given, viz. the inter-
position of the Moon between the Earth and Sun in
the case of a solar eclipse ; and the interposition of the
Earth between the Sun and Moon in the case of a
lunar eclipse. But as the path of the Moon among
the stars does not coincide with that of the Sun, but is
inclined to it at a small angle, the three bodies are
not sufficiently in a straight line for eclipses to occur
at every new and full Moon. The path of the Moon in
the sky is a circle inclined at about 5 degrees to the
ecliptic, the path of the Sun (seep. 23). The two points
of intersection of these circles are called the nodes of the
Moon's orbit. If the Moon is sufficiently near a node
when it is new or full an eclipse of the Sun or Moon
respectively will occur. From our present knowledge
of the movements of the Moon and of its nodes which
move round the ecliptic in 18 years and 7 months it
can be shown that after 223 months the relative posi-
tions of the Sun, Moon, and the nodes of the Moon's
orbit will be nearly the same. Thus after this period
ANCIENT ASTRONOMY 19
eclipses will recur. This very curious cycle, called the
Saros, was discovered by the Babylonian astronomers
from their observations of eclipses of the Moon. The
period is 223 months or 6585 '3 days, or approximately
18 years and 11 days. If, then, the eclipses are
recorded which occur in one period of this duration,
those in the next period may be predicted, and so on.
As the relationship between the numbers is not quite
exact, an eclipse may in some cases occur which is not
predicted by the cycle, and in some cases an eclipse
predicted in this way may not occur, but the extreme
cases where the rule fails from one cycle to the next
are very few. The date of the discovery of the Saros
cannot be fixed with certainty, but must have been
some centuries before the Christian era.
The Planets. Besides the Sun and Moon there are
rive other celestial bodies visible to the naked eye
which move among the stars. Of these Mercury is
only occasionally seen in Great Britain. Venus is best
known as a brilliant evening star which is sometimes
visible in the west about the time of sunset. At
other times it is a morning star and rises before the
Sun. The identity of the evening and morning star is
said to have been discovered by Pythagoras. Venus is
always seen in a direction not far from that of the Sun,
the largest angle between them being 47. The planet
passes from side to side of the Sun as the Sun pursues
its circuit of the sky, and when on one side is seen as
the morning star and when on the other as the evening
c 2
2O
ASTRONOMY
star. Next to Venus, Jupiter is the most brilliant of
the planets. If its position among the stars is plotted
down each day on a celestial globe or on a map of the
stars, it will be seen to be sometimes moving round
the sky in the direction of the Sun's annual motion,
but sometimes to be moving in the opposite direction.
Its total movement in a sufficiently long interval is
in the same sense as the Sun's motion, but the irregu-
larities of its movement will be seen from Diagram
VIII, giving its movement from 1908, Sept. 20, to 1909,
July 10. Mars and Saturn exhibit a similar irregular
^ t movement among
the stars. The
most important dif-
ference between the
movements of these
three planets is that
Mars takes 2 years,
Jupiter 12 years and Saturn 29^ years to complete the
circuit of the sky.
The Greek astronomers succeeded in expressing the
observed movements of the planets, as well as of the
Sun and Moon, by mathematical formulae, so that
their position could be calculated and predicted. This
was an immense step in the progress of astronomy.
A formula, however empirical it may be, which cor-
rectly represents the facts, simplifies their statement
and brings them into orderly arrangement and small
compass. As an example we may take the representa-
XII
Diag. VIII.
ANCIENT ASTRONOMY
Diag. IX.
tion of the movement of Jupiter as given by the Greek
geometricians.
Let the point I in Diagram IX make the circuit of
the sky in 12 years. Represent this by the movement
of I round the circumfer-
ence of the circle whose
centre is E. Meanwhile
let the point J move round
a circle of -t- the radius of
El in the course of one
year. As seen from E,
J when at J\ will be
moving in a retrograde
direction, when at J 2 in a
forward one. This epi-
cyclic movement of I as seen from E presents the
main features of the movement of Jupiter among the
stars, namely, its alternate progression and retro-
gression. Further, by taking the radii of the circles
and the periods in which they are described in suitable
proportions, the movement of J in the diagram as seen
from E agrees in amount with the observed motion
of Jupiter in the sky.
Hipparchus. Hipparchus, one of the greatest of all
astronomers, lived at Rhodes, and made observations
between 146 and 126 B.C. He invented trigonometry,
and by its aid made geometrical representations of the
motions of the heavenly bodies by means of epicycles,
eccentrics, etc., in close numerical agreement with the
22 ASTRONOMY
best and most detailed observations which were then
possible. For example, it was known that the Sun
moved across the sky more rapidly in winter than in
summer. Hipparchus showed that the movement would
be accurately represented if the Sun moved uniformly
round the circle whose centre is O (Diagram X), but the
earth from which it is seen had the slightly eccentric
position E. He fixed the position of E as being V tri
part of the radius distant
from O, and in such a
direction that the Sun was
at A on June i.
Hipparchus made a
great step in unravelling
the motion of the Moon,
which, when observed in
detail and with accuracy,
Diag. X.
is extremely complicated.
As in the case of the Sun he found that its varying
rate of motion could be represented by supposing the
Earth to be placed eccentrically in a circle whose
circumference was uniformly described by the Moon. He
discovered that to represent the motion accurately the
line corresponding to EA of the last diagram revolves
in a time which he fixed at 9 years. This is known as
the movement of the apse. He also determined the
inclination of the Moon's orbit to that of the ecliptic
to be 5, and showed that the points where the circle
which the Moon traced on the celestial sphere cut the
ANCIENT ASTRONOMY 23
ecliptic are not fixed but move round in a period
of 19 years. Thus in Diagram XI, if N 1 AM 1 B is the
ecliptic, and N 1 CM 1 D the Moon's orbit; the angles
at Nj and M! were found to be 5; and the points N x ,
Diag. XI.
M! carrying the circle NjCMjD with them moved
round N 1 AM 1 B in 19 years.
Perhaps the most famous of the discoveries of
Hipparchus is that of the precession of the equinoxes.
In the year 134 B.C. the appearance of a new star
in the constellation Scorpio led Hipparchus to make
a catalogue of 1080 stars for comparison with cata-
logues made at other dates. He determined the posi-
tion of the stars with all possible precision. When
he compared this catalogue with earlier ones he found
that the stars had shifted their positions with reference
to the equinoxes or points in the sky where the ecliptic
cuts the equinoctial. As the stars all showed the same
shift, the change in their positions was attributed by
him to a movement of the equinoxes in an opposite
direction.
24 ASTRONOMY
The meaning of this discovery will be understood
more clearly by reference to the map on pp. 14, 15.
The ecliptic or path of the Sun among the stars does
not change; its course is through the constellations of
Aries, Taurus, etc. But in the map it will be seen
that the Sun is midway between Pisces and Aquarius
at the time when it crosses the equinoctial, i. e. at
the time in spring when the Sun is just 90 from the
pole and the days and nights are equal. In the time
of Hipparchus the equinoctial was in a different posi-
tion and cut the ecliptic at a point in the constellation
Pisces, 28 from its present position. The equinoxes
move round the ecliptic in 26,000 years, a move-
ment discovered by Hipparchus by the differences be-
tween his catalogue and one constructed 150 years
previously. Now the pole of the sky bears the same
relation to the equinoctial as the pole of the Earth does
to the Equator, being 90 away from every part of it.
As the equinoctial moves the pole necessarily moves
too, and thus precession states that the point of the
sky about which the stars turn slowly changes its
position, describing among the stars in 26,000 years
a small circle whose radius is 23^. At present the
pole is near the star Polaris. Its positions 6500 years
ago and 13,000 years ago are shown on the map.
The effect of the precession of the equinoxes is to
change the time of year at which the constellations
are visible. Orion is at present a winter constellation.
We see it due south at midnight in December. 6000
ANCIENT ASTRONOMY 25
years ago it was due south at midnight in the
autumn. In 6000 years more it will be due south at
midnight in the spring. Thesechangesbrought about
by precession in the positions of the stars in relation
to the seasonal changes of the Sun can be in some
instances used for chronological purposes. For
example, Hesiod gives information about the times of
rising and setting of Sirius at certain times of the
year the year being defined by the seasons which
can be used to verify the approximate date at which
he wrote. The approximate dates of some of the
pyramids and some temples have been determined by
more or less conjectural relationships between the
position of the Sun and some bright star at the time
of their erection, the rising of the star having been
used as a warning of the approach of sunrise at the
equinox or at midsummer's day.
The Distance of the Sun, Moon, and Planets. That
the Earth is a sphere was believed by Plato and
Aristotle. Their reasons were the same as those given
in modern books on geography, except the reason
which might be expected to convince even the least
reflective, namely, that people have been round it and
nearly all over it. Eratosthenes, the librarian at Alex-
andria, who lived from 276 to 196 B.C., first determined
its size. He observed that at the summer solstice the
Sun w r as vertically overhead at Syene in lower Egypt,
but at Alexandria made an angle with the vertical of
7! or-J^th part of the circumference of a circle.
26
ASTRONOMY
Diag. XII.
Taking the Sun to be at a distance so much greater
than the distance AS, Diagram XII, that the lines
from A and S to the Sun are
parallel, the angle AOS be-
tween the verticals at the two
places is 7!. Thus AS :
Circumference of Earth =
7 V : 360= i : 50.
The distance between
Syene and Alexandria was
measured and found to be
5000 stadia, and therefore the
circumference of the earth
was 250,000 stadia. The
value of a stadium is not
known exactly, and the accuracy of the result cannot
be stated, but the method is sound and the result not
far from the truth.
Knowing the size of the Earth Hipparchus was
able to measure the distance
of the Moon. When the
Moon is partially eclipsed
the edge of the shadow of.
the Earth is seen as part of
a circle on the Moon, as in
Diagram XIII. The size of
this circular shadow is com-
Diag. XIII. 1-11 e **.
pared with the size ot the
Moon. The apparent diameter of the Moon is J or
30' ; thus it is found that the shadow of the Earth at the
ANCIENT ASTRONOMY 27
distance of the Moon subtends an angle of 80'. Dia-
gram XIV, in which S, E, M are the Sun, Earth and
Diag. XIV.
Moon, shows how the shadow is formed. The angle
AEB is thus found to be 80', while the angle FEG
under which the Sun is seen is 30'. 1 [In the diagram
these angles are necessarily grossly exaggerated.]
With these data, and making the assumption that
the Sun's distance is 20 or 30 or any large number of
times the Moon's distance, Hipparchus found that the
Moon's distance from the Earth was about 59 times
the radius of the Earth, and that the result did not
vary much with the different hypotheses made as to
the Sun's distance provided it was a good many times
larger than that of the Moon.
Ptolemy, who lived at Alexandria about A.D. 150,
determined the distance of the Moon by a method
which is substantially the one now adopted. If at
the same moment the position of the Moon be observed
from two places A and B at a considerable distance
apart on the earth (Diagram XV); and ZAM, YBM,
1 The angle through which we turn in looking from one
direction to a perpendicular one is called a right-angle. If this
angle is divided into 90 equal parts, each is called one degree, and
written i. One-sixtieth part of a degree is called a minute, and
written i'. One-sixtieth part of a minute is called a second,
and written i".
28 ASTRONOMY
the angles between the directions of the Moon, and
the verticals at the two places be measured; knowing
the positions of A and B on the Earth's surface, it
is possible to draw the diagram below to scale and
thus infer how large OM, the distance of the Moon,
Diag. XV.
is as compared with OA or OB, the radius of the
Earth. In actual practice trigonometrical calcula-
tions are used, but that is only because drawing to
scale cannot be done with sufficient accuracy.
The Moon's distance was thus satisfactorily deter-
mined, and Ptolemy tried to use his result in com-
bination with the eclipse method of Hipparchus to
obtain the Sun's distance. He found that the Sun
was 20 times as far away as the Moon. This is much
too small ; we know now that the Sun is nearly 400
times as far away as the Moon. The method used by
Ptolemy is not susceptible of giving the Sun's distance
with accuracy.
The Almagest. Although Ptolemy made several
discoveries of very great importance, the greatest
ANCIENT ASTRONOMY 29
service he rendered to astronomy consists in his
treatise, /^eyaArj awrafi?, or the Almagest, as it was
called later by the Arabian astronomers. This work
contains the whole body of astronomical knowledge
then known, and was for 1400 years an astronomical
bible.
The preceding pages give some idea of the im-
mense progress made by the Greeks in astronomy.
They had reached correct ideas of the shape and size
of the Earth and the distance of the Moon; they knew
that the Sun was much farther away than the Moon,
and guessed from the rates of movement of the planets
round the sky that their distances were of a similar
order of magnitude, Jupiter and Saturn being the
most distant, while the fixed stars were much farther
away. Again, the movements of Sun, Moon and
planets had been studied in considerable detail, and
geometrical and trigonometrical representations of
them had been devised. These representations were
sufficiently accurate for the prediction of their positions
and of eclipses. In these geometrical representations
the Earth was taken as stationary, and movements attri-
buted to the Sun, Moon and planets and the celestial
sphere of the stars. It may well be that Hipparchus
and Ptolemy regarded as formulae what their more
ignorant successors regarded as dogmas. In any case
the skill with which the movements of the heavenly
bodies were traced and brought into relationship with
geometry made astronomy an exact science of great
scope and interest.
CHAPTER II
THE COPERNICAN SYSTEM
Copernicus. From Ptolemy's Almagest in the
middle of the second century, to the De Revolutioni-
bus of Copernicus in the middle of the sixteenth
century, comparatively little progress was made in
astronomy. But the publication of the De Revolu-
tionibus in 1543 was the beginning of a new astro-
nomical era. The 1 change from the ancient to the
modern conceptions of astronomy is associated with
four great names Copernicus, Galileo, Tycho, and
Kepler.
Copernicus stated two propositions
(1) That the diurnal movement of the stars is appar-
ent only, and results from a rotation of the Earth about
its axis in the opposite direction.
(2) That the Earth is one of the planets, and, like
them, revolves round the Sun.
These are the commonplaces of modern astronomy ;
it is, however, both interesting and important to
notice the arguments which were adduced in their
favour, and those brought against them.
Earth's Diurnal Eotation. Copernicus showed clearly
the relative character of motion. The apparent motion
30
THE COPERNICAN SYSTEM 31
of objects as seen from the window of a railway car-
riage is so familiar that it is not necessary to elabor-
ate the proposition that the appearance of motion is
equally produced by a movement of the object or
the observer. The apparent movement of the stars in
parallel circles is identical with the movement which
would be produced by a rotation of the Earth about
its axis. The objections are, the difficulty of believ-
ing in the motion of so large a body as the Earth ;
that we should be entirely unconscious of this move-
ment; and that movable bodies, specially the air,
should not be left behind. Copernicus points out
that these objections would apply with far greater
force to a rotation of the celestial sphere containing
the stars, for this is immeasurably larger than the
Earth, and would need to move at an immeasurably
greater speed to accomplish a diurnal rotation.
Annual Revolution of Earth round the Sun. The
annual motion of the Sun among the stars is as
well explained by an annual revolution of the Earth
about the Sun as by that of the Sun about the Earth.
In Diagram XVI, when the Earth is at E, the Sun
will appear projected against the sky at e ; when the
Earth moves to F, the Sun 'will appear projected
against the sky at /, and the appearance of the Sun's
annual movement among the stars will be produced.
The explanation of the seasons offers no difficulty.
The axis round which the Earth makes its daily
rotation is fixed in a direction not perpendicular to
32 ASTRONOMY
the plane in which the Earth revolves round the Sun,
Diag. XVI.
but inclined at 23^ to this perpendicular. In Dia-
gram XVII the centre of the Earth describes the
Diag. XVII.
circle CCCC about the Sun in the direction shown by
THE COPERNICAN SYSTEM
33
the arrows. As the axis is not perpendicular to the
plane of this circle, in June the northern hemisphere
is more directly under the Sun's rays, or the Sun
appears higher, being directly overhead at a point
north of the equator. Similarly, in December the
point on the Earth where the Sun is directly over-
head is south of the equator. By running a knitting-
needle through a ball of worsted a model can be con-
structed, with which the movement of the Earth round
the Sun can be imitated, and the cause of the Earth's
seasonal changes explained.
The alternations of forward and retrograde motion
of the major planets (see p. 20), which is repre-
sented by an epicyclic motion on the Ptolemaic
system, is accounted for at once by Copernicus. The
movement of Jupiter, for example, is represented in
Diagram IX by a movement of I round E (the Earth)
in twelve years, while J (Jupiter) moves round I in one
year. Diagram XVIII
shows how this would be
represented on the Coper-
nican system. S is the
Sun ; E, the Earth, de-
scribes a circle round it in
one year, J, Jupiter, de-
scribes a circle round S in
twelve years, the radius
" . T , Diag. XVIII.
being fiVe times SE. If
the line El is drawn parallel to SJ and JI parallel to
34 ASTRONOMY
SE, then the points I and J bear the same relation to
E as in the Ptolemaic diagram, for El and IJ are
equal in length and in the same directions in the two
diagrams. Thus in the Copernican system the ap-
parent motion of Jupiter relatively to the Earth, or
as seen from the Earth, is shown to result from a
motion of Jupiter round the Sun in a circle, com-
bined with a motion of the Earth the point from
which Jupiter is viewed in another circle.
The essential features of the movements of the
planets Venus and Mercury are readily explained.
As they move round the Sun in less than a year, they
will necessarily be seen from the Earth first on one
side and then on the other
side of the Sun. In Dia-
gram XIX, if Venus is at V
when the Earth is at E,
looking at the Sun from E,
Venus would appear on the
left hand, while if the Earth
reaches E 7 when Venus
reaches V', it will be seen
Diag. XIX. , , rr<
on the right hand. Thus
Venus will be alternately a morning and evening star,
and can never be more than a certain angular distance
from the Sun, as it will always be within the angle
formed by the two tangents from the Earth to the
circle along which Venus moves.
Copernicus further showed how the relative dis-
THE COPERNICAN SYSTEM 35
tances of the planets from the Sun could be obtained.
As Mercury never gets so far from the Sun as Venus,
it must describe a smaller circle; the knowledge of
the greatest angle its direction can make with that
of the Sun makes it possible to draw this circle to
scale with the one described by the Earth. Similarly
with regard to Venus, if EK is drawn so that SEK
is the greatest angular distance Venus attains from
the Sun, it is only necessary to draw a circle with
centre S to give the orbit of Venus. The distances
of Mars, Jupiter and Saturn are deducible from the
extent of their retrograde motions. Thus Copernicus
was able to draw a plan of the solar system, giving the
planets in their order of distance from the Sun, and
at their proportionate distances. He pointed out that
this order agreed with the order which could be
inferred from their times of revolution. Thus Mer-
cury, the nearest, goes round the Sun in 88 days,
Venus in 223 days, the Earth in a year, etc., and
Saturn, the most distant, in 30 years. Diagram XX,
taken from the De Revolutionibus, gives the order,
but not the correct relative distances. It will be
noticed that the Moon revolves round the Earth as in
the Ptolemaic system, and is carried with the Earth
in its orbit round the Sun.
Difficulties of Copernican System. The CoperniCan
system presented several difficulties. How the Moon
could be carried round the Sun with the Earth is a
mechanical problem which was not at that time
D 2
36 ASTRONOMY
soluble. Another objection arose from the absence
of any appreciable motion of the fixed stars. Their
immense distances are familiar to us now, but at the
time when the Copernican system had to meet
criticism their distances might well have been sup-
posed to be 10, or 20, or 30 times the distance of
Diag. XX.
Saturn. If the Earth described a circle round the
Sun, its positions when on opposite sides are a very
great distance apart. It was to be expected that the
stars, seen from two points so far apart, would show
some differences of relative position. The only reply
which could be given and it is the correct one was
that the distances of the fixed stars are so great that
the distance between the Earth and Sun is inappre-
ciable in comparison with them.
THE COPERNICAN SYSTEM 37
Other objections to the Copernican system were its
supposed opposition to the Bible and its disagreement
with the orthodox astronomy found in the writings
of Ptolemy and Aristotle. Curiously enough the
authority of Greek teachers was its greatest obstacle,
although freedom of thought is a heritage the world
owes so largely to Greek philosophy. It was a
hundred years before the Copernican system com-
pletely superseded that of Ptolemy.
Galileo. Galileo supported the Copernican theory
by arguments which appealed to a wider audience
than the mathematical treatise of Copernicus. In
1609 he learned that a Dutch optician had by a com-
bination of lenses devised an instrument which made
distant objects seem near. Galileo realized the optical
principles which must underlie such an instrument,
and soon made one himself which magnified thirty
times. He pointed this to the sky, and found that the
number of stars visible was much greater than could
be seen with the naked eye.
Seen in his telescope the Moon presented the
appearance of a mountainous country with dark
shadows cast by the mountains. Near the edge
between the bright and dark parts he saw bright spots
where the mountain tops were illuminated by the
rising or the setting sun, while the valleys were still
in darkness. From the lengths of the shadows he
calculated the heights of the mountains. Some of
the dark parts he erroneously supposed to be water.
ASTRONOMY
Thus the Moon, instead of being a crystal globe, as
the old astronomers believed, had mountains and
valleys like the Earth.
Pointing his telescope to the planets he found that
they were not bright points like the stars, but discs of
sensible magnitude like the Sun and Moon. The
appearance of Venus was especially striking. It was
seen to have phases like the Moon, and the conclusion
was irresistible that, like the Moon, it shines by the
reflected light of the Sun, and not by its own light.
This established a resem-
blance between Venus and
the Moon, and afforded
another argument in favour
of the Copernican theory.
On January 7, 1610, he
saw three small stars in a
line with Jupiter (Diagram
XXI). By accident he
examined Jupiter again on
January 8, and found them
in a different position.
January 9 was cloudy. On
January 10 he found two
stars both on the east of the
planet. On the nth he
found two on the east, but
*o
Diag. XXI.
the most easterly one was much the brighter. On
the 1 2th he saw three stars, the third one emerging
THE COPERNICAN SYSTEM 39
from behind the planet during his observations. On
the I3th he saw four stars. Galileo perceived that
these stars were four satellites revolving round Jupiter
just as the Moon revolves round the Earth. He
observed them further, and determined their periods
of revolution. The analogy between Jupiter and his
satellites and the Earth and Moon was another argu-
ment for the Copernican theory. As Jupiter's moons
revolve around and accompany Jupiter, may not
the Earth's Moon accompany the Earth in its revolu-
tion about the Sun ?
Galileo's telescope revealed to him still another
analogy which lent support to the Copernican theory.
He discovered spots on the Sun which did not remain
stationary, but crossed the disc in fourteen days, and
showed changes in appearance which, as he explained,
would naturally arise from perspective when the spots
were seen at an increasing angle. He concluded
that the Sun rotated on an axis. If the Sun, why
not the Earth ?
In 1632 Galileo published his great work, the
Dialogue on the Two Chief Systems of the World
the Ptolemaic and the Copernican. The arguments
in favour of the Copernican system were put forward
with unanswerable force, and the book was received
with applause all over Europe. Unfortunately for
Galileo, he had made many enemies during a life
full of controversy. They procured his trial by
the Inquisition, and he was compelled to abjure
4 o ASTRONOMY
his opinions. But, although his book was condemned,
the Copernican system was effectively established.
There can be no question of the important part
which Galileo's telescope played in the substitution of
a system of the world with the Sun as centre (helio-
centric) for the Ptolemaic one in which the Earth
was the centre (geo-centric). Copernicus put the
geometrical arguments with great force in --the De
Revolutionibus, but he had no new facts to bring
forward. A heliocentric theory had been previously
proposed by the Greek astronomer Aristarchus, and
the Babylonian astronomer Seleucus is said to have
nearly convinced Hipparchus of its truth. Galileo's
telescope transformed the planets from bright points
into worlds, and thus added a force to the arguments
of Copernicus which made them irresistible.
Tycho Brahe. The Copernican system satisfied the
observed planetary motions in broad outline, but for
more accurate representation it. was necessary to add
a number of small epicyclic or eccentric movements.
In 1546, a few years after the death of Copernicus,
Tycho Brahe was born. Tycho became a great astro-
nomical observer as contrasted with a theorist. The
multitude and accuracy of his observations of the Sun,
Moon and planets were destined to furnish the key by
which the Copernican system was freed from the
numerous subsidiary epicycles, etc., and the true
movements of the planets discovered. Apart from
particular discoveries, such as his determination that
the comet of 1577 was more distant than the Moon,
THE COPERNICAN SYSTEM 41
and revolved round the Sun, Tycho's services to
astronomy consist in the great improvements he made
in astronomical instruments and in the accuracy of
observations. He used his instruments with great
skill, and also realized the importance of making long
series of continuous observations.
Kepler. Tycho's observations of Mars passed into
the hands of his pupil and successor, Kepler, who,
unlike his master, was a Copernican. For two
reasons Mars is the most difficult of the planets
for which to construct tables in harmony with the
observations. As Mars sometimes comes near the
Earth, its movements can be determined with great
precision and any irregularities become apparent.
Besides this, the orbit of Mars diverges more from
the circular form than that of any of the other planets.
A very complicated geometrical system of epicycles
and eccentrics (pp. 21, 22) is required in order to
represent the motion in satisfactory accordance with
the facts.
Kepler tried hypothesis after hypothesis, but could
not by systems of epicycles represent Tycho's obser-
vations with sufficient accuracy. He then tried other
forms of curves, a daring innovation, as it was univers-
ally believed that the celestial motions must be com-
posed of circular movements. Each different hypo-
thesis involved an immense amount of labour, as all
the calculations had to be started anew, and in Kep-
ler's time there were no logarithm tables or other
modes of simplifying numerical work. Finally, Kepler
ASTRONOMY
tried the ellipse, and found that with the Sun in
one of the foci he could adequately represent Tycho's
observations. The ellipse is the curve which is ob-
tained when a cone is cut obliquely. It may also be
considered as the curve which a point P describes if
it moves so that the sum of its distances from two
points, S and H, re-
mains the same. The
two points S and H
are called the foci.
If they are a long
way apart the ellipse
Diag. XXII.
is elongated or very
eccentric ; if close to-
gether it approaches more nearly to a circle. But
Mars does not move uniformly in this ellipse, its
velocity being greater when it is near the Sun than
when it is further away. Kepler discovered how the
velocity varies at different points in the planet's orbit.
Kepler's Laws. The results were stated in what are
known as Kepler's first and second laws of planetary
motion.
1. The planets move in ellipses having the Sun in
a focus.
2. The straight line joining a planet to the Sun
sweeps out equal areas in equal times.
Thus in Diagram XXIII a planet will describe the
large angle A'SP 7 in the same time as the small angle
ASP, because the area A'SP 7 equals the area ASP.
THE COPERNICAN SYSTEM 43
These famous laws were published in 1609. They
were first established for Mars,
and in course of time for the
other planets, and even for
the satellites which Galileo
had found to circulate round DJa XXIII
Jupiter.
In 1619 Kepler discovered a third law which shows
the relationship between the distance of a planet from
the Sun, and the time it takes to perform a complete
revolution. The more distant the planet the longer its
period of revolution, but the planets do not move at
the same rate : e.g. Jupiter is five tinges as far away
from the Sun as the Earth, but takes twelve years,
not five years, to complete its revolution.
Kepler's third law is
The square of the time of revolution of any planet
about the Sun is proportional to the cube of its mean
distance from the Sun.
The meaning of this law will be clearly seen by in-
spection of the following" table, in which a is the mean
distance of a planet from the Sun, the Earth's mean
distance being taken as i, and T is the time in years of
its revolution.
Mercury Venus Earth Mars Jupiter Saturn
a -387 723 I 1-524 5-203 9.539
a 3 -058 -378 i 3 -54 140-8 868-0
T '241 '615 i i'88i 1 1 -86 29-46
T 2 -058 -378 i 3-54 1407 8679
44
ASTRONOMY
The agreement of the figures in the second line with
the corresponding figures in the fourth line constitutes
the third law.
The Ptolemaic astronomy gave geometrical repre-
sentations of the apparent movements of the heavenly
bodies. The Copernican system gives their real move-
ments. Kepler's laws, substituting the ellipse for the
circle, gives these real movements with all the accuracy
that Tycho Brahe's refined observations demanded,
and are a concise statement of all the apparently
complicated facts of planetary motion, as far as they
had at that time been elicited by observation.
CHAPTER III
THE LAW OF GRAVITATION
Movement of Bodies in Curved Paths. The science of
dynamics, which may be said to have been founded
by Galileo, led to further inquiry into the elliptic
motion of the planets. Galileo investigated the
motion of falling bodies on the Earth, and Huyghens
showed under what conditions a body could revolve
uniformly in a circle. Put very roughly, the con-
dition is that the tendency to fly off should be counter-
acted by a pull towards the centre. For the Moon to
revolve uniformly round the Earth in a circle, it is
not necessary that it should be pushed in the direc-
tion of its motion, but it is necessary for it to be
constantly pulled towards the Earth, otherwise it
would move in a straight line. Since bodies on the
Earth fall to the ground how y ever high we may go,
the Earth may be regarded as exercising an attractive
force upon them. Might not this force continue to
act, though to a diminished amount, at the distance
of the Moon ? Newton put this question to himself,
and answered that if the attraction diminished accord-
ing to the inverse square of the distance from the
45
46 ASTRONOMY
Earth's centre, the Moon would move round the
Earth in the circle it actually describes. As the
Moon's distance is 60 times the Earth's radius, the
diminution of the attraction according to the inverse
square of the distance from the Earth's centre means
that the attraction on a body at the Earth's surface
would be diminished (^V) 2 at the Moon's distance.
Newton compared the motion of the Moon to that of
a bullet fired from the top of a hill. One fired
horizontally from A with small velocity reaches the
Earth at B ; a
second, fired
with greater
velocity, at C ; a
third at D. If
Diag. xxiv. the bullet could
be fired with sufficient velocity it would not fall to
the Earth, and if the velocity were exactly the right
amount, the bullet would move round the Earth in a
circle.
Movement in Ellipses. Under what conditions will
the planets describe ellipses round the Sun in accord-
ance with the laws discovered by Kepler? Newton
was able to answer this question fully. From the
second law, that equal areas are swept out in equal
times, he proved that the planets were subjected to
attractive forces drawing them towards the Sun.
From the fact that the path of a planet is an ellipse
with the Sun in a focus, he showed that this force
THE LAW OF GRAVITATION 47
varies inversely as the square of the planet's distance
from the Sun. From Kepler's third law he showed
that the Sun's attraction is the same for all the planets,
the amount depending only on the inverse square of
each planet's distance from the Sun.
Law of Gravitation. In this way Newton was led
to propound the law of universal gravitation that
every particle of matter attracts every other with a
force which is proportional to the mass of each and
inversely proportional to the square of the distance
between them. Thus, if at A there is a particle of
matter whose mass is M, > ^
and at B another whose A
A -t *u r Diag. XXV.
mass is m, and if the dis-
tance AB be called r, then each particle exerts on
the other an attractive force which is proportional to
M x m
~2 . It does not matter what the particles are
made of, or whether they are both on the Earth or
both in the Sun, or one on the Earth and the other
on Sun, Moon, or planets.
Consequences of Law of Gravitation. Newton now
put forward the law of gravitation as an hypothesis
whose consequences are to be deduced and compared
with the observed phenomena of the solar system.
Its immense range is seen from the variety of these
consequences. Not only the movements of the Moon
and planets, but the shape of the Earth and the
planets, the ebb and flow of the tides and the preces-
48 ASTRONOMY
sion of the equinoxes, were shown by him to be dedu-
cible mathematically from the law of gravitation. The
verification of this law became one great branch of
astronomy. Irregularities in the lunar and planetary
motions have constantly presented new problems,
which have been resolved ds due to some consequence,
till then unrecognized, of universal gravitation ; while,
on the other hand, the law has been confidently used
to determine the condition of the solar system in past
and future times.
Attraction of Spheres. The total attraction of one
body on another is made up of the attractions of each
particle of one body on each particle of another.
These are in varying directions and of various
amounts. Newton was able to prove mathematically
that spheres of uniform material or made up of con-
centric shells of unifor'm material attract one another
just as if their masses were concentrated at their
centres. This proposition would naturally be ex-
pected to hold for two spheres whose distance apart
was much greater than their radii. Newton showed
that it holds for all distances, and was thus able to
calculate the combined effect of the attractions of all
the particles which compose the Earth on a body at
its surface, and thus verify that the law of universal
gravitation gives a correct relationship between the
attractive force observed in falling bodies at the
Earth's surface, and that required to keep the Moon
in its orbit.
THE LAW OF GRAVITATION 49
Shape of the Earth. In an expedition to Cayenne, in
South America, near the equator, a French astrono-
mer, Richer, found that a pendulum swung more
slowly there than in Paris, thus showing that the
force of gravity is less at the equator than in the
latitude of Paris. Newton proved that this result
necessarily follows from the law of gravitation, and
that the Earth bulges out somewhat from the spherical
form at the equator. If this were not the case, the
water of the ocean would, owing to the Earth's spin,
tend to flow towards and heap itself up near the
equator.
Tides. Newton also gave a general explanation of
the tides. The solid Earth, by virtue of its rigidity,
responds to the attraction of the Moon en masse. But
the actual attractive force varies somewhat from place
to place according to the distance from the Moon.
The result is that when the mean effect of the Moon's
attraction is abstracted, there remains a force which
tends to raise tides on the side of the Earth facing the
Moon and also on the opposite side. The mobile water
yields to this tide-producing force, whereas the Earth's
rigidity prevents it from giving, and the water moves
relatively to the Earth, producing tides. The occur-
rence of two tides a day is thus explained, for the
water tends to rise at the points nearest to and farthest
from the Moon, and as the Moon takes 50 minutes
more than the 24 hours to complete its apparent re-
volution round the Earth, the time of high water is
5 o ASTRONOMY
50 minutes later each day. The attraction of the Sun
also produces tides, but only half as large as those
produced by the Moon. At New and Full Moon
the forces exerted by the Sun and Moon combine,
and spring tides occur, while when the Moon is in a
direction at right angles to the Sun, their tide-pro-
ducing forces are opposed, and neap tides result.
Precession of the Equinoxes. The precession of the
equinoxes, interpreted in the light of the Copernican
system, means that the axis round which the Earth
spins is not fixed in direction, but slowly changes.
In 26,000 years it describes a cone whose axis is per-
pendicular to the ecliptic; the angle between the axis
of the Earth and the axis of the cone is always 23 J.
In Chapter I this was expressed slightly differently,
when it was said that the pole described a small circle
of radius 23^ among the stars in 26,000 years.
Newton showed that this motion of the Earth's
axis is a consequence of its oblate figure. In order
to see the effect of the attraction of the Sun and Moon
on the Earth, consider separately the sphere which
can be just enclosed in the Earth, and the oblate part
which bulges out at the equator. The attraction of
the Sun, for example, on the spherical part produces
a pull in the direction OS (Diagram XXVI), but does
not tend to turn the Earth. The attraction on the
nearer half of the part bulging out at the equator
produces a pull in a direction ES, while the attraction
on the more distant half produces a pull in the direc-
THE LAW OF GRAVITATION
5 1
tion E'S. But as E is nearer to S than E', the pull
along ES is greater than that along E'S, and there
result forces which tend to right the Earth, or bring
OP nearer to OK. But
when the dynamical con-
sequences of this righting
force are investigated, it
is found that owing to the
Earth's spin, the axis
OP, instead of being
moved nearer to OK, Diag. xxvi.
keeps at the same distance, but slowly describes a
cone around it. This result may at first sight appear
paradoxical, but a similar result
from similar causes is familiar in
the peg-top : while the top spins
round its axis, the axis describes a
cone about a vertical line and the
top does not fall down as it would
if it were not spinning. Diag> XXV1L
Comets. The ellipse is not the only curve which
a body can describe about another to which it is
attracted by a force varying inversely as the square
of the distance. If a cone be cut perpendicularly to
its axis, we get a circle; if the plane is not quite
perpendicular, we get an ellipse; as the plane of
section becomes more inclined to the axis of the cone
the curve becomes more and more elliptic, till when
the plane is parallel to an edge of the cone the curve
E 2
Pfcrop
ASTRONOMY
is no longer closed, but becomes an open curve called
a parabola, and at still greater divergence of the cut-
ting plane from perpendicularity a curve called a
hyperbola. The forms of these curves are shown in
Diagram XXVIII. All these conic sections are
possible paths for a body
to describe about the Sun
under the influence of
gravitation. The planets
describe nearly circular
orbits. Newton showed
that comets move in ellip-
tic orbits of great eccen-
tricity or in parabolic
orbits. Thus comets are
brought into the scheme of
the solar system, and are
seen to move like the
Earth and planets under
the dominating influence of the Sun's attraction.
Masses of Heavenly Bodies. A very interesting con-
sequence of the law of gravitation is its application
to determine the masses of heavenly bodies. If the
mean distance between two bodies whose masses are
M and m is a, and they revolve about one another in
a 3
the time T, then the quantity ^ is proportional to
Mi+ra, the sum of the two masses. By taking a to be
the Moon's mean distance, and T the time in which
Dia 2 . XXVIII.
THE LAW OF GRAVITATION 53
the Moon revolves, the formula may be applied to the
Earth and Moon. By taking a to be the Sun's mean
distance and T the year, it may be applied to the Sun
and Earth. The Sun's distance is, let us say, 390 times
that of the Moon, and the year is, roughly, 13 times
as long as a sidereal revolution of the Moon. The
combined mass of the Sun and Earth is, therefore,
greater than that of the Earth and Moon in proportion
of '5zr_. Thus the Sun's mass is 350,000 times that
of the combined mass of the Earth and Moon. By
taking a to be the distance of one of Jupiter's
satellites and T the time in which it revolves round
Jupiter, the formula is applicable to determine the
mass of Jupiter. This is the astronomical method of
determining the masses of the heavenly bodies.
They are measured by the attractions they exert on
one another, and these attractions are proportioned
rt 3
to 2. The method has been applied to all the
planets which have satellites and to double stars,
when the distance between the two stars can be
determined.
Disturbance produced by a third body. The move-
ment of two bodies under their mutual attraction
was completely solved by Newton. When there are
more than two bodies the problem becomes one of
great difficulty. In the solar system the mass of the Sun
is so preponderating that the movement of each planet
54 ASTRONOMY
is very largely determined by the Sun. However,
other planets influence the movement to some extent,
and "perturb" the motion in an ellipse round the
Sun as focus. Newton pointed out some of the effects,
but in the main left this question to his successors.
The Moon's motion is particularly difficult because,
although the Sun is very distant compared with the
Earth, its great mass makes its effect considerable.
Newton showed how the rotation of the apse and the
node discovered by Hipparchus were traceable to the
Sun's action.
The "Principia." Newton's discoveries, though many
of them were made earlier, were published in the
Principia in 1687. The doctrine of universal gravita-
tion did not commend itself to the most eminent of
Newton's scientific contemporaries. In 1738 Voltaire
presented a popular account of it which procured its
acceptance among French scientists. From that time
till the early years of the nineteenth century the idea
of universal gravitation was developed by great
French mathematicians, who applied it in detail to
all the movements of the solar system.
The task was one of extreme difficulty. The law
of gravitation, which gives the forces that different
bodies exert on one another, enables the rate at which
the velocity of any body is changing to be calculated.
When this is done, if the velocities are known at one
particular instant, they may be found a minute later.
In this minute the positions of the bodies have all
55
changed, the forces between them consequently
altered, and the velocities are changing at slightly
different rates. The difficulty consists in devising
mathematical methods for duly integrating the effects
of these varying forces. The greatest mathematicians
have applied themselves to various branches of the
subject, and gravitational astronomy has been a great
stimulus to mathematics.
Stability of Solar System. The work is of too tech-
nical a character for much of it to be referred to here.
One important result may be mentioned. Laplace,
the greatest exponent of gravitational astronomy
since Newton, demonstrated the stability of the
solar system. If the Earth were the only planet, it
would perpetually repeat its path in the same ellipse.
One effect of the attraction of the planets on each
other is to slowly change each other's orbits. For
example, the ellipse in which the Earth moves is at
present gradually becoming more circular from this
cause, and the plane of its motion the ecliptic
is slowly changing. Laplace showed that the mean
distance of each planet from the Sun remains un-
changed, and that the eccentricities and inclinations
of their orbits only suffer periodic changes, and these
between comparatively narrow limits. Thus the
action of the planets can never make the Earth's
ellipse so eccentric that the Earth will at one part of
its orbit approach very near to the Sun. and at the
opposite part go to a correspondingly great distance
5 6 ASTRONOMY
from it. Laplace showed that this result depends on
the fact that the Earth and planets are all moving
round the Sun in the same direction.
Discovery of Neptune. In the year 1846, 160 years
after the publication of the Principia, the law of
gravitation led to the discovery of a new planet.
Uranus, a planet beyond Saturn discovered by Her-
schel in 1781, did not conform exactly to its elliptic
orbit. The perturbations caused by Jupiter and Saturn
did not account for the anomalies in its movement.
The possibility of an exterior planet being the cause
was investigated simultaneously by Adams at Cam-
bridge and Leverrier at Paris. From the researches of
these two astronomers, the position in the sky where the
disturbing body was to be found was pointed out.
Search was made by Dr. Galle at Berlin, and the new
planet (to which the name of Neptune was given) was
duly found close to the predicted place.
Halley's Comet. Another interesting episode con-
nected with the law of gravitation is furnished by the
history of Halley's comet. Halley made observations
of a comet which appeared in 1682, and deter-
mined the position of its orbit. He found that the
comet had moved in much the same path as the
comets which appeared in 1531 and 1607. He con-
cluded that these were the same comet; that this
comet moves round the Sun in a very elliptic orbit,
going to a distance of 33 times the Earth's distance
from the Sun ; and that the comet takes about 75
THE LAW OF GRAVITATION
57
years to complete its revolution, the time varying
somewhat in consequence of perturbations caused by
planets near which it passes. The comet is only
visible at its successive returns to the Sun when it is
Diag. XXIX.
comparatively near the Earth. Halley predicted its
return for the year 1759. Before the reappearance of
the comet, Clairaut, calculating the perturbing effects
of the planets it had encountered in its path, pre-
dicted that the comet would be at the point of its
orbit nearest to the Sun or at perihelion on April 13,
1759. The comet was discovered at the end of 1758,
and Clairaut's prediction found to be only one month
in error. It again returned to perihelion on Nov. 15,
1835, and its coming return in April 1910 was pre-
dicted by Messrs. Cowell and Crommelin of the
5 ASTRONOMY
Greenwich Observatory with an error of only three
days. The early history of this comet is interesting,
as it has been identified with comets of which historic
records are preserved. Diagram XXX, taken from the
Bayeux tapestry, represents a comet which appeared
in 1066, and was accounted an evil omen for King
Harold. Calculation shows that Halley's comet in that
year made one of its periodical visits to the Sun, and
was unquestionably the one which was supposed to
have predicted Harold's de-
feat and death. The comet's
course has been traced back
by Messrs. Cowell and
Crommelin, and is almost
Diag. xxx. certainly the one which
Chinese records state to have been seen in 87 B.C.,
and possibly a still earlier one in 240 B.C.
Movement of the Moon. The determination of the
Moon's movements from the law of gravitation has
been a mathematical problem of great difficulty and
complexity. The problem has a practical bearing,
for if the Moon's position can be predicted with
sufficient accuracy, it may be used to determine longi-
tude at sea. In 1713 a prize of ,20,000 was offered
by the British Government for a method of finding
longitude accurate to within half a degree. This prize
stimulated the manufacture of chronometers on the
one hand, and the formation of accurate lunar tables
on the other. In 1765 ^3000 was paid to the widow
THE LAW OF GRAVITATION 59
of Tobias Mayer for his tables of the Moon tables
which gave the position of the Moon with an accuracy
of about one minute of arc (-jV tn ) f tne Moon's
angular diameter.
Theories of the Moon were developed with great
mathematical skill by Clairaut, Euler, and Laplace,
and various difficulties were removed, but a theory
which will give the position of the Moon's place as
accurately as it can be observed is required before
the law of gravitation can be said to be completely
verified. Elaborate theories of the Moon's motion
have been worked out by many eminent mathe-
maticians. At present Hansen's is used by the
Nautical Almanac for the prediction of the Moon's
place, and gives the position of the Moon for the
period 17501850 with errors not larger than i" or 2"
(i" is about TsVfrth part of the Moon's diameter). As
showing how complicated this question is, it may be
enough to say that the final algebraic expressions
which give the position of the Moon in Delaunay's
Theory occupy a large quarto volume. Not only
does the Sun affect the motion of the Moon round the
Earth, but the planets, too, have their influence, both
directly by their attraction on the Moon, and in-
directly by their attraction on the Earth. The interest
of the problem does not consist entirely in surmount-
ing the mathematical difficulties but in determining
whether, when all its consequences are traced, the
simple law of gravitation is a complete key to these
60 ASTRONOMY
very complicated movements. Compared with what
has been already explained, what yet remains in doubt
is trivial. Still, there are several curious differences
between observation and gravitational theory in the
motion of the Moon, and also of Mercury and Venus,
of which the explanation seems at present to be a
long way off.
Mass of Earth. We have seen how the masses of
the heavenly bodies can be compared with one
another, the Sun with the Earth or Jupiter with the
Earth, by comparing the movements their attractions
produce upon bodies subject to their influence. But
what is the mass of the Earth ? This can be measured
in several ways by comparing its attraction with that
of a smaller body whose mass is known.
Attraction of Schehallien. In 1776 Maskelyne com-
pared the attraction of the Earth with that of the
mountain Schehallien in Perthshire. As shown in
Diagram XXXI, the effect of the attraction of this
peak is to deflect the plumb-line towards it. The
amount of this deflection is measured astronomic-
ally by observing the angle which the direction of
a star makes with the plumb-line at two stations on
opposite sides of the mountain. If there were no
mountain, the angle between the plumb-lines at
the two places would be the angle AOB, got by
joining the places to the centre of the Earth. By
measuring the distance AB this angle can be calcu-
lated. But owing to the attraction of the mountain
THE LAW OF GRAVITATION
61
which pulls the plumb-line in different directions at
A and B, the actual
measured angle is found
to be greater than the
angle AOB. The amount
of the excess is due to the
pull of the mountain,
which is thus compared
with the pull of the Earth.
In this way Maskelyne
found the attraction of the
Earth to be 4.7 times as
large as it would be if the CD
Earth were of the density Dia g- XXXL
of water throughout; or the Earth's mean density is
4'7 times that of water.
Cavendish Experiment. A better and more accurate
determination is obtained by measuring in a labora-
tory the attraction of a metallic ball on a small ball
placed near it. This experiment was first made by
Cavendish, and was carried out later with great skill
by Francis Baily by means of a torsion balance. A
light arm, at the ends of which are two gold balls,
is suspended by a thread. .Suppose the balls rest in
a position due north and south. If two large balls
are brought near them, on the east side of one and
west of the other, the two gold balls will be attracted
slightly, and the force of the attraction is measured
by the twist given to the thread. This experiment
62
ASTRONOMY
was carried out by Prof. Boys in 1893 in the cellar
of the Clarendon Physical Laboratory at Oxford with
the greatest precision. Observations were made on
Sunday nights between midnight and 6 a.m., because
at other times traffic over stony streets and shunting
Diag. XXXII.
of trains set up tremors which interfered with the
delicacy of the experiment. A fine quartz fibre held
the balls, which were of gold, and in different experi-
ments were ^th and j|th of an inch diameter. The
large balls were of lead, and in different experiments
varied from 2\ to 4! inches in diameter. These ex-
periments showed that the Earth's mean density is
5*5270 times that of w~ater.
CHAPTER IV
ASTRONOMICAL INSTRUMENTS
THE stars appear to us as bright points fixed on a
distant globe which turns uniformly. The first task
of practical astronomy is to map their positions on
this globe as accurately as possible. Instruments
have gradually been evolved by which this mapping
is carried out with ever-increasing precision.
Right Ascension and Declination. It is first necessary
to see clearly how positions on the celestial sphere are
defined. Suppose P to
be the pole, and that
there is a star at S. The
distance of the star from
the pole is measured by
the angle POS, or by
what is the same thing,
the arc PS of the sphere.
The plane OPS will pass
through P 7 , the other pole,
and will cut the sphere
in^a circle. The circle D ia g . xxxm.
90 away from P (it is
also 90 away from P 7 ) is called the equinoctial or
63
64 ASTRONOMY
sometimes the equator. PS is called the north polar
distance of the star, and SM the declination. If PS
is known, SM is obtained by subtracting PS from 90.
If S is north of the equator the declination is positive,
and if south negative. To know the position of S on
the sphere, besides knowing SM, we need to know the
position of M. A point on the equator called the First
Point of Aries (T), which moves with the stars, is used
as the point from which to measure, and the arc TM
(or the angle between the planes POT and POM)
is called the right ascension. The direction TM is
measured in the direction contrary to that in which
the Earth rotates, and may have any value from o
to 360. The point T is not chosen arbitrarily, but is
the point in the sky where trie ecliptic or path of the
Sun cuts the equator. It will be seen that this mode
of defining the position of a star in the sky is similar
to the method of defining a spot on the earth by its
latitude and longitude.
Now as the whole sky appears to turn about its
axis in one sidereal day (approximately 4 m. shorter
than the mean solar day which is used in ordinary
life), the star moves in a circle completing its round
in one sidereal day. At the moment when it is at 5
in the diagram, it is on a circle which passes through
the poles and the zenith, or point vertically over the
observer's head. This circle is the intersection of the
celestial sphere with the meridian, or vertical plane
which passes through the place of observation in a
ASTRONOMICAL INSTRUMENTS 65
direction exactly north and south. When S reaches s,
its right ascension circle PSMP' is PsmP', or the
point M has reached m. After a time another star
S' reaches the meridian at s', and M' reaches m', and,
if the interval of time between the meridian passage of
S and S' be measured, we shall obtain the angle of
MM' at the rate of 15 to one sidereal hour.
Clocks. Suppose, now, we have a clock which reads
oh. om. os. when Tis on the meridian, and is rated
so that it completes 24 h. when T returns to the
meridian the next day. The time indicated by this
clock when any star crosses the meridian gives the
star's right ascension, at the rate of 360 to 24 hours,
or 15 to i hour. It is frequently not necessary to
change from time to angle, and the right ascension is
taken as the actual time given by the clock (supposed
to be correct). Thus it is very necessary for an ob-
servatory to possess such a clock, to divide up the time
in which the Earth makes one rotation into 24 hours,
24x60 minutes and 24x60x60 seconds. The time
indicated by such a clock gives the right ascensions of
all stars which are at that moment on the meridian.
Circles. When a star is on the meridian its distance
from the pole is the sum of its distance from the
zenith and the distance of the zenith from the pole.
In Diagram XXXIII sP = sZ + ZP. Now ZP is the
same for all stars, and is obtained by subtracting the
latitude of the place of observation from 90. The
direction of Z is the direction of a plumb line, so that
66
ASTRONOMY
to find sZ it is necessary to observe the angle between
the direction of the star and the direction of a plumb
line. The method adopted by Tycho Brahe, though
not invented, yet brought to a much higher degree of
Diag. XXXIV.
Diag. XXXV.
accuracy by him, consisted in having a large quadrant
of a circle mounted on a wall which pointed accurately
north and south (Diagram XXXIV). The arc of the
quadrant was divided into degrees and further sub-
divided into minutes (as in Diagram XXXV). The
direction of the star was taken along sights, one of
which was at the centre of the quadrant and the other
moved to the required position along the arc for the
star to be seen. In this way Tycho Brahe observed
the positions of stars and planets with errors of not
more than i' or 2'.
The accurate graduation of the arc of a circle is an
art which has been developed with the progress of
astronomy. Quadrants fixed to a wall are no longer
used, but complete circles attached to a telescope.
ASTRONOMICAL INSTRUMENTS 67
An accurately divided circle is as essential for the
determination of declinations as a good clock is for
that of right ascensions. The introduction of tele-
scopes has not altered the method of determining the
positions of stars. The right ascension of a star is
still determined by observing the time" at which it
crosses the meridian, and the north polar distance
from its altitude at this moment.
The Telescope. The telescope has increased the
accuracy and improved the power of the astronomical
observer in a wonderful manner. It has three import-
ant properties
(1) It increases the amount of light which enters
the eye from a star, and thus enables fainter stars to
be seen.
(2) It magnifies the apparent angle between two
stars, and thus greater accuracy can be obtained in
angular measurements.
(3) It obviates the necessity for the use of sights.
The light from a star comes to us in parallel rays.
If these fall on a lens (Diagram XXXVI) their direc-
Diag. XXXVI.
tions are refracted so that they pass through a point F,
F 2
68
ASTRONOMY
the focus of the lens. At F a bright point is fonr.ed,
called the image of the star. If the rays which pass
through F be intercepted by a second lens L', they can
be again converted into a parallel beam of light. If
the diameter of the second beam is no wider than the
pupil of the eye, all the star's light which fell on the
lens L passes into the eye. The telescope, in effect,
supplies the astronomer with an eye as big as its
object glass and thus enables him to see very much
fainter stars.
Now let there be two stars whose images are formed
at F and G (Diagram XXXVII). The cone of light
Diag. XXXVII.
through F will be converted into a beam of parallel
rays which, falling on the eye, will enable the star to
be seen. Similarly the cone of rays through G will
be converted into a parallel beam. The first beam is
in a direction parallel to DF, and the second one
parallel to DG. Thus the eye which receives these
beams will see the two stars in directions parallel to
DF and DG, whereas the actual directions are CF
and CG. Thus the angular distance between the stars
is magnified from FCG to FDG, which is in the pro-
portion CE : DE, or that of the focal length of the
ASTRONOMICAL INSTRUMENTS 69
object lens to the focal length of the eye lens. Thus
the longer the focal length of the object glass of a
telescope and the shorter the focal length of the eye-
piece, the greater the magnification.
Suppose the two lenses are firmly fixed in a tube,
and in the focal plane PEG two pieces of fine wire or
two spider's webs are stretched, crossing at E. When
the telescope is pointed near a star an image is formed
in the plane PEG. Shifting the telescope a little the
image can be made to fall at E, the intersection of the
two fine spider's webs. In this case the telescope is
pointing accurately to the star, for the line EC then
passes through the star. As E is fixed and C is
fixed, the line EC serves the same purpose as sights
at E and C ; and it is much easier to secure accurate
pointing in this way. This important improve-
ment of the telescope was introduced by Gascoigne in
1640.
Refracting Telescope. Telescopes have been gradually
improved from the small and imperfect one of Gali-
leo's to the large refractors and reflectors of the present
day. A simple lens does not bring light of all colours
to the same focus, and the image formed is con-
sequently coloured and indistinct. Newton, who first
resolved white light into a coloured band by means of
a prism, supposed that this defect was irremediable.
But in 1758 Dollond, an English optician, found that
by combining a convex lens of crown glass (a dense
glass with large refracting power) with a concave lens
of flint glass (a lighter glass of less refractive power),
7 o ASTRONOMY
the defect can be largely remedied. The light from a
star falling on the crown lens is refracted into a con-
verging beam, and is also dispersed into the different
colours of the spectrum : the
concave lens of flint glass neutral-
izes the dispersion and makes the
Din xxxvin ' ra y s ^ different colours converge
to the same point. This combina-
tion of lenses is called an achromatic object glass
(Diagram XXXVIII). It is not possible to com-
pletely banish all trace of colour in this way, and
there are other imperfections arising from the fact
that the curvature of the surfaces does not bring all
parallel rays of the same colour absolutely to a point.
These "aberrations," chromatic and spherical, are
reduced to small dimensions by careful choice of the
kinds of glass and by calculating the most appropriate
curvatures for the surfaces of the two lenses. The
single lens at the eye-end of a telescope has also been
replaced by two separated from one another by a
distance in suitable relation to the curvatures of the
two lenses. In this way an increase in clearness is
obtained in the parts of the image which are near the
edge of the eye-piece.
Before the invention of the achromatic object glass
very long telescopes were used, because they gave
greater magnification without much indistinctness
from the confusion of colours. With an achromatic
object glass much more magnification of the image
ASTRONOMICAL INSTRUMENTS 71
by the eye-piece is possible, and telescopes are not so
cumbersome.
For a long time it was not possible to procure glass
discs of sufficient uniformity and clearness to make
object glasses of more than 3 inches in diameter. The
largest object glass constructed by Dollond had a
diameter of 3! inches. Early in the nineteenth cen-
tury a Swiss artist, Guinand, succeeded in making
larger discs. He was employed by Fraunhofer, who
constructed object glasses of great perfection of 6 to 9
inches aperture. In 1840 a i5-inch object glass was
constructed by Merz for the Imperial Observatory at
Pulkowa; in 1870 a refractor of 25-inches aperture
was made by Messrs. Cooke for Mr. R. S. Newall,
and there are at the present time a considerable number
of telescopes whose object glasses are as large or larger
than this. The largest refracting telescopes are those
of the Lick Observatory of 36-inches aperture, and of
the Yerkes Observatory of 4o-inches aperture, both
made by the American opticians, Alvan Clark & Sons.
Reflecting Telescope. In 1668 Newton made a small
reflecting telescope which magnified thirty times. In
this instrument the light from a star falls on a concave
mirror of speculum metal an alloy of copper and
tin approximately in the proportions of four atoms of
copper to one of tin. The light is reflected by the
mirror so that parallel rays from a star are brought
to a focus forming an image of the star. By the
insertion of a small flat mirror, placed diagonally in
7 2 ASTRONOMY
the tube, this image is shifted to the side of the tele-
scope, where it can be viewed by an eye-piece (Dia-
_ gram XXXIX). In
1723 Hadley, the in-
ventor of the sextant,
made a reflector with a
f
Diag. XXXIX.
a focal length of 62
inches with which a magnification of 200 times could
be obtained. The great development of reflecting
telescopes was made from 1776-1787 by Sir W.
Herschel, who constructed specula of 6, 8, 12, 18, 24
an'd 48 inches, with focal lengths of 7, 10, 14, 20, 25
and 40 feet. These great telescopes were exceeded
by Lord Rosse who, in 1848, constructed a reflecting
telescope of 6 feet diameter and 53 feet focal length.
In 1851 Liebig discovered a process of depositing
silver on glass so as to give a highly reflecting surface.
Since that time reflecting telescopes have usually been
made of glass with a fine film of silver deposited on
them chemically. The advantages are a more highly
reflective surface, less weight, and the facility with
which a tarnished silver film may be dissolved and a
fresh one deposited without in any way interfering
with the carefully figured surface of the glass.
Astronomy is greatly indebted to Dr. Common, an
English amateur astronomer, for introducing the use
of large silver-on-glass reflectors. With a 36-inch
mirror he obtained in 1883 a beautiful photograph of
ASTRONOMICAL INSTRUMENTS 73
the Orion nebula. He completed in 1890 a mirror of
5 feet diameter, and showed how to grind, polish and
test a mirror so as to obtain the best results. The
greatest living exponent of the art of making very
large mirrors is Mr. Ritchey, who has constructed
extremely perfect ones for the Yerkes and Mt. Wilson
Observatories in America. He has recently constructed
one of 60 inches diameter, and is now engaged on one
of 100 inches.
There has been throughout the long period of their
development a friendly rivalry between the refracting
and reflecting telescopes. The uses of the two instru-
ments are now pretty well defined. Where accurate
measurements are required the refractor is generally
to be preferred. Where the object observed is ex-
tremely faint the reflector has the advantage, for in
proportion to size reflecting telescopes are of much
shorter focal length, thus producing a smaller but
brighter picture.
Mounting of Telescopes.; A small telescope, which is
used simply to look at the stars, can be held in the
hands, but it will be found much easier to rest it on
something, and for one of moderate dimensions
some form of mounting which holds the telescope
firmly and yet admits of its being easily pointed to any
part of the sky is indispensable. When accurate
measurements of any kind are to be made, the mount-
ing is a matter of great importance. There are two
classes of observations for which the telescope is used.
74 ASTRONOMY
which require it to be mounted in entirely different
ways. The actual position of the heavenly bodies in
the sky may be required, as for instance in finding
day by day the positions of the Sun, Moon or planets,
or determining the positions of the stars. On the
other hand, the position of the object in the sky may
be of no interest, as in observations of the revolution
of Jupiter's satellites about the planet or the rotation
of Jupiter itself.
When the actual position of a star in the sky is to
be determined, the telescope is fixed during the time
of observation, and the star is watched as it moves in
front of the telescope. The image of the star is seen
as a bright point moving in the focal plane of the
objective; in this focal plane spider's webs are
stretched, and the observation consists in a determina-
tion of the exact position of the telescope, and the
exact time at which certain threads are crossed by the
star's image.
Transit -Circle. The most important instrument of
this kind is the transit-circle (Diagram XL). It
applies the advantages the telescope gives in visibility,
magnification and accuracy of sighting to the method
used by Tycho Brahe of observing the time when a
star crosses the meridian and its altitude at that
moment. The telescope is fixed perpendicularly to
a horizontal axis which ends in two accurately turned
pivots. These pivots rest in bearings due east and
west, so that the telescope can be turned to any point
ASTRONOMICAL INSTRUMENTS
7 6
ASTRONOMY
in the meridian (or vertical plane pointing north and
south), but is always confined to this plane. In the
focal plane of the objective are two fairly close
horizontal parallel wires and several equally distant
perpendicular ones (so-called wires, but in reality
spider's webs) (Diagram XLI). The middle wire is
so placed that it is the "sight" of the meridian, i.e.
when a star crosses the meridian its image will be
seen in the telescope crossing the middle wire. A
little before the time when a star should cross the
meridian the observer turns the telescope about its
axis to the right altitude. In due time he sees the
star enter the field of his telescope, and moves the tele-
scope so that the star may come accurately in the
middle of the two horizontal wires. The star is
watched as it moves and the exact time is noted when
the several vertical wires are crossed. Formerly the
timing was done by the observer listening to the beats
of a clock, carrying the
seconds in his head and
estimating the tenths of
seconds. An easier method
now in general use is to
register the time electrically
on a chronograph, the ob-
server pressing a button
when the star crosses the
wires. The mean of the
Diag. XLI.
times across these wires
gives, subject to some small corrections which are
ASTRONOMICAL INSTRUMENTS 77
easily calculated, the exact moment at which the star
crosses the meridian, i. e. the right ascension.
To obtain the star's declination it is necessary to
determine the altitude at which the telescope is
pointed. For this purpose a large graduated circle is
fixed centrally on the axis of rotation of the telescope ;
the position of the telescope is determined by the par-
ticular division on the circle which comes to some
fixed point. To secure greater accuracy microscopes
are firmly fixed in positions for viewing the graduated
limb of the circle.
In the focal plane of each microscope are placed
wires, and the intersection of these wires will be seen
between two divisions of the graduated circle. The
exact distance of this point from a division is obtained
by mounting the wires on a frame carried by a screw
and reading the turns and fractions of a turn of this
screw necessary to bring the cross to the nearest
division of the circle. The divisions of circles are
generally 5' apart (so that there are 12x360 on the
whole circle), the fractions of 5' being read by means
of the micrometer screw. For greater accuracy four
or six microscopes arranged round a circle are used.
In actual practice there are a number of modifica-
tions and complications. With a good instrument, a
good clock and good observer, the right ascension
and declination of a star can be determined with an
error which is seldom more than 2" '. To form an idea
of 2" comparison may be made with the angular dia-
meter of the Sun, which is 30' or 1800". By taking
78 ASTRONOMY
the mean of several observations on different nights,
stars' positions are found with greater accuracy.
Equatorial. In order that a telescope may be kept
pointing to a star as it crosses the sky the telescope
must be given a suitable movement. The movement
Diag. XLII.
required is easily demonstrated by a pair of compasses.
If one leg be pointed towards the pole, the other leg
ASTRONOMICAL INSTRUMENTS 79
can be opened out to an angle equal to the polar
distance of the star; then by turning about the leg
pointing to the pole the other leg may be brought to a
position in which it points to the star. If now the
compasses are turned uniformly around the leg point-
ing the pole so as to go completely round in one
sidereal day, the other leg will point to the star all the
time. This is exactly the principle of the equatorial
mounting of a telescope. The telescope is perpen-
dicular to, and can turn about, the declination axis.
The declination axis is perpendicular to, and turns
about, the polar axis (Diagram (XLII). The tele-
scope is first placed in the required position and then
turned by clockwork.
In the mounting of a large telescope there are neces-
sarily many important details to be arranged in order
to make it easy of manipulation and regular in its
movement. It is also necessary to be able to correct
for any want of precision in the driving clock, espe-
cially when the telescope must be kept pointing to
the same part of the sky for a long time. These
details are satisfactorily surmounted by the engineer-
ing skill of the instrument makers combined with care
and patience of the astronomer who uses the equatorial.
Thus a picture of the part of the sky to which the
telescope is pointed is formed in the focal plane of the
object glass. By means of the equatorial movement
this picture is kept at rest, and the observer looking
through the eye-piece of the telescope can examine it.
So
ASTRONOMY
Position-Micrometer. This examination usually in-
volves measurement of some kind, and other instru-
ments are required for this purpose. For example,
to measure the distance between two very near stars
or the diameter of one of the planets, a micrometer of
some kind is needed. A very simple form is the posi-
tion-micrometer, which gives means of moving fine
wires (webs of spiders stretched on frames) in the focal
I
Diag. XLIII.
plane of the telescope. In Diagram XLIII, which
represents this instrument, there are three lines, AB,
CC and DD, of which CC and DD can be moved
nearer or farther apart by means of screws P and O,
the distance between them being known from the
readings of the screw-heads. In addition the micro-
meter, which is mounted in the telescope tube, can be
turned to any required position. Thus if two stars
ASTRONOMICAL INSTRUMENTS 81
are in the field of view, by turning the micrometer and
moving the screws, the intersection of AB and CC
can be placed on one star and the intersection of AB
and DD on the other.
The distance between the images of the two stars is
measured in linear measure, let us say, in fractions of
an inch; the angle between them is found by dividing
this distance by the focal length of the telescope.
Referring to Diagram XXXVII, the distance FG
is measured, and to find the angle FCG it is sufficient
to divide by the length CE, as we are only dealing
with very small angles.
Heliometer. A position-micrometer is suitable for
measuring the distance between two stars which are so
near that both can be seen at the same time. With a
large telescope this means angles less than one minute
of arc or less than -J$th of the diameter of the Sun or
Moon. For angles comparable in size with the Sun's
diameter the most accurate visual observations are
made with a heliometer. This is a telescope equatori-
ally mounted, but having its object glass divided into
two halves. The two halves can be moved, as shown
in Diagram XLIV, by means which admit of the
distance from the central position being accurately
determined. Each half gives a picture of the part
of the sky which is being observed; the two images
are exactly alike, but they are at a distance apart
equal to the separation of the two halves of the
object glass. If, for example, two stars are looked at,
G
82
ASTRONOMY
Diag. XLIV.
and the glass is turned so that the direction in which
the halves are separated is parallel to the line joining
the stars, there will be seen, as in Diagram XLIV, four
images in a straight line,
viz. A and B, the images of
the two stars formed by
one half of the glass, and
A' B', the images formed by
the other half. The halves
of the glass are separated by
1 a distance AA' or BB'. If
now they are still farther
separated till A' coincides
exactly with B, the distance between the stars is
exactly equal to the amount by which the two halves
of the glass are separated. In practice a good
deal of refinement is necessary in carrying out these
observations, and it is, besides, a very delicate matter
to cut an object glass in two. To instruments of this
class we are largely indebted for the accurate measures
by which the distances of the Sun and of the stars
have been determined.
Photographic Telescope. The telescope is seen in its
simplest form when it is used for photography. A
photographic plate is placed in the focal plane of the
object glass or reflector, and gives a permanent record
of the image formed there.
A reflector may be used for visual or photographic
observations because the light of all colours is brought
to the same focus, but an object glass to be used for
ASTRONOMICAL INSTRUMENTS 83
photography must be constructed so that blue light
which affects the plates most powerfully is brought to
a sharp focus, and not the red, green and yellow to
which the eye is most sensitive. A photographic
telescope is merely a large photographic lens of corre-
spondingly long focus. Typical telescopes are those
used in the International Chart of the Heavens,
initiated at Paris in 1887, of about 13 inches diameter
and ii feet 3 inches focal length. The scale of these
telescopes is such that the photographs of the Sun or
Moon are about i\ inches in diameter. The field
over which good pictures are taken has a diameter
of about 5 inches. Using fast plates, stars visible to
the naked eye require exposures of less than one
second, and the number of stars shown increases
largely with the length of the exposure. Long
exposures are necessary to photograph very faint
stars, and therefore the clock movement should be
very accurate. If the telescope moves to follow the
motion of the stars exactly their images will be round
dots, but if it is moving too slowly or too fast they will
be short lines. To secure the correct movement of the
telescope arrangements are made for the observer to
guide and control it.
When a photograph of the stars has been taken,
it will contain a small number of bright stars whose
positions are already known and a large number of
fainter ones which are unknown. It therefore serves
to fill in the fainter stars into a map on which the
brighter stars are already delineated. Like the helio-
c 2
84 ASTRONOMY
meter, a photograph can be used for finding the
distances and relative directions of stars whose
distance apart is less than one or two degrees.
We have so far considered astronomical instru-
ments simply as means for the accurate measure of
angles the transit circle being typical of the methods
by which the relative positions of stars distant from
one another on the celestial sphere are obtained, and
the equatorial mounting with its various adjuncts
giving the relative positions of near bodies. But a
telescope mounted equatorially can be used for many
other purposes. For example, a photometer may be
used, and the quantity of light received from different
stars may be measured and compared. In one or
two cases an instrument has been attached to the
telescope by which the amount of heat received from
the stars has been measured. But by far the most
important instrument of physical research used by
the astronomer in conjunction with the telescope is
the spectroscope. When applied to the stars it is
mounted on an equatorial telescope with the slit in the
focal plane of the object glass. The telescope is so
pointed that the image of a star may fall on the slit
and part of it enter the spectroscope. The function
of the object glass is to collect the light, and that of
the equatorial to keep the telescope accurately pointed.
The way in which a spectroscope analyzes the light
which passes through it will be described in the chapter
on the Sun.
CHAPTER V
THE SUN'S DISTANCE
THE determination of the Sun's distance is one of
the most important problems of astronomy. As we
have seen, it is possible, by means of Kepler's third
law, to determine the distances of the other planets
from the Sun in terms of the Earth's mean distance.
For example, the mean distance of Jupiter from the
Sun is 5*2028 times the Earth's distance. A model
of the solar system can be constructed, but till the
Earth's distance from the Sun is found we cannot
give the scale. More than this, the distances of the
stars are determined in terms of the distance of the
Sun, so that this is the standard length with which
all astronomical distances are compared. Naturally
such an important problem has received a great deal
of attention.
A Greek astronomer, Aristarchus of Lamos, realiz-
ing that the Moon shone by reflected light from the
Sun, argued that the Moon would be exactly half full
when the directions of Sun and Earth, as seen from the
Moon, were at right angles. Thus in Diagram XJ^V
85
86 ASTRONOMY
the angle EMS is exactly a right angle. If the exact
moment when the Moon is half full could be deter-
mined by observation, it would then be possible, by
measuring the angle between the Sun and Moon, as
seen from the Earth
(the angle SEM of the
diagram), to determine
XLV ^ ie exact shape of the
triangle SME, and
thus find SM in terms of EM. He found in this way
that the Sun's distance was nineteen times that of the
Moon. The method is extremely rough, because it is
impossible to say exactly when the Moon is half full.
Till the time of Kepler this was the generally
accepted distance of the Sun, but Kepler showed that
it must be at least three times as far away.
Cassini's Measure of Sun's Distance. The first deter-
mination which approaches to what we now know to
be the distance was made by the French astronomer
Cassini, between 1670 and 1680. He did not measure
the distance of the Sun directly, but chose the planet
Mars when in opposition, i. e. in a direction opposite
to the Sun. Now, the Earth describes a circle of
radius i about the Sun, while Mars describes one of
radius ij, and therefore Mars, when in opposition, as
at M (Diagram XLVI), is only at one-half the Sun's
distance. The shorter distance is measured twice as
easily. But more than this, Mars is seen at night with
a background of stars, ancl its position can be deter-
THE SUN'S DISTANCE 87
mined very accurately in relation to these stars.
Cassini sent out an expedition to Cayenne, and the
positions of Mars were observed simultaneously from
Paris and Cayenne. In Diagram XLVII, E is the
centre of the Earth, EP^> a radius through Paris, and
ECc one through Cayenne, while M is the position of
Mars. If at Paris the angle MP/> is measured, and
Diag. XLVI.
Diag. XLVII.
simultaneously at Cayenne the angle MCc, then, since
the radii of the Earth, EC and EP, are known, and
also the angle PEC from the positions of Paris
and Cayenne on the Earth's surface, there is enough
determined to draw the diagram accurately to scale,
and thus find the distance EM. In actual practice the
diagram would not be drawn to scale, but trigono-
metrical calculations made instead, but this is merely
a substitute which avoids the difficulties and uncer-
tainties of drawing the angles correctly.
Cassini's result was 84 million miles, and as we now
know th'e distance to be 93 million miles it will be
88 ASTRONOMY
seen that he was within about 10 per cent, of the true
value.
Transit of Venus. Another and very famous
method of determining the Sun's distance is by the
transit of Venus. As the orbit of Venus lies within
that of the Earth, it happens on very rare occasions
that Venus passes between the Earth and the Sun,
and is actually seen crossing the Sun's disc as a black
spot. As at these times Venus is about 25 million
miles from the Earth, while the Sun is much farther
away, it follows that, seen from two points as distant
Diag. XLVIII.
from one another as possible on the Earth's surface,
Venus traces a slightly different path across the Sun's
disc. This is shown in Diagram XLVIII, but im-
mensely exaggerated. By observations of the exact
times at which Venus enters and leaves the Sun's disc
at the two stations, it is possible to determine the dis-
tance apart in angle of the two chords aa' and bb r
and thence to find the distance of Venus the distance
AB Between the two stations serving as the base-line.
Observations made at the transits of 1761 and 1769
gave the distance of the Sun 95 million miles, An
THE SUN'S DISTANCE
89
attempt was made at the transits of 1874 and 1882 to
obtain the distance with greater accuracy. Extensive
preparations were made, and many expeditions were
dispatched by the governments of Europe and the
United States. Although every care was taken, the
expeditions were a comparative failure, owing to the
impossibility of saying with certainty what w 7 as the
exact moment at which Venus was seen touching the
Sun's disc.
Mars near Opposition. In the year 1877 Sir David
Gill made observations of Mars near opposition from
the island of Ascension. As the Earth turns round,
bringing the observer
from A in the early
evening to B in the
early morning (Dia-
gram XLIX), the di-
rection in which Mars
is seen changes slightly. Instead of observing Mars
simultaneously from two different places on the Earth's
surface, it was observed evening and morning from the
same point the point of observation swinging in con-
sequence of the Earth's rotation from one side to the
other of the direct line from the Earth's centre to
Mars. Are there any means of measuring the angle
AMB? If so, the distance can be found. Now
Mars is seen projected on the sky in the midst of the
fixed stars. These are so distant that they are seen
in the same direction from all points of the Earth's
. XLIX.
9 o ASTRONOMY
surface. Suppose there were a star exactly in the
line of EM. As seen from A, Mars would appear
to the right of this star, but when the Earth's rotation
will have carried A to B, then it will appear to the
left. Measuring the angular distances between Mars
and the star, the angles MAS and MBS are found,
and by addition the angle AMB. Then, as the length
AB can be easily determined, the distance EM is
calculated at once.
The geometrical principles underlying this are easy
enough, but observations necessary to obtain a good
determination of the distance must be of extreme
accuracy. The angles to be measured are so extremely
small that the slightest errors make a considerable
difference in the result. The measures of angles were
made with a heliometer, and errors arising from the
instrument and the observer were guarded against, and
where possible their effects eliminated by further ob-
servations. An additional difficulty is found in the
movement of the planet. Mars does not stay still
between evening and morning to suit the observer's
convenience, so its motion has to be carefully calcu-
lated and allowed for. As Mars is near opposition for a
considerable time, long series of observations are car-
ried on night after night and morning after morning,
and the final result derived from the mean of the whole
series. Although a very accurate result was obtained,
the fact that Mars has a disc of considerable size gave
rise to a. little uncertainty. It is much easier to
THE SUN'S DISTANCE 91
measure the distance of a bright point from another
than to measure the distance of a bright point from
the edge of a disc, where one is liable to measure
from a little inside or a little outside of the edge.
Now, there are among the small planets whose orbits
are rather further from the Sun than that of Mars,
some which, owing to the eccentricity of their orbits,
come sufficiently near to the Earth for them to be
available to determine the Sun's distance. From these
Sir David Gill picked out Victoria, Iris and Sappho
as being the most suitable, and made an extensive
series of observations at the Cape of Good Hope in
the years 1888 and 1889, and also secured the assist-
ance of observers at northern observatories in the
observations of the planets, and in the extensive sub-
sidiary observations necessary to determine the posi-
tions of the stars from which the angular distances of
the planets were measured. The details of the ob-
servations and the determination of the Sun's distance
from them occupy two large quarto volumes. The
final result is that the Sun's distance is 92,874,000
miles, and from the agreement between the different
observations it is concluded that the error is probably
not more than 50,000 miles. This error corresponds
to an error of one yard in measuring a mile.
Eros. On August 13, 1898, Dr. De Witt of Berlin
discovered a small planet, to which the name Eros was
subsequently given, which at times comes to within
14 million miles of the Earth. This small body, only
92 ASTRONOMY
28 miles in diameter, is our nearest neighbour among
the planets, and is admirably suited to determine the
Sun's distance. At the end of 1900, when Eros came
to within 30 million miles of the Earth, a very exten-
sive series of observations was undertaken in co-
operation by many observatories. The method em-
ployed was essentially the same as the one just
described with regard to Victoria, Iris and Sappho ;
the main difference being that photographs of the
planet and surrounding stars were taken, and after-
wards measured, instead of the planet's distances
from neighbouring stars being measured with the
heliometer. The photographic telescopes employed
were of long focus from njft. to 22^ ft. and con-
sequently the photographs were on a large scale, and
admitted of the accurate determination of the position
of Eros among the surrounding stars. The result
derived by Mr. Hinks of the Cambridge observatory
from the combined observations of Eros is approxim-
ately 92,800,000 miles, agreeing very closely with the
distance found by Sir David Gill.
It should be noticed that the methods of determin-
ing the Sun's distance just described, though very
complicated in the details which must be considered
when a result of high accuracy is aimed at, are very
simple in principle. The distance of the Sun is
measured just as a surveyor might measure the dis-
tance of a tree on the opposite bank of a river. The
difficulty arises from the fact that the astronomer
THE SUN'S DISTANCE 93
cannot obtain a base-line larger than the diameter of
the Earth. This, in comparison with the distance of
Eros, is very small, and gives a triangle with very
long sides and a very short base. A small error in
the determination of the vertical angle makes a large
error in determining the lengths of the long sides of
the triangle.
The distance of the Sun may be determined in an
entirely different way by observing the time which
light takes to travel across this distance, and again by
comparing the velocity of the Earth in its orbit with
the velocity of light.
Velocity of Light. In the year 1675 the Danish
astronomer Roe'mer discovered that light is not trans-
mitted instantaneously, but moves with a measurable,
though very great, velocity. He was led to this dis-
covery by observations of Jupiter's satellites. The
Sun's light causes Jupiter to cast a shadow, and the
satellites may be seen entering or emerging from this
shadow. From numerous observations it became pos-
sible to construct tables predicting the times of these
occurrences. Roe'mer found, however, that when the
Earth was near to Jupiter the eclipses occurred before
the predicted times, but after them when the Earth was
more than its mean distance from Jupiter. He ex-
plained these differences between the observed and pre-
dicted times by the difference of time taken by the light
to travel a longer or shorter distance. Thus in Dia-
gram L, if E x , E 2 , E 3 , E 4 , be four positions of the
94
ASTRONOMY
EJ
Earth, S and J the positions of the Sun and Jupiter,
the distances to be traversed in these four cases are
and it is clear that the difference
between the times taken
\ to traverse E 3 J and EJ
* gives twice the time it
> takes for light to travel
from the Sun to the
Earth. The actual time
taken by light to travel
between the Earth and Sun is
Diag. L.
the mean distance
8m. 18-55.
Aberration. Fifty years later, Bradley, while at-
tempting to measure the distance of one of the fixed
stars, y Draconis, discovered the "aberration of light."
He found that this star's declination changed in the
course of the year. From December 1725 to March
1726 the star moved 20" towards the south; it was
stationary for a short time, and then moved north-
wards, reaching by the middle of June the position it
had at the beginning of December. It continued to
move northwards, till at the beginning of September
it was 20" to the north of its position in December
and June. Again it was stationary for a short time,
and then moved southwards, till at the beginning
of December it was in the same position as in the
previous year.
Although the movements of the star were exactly
opposite to Bradley's anticipation, their regularity
THE SUN'S DISTANCE 95
showed that they were not accidental. At first Bradley
looked for the explanation in a movement of the
Earth's axis. But by making observations of stars
in different parts of the sky he found that this could
not be the cause, and after some other attempts he
discovered that the velocity of the Earth in its orbit,
combined with the velocity of propagation of light,
afforded a complete explanation of the phenomena.
A very familiar example will help to make this clear.
. If rain is falling vertically a person who is standing
still holds his umbrella directly over his head, but if
he is walking fast the rain appears to meet him, and
he holds his umbrella slightly in front. In a similar
manner, if the light moves over a distance equal to BA
(Diagram LI), while the observer moves
over a distance AC, the light will appear
to come in a direction DA, instead of
the direction BA. Let us further sup-
pose that the gentleman with the
umbrella walks round a circular track.
When he is walking northwards his
umbrella will be pointed a little to the
north, when eastward a little east,
when southward a little south the di-
rection in which he holds the umbrella
being constantly changed. Now as the Earth is moving
round the Sun its direction is constantly changing
throughout the year. The direction from which the
light appears to come from a star, i. e. the direction
96 ASTRONOMY
in which the star is seen, is constantly changing
being always inclined slightly from the star's mean
direction towards the direction in which the Earth at
the moment is travelling, and in consequence the
stars are seen to describe small ellipses in the sky
about their mean positions. The semi-major axes of
these ellipses are all the same, namely, 20" (approxi-
mately), this being the angle of a right-angled tri-
angle of which the longest side is proportional to
the velocity of light, and the shortest proportional
to the velocity of the Earth in its motion round the
Sun.
Sun's Distance determined from Velocity of Light.
Roemer's observations showed that light was pro-
pagated with a finite velocity, and Bradley's discovery
of aberration was the first absolute proof that the
earth revolved round the Sun. But in the middle of
last century methods of measuring the velocity of
light on the Earth were devised by Fizeau and Fou-
cault; the method of Foucault by which the velocity
of propagation of light is measured in a laboratory
has been so perfected that Michelson and Newcomb
have determined it as 186,330 miles a second, with an
error probably not exceeding 25 miles. Knowing the
velocity of light, if the time which light takes to travel
across the Earth's orbit be accurately determined from
the times of the eclipses of Jupiter's satellites, it is
but a matter of simple division to find the radius of
this orbit or the distance of the Sun. The accuracy
THE SUN'S DISTANCE 97
attainable by this method is considerable, but not
nearly equal to that given by the trigonometrical
methods described above.
The constant of aberration has been determined with
very great accuracy by observation. This constant is
the ratio of the Earth's velocity to that of light.
Knowing the velocity of light, the velocity of the
Earth is deduced, and from it the distance through
which the Earth moves in a year, and then the mean
distance of the Earth from the Sun. The value thus
found for the Sun's distance is slightly greater than
the result given on p. 92.
Quite recently another method has been employed
for determining the ratio between the Earth's velocity
and that of light. As will be explained in the next
chapter, when the light from a star is analyzed by a
spectroscope, the lines in the spectrum are slightly
shifted towards the red or the blue if the source emit-
ting the light and the spectroscope receiving it are
moving away from or towards each other. This
principle was applied by Sir William Huggins to
determine the velocities with which stars are appar-
ently approaching, or receding from, the Earth. Now,
if the Earth's orbital motion is at one time of the
year directed towards a star, it will six months later
be directed away from it. At the first of these times
spectroscopic observations give the velocity of the star
away from the Solar System diminished by the velo-
city of the Earth in its orbit. Six months later they
9 8 ASTRONOMY
give the velocity of the star added to the velocity of
the Earth. The difference of the two results is twice
the velocity of the Earth in its orbit. Thus we find
how fast the Earth is travelling, and as we know that
it completes its journey in one year, the length of that
journey can be found, and the Sun's distance derived.
Gravitational Methods. There are at least three other
ways of determining the Sun's distance. One de-
pends on the fact that the Earth every month describes
a small circle about the centre of gravity of the Earth
and Moon, and this slightly affects the direction in
which we see the Sun. A second arises from the fact
that when the Moon is between the Earth and Sun,
the attraction of the Sun upon it is greater than when
the Moon is on the side of the Earth away from the
Sun. The effect of this can be traced in the Moon's
motion, and leads to a determination of the Sun's
distance. A third method depends on a disturbance
which the Earth makes in the elliptic motion of
Venus about the Sun : this leads to a determination
of the Earth's mass, and through it of the Earth's
distance.
The Sun's distance may therefore be found in a
variety of ways. The methods may be classified as
(i) surveyor's or trigonometrical methods applied to
the nearest of the planets; (ii) methods which take
the velocity of light as known, and compare the
Earth's velocity with it, or else find directly the time
light takes to travel the Sun's distance; and (iii) by
THE SUN'S DISTANCE 99
effects due to gravitation seen in the motion of the Sun,
Moon, and especially of Venus, in which the Earth's
distance from the Sun enters as a factor. The sur-
veyor's or trigonometrical method applied to minor
planets when nearest to us is the simplest, and at
present gives the best results. But it is important to
use as many methods as possible based on different
principles in determining what is the astronomer's
standard of length, in terms of which he measures all
other celestial distances.
H 2
CHAPTER VI
THE SUN
WE think of the Sun as the centre and seat of
government of the planetary system, and particularly
as the source from which the Earth derives the heat
and light required for the existence of man upon its
surface. But we may also regard the Sun as a star
much nearer to us than any of the others. For the
stars are suns at such great distances that in the
largest telescopes they appear to be only bright
points. If the Sun were a million times as far away,
we should see it as a star of the third or fourth magni-
tude in no respect specially remarkable. Owing to
its proximity, a more detailed knowledge can be
obtained of the Sun than of other stars, and it there-
fore serves as the sample by which we judge of them.
Both on account of its relationship to our planet and
ourselves, and of its being the representative of the
millions of stars in the sky, the Sun is a supremely
interesting subject for study and research.
Size. When the distance of the Sun has been deter-
mined there is no difficulty in finding its size and mass.
If we draw lines to two points at the opposite extrem-
ities of a diameter of the Sun, the angle between these
THE SUN 10 1
lines will be rather more than half a degree. It
follows from this that as the Sun's distance is 93
million miles, its diameter is 865,000 miles, or about
no times that of the Earth. Its volume will, there-
fore, be 110 cubed, or 1,331,000 times that of the
Earth.
Mass. The Sun's mass is determined from the effect
of its gravitation. The Earth describes a circle of 93
million miles radius in one year. It follows that in one
second it is pulled inwards from the tangent by Tt)i> tri
of a foot. In Diagram LII, S being the Sun,
'f e
E the Earth, and EG the distance travelled
in one second, then EG = y^ ft. Now the
Earth's gravitation causes a stone to fall
1 6 ft. in the first second after it is dropped.
At the Sun's distance the stone would fall
16 x (mriw.inny) 2 ft. = -& x one millionth
of one foot.
Thus the Earth's attraction would only produce
Tmnnnrth of the effect produced by that of the Sun,
and consequently the Sun is 330,000 times as massive.
Density. As the ratio of the Sun's volume to that
of the Earth is much greater than the ratio of their
masses, it follows that the Sun is much less dense
than the Earth. The figures are T ;Wf innr or about J.
Now the Earth's mean density is 5j times that of
water; therefore the mean density of the Sun is only
1 1 times that of water, or about half the mean density
of rocks at the Earth's surface. The pressure inside
102 ASTRONOMY
the Sun caused by the mutual gravitation of so huge
a mass is enormous. The low density shows that the
enormous pressures are accompanied by extremely
high temperatures, and that the matter in the body
of the Sun is in a gaseous condition.
Solar Radiation. The Sun is constantly radiating
its heat into space. A very small portion of this is
intercepted by the Earth and planets. What becomes
of the rest we do not know. The rate at which this
radiation is proceeding can be measured by finding
how much heat falls each minute on a given area
exposed perpendicularly to the Sun's rays. An
instrument for measuring the amount of heat received
from the Sun is called a pyrheliometer. Such an
instrument is constructed so that it shall retain all
the heat which falls on it from the Sun, and it is
shielded from receiving heat in other ways. As a
great deal of heat is absorbed by the Earth's atmo-
sphere, allowance is made for this, and when possible
observations are made at a high altitude, such as
Pike's Peak or the Corner Grat, where less atmo-
sphere has been traversed. The "solar constant" is
the name given to the quantity of heat which would
be received per minute on a square centimetre
( T V inch x y^ inch) exposed perpendicularly to the
Sun's rays if there were no atmosphere. Experiments
show that this is 2*25 calories, or sufficient to raise the
temperature of one cubic centimetre of water by 2*25
Centigrade,
THE SUN 103
If we imagine a sphere with the Sun as centre and
a radius of 93 million miles, every square centimetre
of the surface of this sphere receives each minute 2*25
calories. All this heat is radiated from the Sun's
surface. Now the surface of the Sun is only T ^oir tri
part of the surface of a sphere whose radius is 93
million miles. Consequently the Sun must radiate
heat at the rate of 2^25 x 46,000 calories per minute
per square centimetre, or more than 100,000 calories.
Every square centimetre of the Sun is turning out
work at the rate of an n -horse-power engine. Pro-
fessor Young illustrates the immense output as
follows: if the Sun were frozen over completely to
a depth of fifty feet, the heat emitted is sufficient to
melt the whole of this in one minute of time. The
mechanism by which this radiation is maintained is
a constant flow of heated matter from the interior to
the surface of the Sun, and a corresponding flow
inwards of the cooled matter from the surface. Prof.
Schuster gives an idea of the magnitude of the pro-
cess as follows : In every second a fresh layer of hot
gaseous matter will have to be brought to the surface,
a layer a quarter of a mile thick if the gas is at atmo-
spheric pressure. And the matter brought up in the
preceding second must be got out of the way when it
has parted with all its heat.
Maintenance of Heat How is the Sun able to con-
tinue this prodigal expenditure of heat? It cannot
be by combustion, for if the Sun were made of coal,
104 ASTRONOMY
the heat obtainable would not be sufficient to main-
tain this expenditure for more than 6000 years, and
geology teaches us that the Earth has been receiving
heat from the Sun for millions of years. But every
time a meteorite falls into the Sun it contributes heat,
for the velocity of a body pulled into the Sun from
a great distance will approach 400 miles a second,
and the energy of such a body will by the collision
be turned into heat. Though some heat is doubtless
acquired by the Sun in this way, calculation of the
amount shows that it is probably only a small per-
centage of the total. Helmholtz showed that the slow
contraction of the Sun under the influence of its own
gravitation would supply a much larger amount.
This process is essentially similar to that by which
a meteorite falling into the Sun contributes to its
heat. In the case of a meteorite, the motion of a
small body is checked suddenly. In that of the con-
traction of the Sun, a very large mass is continuously
forcing its way inwards. In both cases energy ac-
quired by gravitation is converted into heat. Helm-
holtz showed that if the Sun's radius contracted one
mile in 40 years, sufficient energy would be obtained
to supply the output by radiation. It would be
thousands of years before such a small shrinkage
could be detected. Still, this process cannot go on
for ever, and if the Sun has no other way of
replenishing its stores, the Earth will not continue
to receive the amount of heat necessary for the
THE SUN 105
support of life on its surface many million years
longer.
We may also ask how long the Sun has been
radiating heat at this tremendous rate. Supposing
the Sun to have been formed by matter falling to-
gether from very great distances, the supply of heat
thus generated would be sufficient to maintain the
present rate of radiation for 18 million years. We
cannot say that this is the only way in which the
Sun has obtained heat. It is known, as we shall see
later, that helium exists in the Sun. Now, helium is
formed from the disintegration of radium, a process
which is accompanied with a great liberation of heat.
The Sun's heat may have been partly acquired in
this way, or in others of which we know nothing. It
is generally believed by scientists that the Earth has
been receiving heat from the Sun for a much longer
period than 18 million years.
Temperature. Very different estimates have been
formed of the temperature of the Sun. It is seen to
be very high because with a very powerful burning-
glass all metals can be liquefied and vaporized. The
difficulty in determining the temperature has been
principally due to want of knowledge of the law con-
necting the amount of heat radiated with the tempera-
ture of the radiating body. In 1879 Stefan enunciated
the law that the radiation varies as the fourth power of
the temperature reckoned from absolute zero, or 273
Centigrade. Messrs. Wilson and Gray heated a
io6 ASTRONOMY
definite surface of platinum electrically to a known
temperature, and compared the heat radiated by this
with the heat radiated by the Sun. Making necessary
allowances for the amount of the Sun's heat absorbed
in the Earth's atmosphere, they were in this way
able to determine the Sun's temperature. The results
formed by different observers agree in giving the
temperature of the Sun at from 6000 to 10,000
Centigrade.
The Spectroscope. During the last 50 years our
knowledge of the Sun and stars has been extended in
unexpected directions by spectrum analysis. Just as
the ear can detect and separate several notes of a
piano played simultaneously, so the spectroscope
analyzes the vibrations which are transmitted in a
beam of light. A beam of light may be, and often is,
extremely complex, but by this analysis the different
notes, so to speak, are separated, and a great variety
of information is in certain circumstances obtained of
the source from which the light proceeds. If a beam
of sunlight be allowed to fall on a prism, it is split
up into a coloured band in which the colours are
arranged in the order violet, indigo, blue, green,
yellow, orange, red. Each gradation of colour cor-
responds to a particular length of wave and time of
vibration of the light the whole consisting of an
infinite number of different waves. A much more
perfect analysis of a beam of light is obtained as
follows : the light of the Sun (for example) is made
THE SUN
107
to pass through a very narrow slit A in the focal
plane of an object glass B (Diagram LIII). The light
falls on B and
emerges as a
parallel pencil of
rays. This falls
on the prism C,
whose edge is
Diag. LIII.
parallel to the
slit A. All the rays of any one wave-length emerge
in parallel directions from the prism, and, falling on
the object glass D, are brought to focus. The rays
of each colour are brought to a different focus, and
a coloured band rv, called a spectrum, is formed.
When this experiment is carefully performed, the
bright band is found to be crossed by a large number
of dark lines.
If, instead of sunlight, the light from a Bunsen
burner in which some sodium chloride (common salt) is
sprinkled is admitted into the spectroscope, two bright
yellow lines are seen, and these two lines are coinci-
dent in position with two of the dark lines in the solar
spectrum. The light from other substances when
vaporized gives bright lines characteristic of the
substances emitting them. The relation between the
spectra of sunlight and of light from terrestrial
sources was explained and developed by Kirchoff.
He found that when sunlight streamed through a
flame in which salt had been sprinkled into the
io8 ASTRONOMY
spectroscope, the yellow lines disappeared, being com-
pletely swallowed up by the solar dark lines which
coincided with them in position, and which were
much stronger than when the sunlight had not passed
through the flame containing sodium vapour. He
was thus led to explain the existence of the two dark
lines in the solar spectrum which coincide in position
with the yellow lines given out by the vapour of
sodium, by saying that light from the hot interior of
the Sun passed through a layer of lower temperature
at the Sun's surface in which there was the vapour of
sodium ; that the sodium vapour in this layer absorbed
the vibrations of the same period as those it could
itself emit, just as a tuning-fork responds when its
own note is played on a piano. He verified this pro-
position experimentally in his laboratory, by allow-
ing light containing sodium vapour from a flame at
a high temperature to pass through a flame at lower
temperature also containing sodium vapour before
entrance into the spectroscope. The yellow lines
from the flame at lower temperature were darkened.
Spectra are of three kinds
(1) Continuous coloured bands with no dark lines.
These are given by the light emitted by glowing
solids or liquids or gases subjected to great pressure.
(2) A number of definite bright lines. These
spectra are obtained from glowing matter in a gaseous
condition. They may be produced by volatilizing
metals in flames or the electric arc; from an electric
THE SUN 109
spark, in which cases matter from the terminals is
carried across the gap between them ; or by an electric
discharge in vacuum-tubes containing a small quantity
of such gases as hydrogen, nitrogen, etc.
(3) Absorption spectra. These consist of bright
bands traversed by dark lines. They are formed when
light from a source at higher temperature passes
through a medium containing glowing vapours which
would themselves yield a bright line spectrum. The
spectrum is the reversal, dark lines for bright, of that
which would be given by the medium through which
the light passes.
Solar Chemistry. -- Kirchoff's discovery was the
beginning of solar and stellar chemistry. The spec-
trum of the Sun was carefully mapped by him, and
the positions of certain dark lines shown to be
identical with those in the spectra of sodium, calcium,
magnesium, barium, iron and nickel. Sunlight has
therefore traversed a layer surrounding the Sun in
\vhich vapours of these elements exist. To make sure
of the exact coincidence in position of the solar lines
and those of terrestrial elements it is necessary to
spread out the spectra as far as possible. This is done
by having a number of prisms instead of one, or, still
better, by using a "grating" instead of prisms to
disperse the light. A "grating " consists of a polished
surface on which a large number of equally spaced
parallel lines are ruled by a diamond. The art of
ruling gratings was brought to great perfection by
[io ASTRONOMY
Rowland of Baltimore. A typical grating of Row-
land's is of speculum metal 6 inches long by 4 inches
high, and on it are ruled 14,468 lines to the inch, so
that altogether the grating contains 86,800 minute
furrows. When light falls on such a surface, part
of it is dispersed into a series of spectra.
With gratings of his own construction Rowland
made a magnificent catalogue and map of the lines in
the solar spectrum. It extended from the red end of
the spectrum through the yellow, green, and blue far
beyond the violet. The human eye is not sensitive to
the rays of ultra-violet light, but the spectra can be
photographed, as photographic plates are very sen-
sitive to this light. Altogether he measured the in-
tensities and positions of 16,000 lines and mapped
them. Diagram LIV shows a small part of Rowland's
5(60
5)80
1
I
ii
i
5200
Diag. LIV.
map in the green part of the spectrum, many very faint
lines being omitted. The numbering gives the length
of the waves of light belonging to that exact colour.
THE SUN in
Thus 5 160 stands for 5160/1 o 10 of one metre, or, approxi-
mately, '00002 of one inch. The chemical origin of
the separate lines is given with them : C, carbon ; Fe,
iron; Cr, chromium, etc. By comparison with the
spectra of terrestrial elements a very large number,
in fact, nearly all the more intense lines in the solar
spectrum, have been identified, and their origin traced
to the existence in the Sun of some chemical element
with which we are familiar on the Earth. More than
2000 lines in the solar spectrum arise from the pre-
sence of iron. The Sun contains hydrogen, oxygen;
carbon, silicon; sodium, potassium, magnesium, cal-
cium, strontium, barium; aluminium, chromium,
iron, nickel, cobalt, manganese; lead, zinc, tin,
copper, silver, palladium; titanium, vanadium; scan-
dium,, ytrium, zirconium, lanthanum, cerium,
erbium, yterbium, europium, neodymium, gallium,
and some other rare metals. The principal elements
which have not been found in the Sun are nitrogen,
phosphorus, sulphur, fluorine, bromine, chlorine and
iodine, but, as Professor Rowland says, we cannot
infer the non-existence of these substances in the
Sun. In some instances their spectra do not con-
tain any very strong lines, and their discovery is
rendered difficult. It seems remarkable that rare
metals, such as scandium, which it is difficult to pro-
cure on the Earth, should make their presence in the
Sun so plainly visible.
It must be added that not all the dark lines in the
ii2 ASTRONOMY
solar spectrum are caused by absorbing gases in the
Sun's surface. The Earth's atmosphere in certain
parts of the spectrum absorbs certain special rays and
causes additional dark lines. These are mainly
caused by oxygen and. water vapour, and are specially
prominent when the Sun at the time of observation
is low, so that its light has traversed a long path in
the Earth's atmosphere.
The Sun's Surface. To observe the Sun at the tele-
scope precautions must be taken by suitable eye-pieces
to cut down a great part of the heat and light. The risk
of accident to the eye may be avoided and an equally
good observation obtained by drawing out the eye-piece
of the telescope a short distance and projecting an image
TeJetceft
Diag. LV.
of the Sun on a screen. This was the method adopted
by Carrington, who made an extensive series of ob-
servations upon sun spots during the years 1853-61 . It
is more usual now to photograph the Sun, enlarging
the image formed by the object glass by means of a
second lens. Besides giving a larger picture, this
has the advantage of diminishing the brightness of
the image. Even then it is necessary to give very
short exposures and to use very slow plates. Photo-
graphs of the Sun are taken daily at Greenwich, the
THE SUN
gaps caused by cloudy weather being filled in by
photographs taken in India. A copy of one of the
Greenwich photographs is reproduced here.
Diag. LVI. Photograph of Sun.
This photograph shows that the light of the Sun
is more intense near the centre of the disc than at the
edge, pointing to an absorbing smoky atmosphere
surrounding the photosphere, or luminous body of
the Sun. The light from near the limb passes through
a greater depth of this layer just as near sunset on
the Earth the sunlight traverses a greater extent of the
Earth's atmosphere. This "dusky layer" absorbs
violet and blue light to a greater extent than yellow
u 4 ASTRONOMY
and red, and if it did not exist, the Sun, instead of
being yellow, would have a bluish tinge.
Apart from the spots sometimes seen on it, the
Sun's surface presents a mottled appearance. Nasmyth
compared the appearances to willow leaves, Langley
and Janssen to rice grains. These "rice grains " are of
perhaps 400 miles diameter. They rapidly change
their form. It is far from certain what thev are.
Ding. LVII. Granules on Sun.
Langley regarded them, and his view appears to be
shared by Prof. Hale, as the tops of long columns in
which the heated matter from the Sun's interior rises
to the surface.
Observations of these curious granules have been
made recently by M. Hansky, and still later by M.
Chevalier. They found that on photographs taken
THE SUN 115
in quick succession individual granules could be
recognized. They appeared to be moving about at
random with velocities of from 5 to 20 miles a second.
As M. Chevalier points out, it is difficult to believe
that what we see arises from real horizontal move-
ments. He compares the white granules to the sum-
mits of waves on a choppy sea. The white tops
move, but the particles of water which form them are
changing all the time.
Sun-spots. Sun-spots were one of the first discoveries
of Galileo's telescope. Occasionally a spot is large
enough to be seen through dark glass with the naked
eye. The best way of seeing them is to project the
Sun's image, as explained on p. 112. The inner part
of a spot, or umbra, is apparently black, and is
surrounded by a greyer penumbra, but it must be
borne in mind that a spot is only dark in comparison
with the Sun. If the spot could be seen away from
the Sun, it would be found to be brighter than an
electric arc-lamp. Diagram LVI shows also near the
limb bright patches, known as faculae. These faculae
are always abundant near Sun-spots, and seem to be
raised somewhat above the level of the photosphere.
The nature of Sun-spots is a vexed question. They
were for long supposed to be depressions in the Sun's
surface, but this is not now regarded as at all certain.
When the spectra of Sun-spots are observed, it is
found that, as compared with the solar spectrum,
some lines are strengthened and others weakened.
I 2
n6 ASTRONOMY
These changes are doubtless due to the physical
differences of pressure and temperature between spots
and the generality of the photosphere, but their exact
interpretation is not easy. Some recent observations
seem to show that spots are of lower temperature.
Titanium oxide was found in their spectra by Mr.
Adams at Mount Wilson, and magnesium hydride by
Mr. Fowler at South Kensington. The conditions
of temperature and pressure in spots are therefore
such as to admit of the formation of these compounds
which do not exist in the photosphere. This certainly
implies either a lower temperature or a higher pres-
sure than in the photosphere, and has been generally
interpreted as a sign of lower temperature. Some
remarkable observations made by Prof. Hale in 1908
show that an intense magnetic field exists in Sun-
spots.
Prominences and Chromosphere. Reference has been
made in previous chapters to eclipses of the Sun.
At times the Moon is in such a position that
it completely shuts out the view of the Sun for a
few minutes from certain parts of the earth. These
occurrences give opportunities of seeing the imme-
diate surroundings of the Sun, which are gener-
ally invisible to us owing to the glare produced by
the diffusion of sunlight in the Earth's atmosphere.
A total solar eclipse discloses two remarkable features
of the Sun, the prominences and the corona. The
prominences are great tongues of flame which stand
THE SUN 117
out from the Sun's limb, sometimes reaching to such
great heights as 50,000 miles. Diagram LVIII shows
one which was seen in the eclipse of 1900. The most
Diag. LVIII. Solar Prominences.
important feature of the prominences is that they give
a spectrum made up of a number of bright lines, and
not a bright band crossed by dark lines, like the Sun.
This was discovered in the eclipse of 1868, and estab-
lished the fact that prominences consist of luminous
gases, and the identification of the lines showed that
hydrogen was one of their main constituents. The
French astronomer Janssen, who observed this eclipse
in India, was so impressed by the brightness of these
lines that on the day after the eclipse he again
examined with his spectroscope the part of the Sun
where he had seen a great prominence, and saw the
bright lines in full daylight. He verified that a line
in the red was coincident with one caused by hydro-
gen, and found a bright yellow line near to, but not
quite coincident with, the position of the lines due
to sodium. Sir Norman Lockyer, who was not at the
eclipse, simultaneously discovered how these bright
lines could be observed at all times, without waiting
nS ASTRONOMY
for the rare opportunities afforded by eclipses. The
light which hinders these prominences from being
seen with the naked eye being diffused sunlight
reflected by particles in our atmosphere, its spec-
trum consists of a bright band crossed by dark
lines. Sir Norman Lockyer argued that if he used
a spectroscope of high dispersion, the diffused
sunlight would be spread out into a long band of
weak intensity, which would not obscure the spectrum
of the prominences which is concentrated in a few-
bright lines. By bringing different parts of the Sun's
image tangential with the slit of the spectroscope, the
existence of a layer all round the Sun of the same
constitution as the prominences was discovered. To
this the name of chromosphere was given by Lockyer.
When the study of prominences thus inaugurated was
carried on regularly, it was found that prominences
were of two kinds, quiescent and eruptive. Quiescent
prominences are generally to be found on the Sun's
limb ; they change their form slowly, and are taken
out of sight generally by the Sun's rotation. The
eruptive prominences, on the other hand, shoot up
with amazing rapidity, sometimes moving hundreds
of miles per second.
Although the chromosphere can be studied at all
times, the moments of the beginning and ending of
total eclipses are the most favourable. The chromo-
sphere contains most of the elements found in the
Sun, but there are differences between its spectrum
THE SUN 119
and that of the Sun which arise from the different
physical conditions of the chromosphere and the part
of the Sun below it where the absorption which pro-
duces the dark lines in the spectrum takes place.
One interesting difference is the presence of bright
lines due to helium in the spectrum of the chromo-
sphere, whereas there are no dark lines due to helium
in the solar spectrum. Reference has been made to a
bright yellow line seen by Janssen near but not co-
incident with the lines of sodium. This line was
found to be characteristic of the solar prominences
and chromosphere, and the name helium was given to
the unknown element which produced these lines. In
1895 Sir William Ramsay found this element in some
terrestrial minerals, twenty-seven years after its pre-
sence in the chromosphere had been revealed to
Janssen' and Lockyer.
The Corona. The corona is of an altogether differ-
ent character from the prominences. While the latter
rarely extend to more than one-tenth of the Sun's
diameter from the limb of the Sun, the corona some-
times shows rays reaching to several diameters from
the Sun. The instant an eclipse becomes total the
corona is seen as an aureole surrounding the eclipsed
Sun. It is of a pearly white colour, and brightest
close to the Moon's dark limb. It is of a very com-
plex form, which is only well shown by a series of
photographs taken during the few minutes of total
eclipse. A short exposure shows detail near the Sun,
120 ASTRONOMY
while longer ones show the structure and extension at
greater distances. Diagram LIX shows roughly the
form of the corona in the eclipses of 1898 and 1901.
When the nature of the corona is investigated bv
Sun's Corona 1898. Diag. LIX. Sun's Corona igor.
means of the spectroscope, a faint continuous spec-
trum is found such as would be given by incandescent
solids or liquids, and also some bright lines caused
by glowing gases. If the light of the corona were
to any extent reflected sunlight, then its spectrum
would be like that of the Sun, a continuous spec-
trum with dark absorption lines. But the exist-
ence of absorption lines like those in the solar spec-
trum has not been established, and we therefore
cannot say that any considerable part of the light of
the corona is reflected sunlight. The bright lines, of
which more than a dozen are known with certainty,
do not belong to any element with which we are
acquainted. The name coronium has been given to
the element which produces a very prominent line in
the green part of the spectrum, Like helium, this
THE SUN 121
may be discovered on the Earth, but at present, at any
rate, it is unknown.
The Spectroheliograph. The photography of promi-
nences in full daylight has been developed by Prof.
Hale and M. Deslandres. The instrument by which
this is accomplished is called the spectroheliograph.
A prominence is photographed by excluding all light
except that of some definite wave-length which is
specially characteristic of the prominence itself. Thus
a photograph rray be taken in the light of C the red
line of hydrogen and such a photograph will show
the prominences as far as they consist of hydrogen.
Similarly, a photograph can be taken which shows
the forms of the prominences as far as they consist
of glowing calcium.
The spectroheliograph has been developed further
so as to photograph not only the limb of the Sun, but
the whole face of the Sun in the light of one particular
wave-length. Special interest attaches to the photo-
graphs taken in the light of K a line in the violet
due to calcium vapour. In the photograph of the Sun
on p. 113 the faculae are seen near the Sun's edge.
The spectroscope shows that these faculas are asso-
ciated with glowing calcium vapour. When a photo-
graph (of the Sun) is taken in K light, a picture is
obtained of the calcium clouds over the photosphere.
Such photographs were found to show more than the
facuke, and the name flocculi (fleeces) was given to
them by Prof. Hale. The illustration (Diagram LX),
122 ASTRONOMY
taken from one of Prof. Hale's photographs, shows
how widely these flocculi are distributed over the
whole Sun.
Diag. LX. Calcium Flocculi.
The structure of the Sun is thus seen to be ex-
tremely complicated. The lowest part emits a con-
tinuous spectrum; this passes through an absorbing
layer which gives the dark Fraunhofer lines. Next
there is a dusky layer which cuts off a great deal of
the light, the existence of this layer being shown by
the diminishing brightness of the Sun as we go from
the centre to the limb. Above these are the flocculi,
or clouds of calcium. Then we come to the chromo-
sphere with its bright line spectrum, and outside this
THE SUN 123
we have the corona. In addition, there are the more
local phenomena of spots and facuke and of the pro-
minences rising out of the chromosphere.
There are still two points with regard to the Sun
which should not be omitted even in such a short
sketch as the present, namely, (i) its peculiar law of
rotation, and (2) the periodic fluctuations in the
number of spots and associated phenomena.
Rotation of Sun. Galileo found from the movement
of spots across the Sun's disc that the Sun rotates.
Prolonged examination of the spots shows its axis
to be fixed in direction, but not perpendicular to the
ecliptic. We therefore see the Sun under a slightly
different aspect at different times of the year. The
axis is inclined at an angle of 7 to the perpendicular
to the ecliptic. From June 3 to Dec. 5 the plane of
the ecliptic is north of the Sun's equator, and thus
for this half of the year the Sun's north pole is on the
visible side of the Sun, and in the other half of the
year its south pole is visible. Between 1853 and
1 86 1 Carrington made an exhaustive study of the
movements of Sun-spots. He found that the Sun does
not rotate as a solid body would, but that the period
of rotation is greatest on the Sun's equator and
diminishes as the poles are approached. At the
equator a complete revolution occupies 24^ days, but
at 30 from the equator 26^ days. As Sun-spots do
not occur at great distances from the equator, the
slowing of the time of rotation could not be observed
i2 4 ASTRONOMY
in this way to greater distances than 45 north and
south of the Sun's equator.
In 1891 Prof. Duner determined spectroscopically
the law of the Sun's rotation in different latitudes
between the Sun's equator and 15 from the poles.
The spectroscope enables the motion of bodies to or
from the observer to be determined. The position of
a line in a spectrum is determined by the number of
vibrations per second which light of that exact colour
executes. If the source of the light is moving towards
the observer or the observer towards the source of
light, more than the normal number of vibrations
reach the observer each second. The position of the
line in the spectrum is shifted slightly towards the
blue. The amount of shift is a measure of the ratio
of the relative movement of observer and object to the
velocity of light. A similar phenomenon takes place
with regard to sound. If a horn were being blown on
a railway train which was rapidly approaching a
station, then to a person in the station the note of the
horn would be slightly raised. This principle (called
Doppler's principle) was first applied astronomically
by Sir W. Huggins to determine the velocities with
which stars were approaching or moving away from
the Earth. Duner applied it to determine the rotation
of the Sun, by comparing the positions of the lines
in the spectrum given by one end of a diameter of the
Sun with the opposite end. He chose a part of the
spectrum in which there are two dark lines caused by
iron in the Sun and also two dark lines caused by the
THE SUN 125
absorbing influence of oxygen in the Earth's atmo-
sphere. Diagram LXI shows the two spectra. The
lines i and 3 are atmospheric, and the lines 2 and 4
solar. The former are in the same
position whatever part of the Sun the
light comes from. The latter are
shifted a little towards the violet if
they come from a part which by Es= .
J Diag. LXI.
the Sun's rotation is at the moment
approaching us, and towards the red end if the light
comes from a part of the Sun which is at the moment
being carried away from us. The careful measure-
ment of the distances between the lines enables the
relative velocities of opposite ends of any diameter to
be measured in miles per second. Observations of
similar character were made by Dr. Halm at Edin-
burgh and Mr. Adams at the Mount Wilson Observa-
tory in California. The following table shows the rate
at which the Sun is rotating in different solar latitudes
Lat. Time of Rotation.
o 24-5 days
20 25-5 ,,
40 27-6 ,,
60 29^6 ,,
80 30-6 ,,
The cause of this slowing down as we proceed from
the Sun's equator to its poles is difficult to understand.
There can be no doubt of its reality, for the results
given by spots and by the spectroscope are confirmed
by the photographs of faculas and the spectrographs
of flocculi. Spectroscopic determinations by means of
126 ASTRONOMY
the hydrogen lines do not, however, show these differ-
ences in different latitudes. The light in this case
probably comes from a higher level, and thus gives
the rotation of a different layer of the Sun.
Periodicity of Sun-spots. In some respects the
appearance of spots on the Sun is a very irregular
phenomenon. A spot may last for a few days or for
several rotations of the Sun. In the latter case it will
be visible for 14 days, then disappear owing to the
Sun's rotation, then reappear and cross the visible
disc of the Sun in 14 days, then disappear again, and
so on. The number of spots on the Sun on any par-
ticular day is not subject to any easily definable law.
But if the average is taken for a fairly long period,
say a year, it is seen that the number of spots fluc-
tuates in a fairly regular manner. The same result
holds if the fraction of the Sun's area covered with
spots is tabulated. The following table from the
measures made at Greenwich shows the mean area of
spots in millionths of the Sun's visible hemisphere for
a number of years
Area covered
Area covered
Year.
by Spots
Year.
by Spots.
1889
78
1898
376
1890
97
1899
III
1891
421
1900
75
1892
1214
1901
29
1893
1458
1902
63
1894
1282
1903
339
1895
974
1904
488
1896
543
1905
1191
I8 97
5'4
1906
778
THE SUN 127
The increase in the area of the Sun covered with
spots from 1889 to 1893 and the diminution to 1901 is
a fair sample of a fairly regular fluctuation which has
been traced in records of Sun-spots from the year 1610
to the present time. Roughly speaking, Sun-spots go
through a cycle in a period of about n years.
As we have seen, spots are seldom found at more
than 45 from the Sun's equator. On the other hand,
they are rarely close to the equator. Their distances
from it generally are between 30 and 10. When the
number of spots is at a minimum, the few there are
occur either near the Sun's equator or at a consider-
able distance from it. As the number of spots in-
creases the distribution changes, the number near the
equator becoming less and less, and those at a distance
from the equator coming rather nearer to it.
Attempts have been made, without much success,
to connect these changes in Sun-spots with the move-
ments of some of the planets. A very remarkable
connection has, however, been clearly demonstrated
between Sun-spots and magnetic storms on the Earth,
and with the extent of the oscillations which magnetic
needles go through day by day. When the Sun has
many spots magnetic storms are frequent; when the
Sun has few spots they are rare. This is as much
as can be said with certainty. It does not follow that
because there is a large spot on the Sun there will be
a magnetic storm. It has been pointed out by Mr.
E. W. Maunder that magnetic storms frequently recur
after intervals of from 25 to 27 days. This is the
128 ASTRONOMY
time in which by the Sun's rotation a spot is brought
to the same position on the Sun's visible disc again.
He is thus led to suppose that streams of electrified
particles shot out from the neighbourhood of Sun-
spots may reach our atmosphere and start magnetic
storms.
Another phenomenon related to Sun-spots is the
form of the Sun's corona. The corona has been
observed at numerous eclipses, and it is found that
the forms of the corona go through a cycle in the same
period as the Sun-spots. Two of these forms are
illustrated on p. 120, that of 1898 being characteristic
of a time when spots are decreasing, and 1901 when
they are at a minimum.
Summing up this chapter, we see that the size,
mass, density and chemical constitution of the Sun
are known. Its temperature is also know : n approxi-
mately, and a reasonable explanation can be given
of how its heat is maintained. Its physical constitu-
tion presents difficult problems which have not yet
been solved. The nature of and relationship between
the different layers which different classes of observa-
tion show to exist in the Sun are only very partially
known. For the present, the law of the Sun's rotation
and the periodicity of Sun-spots are observed facts
for which no satisfactory explanation has been given.
CHAPTER VII
THE SOLAR SYSTEM
THE solar system comprises all the bodies, great
and small, which are clustered around the Sun. They
form a small CO.T munity of their own, too far distant
from the fixed stars to be appreciably affected by
them, but all dominated by the attraction of the
Sun which keeps them revolving in orbits around
himself. The system includes the Earth, with its
satellite the Moon, the five planets known to the
ancients, and the outer planets Uranus and Neptune,
with their satellites. Then there is a large number of
small planets whose orbits lie between those of Mars
and Jupiter. In addition there are periodic comets
and meteor-streams, and a certain amount of finer
matter whose existence is made apparent by the Zodi-
acal light.
The largest and most important members of the
solar system are the eight planets : Mercury, Venus,
the Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
The positions of these planets in the sky can be cal-
culated for many centuries backwards or forwards, as
their paths and velocities are known with great accur-
acy. Three remarkable characteristics of them
should be noticed
K 129
1 3 o ASTRONOMY
(1) These eight planets move in nearly the same
plane.
(2) The ellipses described by the planets are nearly
circular in shape.
(3) The planets all revolve in the same direction.
The mean distances of the planets from the Sun
are readily remembered in terms of the Earth's mean
distance. They are as follows
Mercury '4 Jupiter 5
Venus 7 Saturn 10
The Earth i 'o Uranus 20
Mars i '5 Neptune 30
To obtain their periods use Kepler's third law, that
the squares of the periodic times are proportional to
the cubes of the mean distances. In the case of Nep-
tune, the mean distance = 30. The cube of 30 is
27,000, and the square root of this is 164. The period
is therefore 164 years.
Minor Planets Between the orbits of Mars and
Jupiter lie the orbits of the minor planets. There are a
large number of these bodies, and every year fresh ones
are discovered. The first of these small bodies, Ceres,
was found by Piazzi on the first day of the nine-
teenth century. The discoveries of Pallas, Juno and
Vesta soon followed. These planets are just large
enough to be seen as discs in the most powerful tele-
scopes. The diameter of Ceres, the largest of them,
is not far short of 500 miles, and that of Pallas,
the smallest, about 100 miles. No more minor
THE SOLAR SYSTEM 131
planets were found till 1845, but since that date
the numbers discovered annually have steadily in-
creased, especially since photography has been used
in the search. The total number at the end of 1900
was 452. Since that date 200 have been added to the
list. Most of them are extremely minute. Probably
the larger ones have been nearly all discovered. Some
of them, particularly Eros, have been of great use
in the determination of the Sun's distance; one has
served to determine the mass of Jupiter; and several
of them illustrate interesting mathematical points in
gravitational theory.
It is a striking and interesting fact that these small
planets should be confined to this particular region
of the solar system ; Olbers suggested that they are
fragments of a larger planet, but this explanation is
very doubtful.
Diameters of the Planets. The determination of the
size of a planet is very simple. As the planet's dis-
tance from the Earth is known, it is only necessary
to measure the angular diameter
seen in the telescope to deter-
mine the real diameter. The
angle AEB is measured and
this value, with the knowledge of the length EA,
gives the length AB (Diagram LXII).
Mercury is the smallest of the major planets, having
a diameter of 3000 miles, or f that of the Earth ; Mars
comes next with a diameter about J, while Venus is
K. 2
i 3 2 ASTRONOMY
very nearly the same size as the Earth. The other
four planets are very much larger; Jupiter's diameter
is ii times, Saturn's 9 times, those of Uranus and
Neptune 4 and 5 times that of the Earth.
Masses. The masses of the planets which have
satellites are readily determined from the distances and
times of revolution of these satellites. The angular
distance of a planet from its satellite is seen and
measured in the telescope.
Taking the simplest case
where a satellite describes
Diag. LXIII. a cirde about hs primarV)
we can, as in Diagram LXIII, measure PES, the great-
est angular distance to which the satellite goes from its
planet. Knowing the distance EP, the distance PS
is found. Let us call this distance a, and let the time
the satellite takes to complete its revolution be T. If a
is expressed as a decimal of the Earth's distance from
a*
the Sun, and T as a decimal of a year, then ^ 2 will
give the mass of the planet as a fraction of the mass
of the Sun. This method is applicable to all the
planets which have satellites. The masses of Venus
and Mercury are more difficult to determine, and are
found from the small disturbances they produce on
the movements of one another, or of the Earth, or of
comets which pass near them. The masses of the
planets are generally expressed as fractions of the
mass of the Sun. Jupiter, which is by far the largest,
THE SOLAR SYSTEM 133
is less than T oVo tn of the Sun 5 Saturn comes next,
being between a third and a quarter of Jupiter, while
Uranus and Neptune are each about w tri - The inner
planets are much smaller; the Earth, which is the
largest of them, is only Tnnyjnny tri f trie Sun, while
Venus is about three-quarters of the Earth, Mars a
little more than T Vth, and Mercury about a quarter.
Densities. Knowing the sizes and the masses of
the planets, their densities are at once determined.
The inner planets do not differ much in this respect
from the Earth, whose density is 5j times that of
water. The outer planets are much less dense, Jupiter,
Uranus, and Neptune being slightly denser than
water, and Saturn not so dense. The differences in
density point to great difference in physical state,
which arise from the fact that the process of cooling,
and its accompanying process of shrinking, have pro-
ceeded more rapidly in the small planets than in the
large ones.
Rotation. The planets all rotate about their axes.
The definite markings on Mars make its period of
rotation easy to determine. It is rather longer than
that of the Earth, being 24 h. 37m. 22*7 s., and is
accurately known to T Vth of a second. The periods of
rotation of Jupiter and Saturn are determinable with
fair accuracy, and are both not far from ten hours.
Owing to their rapid rotation the figures of these
planets are very oblate so much so that the difference
between the equatorial and polar diameters can be seen
i 3 4 ASTRONOMY
in a small telescope. The times of rotation of Uranus
and Neptune cannot be given, but they are probably
less than twenty-four hours. Owing to the absence
of definite markings on Mercury and Venus, their
periods of rotation are not known with certainty.
The opinion was held for a long time that they rotated
in about twenty-four hours, but about twenty-five
years ago a very careful examination was made by
Schiaparelli, who detected some very faint markings.
He concluded that both planets rotate very slowly, so
slowly, in fact, that they always present the same
face to the Sun. Schiaparelli 's results have been con-
firmed by Lowell. Both these observers have ob-
served the planets assiduously under the irost favour-
able conditions nnd in the best of climates. Attempts
have been made to determine the rotation by spec-
troscopic observations, but no decisive results have
yet been obtained in this way.
Satellites. The discovery of the satellites belong-
ing to the various planets of the solar system has pro-
ceeded from the time of Galileo to the present time.
As telescopes have become more powerful, fainter
satellites have been discovered. As far as we know,
Mercury and Venus have no satellites. The Earth has
its one satellite, the Moon, which revolves round its
axis in one month, and in consequence always turns
the same face to the Earth. Mars has t\vo very small
satellites, whose diameters are not more than 6 or 7
miles. They were discovered in 1877 by Asaph Hall
THE SOLAR SYSTEM 135
with the large refracting telescope of the Washington
Observatory. These satellites, which are named Phobos
and Deimos, are very near to Mars, their distances
being only 5800 and 14,600 miles respectively, while
the diameter of the planet itself is 4200 miles. They
necessarily revolve very rapidly, their periods being
7 h. 40 m. and 30 h. 18 m. It is interesting to notice
that Mr. Lemuel Gulliver relates that the astronomers
of Laputa "have discovered two lesser stars, or satel-
lites, which revolve about Mars, whereof the innermost
is distant from the centre of the primary planet exactly
three of his diameters, and the outermost five ; the
former revolves in the space of ten hours, and the latter
in twenty-one and a half; so that the squares of their
periodical times are very near in the same proportion
with the cubes of their distance from the centre of
Mars, which evidently shows them to be governed by
the same law of gravitation that influences the other
heavenly bodies."
The four large satellites of Jupiter were discovered
by Galileo in 1610. They can be easily seen with an
opera glass, and \vith a small telescope their transits
in front of Jupiter and their eclipses in his shadow
can be watched. The smallest is nearly as large as
the Moon, and the largest has a diameter nearly half
that of the Earth. The nearest is as far from Jupiter
as the Moon is from the Earth, and the farthest 4!
times this distance. Their periods round Jupiter are
!f> 3i> 1\ and i6f days. A fifth and extremely small
136 ASTRONOMY
satellite was discovered by Mr. Barnard with the great
telescope of the Lick Observatory in 1892. This little
body is nearer to the planet than the four large
satellites, and revolves in 12 hours. It can only be seen
with the largest telescopes. In December 1904 a sixth
satellite, and in January 1905 a seventh were found
photographically by Mr. Perrine at the Lick Observa-
tory. They are very small, and are a long way from
Jupiter, revolving in 251 and 265 days. An eighth
satellite, still fainter and more distant, was discovered
photographically by Mr. Melotte at Greenwich in
February 1907. This satellite's distance from Jupiter
varies from 10 million to 20 million miles; its period
is two years, and its direction of revolution is opposite
to that of all the other satellites.
Saturn presents a new feature in its ring. This was
a great puzzle to the early astronomers with poor
telescopes, who saw Saturn with what seemed like
wings, which, moreover, changed their appearance
and were sometimes invisible. Huyghens made out
clearly in 1655 that Saturn's strange appendage was a
luminous ring in the plane of the planet's equator,
nowhere touching the planet, and extremely thin.
The plane of this ring, like the plane of the Earth's
equator, retrains always in the same direction, and is
inclined at an angle of nearly 27 to the ecliptic. Now,
Saturn makes its revolution round the Sun in 2q|
years. Like the Earth, Saturn has equinoxes and
solstices, and the Sun's position changes from 27
THE SOLAR SYSTEM 137
north to 27 south of its equator. When the Sun is
north of the equator, the north side of the ring is
illuminated ; \vhen south, the south side ; while when
the Sun is on the equator, only the edge of the
ring. The ring is so thin that it is invisible to
us when the Sun is in such a direction that it only
shines on the ring's edge. Generally the Earth and
Sun are both north or both south of the ring, but it
may happen, near the time when the Sun passes from
north to south, that they are on opposite sides, in
which case the ring is also invisible. A division in
Diag. LXIV. Saturn.
the ring was discovered by Cassini in 1675 separating
it into two, and in 1850 it was seen to be con-
tinued on its inner rim by a "dusky" ring. The
138 ASTRONOMY
nature of Saturn's ring was trade clear by Clerk
Maxwell in 1856. He showed that it could be neither
a solid nor a liquid, but must consist of a swarm of
little satellites circulating round the planet. If the
ring were solid the outer parts would rotate faster
than the inner, but if made of separate particles, more
slowly. Keeler, at the Lick Observatory in 1895, put
this to the test by determining spectroscopically the
rates at which different parts of the ring were moving,
and thus confirmed experimentally what Maxwell had
proved mathematically.
Besides its ring, Saturn has no less than ten satel-
lites. The largest of these, Titan, was discovered by
Huyghens in 1655. Its diameter is about 3500 miles.
It revolves round Saturn in about 14 days, and is
distant about 20 radii of Saturn. Four more satel-
lites were discovered by Cassini between 1671 and
1684. A hundred years later, Sir W. Herschel dis-
covered two smaller ones distant 3 and 4 radii from the
planet. An eighth small satellite at a distance some-
what greater than Titan was found independently by
Bond and Lassell in 1848. A ninth was discovered
in 1899 by Prof. W. H Pickering from photographs
taken at Arequipa. This satellite is so distant that
it takes one and a half years to complete its revolution.
It moves in a retrograde direction in a very elliptic
orbit. Still another very small satellite has been
found by Mr. Pickering.
Uranus, the planet discovered by Sir William Her-
THE SOLAR SYSTEM 139
schel in 1781, has four satellites. Two of these were
discovered by Herschel in 1787, and the remain-
ing two by Lassell in 1851. They are remarkable
because they move in a plane almost perpendicular to
the plane of the motion of Uranus round the Sun.
Neptune has one satellite, discovered by Lassell,
which moves in a retrograde direction in a plane in-
clined at 35 to the plane of Neptune's motion.
It is important to notice that the satellites generally
move in planes not far removed from the ecliptic,
and revolve around their primaries in the same direc-
tion in which these revolve round the Sun. The ex-
ceptions are the satellites of Uranus, the satellite of
Neptune, and the small and distant ninth satellite of
Saturn and the eighth satellite of Jupiter.
We come now to the consideration of the physical
conditions of the planets. What are their tempera-
tures? Are they solid bodies like the Earth? Have
they atmospheres ?
Temperatures of the Planets. The four inner planets,
Mercury, Venus, the Earth and Mars, receive
most of their heat from the Sun. It is possible
to form an idea of their temperatures from the
consideration that the heat they receive from the
Sun just balances the heat which they radiate into
space. The uncertain factor in drawing definite con-
clusions lies in our ignorance of the extent to which
the temperatures of planets are regulated by their
atmospheres. How greatly an atmosphere affects
140 ASTRONOMY
temperatures is seen at once from the small average
difference between day and night temperature on
the Earth. Professor Poynting, who has con-
sidered the temperatures of the planets from this
point of view, has shown that it is very probable
that, whether Mars has an atmosphere like the Earth
or is like the Moon and has none, the temper-
ature is everywhere below the freezing point of
water. The only escape from this conclusion in his
view is that an appreciable amount of heat is issuing
from beneath the surface. But we see by comparison
of the equatorial with the polar temperatures on the
Earth to what an inappreciable extent the internal
heat of the Earth modifies its surface temperature.
There is thus no reason to suppose that the internal
heat of Mars has any considerable effect on its surface
temperature. The temperatures of Venus and Mer-
cury, if they revolve round their axes and have atmo-
spheres, are 100 and 300 Fahrenheit respectively
hotter than the Earth. If they revolve so as to pre-
sent the same faces to the Sun always, then the hemi-
spheres which look at the Sun are much hotter than
this, and the hemispheres which look away from the
Sun are at very low temperatures indeed. When we
come to the major planets it would seem that their
surface temperatures are determined by the internal
heat of the planets themselves, rather than by the
radiant heat received from the Sun. Jupiter is prob-
ably at something like a red-heat, but it does not emit
THE SOLAR SYSTEM 141
sufficient light to illuminate its satellites when they
are shaded from the Sun. Saturn, Uranus and Nep-
tune are probably at higher temperatures.
Atmospheres of the Planets. A bright rim of light, as
shown in Diagram LXV, which has been seen round
the dark disc of Venus a little before it passed in front
of the Sun at the transits of 1874 and 1882 shows that
the planet has an atmosphere. It would seem likely
that both Venus and Mercury are surrounded by very
dense clouds which hide the solid body of the planet.
The spectra of Mercury and Venus are
very like that of the Sun, and do not
suggest that the light, after leaving
the Sun, has passed through any
absorbing atmosphere besides the
Earth's. The explanation may be that
the light by which we see these planets
is reflected by high clouds, and does not traverse the
densest parts of their atmospheres. The question of
the atmosphere of Mars is one of great interest as well
as one of considerable -difficulty. The spectrum of
Mars apparently shows no lines which are not in the
solar spectrum. The question which has to be decided
is, "Are certain lines which we know to be produced
by absorption in the Earth's atmosphere more intense
than can beaccounted for by this terrestrial absorption
alone?" To answer the question the spectrum of the
Moon, taken as far as possible under the same instru-
mental and atmospheric conditions, is compared with
142 ASTRONOMY
that of Mars. Sir W. Huggins and Dr. Vogel con-
sidered that the evidence pointed to the existence of
water-vapour in the atmosphere of Mars, but Prof.
Keeler at Allegheny, and Prof. Campbell at the Lick
Observatory, found no appreciable difference between
the spectra of Mars and the Moon, and therefore no
direct evidence of any atmosphere. Recently Mr.
Slipher at the Lowell Observatory has found that a
band in the red end of the spectrum, caused by water-
vapour, is intensified in the spectrum of Mars. Still
more recently Prof. Campbell, observing from the top
of Mt. Whitney, the highest mountain in the United
States, in order to reduce as far as possible the effect
of the Earth's atmosphere, found no difference be-
tween the spectra of Mars and the Moon. These
observations, made under most favourable conditions,
prove that the Martian atmosphere must be extremely
rare. In the spectrum of Jupiter there appears to be
one line not in that of the Sun, pointing to a con-
stituent of its atmosphere with which we are
unacquainted on the Earth. The spectra of Uranus
and Neptune show very considerable differences from
that of the Sun, from which the inference is drawn
that they are surrounded by dense atmospheres totally
different from our own.
Mars. Mars and Jupiter are the only planets which
show any considerable detail when carefully observed.
Mars shows white caps at the poles which diminish
in the Martian summer. If we take the view that Mars
has an atmosphere like the Earth, but much less
THE SOLAR SYSTEM 143
dense, containing water-vapour, these white caps
would naturally be interpreted as snow. The rapidity
with which they disappear is sufficient proof that they
cannot be thick masses of ice and snow such as we
find at the Earth's poles, but a very thin deposit of
snow or hoar frost. The drawings by Prof. Bar-
nard, made with the 36-inch reflector of the Lick
Observatory, show the melting of the snow (if snow-
Ding. LXVL Mars.
it be) at the south pole of Mars in the year 1894. The
features we see in Mars were for a time supposed to be
land and seas. We may be pretty confident from the
absence of clouds, and the probable low temperature
of the planet, that the dark parts are not seas,
but solid land of a different colour. A long con-
144 ASTRONOMY
troversy has raged about the so-called canals, or thin
lines, first discovered by Signer Schiaparelli, and since
delineated and mapped by Prof. Lowell. The atmo-
spheric conditions of both these observers have given
them opportunities which few others possess, and they
have devoted a great deal of time and attention to the
study of the planet. But, on the other hand, Prof.
Barnard at the Lick Observatory failed to see the
"canals," although he could see (at moments when
the atmospheric conditions were very favourable) a
much greater wealth of detail than he could delineate.
Prof. Barnard's observations have been confirmed by
observers with the largest telescopes in America and
Europe. Recently very fine photographs of Mars
have been taken at the Mt. Wilson Observatory in
California, and do not show the sharp thin lines
which have been named "canals." It has been sug-
gested that the canals are really subjective, and arise
from the tendency of the eye to join up by lines mark-
ings which are only seen with difficulty.
A very small telescope is sufficient to show the
belts of Jupiter. Diagram LXVII shows the planet
as seen with the 36-inch telescope of the Lick Observa-
tory, and drawn by Prof. Barnard in 1890. The
surface of the planet is continually changing. Bright
and dark spots appear, last a few months, and dis-
appear. One of the most permanent features is a
large red spot which appeared in 1878, and continued
without much change of brightness till 1888, when it
THE SOLAR SYSTEM 145
became much fainter, but recovered its distinctness in
Diag. LX VII. Jupiter.
1890, and still more in 1891. It has since gro\vn
fainter again, but was just visible in 1907.
Observations of spots show that the velocity of
rotation of Jupiter, like that of the Sun, varies in
different latitudes. The following table and diagram
is given by Mr. Stanley \Villiams.
No. of Spots observed.
27
21
I
2
Latitude.
Period of Revolution,
+ 60 to + 25
9 h 55 m 39'43 S
+ 25 to + 10
9 h 55 m 39'9 2S
+ 10 to O
gh 5001 23-883
to -12
gh 50111 27-858
- 1 6 to - 28
gh 55m 8-2s
- 28 to - 45
9h 5501 o-gs
Red Spot
9 h 55 m 4'5 8s
L
146
ASTRONOMY
The large and sudden difference between the velo-
city of the equatorial current and the currents in the
adjacent zones is most remarkable. A difference of 5 m.
SURFACE CURRENTS OF JUPITER IN 1887-8.
SOUTH
H. M. s.
R = 9 55 oo
R = 9 55 17
R = 9 55 40
Southern Current.
S. Temperate Current
R Red Spot Current.
| EQUATORIAL CURRENT
w _ o EQUATORIAL CURREN
R _ Q ,. ,0
i N Tropical Current
: : ^Mm^iimmSm^'-'\
R = 9 55 39 Northern Current
KX->:-' :;:>::: :-:-'-:-:-:-:-"-v-v.v.v.r.v'
Diag. LXVIIf.
in the time of rotation means a difference of velocity
of the adjacent currents of more than 200 miles an
hour. Jupiter is clearly not a solid body, and it would
be easier to explain this great difference of velocity on
the assumption that it is gaseous rather than liquid.
But the permanence of the red spot is favourable to
the view that Jupiter is liquid. The spot seems to be
of the nature of an enormous floating island, the base
of which extends down into the denser or more solid
regions of the planet.
The Moon. Our knowledge of the Moon is far more
extensive and certain than our knowledge of Jupiter
and Mars. It is more than 100 times nearer than Mars,
THE SOLAR SYSTEM 147
and with the highest magnification of our telescopes
can be seen as it would appear to the naked eye at a
distance of about 200 miles. At this distance a circle
a mile and a half in diameter would appear as large
as the whole Moon does at its distance of 240,000
miles, so that towns, lakes, etc., if they existed on the
Moon, could be distinguished. The most conspicu-
ous features on its surface are the craters. Some of
these are 50 to 100 miles in diameter, and frequently
have a small peak in the centre. They can be well seen
\\ith a small telescope. The best time to look at the
Moon is when it is nearly half-full ; near full-moon the
Sun's illumination is too direct to produce shadow's,
and there is not sufficient contrast for the details of the
surface to be seen. Besides the craters, there are moun-
tain ranges and the flat plains which Galileo named
seas. The surface of the Moon has been very carefully
mapped and studied, and in recent years very beautiful
photographs, capable of a large magnification, have
been taken, especially at the Observatory at Paris by
MM. Loewy and Puiseux. Diagram LXIX shows
"CopernicuSj" one of the most conspicuous of the
craters, and is taken from a photograph by Prof.
Ritchey.
There is very conclusive evidence that the Moon
can have but a very slight atmosphere, not more
than one thousandth part of that which the Earth
possesses. Moonlight when examined by the spec-
troscope is found to be a faint copy of sunlight.
L 2
148
ASTRONOMY
No absorption is found such as would occur if the
light before reaching us had passed twice through
an atmosphere at all comparable with that of the Earth
Diag. LX1X. Copernicus.
in depth and density. The absence of any refraction
when the Moon passes in front of and occults a star
is further evidence that it has no atmosphere, or
at most an extremely small one. No clouds or hoar
frost are seen, and \ve therefore conclude there is no
water. Without air and water one would naturally
THE SOLAR SYSTEM 149
suppose few changes to occur on the Moon's surface.
With one very doubtful exception, none have been
observed.
Comets. We have seen that Newton showed (a fact
afterwards confirmed by Halley in a striking manner)
that comets moved round the Sun under the influence
of gravitation, and are therefore to be regarded for
the time being, at least as members of the solar
system. The name comet, or "hairy star," was given
to those nebulous bodies usually possessing a tail, or
tails, which occasionally appear in the sky for a few
weeks or months, and then disappear sometirres for
ever, and sometimes to be seen again after an interval
of years. They move, as Newton found, in highly
elliptic orbits, in which case they return to the Sun
after an interval of years, or in parabolic or hyper-
bolic orbits, in which case their velocity is sufficient
to carry them beyond the restraint of the Sun's gravi-
tation. Since the invention of the telescope many
comets have been found, and usually four or five are
discovered every year. These telescopic objects are,
as a rule, faint, insignificant, nebulous patches without
tails. But every few years one appears which is visible
to the naked eye. The total number of such recorded
during the Christian era probably exceeds 500. A few
of these have had such bright and extensive tails that
they have frightened beholders, who regarded them as
portents by which
"The heavens themselves blaze forth the death of princes."
150 ASTRONOMY
The death of Julius Caesar and the battle of Hast-
ings among other historical events were believed to
have been heralded by comets.
When a comet is examined carefully it is seen that
it may be divided into three parts, although these parts
run into one another so gradually that it is impossible
to say where the exact limits between them are situ-
ated. There is first a bright nucleus, which is merely
a bright point in the telescope just like a star. Sur-
rounding the nucleus is the coma, a hazy, cloudy area
of light. It is brightest near the nucleus, and gradu-
ally grows fainter. The nucleus and coma together
constitute the head of the comet. Shading away from
the head, and growing fainter and fainter till it can
be no longer seen, is the tail. The tail streams away
from the head in a direction opposite to that of the
Sun.
The most striking comet of last century was Donati's
of 1858. When discovered on June 2 it was faint and
without a tail, and it was not till September that its
brilliant tail developed. By the middle of October
this stretched over nearly a quarter of the sky, being
40 long and about 10 wide in its widest part. The
illustration (Diagram LXX) shows its naked eye ap-
pearance. This comet may return in about 2000 years.
By far the larger number of comets move in orbits
not very different from parabolas, but a considerable
fraction have an orbit which is sensibly elliptic. Such
comets are periodic, and are seen at each return to
THE SOLAR SYSTEM 151
perihelion, or point of the orbit nearest to the Sun.
Halley's comet is an instance of this class, and is
visible at intervals of 75 years. But some have much
shorter periods. The shortest of all is Encke's, with
Diag. LXX. Donati's Comet, October 1858.
a period of three and a half years. This comet, though
a faint one, is of special interest, as a diminution of
its period of revolution seems to show that in its
course it is impeded by a resistance of some kind,
possibly of meteoric or gaseous matter.
Halley's comet and several others have periods
of a little over 70 years, and the furthest distance
from the Sun to which they reach is beyond the
orbit of Neptune. Their orbits are such that these
comets have at some time been near to Neptune.
152 ASTRONOMY
Similarly, Encke's comet, and all those whose periods
are less than eight years, move in orbits which at some
point are comparatively near to that of Jupiter. The
orbits of several others are related in a similar way to
the planets Saturn and Uranus. It is clear that these
planets have been in some way instrumental in deter-
mining the orbits which their respective families of
comets describe. Several hypotheses have been put
forward to assign more definitely the parts played by
the planets. The favourite one, though not free
from difficulty, is that the comets which were, so to
speak, moving past Jupiter or Neptune, as the case
may be, were "captured" by the gravitation of the
planet. If a comet at any time in its history passed
very near Jupiter, its velocity might be increased or
might be retarded. Those whose velocities were suffi-
ciently retarded would move in more restricted orbits.
Comets are only seen when they are comparatively
near the Sun. From their high velocities it is in-
ferred that they travel to great distances from the
Sun. But we cannot say with certainty that any have
been observed to be moving sufficiently fast to get
clear away from the solar system. The converse pro-
position also holds that comets have not been swept
into the solar system as it is moving through space,
but are bodies which accompany it on that journey.
Comets are of great volume but small mass. The
head is often more than 100,000 miles in diameter.
Nevertheless, no disturbance in the movement of any
THE SOLAR SYSTEM 153
of the planets or satellites has been detected in con-
sequence of their proximity to a comet. Several have
been near the Earth and had their movement modified
appreciably, but yet have made no sensible modifica-
tion in the movement of the Earth. Thus their masses
are small compared with the Earth, probably less than
one hundred thousand times. We cannot say how
much less, and measured by other standards the mass
may be very great. If the mass were one millionth
of that of the Earth, it would be the same as that of
a globe as dense as the Earth and 80 miles in
diameter.
The spectroscope was first applied successfully to
determine the constitution of comets by Sir William
Huggins in 1868. He found bright bands in the spec-
trum of the head which indicate the presence of hydro-
carbons. These bands have since been found to be
characteristic. In addition there is a faint continuous
spectrum, and occasionally the dark Fraunhofer lines
are seen, showing that a small part of a comet's light
is reflected from the Sun. When a comet is very near
the Sun, bright metallic lines are sometimes seen in
the spectrum of the nucleus, especially those of
sodium. We may infer that the nucleus of a comet
probably consists of a collection of solid and metallic
bodies surrounded by gaseous hydrocarbons.
The formation of the tail is very interesting. At a
considerable distance from the Sun a comet is usually
a hazy, nebulous object. As it approaches the Sun
154
ASTRONOMY
it brightens, the nucleus becomes more distinct,
and sends out gaseous matter in the direction of the
Sun. This is repelled by some force from the Sun,
and driven backwards so that a tail or tails are pro-
duced on the side of the nucleus away from the Sun.
Diag. LXXI. Morehouse's Comet, 1908.
These tails are not straight, but are curved because
the matter driven from the nucleus shares its orbital
motion round the Sun. The curvature is shown in
the illustration of Donati's comet on p. 151. In recent
years very beautiful photographs have been taken
which show the details of the tails for a short distance
from the head. Diagram LXXI shows a photograph of
Comet Morehouse, taken at Harvard. The feature
which first strikes the eye in these photographs is one
which is irrelevant to the tail of the comet, namely, the
short parallel lines which are strewn all over the picture.
THE SOLAR SYSTEM 155
They are merely the "trails " of stars which are photo-
graphed with the comet. The camera or photographic
telescope is kept pointing at the comet during the
exposure, but as the comet is moving among the stars,
the telescope is moving slightly relatively to them,
and they come out on the photograph as short lines.
The direction and length of the lines show the
direction and amount of the movement of the comet
in the sky while the photograph was being exposed.
Some comets are seen to have several tails issuing
from the head which change from night to night.
In Comet Morehouse, of which an extensive series
of photographs was made at the Observatories of
Greenwich, Yerkes, Heidelberg and others in 1908,
it w r as seen that tails were being constantly shed and
new ones produced. Comparison of photographs
taken at short intervals of time showed parts of the
tail to be moving with large and increasing velocities
away from the comet's head.
The movements and changes of a comet's tail are
caused by forces in the solar system other than gravi-
tation, and are on this account of great interest.
The most detailed theory as yet advanced is due to
Bredichin, a Russian astronomer, who concluded that
the matter which issues from the nucleus of the comet
is driven away by a repulsive force from the Sun.
The amount of this repulsive force is not propor-
tional to the mass of the particle of matter, but to
the area which is exposed to the Sun. If a small
156 ASTRONOMY
spherical particle be of the right size, the repulsive
force will just balance the attraction of gravi-
tation. For a particle of half this radius, the repulsive
force will be one quarter as large, but the attraction
only one eighth ; for when the radius is halved, the
area is one quarter and the volume one eighth as large.
The repulsive force is thus most effective for the
smallest particles. Bredichin examined the tails of a
large number of comets, and found them to be of three
types : (i) Long ones showing very slight curvature
in a direction away from the Sun ; (ii) a
plume-like tail curving away more
rapidly; and (iii) a short tail curving
away very rapidly. The curvature of
the tail affords a means of comparing
the repulsive forces with the attraction
of gravity. Bredichin supposed the
long straight tail to be composed of
molecules of hydrogen gas ; the plume-
Diag. LXXII. J
Types of Comets' like tail, which is usually the brightest
and most important, to be composed of
hydrocarbons; and the short one to consist of metallic
vapours (Diagram LXXII).
We know of two different repulsive forces which
the Sun may possibly exert on the matter issuing
from the nucleus of a comet. The light radiated from
the Sun exerts a pressure on small particles of
amount proportional to the surface exposed to it.
The difficulty of accepting this as the explanation lies
in the fact that the molecules of gases are so very
THE SOLAR SYSTEM 157
small that they escape the pressure of radiation. The
tails would have to consist of particles one thousandth
as y small as pin-heads, but very large compared with
the sizes of molecules. The in:mense size and tenuity
of a comet's tail favours the hypothesis that it is an
extremely attenuated gas, and that the luminosity is
to be regarded as a glow produced in this rarefied
gas under electrical stimulus. This view has been con-
firmed by spectra which have recently been obtained
of the tails of Daniel's (1907) and Morehouse's (1908)
comet. The spectra are made up of bright lines and
bands, which prove the tail to consist of glowing gas
and not of small solid particles. Spectra which appear
to be identical with those of comets' tails have been
shown by Prof. Fowler to be given when an electric
discharge is passed through vacuum tubes in which
certain gaseous compounds of carbon are present,
when the vacuum is so high that the pressure is only
one 5o,oooth of that of the atmosphere. Further, one
of the lines has been identified by M. Deslandres with
the principal line in the kathode spectrum of nitrogen,
and the others by Prof. Fowler with the kathode
spectrum of a compound of carbon.
Meteors. Our views on the physical nature of comets
have been derived from the study of meteors almost
as much as from that of comets themselves. It be-
comes necessary to interrupt the account of comets
till some of the facts with respect to meteors have
been presented. On any bright night a few minutes'
watching will be rewarded by the sight of a shooting
1 58 ASTRONOMY
star. Sometimes a very bright one is seen by two
observers situated in different towns. It is then pos-
sible, from the different directions in which the meteor
was seen when it burst out and when it disappeared,
to calculate its height and path. In this way meteors
are found to be at some such height as 80 to 100 miles
when they become luminous, and to be at a height
of about 10 miles when last seen.
Their luminosity is caused by friction in the Earth's
atmosphere, which they enter with velocities which
sometimes reach 40 miles a second. A considerable
number which have fallen to the Earth have been
found. They consist of metallic stones, and contain
carbon, iron, nickel and other elements with which we
are familiar. Those which fall to the Earth usually
weigh a few pounds, while the small shooting
stars which are visible almost any night are dis-
sipated into dust while passing through the Earth's
atmosphere.
Meteoric Showers. It sometimes happens that on a
particular night a large number of meteors are seen
shooting across the sky in all directions. If the paths
which they appear to describe as projected against
the starry background be drawn on a globe or star
map, it will be seen that the paths all radiate or
diverge from a common point. This point is called
the radiant point. The existence of a radiant point
shows that all the meteors are moving in parallel
directions. If, for example, meteors were falling per-
pendicular to the Earth, their paths when drawn on a
THE SOLAR SYSTEM 159
globe would all pass through the zenith. The position
of the radiant point gives the direction in which the
meteors are moving relatively to the Earth. In Dia-
gram LXXIII the paths of meteors observed at Green-
Diag. LXXIII.
wich on November 13, 1866, are plotted. It will be
seen that they all appear to come from nearly the
same point of the sky.
The Leonids. One of the most interesting of these
swarms of meteors has its radiant point in the con-
stellation Leo. Meteors diverging from this radiant
may be seen on the i3th or i4th of November.
The reason they are seen about these dates is that
the Earth is then in a part of its orbit where these
160 ASTRONOMY.
meteors are to be met with. The meteors are all
moving in nearly the same orbit round the Sun. This
orbit and the Earth's intersect at the point where the
Earth is situated on November 13 and 14. The key
to the question of the cause of the November meteors
was found in the recognition of the fact that showers
of unusual brilliancy occurred at intervals of about
33 years, or more exactly, three a century. A very
brilliant shower was seen in 1833. Records inves-
tigated by Prof. Newton of New Haven led him to
predict a shower in the year 1866. He concluded that
the November meteors were all moving in an orbit
round the Sun, but that instead of straggling uni-
formly about this orbit they were specially thick in
one particular part. He found that there w~ere several
different orbits which would give rise to a specially
brilliant shower about every 33 years. The fact that
the date of the shower was gradually getting later, for
it was Oct. 19 in A.D. 902, and Oct. 24 in 1202, and
Nov. 12 in 1833, enabled Prof. Adams to decide which
of these orbits w~as the true one. In this way it was
settled that the November meteors move in an
eccentric elliptic orbit \vhich stretches beyond Uranus,
and that their period is 33^ years.
Comets and Meteors. In 1867 it was shown by the
researches of Oppolzer and Leverrier that a comet
discovered by Tempel in 1865 moves in the same
orbit as the November meteors. Schiaparelli showed
that the orbit of the Perseid meteors which are seen
THE SOLAR SYSTEM 161
in August is probably identical with that of Tuttle's
comet of 1862. A third relationship between comets
and meteors was shown by the strange behaviour of
Biela's comet. This comet was discovered in 1826,
and found to have a period approximately six and a
half years. In 1846 this comet was seen to split into
two, which kept at a distance of about 200,000 miles
from each other. In 1852 the two parts were at a
distance of two million miles. In 1859 and 1865 the
comet was not seen, but in 1872 its place was taken
by a shower of meteorites radiating from a point in
Andromeda.
We are thus led to regard a comet as made up of a
loose collection of meteorites, gathered possibly
around a larger central nucleus. When the comet
approaches the Sun, heat and other radiative influ-
ences tend to disintegrate the mass, and to drive off
gaseous constituents. The gaseous constituents thus
driven off form the tails.
Nebular Hypothesis. The Sun, with the planets and
comets which circulate round it, forms a system so far
from any other celestial bodies that their influence
upon it is imperceptible. It pursues its course and
undergoes its development entirely apart from them.
In a famous hypothesis which he propounded in the
Systeme du Monde, Laplace attempted to trace the
process of its evolution. He was struck by the facts
that the larger planets are nearly in the same plane,
that they and their satellites revolve in the same direc-
1 62 ASTRONOMY
tion, and that the Sun and planets are rotating in this
same sense. These coincidences are too many to be
the result of chance, and point to some common cause.
He put forward the theory that a vast nebula diffused
tenuous matter once extended to the confines of the
solar system, and under the influence of gravitation
slowly contracted. He further supposed that this
nebula was endowed originally with a slight rotatory
motion. As the contraction proceeded the rotation
necessarily increased, and rings or other masses were
thrown off which collected and formed planets. This
theory received fresh support when it was discovered
that heat was developed in the process of contraction.
The existence of nebulas in the sky, and the discovery
of their gaseous condition, which we shall come to
in a later chapter, was regarded as fresh evidence in
its favour. Discoveries made since Laplace's time
have shown that there is not quite so much unanimity
as he supposed in the directions of planets' rotations
and the movements of their satellites. Besides this
there are dynamical difficulties, for from the present
state of the solar system it is possible to calculate
the speed of rotation the nebula had when it extended
let us say as far as Jupiter, and this speed is not
nearly sufficient for any part of the nebula to have
been whirled off. The process of evolution cannot be
traced by following the simple principle which La-
place enunciated. It has been pointed out recently by
Prof. Jeans that "gravitational instability," or a tend-
THE SOLAR SYSTEM 163
ency of matter to accumulate around nuclei of slightly
greater density, and for these nuclei to increase and
gradually collect more and more nebulous matter
around them is probably a more important cause
than rotation in the development of a planetary system
from a nebula. A very careful criticism of Laplace's
hypothesis has been given by Messrs. Chamberlin
and Moulton. They consider that the solar system
has been derived from the aggregation of meteoric
dust and fragments, which had possibly resulted from
the collision of previously existing bodies.
Sir George Darwin has attempted to trace in detail
the birth of the Moon. He supposes that the Earth
and Moon were once part of the same fluid body.
Owing to its rotation about an axis this body had a
spheroidal form. In consequence of the contraction
caused by cooling, the speed of rotation increased and
the body bulged out more and more at its equator till
it reached the limit at which a spheroidal form is
possible. As the contraction continued the form
changed to an ellipsoid with three unequal axes,
then to a pear-shaped figure, and finally split into two
bodies. Large tides were generated in these bodies
by their mutual gravitation, and the friction of these
tides caused the tw 7 o bodies to separate further. This
very complicated question has been mathematically
worked out in detail by Prof. Darwin, but there are
still some difficulties to be overcome before we can be
certain that it is a true account of the Moon's history.
M 2
CHAPTER VIII
DISTANCES AND MOVEMENTS OF THE STARS
THE last thing astronomers have learned from the
study of the stars has been the nature of the stars
themselves. Their vast distances make them appear
"fixed" in the firmament, and they have served as
reference points from which the movements of other
bodies have been inferred and measured. Thus the
rotation of the Earth, the movements of the Earth's
axis, the velocity of light have all been discovered
directly or indirectly by the help of observations of
the fixed stars. The fixity of the stars showed the
movements of the planets and thus led to the Coper-
nican system. The bright points called planets or
wandering stars on the dome of the sky have been
shown to be large bodies resembling the Earth w ? hich
circulate about the Sun. Their sizes, positions and
movements have all been determined. The "fixed"
stars present a similar but more difficult problem.
They appear as bright points projected on the sky.
Can they be made to stand out in three dimensions ?
Can the points on the sky be replaced by material
bodies in space whose positions and movements
relatively to the Sun are known? Further, can the
masses and sizes of the stars be determined?
164
DISTANCES AND MOVEMENTS OF STARS 165
If the distances of stars were as easy to determine
as their directions these questions would be simplified
very much. As we have seen, a star's right ascension
and declination fixes its direction, just as the longitude
and latitude of a place on the Earth fix the direction
in which the place would be seen from the Earth's
centre. If the distances of the stars from the Earth
were known as well as their directions, we should be
at once in a position to construct a model of the
sidereal universe so far as the positions of the stars are
concerned. But the determination of stellar distances
is a difficult problem which has lured and baffled
astronomers for centuries.
Before we approach this question, it w-ill be con-
venient to refer briefly to the nomenclature by which
stars are identified and to indicate what is meant by
the magnitude of a star.
Nomenclature of Stars. A small number of the
brightest stars like Sirius, Arcturus, Aldebaran have
been given special names. Next to these come a large
number of the stars visible to the naked eye which are
named from the constellation to which they belong,
being distinguished either by Greek letters or num-
bers. Bayer in his Uranometria, a star atlas published
in 1601, used Greek letters, the stars being arranged
approximately in order of brightness for each con-
stellation. Thus we have a, /3, y Leonis, etc. Flam-
steed, the first English Astronomer Royal, made an
accurate catalogue of the stars' positions in which he
1 66 ASTRONOMY
designated the stars by numbers as i, 2, 3 Leonis, etc.
The names given by Bayer and Flamsteed have been
generally adopted. For fainter stars the number in
some well-known catalogue serves as a name. Thus,
Br. 3147, Gr. 1830, and Lai. 21185 re f er to stars which
are respectively No. 3147 in Bradley 's catalogue,
made in 1755, No. 1830 in Groombridge's catalogue
of 1810, and No. 21185 in Lalande's catalogue of
1800.
Positions of Stars in the Sky. The direction of a
star, if it is a bright one, can be obtained roughly from
a celestial globe. If the accurate direction is required
reference must be made to a star catalogue. The
earliest star catalogue in which the positions that
is, the right ascensions and declinations are
given with sufficient accuracy for modern require-
ments, was made by Bradley from observations at
Greenwich about 1755. Since that time the results
of many observations with transit circles have been
embodied in star catalogues. Throughout the whole
of last century, for example, catalogues giving the
positions of the brighter stars derived from the most
accurate observations were repeatedly made at Green-
wich and other national observatories. One of the
largest star catalogues, giving the accurate positions
for the date 1875 of all northern stars as bright as the
ninth magnitude and many fainter ones, was the result
of the combined effort of 15 observatories under the
auspices of the German Astronomical Society.
Stellar Magnitudes. The brightness of a star as seen
DISTANCES AND MOVEMENTS OF STARS 167
from the Earth, like its position, is a quantity which
admits of immediate measurement. Evidently a
knowledge of the stars' distance is required before the
intrinsic brightness of stars can be compared. If a
star's distance were doubled the light received from
it would be diminished fourfold, or more generally
the light received from equally bright stars varies
inversely as the squares of their distances. The quan-
titative measurement of the light received from stars
is a comparatively recent astronomical work, which
has been extensively pursued under Prof. Pickering's
direction at the observatory at Harvard College, and
by Messrs. Miiller and Kempf at Potsdam. Various
photometric methods have been devised for this pur-
pose, and these have replaced and given precision to
the eye-estimations previously made by astronomers.
The brightness of a star is indicated by its magnitude,
and the photometric scale is such that a difference of
one magnitude between two stars corresponds to 2*5
times the amount of light. Thus from a star of mag.
ro, 2'5 times as much light is received as from a star
of mag. 2'o; while from a star of mag. 2'o, 2'5 times
as much light is received as from a star of mag. 3*0,
and so on. Thus the brightness or amount of light
received from a star is related to its magnitude by a
formula
Amount of light = C x (^V^" 1 , where ra is the star's
magnitude, and C is the amount of light re-
ceived from a star of magnitude o'o, i, e. a
star slightly brighter than Vega.
168 ASTRONOMY
Aldebaran is of magnitude ri, or slightly fainter
than the first, while Altair is of magnitude o'g, or
slightly brighter. The stars brighter than first mag-
nitude are
Mag. Mag.
Sirius -!'4 Rigel 0*3
Canopus 1*0 Procyon o'5
Vega o'i Achenar 05
a Centauri 0*2 /? Centauri o - 8
Capella o'2 Altair 0-9
Arcturus 03
Thus Vega gives nearly 2*5 times the light of a
first magnitude star, and Sirius gives (2'5) lt5 , or 4
times the light of Vega.
With the naked eye stars slightly fainter than 6'o
mag. can be seen. A very small telescope will show
stars down to 9*0 mag., and with the largest telescopes
the sixteenth magnitude can be reached. A convenient
rule which connects the brightness of a star with its
magnitude is that a difference of 5 magnitudes corre-
sponds to a ratio of 100:1 in the amount of light
received.
Thus from a star of I'D mag. 100 times as much
light is received as from a star of 6'o mag. ; from one
of 6'o mag. 100 times as much as from one of iro
mag., and from one of u'o mag. 100 times as much
as from one of i6'o mag. Thus one millionth of the
light of a first magnitude star is received from one of
the 1 6th magnitude.
Number of Stars. A very interesting question natur-
ally arises as to the number of stars of each magnitude,
DISTANCES AND MOVEMENTS OF STARS 169
About 1855 Argelander at Bonn made a very complete
list of all the stars as bright or brighter than 9*5 mag.
between the north pole and 2 south of the equator. He
enumerated altogether 324,000 stars. This work was
continued as far as 23 south declination by Schonfeld,
who enumerated in this part of the sky 134,000 stars.
From 22 south declination to 52 south declination
an enumeration of all stars down to lO'o mag. made at
Cordoba contains 490,000 stars. At the Cape Observ-
atory similar work has been accomplished photo-
graphically extending from 19 south declination to
the south pole, giving approximate positions and
magnitudes of 455,000 stars. The difficulty in
researches of this class is in keeping a constant scale
of magnitudes, as the magnitudes are necessarily
determined by eye-estimation in visual observa-
tions, and by what amounts to a very similar process
in photographic observations. When corrections are
made so that the estimates may be as far as possible
according to the photometric scale, the following
results are found for the total number of stars of
different magnitudes.
Mag-.
No. of Stars. Mag.
No. of Stars.
>ro
1 1 6*0 - 7-0
10,275
I'O 2"O
28
7-0- 8-0
31,000
2 O - 3'O
>5
8-0- 9-0
93,000
3-0-4-0
300
9-0 - io'o
271,000
40-5-0
1016 io'o - i i'o
710,000
5-0-6-0
3 26 5
Our knowledge of the immense number of very
1 70 ASTRONOMY
faint stars begins with the Herschels who counted
the stars in sample areas in different parts of the sky.
The limiting magnitude to which Sir J. Herschel went
was approximately 14*0 m. The estimated number of
stars down to this limit is nearly 24 millions. With
some of the modern reflecting telescopes stars three
or four magnitudes fainter than 14*0 mag. can be
photographed, and the total number down to i8'o mag.
may be estimated at about 1000 millions.
The increase of the number of stars per magnitude
is very interesting. It is seen to be roughly 3 times.
Now, as the amount of light received from a star is^V
times as much as that received from a star a magnitude
brighter, it follows that as far as u'o mag. the total
light contributed by all the stars of any one magnitude
is greater than that contributed by the class a magni-
tude brighter. This cannot go on indefinitely, or the
total amount of light received from the stars would be
infinite. The ratio of the number of stars per magni-
tude to the number a magnitude brighter does not
appear to fall off very fast for several magnitudes
fainter than ii'o m.
Distance of Stars. We have seen how the distance
of the Moon may be determined by observing the
difference of its direction from two points on the
Earth's surface; and how the same method carried
out with greater refinement enables the distance of
Mars and of certain minor planets when nearest the
Earth to be measured, and the scale of the planetary
system to be derived,
DISTANCES AND MOVEMENTS OF STARS 171
But the distance of the stars is so vast that the
most refined instruments show no trace of any differ-
ences in their directions as viewed from the north of
Europe or South Africa. Such a base-line for their
triangulation is absolutely inadequate. When Coper-
nicus showed that the Earth revolved round the Sun,
astronomers realized at once that they could use a
very much larger base-line. After an interval of six
months the Earth has moved from a position go
million miles on one side of the Sun to one 90 million
miles on the other. With such a large base-line as
1 80 million miles some differences in the directions of
the stars which would permit of the determination of
their distances was surely to be anticipated. Diagram
LXXIV, which consists of rough sketches of Edin-
burgh from two different points in the grounds of the
Royal Observatory, shows the change produced by
a slight difference of point of view. The church spire
on the left, which is only half as distant as the Castle,
is in one sketch seen projected against the right edge
of the Castle, but in the other near the middle of it.
The chimney on the right, which is a little nearer to
the observatory than the crown-like spire of St. Giles'
Church, appears in one sketch to the right and in the
other to the left of this spire.
But the contemporaries and successors of Coper-
nicus could not find the slightest trace of any paral-
lactic effect of this kind among the stars. Some
concluded that Copernicus was wrong, others that the
distances of the stars were so great that the distance
172
ASTRONOMY
of the Sun was inappreciable in comparison with
them. As means of measuring angular positions
were improved, attempts were renewed to find some
Diag. LXXIV.
small differences in the relative positions of the stars
which would show that though very large the distances
were not immeasurably great. Of these unsuccessful
attempts the most notable are Bradley 's, from 1729
to 1748, which led to the discovery of the aberration
of light and of a small oscillatory movement of the
Earth's axis called Nutation, and Sir William Her-
schel's, which led to the discovery of double stars
DISTANCES AND MOVEMENTS OF STARS 173
revolving about one another under the influence of
their mutual gravitation.
Before the distance of any star was actually measured
indications were found that some of the stars though
at great were still at appreciable distances. Halley
found that the three bright stars, Sirius, Arcturus
and Aldebaran, w<ere placed in Ptolemy's catalogue
in positions slightly to the north of those they occu-
pied in his own time. He guarded against this being
due to errors of Ptolemy's catalogue by observing that
the positions of other and fainter stars agreed with
those assigned to them by modern observations. In
a communication to the Royal Society in 1718 Halley
remarks, "These stars, being the most conspicuous
in heaven, are in all probability nearest to the Earth;
and if they have any particular motions of their own
it is most likely to be perceived in them, which in
so long a period as 1800 years may show itself by an
alteration of their places, though it be utterly im-
perceptible in the space of a single century of years."
Halley's conclusions were confirmed by other astron-
omers, and in 1756 Mayer, a German astronomer,
gave a list of 57 stars whose positions had changed
perceptibly in half a century due to the movement of
the stars themselves relatively to the solar system.
At the middle of the eighteenth century it was fully
realized that the Sun and stars were similar bodies,
but that the stars were vastly more distant. The
discovery of movements among them showed that,
174 ASTRONOMY
though great, their distances were not infinite, and
held out hopes to astronomers that with more refined
measures these distances might be determined.
Success in measuring the distance of a star was
attained almost simultaneously by three astron-
omers, Bessel, Struve and Henderson. Bessel chose
61 Cygni, a star of only the 5th magnitude, on
account of the rapidity of its motion across the sky.
Near to this star were two others which did not share
this large motion, and were presumably at a much
greater distance. He commenced a series of measures
with a heliometer in August 1837 and continued them
till October 1838. He found a very small movement
of the star with reference to both the small comparison
stars, analogous to the change in position shown in
the diagram of p. 172, arising from the fact that his
point of view was changed by the motion of the
Earth around the Sun. He concluded that the "paral-
lax " of 61 Cygni was D'32".
The parallax is the small angle which the radius
of the Earth's orbit subtends at the star's distance.
3 , If E (Diagram LXXV) be the
P ___________ position of the Earth, of the
Sun, and the line QS is drawn
Diag. LXXV.
perpendicular to LQand carried
till QS represents the star's distance on the same
scale, then the small angle ESQ is called the star's
parallax. If SQ is 200,000 times EQ, then the angle
ESQ will be i". Bessel found the angle to be o'32"
DISTANCES AND MOVEMENTS OF STARS 175
in the case of 61 Cygni, and therefore 61 Cygni is
^^ x 200,000 times, or more than 600,000 times the
distance of the Sun.
Meanwhile Struve at Pulkova had from 1835 to
1838 been making a similar series of observations
on the bright star Vega. This star, though not
moving so fast as 61 Cygni, indicates, both by its
movement and its brightness, that it is probably one
of the stars nearest to the Sun. Struve found for this
star a parallax of o'26", indicating a distance of
800,000 times that of the Sun. Later observations
have shown that the parallax is not so large as this,
but nearer to o'io", so that its distance is two million
times that of the Sun.
Henderson's observations were made by a different
method. Appointed H.M. Astronomer at the Cape of
Good Hope in 1831, he made a series of observations
to determine the declination of the bright double star
a Centauri. This star, which is the fourth brightest
in the heavens, only Sirius, Canopus and Vega being
brighter, has a very large proper motion. Henderson
examined his observations and found that they showed
the star to have a parallax of i". His calculations
were not made till he had left the Cape on his
appointment as Astronomer Royal for Scotland, and
he did not announce the result till it had been con-
firmed by observations of the right ascension of the
same star. He published his determination of the
parallax of a Centauri two months after Bessel had
1 76 ASTRONOMY
published that of 61 Cygni. Later and more accurate
observations have shown that the parallax is not quite
so large but only Q'75". Nevertheless this star is, as
far as we know, our nearest neighbour among the
stars, its distance being 270,000 times that of the
Sun.
The work of determining the parallax of a star is
extremely delicate and very laborious owing to the
care which needs to be taken to obtain the necessary
accuracy. In recent times the parallaxes of a number
of southern stars have been carefully determined by
Sir David Gill at the Cape. Among other stars he
finds that Sirius has a parallax of o'37 // , but that
Canopus is too far away to show any sensible paral-
lax. The star with the largest parallax next to a
Centauri is a faint star of magnitude 7'6, situated
in the Great Bear. The parallax of this star is o'^6".
There are about twenty stars whose parallaxes are
known to be greater than o'2o", i. e. whose distances
are less than one million times that of the Sun. On
the other hand, even some of the brightest stars, such
as Canopus and Rigel, are at such a great distance
that they show no certain parallax. The fact that
some faint stars are comparatively near, while some
bright ones are too far away for their distances
to be measured with certainty, shows that there is
very great diversity in the actual luminosity of the
stars. If all were at the same distance some would
appear thousands of times brighter than others.
DISTANCES AND MOVEMENTS OF STARS 177
It is not easy to form any conception of the great
distances the stars are from us. If the distance
between the Sun and Earth were represented by the
distance between two railway lines, the distance of a
Centauri, our nearest neighbour among the stars,
would be 245 miles, and the distance of Sirius would
be 500 miles. Thus if two railway lines starting from
London instead of keeping parallel at a distance of
4 feet 8J inches, converged so gradually that they
met at Durham, the long triangle thus formed would
be similar to that formed by the Sun, the Earth, and
a Centauri. For more distant stars the triangle
would be proportionately longer. The measurement
of stellar distances rests on the determination of the
small angle at the vertex of the triangle, and as
this angle is extremely small the utmost care is
necessary to avoid any error due to instrumental
causes. For this reason the differential method of
determining stellar parallaxes has generally been
used; that is, a small change ftf
in the position of a star
relative to neighbouring stars
has been looked for. In Dia- Diag> LXXVL
gram LXXVI if E x and E 2 are the positions of the
Earth when on opposite sides of the Sun (marked O
in the diagram), and if o- is a comparatively near star
ando^ a distant one, then E^ and E 2 <r 1 are sensibly
parallel, and the angle E^E^ which is twice the paral-
lax of the star <r, is the sum of the two small angles
178 ASTRONOMY
o-EjO^ and o-E^. It is easier to determine the angle
Ej/rEg accurately in this way than in any other, as the
many causes except parallax which affect the position
in the sky of <r as seen from E and six months later
from E 2 , equally affect the position of o- x , but not the
relative positions of the two stars.
Unless the stars of reference are much more distant
than the star whose parallax is sought, the differential
method will fail, but if they are 10 or 20 times as
far off the result will be T Vth or-^th part too small.
The stars whose distances have been satisfactorily
determined number from 150 to 200. Those whose
distances have been investigated are in nearly all
cases very bright or with very large proper motions.
The brightness and the proper motion have been
clues which have guided astronomers in the choice
of stars whose distances they should attempt to
determine. This manner of selection makes it diffi-
cult to deduce from the results correct views as
to the average distances of stars. Prof. Kapteyn,
realizing the importance of an increase in our know-
ledge of the parallaxes of stars, has set on foot a
scheme by which certain selected areas well dis-
tributed over the sky shall be photographed at such
times of the year that any stars of large parallax will
be detected by their slight movements relative to the
general mass of the stars photographed on the same
plate. When stars of large parallax let us say greater
than o'i" are picked out in this way, a great deal
DISTANCES AND MOVEMENTS OF STARS 179
of information will be obtained on many important
points on which our knowledge is at present very
scanty. For example, the percentage of stars of differ-
ent magnitudes, having parallaxes of this amount, will
show to what extent the apparent brightness of a
star is due to its intrinsic brightness, and to what
extent it is due to nearness to the Earth. Similarly
we shall be able to judge to what extent a large proper
motion is due to a large velocity, and to what extent
it arises from the star's proximity to the Earth. These
and other questions bearing on the geometry of the
stellar system depend largely for their answer on the
increase of our knowledge of the parallaxes of stars.
Proper Motions of Stars. Although only a small frac-
tion of the stars are sufficiently near for their dis-
tances to be separately determined, there are a large
number of stars sufficiently near for their proper
motions or angular motion on the face of the sky
to be determinable. With the lapse of time the
number will increase, for if motion cannot be detected
in one year it may be in ten, if not in ten
a century may be sufficient. The existence of a
proper motion clearly shows that a star is not at an
infinite distance, otherwise its velocity would need to
be infinite for any change in its position to be
produced.
The magnitude of the proper motion does not
enable a star's distance to be determined unless the
actual velocity of the star is known. The study of
N 2
i8o ASTRONOMY
proper motions does, however, give information
about the average distances and movements of stars
which are too far distant for their parallaxes to be
determined individually.
The proper motions of many stars have become
known during the last quarter of a century because a
sufficient interval of time has elapsed since the posi-
tions of the stars were accurately catalogued for
changes in their position to be apparent. Modern
determinations of proper motion date from the
revision by Dr. Auwers of the catalogue executed by
Bradley at Greenwich in 1755 and its comparison
with catalogues made a hundred years later. By this
work the angular movements on the face of the sky of
more than 3000 stars were made known. The proper
motions of thousands of stars have since been investi-
gated by different astronomers. As examples of the
actual amount of stellar proper motions we may take
the very bright stars given on p. 168. The number
of seconds they move over the face of the sky per
century are as follows
Sirius 132"
Canopus 2"
Vega 35"
a Centauri 368"
Capella 44"
Arcturus 228"
Rigel o"
Procyon 125"
Achenar 9"
/? Centauri 4"
Altair 65"
Canopus and Rigel show practically no movement,
and are probably at a very great distance. As we have
seen, attempts to determine their parallaxes have been
DISTANCES AND MOVEMENTS OF STARS 181
unsuccessful . It follows that their actual luminosity must
be immense. On the other hand, Arcturus is an instance
of a star moving with a very great velocity. Its paral-
lax has been determined as o'O3". While this is the
small angle the distance from the Earth to the Sun
subtends at Arcturus, its movement in a year on the
face of the sky subtends an angle 2'28". In one year,
therefore, it moves : trt times the distance from the
Earth to the Sun. This works out to be 76x93
million miles a year or more than 200 miles a second.
Large proper motions are not confined to bright
stars. Till a few years ago Gr. 1830, a star of 6'g mag.
was the most rapid known; but in 1897 a faint
southern star of 8'5 mag. was found to be moving still
more rapidly. The following five stars have proper
motions greater than 500" a century.
Mag. Prop. Parallax.
Motion.
Cordoba V, 243 8*5 870' o'3i"
Gr. 1830 6*9 704" <xi2"
Lac. 9352 7-5 694" 0-28"
Cor. 32416 8-5 607"
6 1 Cygni 57 520" 0-33"
The parallaxes show that four of these five stars
are comparatively near. The faintness of the stars is
therefore a proof of their small absolute luminosity,
and illustrates the great variations among the stars in
this respect.
Altogether about 100 stars are known to have proper
motions of more than 100" a century, and about 2000
1 82
ASTRONOMY
of more than 20" a century, but the latter list is very
incomplete. The probable number of those which
have proper motions greater than 5" a century is
given by Newcomb as 20,000, but the data are as
yet insufficient for a precise estimate.
Motion of Sun in Space. The proper motion of a
star may arise from its own motion or from a motion
of the solar system in space. In the former case there
is, a priori, no reason to expect any regularity among
the proper motions; but in the
latter case there would be a
general drift of the stars in an
opposite direction to the move-
ment of the solar system. In
Diagram LXXVII let O be the
centre of a large circle, and let
O move a small fraction of the
Diag. LXXVII. radius to O' in the direction
OG. The direction in which A is seen has
changed from OA to O'A ; A has apparently moved
in the direction of the arrow through an angle
COA CO'A or OAO'. Similarly E has apparently
moved through an equal angle. G and C, which
are in the direction of and the direction opposite to
the movement of O, have not changed their directions
at all. A point B has apparently moved through an
angle COB CO'B or OBO'. This angle is largest
when B is like A or E, perpendicular to OO', and
becomes smaller as B approaches C, the point from
DISTANCES AND MOVEMENTS OF STARS 183
which O is moving or the point G to which O is
moving. If, instead of dealing with a circle, we
take a sphere like the sky, the apparent angular
movement of the stars arising from the real movement
of the Sun (carrying the Earth with it) will be towards
the point from which the Sun is moving. The move-
ment will be imperceptible in stars near this point or
1 80 away from it, and will be largest for those 90
distant. There are two complications when this geo-
metrical conception is applied to the stars. First,
part of a star's proper motion arises from the star
itself; and secondly, the unknown and irregular dis-
tances of the stars prevent the effect from being as
regular as in the geometrical illustration just given.
One of Sir William Herschel's greatest discoveries
was his perception of a certain amount of regu-
larity in the proper motions of stars, and his
attribution of this to a translation of the solar
system in space towards a point in the sky which
he fixed in the constellation Hercules near the star
A. Herculis.
Herschel's first determination of the direction of
the solar motion was made in 1783. He obtained
from very little material a result in very good agree-
ment with modern determinations. He made a new
determination in 1805, and found for the Sun's apex
or point towards which the Sun is moving a position
30 distant from A Herculis. This discordance led some
astronomers, and among others Bessel, to doubt
1 84 ASTRONOMY
whether a movement of the solar system had really
been established.
In 1830 Argelander made very exact observations
of a number of bright stars. He compared the posi-
tions of 390 of these with those found by Bradley
in J 755- The interval of 75 years between the obser-
vations provided him with a very considerable change
of base the distance through which the solar system
had moved in 75 years. His research, which was
carried out with considerable mathematical refine^
ment, confirmed Herschel's earlier result. Many
determinations of the solar motion have been made in
comparatively recent years. The comparison of
modern observations with the older ones of Bradley
and others have given the proper motions of a large
number of stars, so that bright stars and faint stars,
stars of large and of small proper motions have been
used in different determinations. Further, the diffi-
culties and uncertainties of the problem have given
rise to the development of somewhat different mathe-
matical methods of treatment. The results were not
as accordant as might have been anticipated, and in
searching for the cause of the discrepancies Professor
Kapteyn discovered an interesting feature in the
proper motions arising from peculiarities in the
motions of the stars themselves. The different
methods by which the problem had been treated
assumed that, apart from the apparent movements
arising from the real movement of the solar system
DISTANCES AND MOVEMENTS OF STARS 185
in space, the movements of the stars themselves were
haphazard. It has been clearly demonstrated that this
is not the case, but that the stars' movements exhibit
a bias towards a direction whose right ascension is
about 90 and declination about + 15 and the direction
diametrically opposite. The point in the sky towards
which the solar system is moving has right ascension
275 and declination + 30, and is not far from the
bright star Vega. It is to be understood that there is
an uncertainty of several degrees in the positions
determined for both of these points.
Motion in the Line of Sight. The information derivable
from the proper motions of stars has in recent years
been supplemented by determinations of the actual
velocities with which stars are moving to or from the
Earth. The application of the spectroscope for this
purpose was first made by Sir William Huggins in
1868. The position of a line in the spectrum is deter-
mined by the number of vibrations which are received
each second. If the source of light is approaching the
observer, more vibrations are received per second than
is the normal case when the source of light is at rest.
Suppose the spectrum contains known lines, for in-
stance, those due to Iron. These will all be displaced
slightly to the violet side of their positions in the
normal spectrum of Iron; and the amount of the dis-
placement affords a means of comparing the velocity
of the source of light towards the observer with the
velocity of light. If the source of light is receding
1 86 ASTRONOMY
from the observer the lines are displaced towards the
red.
The initial difficulties of applying this principle to
determine the velocities of the stars to or from the
Earth were very considerable owing to the small
amount of light from a star and also on account of
the minuteness of the displacement. Sir William
Muggins showed that the method was feasible, and
Dr. Vogel, by substituting photographic for visual
observations, substantially increased its accuracy.
Later with the large telescope of the Lick Observ-
atory, Prof. Campbell obtained still higher accuracy,
and at the present time there are half-a-dozen observ-
atories where the velocity of a bright star to or from
the Earth can be obtained with a probable error of
not more than half-a-mile a second. It is to be noted
that, provided there is enough light for an observation
to be made, the information we derive of the stars'
velocities in this way is irrespective of their distance.
As might be expected the velocities with which the
stars are approaching or receding from the Earth
vary considerably. Those with the greatest velocity
determined at the Lick Observatory are
rj Cephei 55 miles per second towards Sun
Herculis 45 ,, ,, ,, ,,
e Andromedae 53 ,, ,, ,, ,,
p. Cassiopeiae 61 ,, ,, ,, ,,
8 Leporis 59 ,, ,, from Sun
0Canis Majoris 59 ,, ,, ,, ,,
DISTANCES AND MOVEMENTS OF STARS 187
From the velocities of 280 stars Prof. Campbell
determined the direction and amount of the solar
motion. The method is essentially the same as that
employed in the case of proper motions. The
velocity found for each star is supposed to be com-
pounded of the velocity of the solar system and of
the star itself, and from the manner in which stars
at one part of the sky are systematically found to be
moving towards the Sun, and in a diametrically
opposite part of the sky to be moving from the Sun,
the velocity with which the solar system is moving
through space is found to be about 12^ miles per
second.
Average Distances of Stars. This velocity of 12^
miles per second in a year carries the solar system for-
ward a distance equal to 4# where a is the distance of
the Earth from the Sun. In 100 years, therefore, the
solar system moves a distance 4000, and the stars are
seen from points 200 times as far apart as the extreme
distance which the revolution of the Earth about the
Sun supplies.
Referring to the figure on p. 182, we may take O
to be the position of the Sun in 1800 and O' in 1900.
Let us suppose a number of stars at equal but un-
known distances from the solar system to have had
their positions in the sky observed in 1800 and again
in 1900. From comparison of these observations the
angle OAO' may be determined, and then as the
length OCX is known, the distance OA of these stars
1 88 ASTRONOMY
can be found. As the stars are not all at the same
distance, the application of this method in practice
only gives the average distance of the stars considered.
As an illustration, take the stars observed by Groom-
bridge in 1810 and re-observed at Greenwich about
1890. There were 200 stars brighter than 5*0 mag.,
454 between mags. 5'o and 6'o, 1003 between mags.
6'o and 7*0, 1239 between mags. 7'o and 8'o, and 811
between mags. 8'o and 9'o. Treating each group as if
all the stars belonging to it were at the same distance
from the solar system, the angle OAO' or the paral-
lactic angle was found to be 3*17", 2'54 // , 2' 28", 179",
i '86" for the several groups of stars. But in 80
years the actual displacement of the solar system is
32oa, where a is the Sun's distance from the Earth,
and thus the average parallaxes of these groups of
stars are found by dividing trie above angles by 320,
and are therefore Q'0099", o'ooSo", 0*007 1", o'oo56",
and o'oo$8 ff . The distances corresponding to these
parallactic angles are 20, 25, 30, 36 and 34 million
times the distance of the Earth from the Sun. No
stress is to be placed on these exact figures, which are
only given to indicate roughly a method by which the
distances of the stars may be approximately arrived at.
Another method of obtaining an idea of the dis-
tances of the stars is based on the very simple assump-
tion that the density of the stars in space is the same
at greater distances as it is near the Sun. If we take
a sphere whose radius R is one million times the
DISTANCES AND MOVEMENTS OF STARS 189
Sun's distance, we know that there are 20 stars within
this sphere, we should expect to find 20,000 stars
within a sphere of radius loR, and 20 million stars
within a sphere of radius lOoR. Precise results can-
not be given till we are certain that all the stars
are known which are within the smallest of these
spheres. For this it will be necessary to wait till the
results of the organized search for stars of large
parallax have been obtained. The simple argument
just given shows that while there are only a few stars
nearer than a million times the Sun's distance, a very
considerable number are within ten times the limit,
and probably a large fraction of those visible to the
naked eye are within a hundred times this limit.
Only a very rough indication has been given of
methods which may be applied with considerable
detail. The brightness of a star, other things being
equal, is an indication of its distance. Similarly a
star with large proper motion is probably nearer than
one in the same part of the sky with a small proper
motion. It has been established that the stars differ
very much in intrinsic brightness, and thus the proper
motion generally is a safer guide than the magnitude
to the distance of a star. But magnitude and proper
motion are not the only classifications which need
to be considered in connection with stellar distances.
As we shall see later the spectroscope enables stars
to be classified according to their physical conditions.
Most of the stars fall into one of two types: those
igo ASTRON&MY
whose spectra exhibit broad lines due to hydrogen and
sometimes to helium, such as Sirius, Vega and Rigel,
and those whose spectra are, like the Sun, full of
metallic lines, such as Capella and Arcturus. It is
found that the yellow or solar stars are much nearer
to us than the blue or Sirian stars. The following
table by Kapteyn gives the mean parallaxes of stars
of different magnitudes
Mag. Type I. Type II.
2'0 0*032" 0-072"
4-0 o'oi6" 0-036"
6*0 0*008" 0*018"
8*0 0-004" 0*009"
io'o 0-002" 0-0045"
The table shows that the mean distance is doubled
as we pass from second to fourth magnitude stars,
and so on; and that the mean distance of blue stars
is more than twice that of yellow stars of the same
magnitude. But it must be clearly understood that
these are only average results, and that there are great
differences in the distances of stars of the same
magnitude.
Velocities of the Stars. It is beyond the scope of this
book to go into the rather difficult statistical processes
by which the average velocities of the stars are deter-
mined. The following table by Professor Newcomb
gives in a simple form some of his conclusions. It
should be remembered that a velocity of three miles
a second would cover the distance from the Earth to
DISTANCES AND MOVEMENTS OF STARS 191
the Sun in one year. Taking 1000 stars, an estimate
is made of the number of stars moving 3, 6, 9, etc.,
miles a second.
Velocity
in miles
per sec.
No. of
Stars.
Velocity
in miles
per sec.
No. of
Stars.
Velocity
in miles
per sec.
No. of
Stars.
O
5
27
75
54
2
3
36
3
59
57
I
6
66
33
44
60
I
9
92
36
32
66
I
12
107
39
22
75
I
15
114
42
'4
90
I
18
I 12
45
9
1 20
I
21
I0 3
48
6
^o
I
2 4
9 1
5 1
3
180
I
As the velocity of the Sun in space is about twelve
miles per second, it is seen that the Sun's velocity is
rather below the average of stellar velocities.
Absolute luminosity of the Stars. If the Sun and stars
were all at equal distances from the Earth, how would
their luminosities differ ? It is not easy to determine the
ratio with accuracy, but we may take it that the light
from the Sun is 40,000,000,000 times the light from the
bright star Vega. Now, Vega is of magnitude o'l,
and a little calculation from these figures shows that if
the Sun were removed to two million times its dis-
tance, when its parallax would beo'i", it would appear
to us as a star of 5'i mag., that is to say, would be just
visible to the naked eye. As showing how much the
stars vary in absolute luminosity the following table
1 92 ASTRONOMY
of Professor Kapteyn's may be quoted. In a space
containing two million stars of the same luminosity as
the Sun there are
i star with 100,000 times its luminosity.
38 stars ,, 10,000 ,, ,, ,,
1800 ,, ,, 1000 ,, ,, ,,
3600 ,, ,, loo ,, ,, ,,
440,000 ,, ,, 10 ,, ,, ,,
5 million stars with T V^ n f the Sun's luminosity.
/2f > " " Til(T > jj
Naturally figures of this kind do not pretend to any
great degree of exactitude; but the table given above
is based on a careful discussion of such material as
exists, and may be taken as an approximate statement
of the great diversity which exists in the intrinsic
brightness of the stars.
CHAPTER IX
STARS AND NEBULAE
IN the last chapter the questions to be answered
were : Where are the stars ? and How are they mov-
ing ? Another series of questions which naturally
present themselves are concerned with their chemical
and physical nature. What are the stars made of ?
What are their temperatures ? How far do they
resemble the Sun and in what respects do they differ
from it ? Partial answers to these questions can be
obtained from a study of stellar spectra, which teach
us three distinct things, (i) By comparison with
terrestrial spectra something is learned of the chemical
composition of the stars. Hydrogen and helium,
sodium and calcium, iron and titanium are perceived
in stars 100 million million miles away. (2) By slight
displacements of the spectral lines from their normal
positions, movements in these distant bodies towards
or from the Earth are detected and measured. (3;
By the differences in character of the spectra, facts
about the physical condition of the stars, such as their
temperatures and the extent of the atmospheres sur-
rounding them, may be gathered. These three lines
of research are not entirely distinct, though they are
o 193
194 ASTRONOMY
so to a large extent. The interpretation of the
physical conditions which give rise to the peculiar-
ities in stellar spectra is a matter of difficulty. This
is not to be wondered at, for the spectrum of a sub-
stance observed in a laboratory differs according to
the temperature, pressure, and electrical conditions of
the source from which the light is obtained. In the
stars these conditions are varied far more than our
means of experiment will permit.
Stellar spectroscopy practically dates from 1863 with
the researches of Sir William Huggins in England
and Father Secchi in Rome. The very considerable
difficulties to be overcome arise primarily from the
limited quantity of light a star affords. Only a por-
tion of this passes through the narrow slit (say
2-tr^th inch wide) of a spectroscope; it is then spread
out into a line of several inches in length from the red
at one end to the violet at the other; and further, in
order to see the structure of the line, it is necessary
that it should be broadened into a narrow band by
means of a cylindrical lens. When the light is spread
out in this way its intensity is greatly diminished.
The introduction of photography made a great
advance in the accuracy and the range of stellar
spectroscopy. Difficulties still arise, though in an-
other form, from the small quantity of light which is
submitted for analysis. Long exposures are necessary,
and therefore the light of the star must be kept con-
tinuously on the slit of the spectroscope. Further,
STARS AND NEBULA 195
the spectroscope must be so mounted that no flexure
occurs in the different positions which it takes when
the telescope follows the same star for several hours;
and again, arrangements have to be made to keep the
temperature of the prisms constant (to within a small
fraction of a degree), so that their density may not
change and give a blurred picture of the spectrum.
As the result of an examination of the spectra of
more than 4000 stars, Secchi made an empirical classi-
fication of the stars into four types. In the first type
he included white and blue stars, such as Vega and
Sirius, whose spectra show broad dark lines due to
absorption of certain rays by hydrogen. The second
type contained yellow stars, like the Sun, Capella and
a Centauri, whose spectra show many fine metallic
lines and two broad lines in the violet part of the
spectrum due to calcium. The third type contained
red stars, of which Antares is an example, whose
spectra contain a number of dark bands, sharp on the
violet side and fading off gradually to the red. The
fourth type also consisted of red stars, whose spectra
consist of dark bands due to the presence of carbon,
sharp on the red side and fading off towards the
violet. A fifth type was added later by Messrs.
Wolf and Rayet of the Paris Observatory consisting
of stars whose spectra contained dark bands and
bright lines as well.
In the Draper catalogue of the Harvard Observa-
tory the spectra of more than 10,000 stars are classified
o 2
196 ASTRONOMY
by Mrs. Fleming. Still more recently, from an ex-
amination of 4800 spectra of 68 1 stars taken with a
larger telescope and greater dispersion, a careful and
elaborate division of the stars into 22 groups has been
made by Miss Maury. This subdivision into 22
groups emphasizes the gradual change from type to
type. The most important difference between this and
Secchi's classification is the subdivision of the stars of
Type I.
All the stars of Secchi's first type are marked by
the series of hydrogen lines which gradually close up
to a point in the ultra-violet part of the spectrum.
About 30 of these lines are seen ; they were discovered
in the photographs taken by Sir W. Huggins. The
wave-lengths were shown by Prof. Balmer to follow
a very simple law
A = 3647'i4 x ~2 - , where n = 3, 4, 5, 6, and so on.
7? ~ ~ A.
The appearance of these broad hydrogen lines in the
spectra of certain stars is shown in Diagram
LXXVIII.
39 _ 19
\
i
i
mil 1 1
1 1
Diag. LXXVIII.
Helium Stars. When helium was discovered in 1895
by Sir W. Ramsay, it was found that some of these
stars with broad hydrogen lines showed a large
STARS AND NEBULA 197
number of helium lines as well. The helium stars
also contain lines due to oxygen, silicon and nitrogen.
But lines due to metals are found in very few of them.
Many of the bright stars of Orion belong to this
class, Rigel and Bellatrix among them. Another
helium star is /3 Crucis, in the Southern Cross -the
first star in which the presence of oxygen was recog-
nized (by Mr. McClean in 1897).
Hydrogen Stars. Sirius and Vega are the brightest
of the hydrogen stars. In the spectra of this group
the helium lines are not present. Between the broad
lines of the hydrogen series a number of metallic
lines are faintly shown in some of the stars. Thus in
Sirius are seen lines due to sodium, calcium, mag-
nesium, silicon, iron, titanium, vanadium. Oxygen
and nitrogen are not shown.
More than half the stars in the sky belong to
Secchi's first type. A remarkable feature about them
is their small proper motions, indicating that as a
class they are very distant from the Sun. This is
specially true of the helium stars. Many of these
stars are, however, of very great brilliancy. Sirius,
for example, gives us 20 times as much light as the
Sun would if placed at the same distance, but is only
between two and three times as massive as the Sun.
This may result from great intrinsic brightness or
very large surface. Again, the blueness of these
stars may be taken as evidence that they are not sur-
rounded by a dusky veil like the Sun.
198 ASTRONOMY
Solar Stars. The most conspicuous stars of this type
are Capella and Arcturus. Their spectra are almost
exactly similar to that of the Sun. Procyon and
Canopus are intermediate between the Sirian and solar
stars, as they show the hydrogen series as well as
strong metallic lines. A very large number of stars
belong to this group. Some, like Arcturus, are at
a very great distance, while a Centauri is very near.
The similarity of their spectra to that of the Sun
shows that these stars are of similar intrinsic bril-
liancy. The great differences in their apparent
brightness is therefore to be attributed solely to
distance and actual size. Making allowance for
distance, Arcturus is found to be many thousand
times more bulky than the Sun, a Centauri to be
nearly the same size, and some other stars much
smaller.
Stars of the Third Type. When we come to stars of
the third type, it is found that a larger proportion of
their total light is in the red end of the spectrum
the blue light is absorbed as in solar stars, but to a
greater extent. The bands, sharp at their violet edges
and fading off towards the red, which are the charac-
teristic feature of this type, have recently been shown
by Prof. Fowler to be due to titanium oxide. The
same bands have been found by Prof. Hale in Sun-
spots. The general appearance of the bands is given
in Diagram LXXIX. The existence of an oxide is
taken as an indication of comparatively low tempera-
AND NEBUL/E 199
ture. Besides the bands, there are a great many lines
due to metals. Antares and Betelgeux, the brightest
stars belonging to this type, are at very great dis-
tances, and appear to be very much greater than the
Sun.
h te la b
33
i N
Diag. LXXIX.
Stars of the Fourth Type. These are comparatively
few, and none are brighter than the fifth magnitude.
They are characterized by three bands sharp towards
the red and fading away towards the violet, which
were identified by Secchi as due to carbon com-
pounds. The spectra of this group of stars have
been carefully studied by Prof. Hale and Mr. Eller-
man at the Yerkes Observatory. They are shown to
contain, in addition to the bands, a large number
of dark lines and a few bright ones. The presence
of sodium and iron, among other bodies, is indicated
by the absorption lines.
Stars of the Fifth Type. The Wolf-Rayet stars
have complex spectra, consisting of the superposition
of a continuous, bright line and a dark line spec-
trum. Some of the lines are due to helium and
hydrogen, but the rest are unidentified. There are
no metallic lines. The brightest star of the class is
y Argus. In it the first line of hydrogen is bright,
200 ASTRONOMY
the second neutral, and the rest dark. A remarkable
feature about these stars is the existence of a series
of lines, whose wave-lengths can be derived from the
formula for the hydrogen series on p. 196 by giving
n the values 3^, 4^, 5j, etc. This points to the exist-
ence of hydrogen under conditions which have not
been obtained in any laboratory experiments. These
Wolf-Rayet stars are all found in the neighbourhood
of the Milky Way.
In addition to these stars, Miss Maury has a class
whose spectra are like the helium or Orion stars, but
in which some of the lines are bright instead of dark.
The following table, taken from the Harvard
Annals, shows how the 68 1 brightest stars between
the north pole and 30 S. declination are divided
among the different classes
Helium . . . . . . 117
Intermediate . . . . . 31
Type I. Hydrogen . . . . 185
Intermediate ..... 35
Type II. Solar . . . . 218
Type III. Titanium Oxide . . 55
Type IV. Carbon .. 4
Type V. Wolf-Rayet ... 4
Helium stars with some bright lines . 14
Composite spectra (probably binaries) 18
The table shows that a very large percentage of the
stars are included in the three types of helium, hydro-
gen and solar stars. The same result is found when
the classification is extended to include fainter stars.
STARS AND NEBULAE 201
Nebulae. The relationship of these various classes
of stars to one another cannot be understood without
reference to an apparently very different kind of body.
With his small telescope Halley found two nebulous
patches of light in the constellations of Andromeda
and Orion. Herschel with his great telescopes dis-
covered thousands of faint nebulous areas. Some
were irregular and diffuse, others nearly circular and
small. He could not say certainly whether they
consisted of faint stars crowded together, or were
continuous bodies of luminous fluid. Most of the
nebulae discovered by Herschel are faint and invisible
except with large telescopes, so much so that the Bonn
Durchmusterung, which contains more than 300,000
stars visible in a small telescope, gives no more than
64 nebulae.
The key to the nature of these bodies was found by
Sir William Huggins in 1864. Light from the bright-
est of the nebulae, that of Orion, was collected by the
object glass of a telescope, and a small part of it sent
through the slit of his spectroscope to be analyzed.
The spectrum was not a bright band with dark absorp-
tion lines across it like the solar spectrum, but con-
sisted simply of four bright lines, of which the bright-
est was green. The nebula, therefore, was composed
of glowing gas of low density. Other nebulae were
found to contain the same lines, two of which were
identified with hydrogen, and the brightest of all was
at first thought to be due to nitrogen. Larger tele-
202 ASTRONOMY
scopes and spectroscopes of greater dispersion have
since been employed, and show that this is not the
case, and the origin of two of the lines is still un-
known. An unknown element nebulium may give
rise to them, or possibly some known element, but
under conditions which have not yet been reproduced
in our laboratories. A number of fainter lines have
since been discovered in the spectra of nebulae,
among others the yellow line due to helium identified
by Prof. Copeland. The most extensive study of
nebular spectra has been made at the Lick Observa-
tory by Prof. Keeler, who succeeded in determining
the velocities with which 14 were approaching or
receding from the Earth, as well as the exact 'wave-
length of nebular lines of unknown origin.
Nebulas do not all show a spectrum consisting of
bright lines. The Andromeda nebula and a very
numerous class of spiral nebulas show a continuous
spectrum.
Our knowledge of nebulas has been largely increased
by the beautiful photographs which have been taken
in recent years. When a telescope is used with a
high magnifying power only a very small area of the
sky can be seen at one time. This is of no conse-
quence if we are measuring a close double star or
examining a planet, but with extended bodies like
some of the nebulas it is a great advantage to have
the whole object before the eye at one time in a
photograph. Again, a photographic plate with a
STARS AND NEBULA 203
sufficiently long exposure receives impressions which
make no perceptible effect on the retina, and thus
faint nebula? and the faint details of bright nebulae
are recorded which could not be observed visually.
A third advantage is that the photograph itself is an
unbiassed and permanent record of the observations.
An English amateur astronomer, Dr. Common,
succeeded in 1883 in obtaining a beautiful photograph
of the great nebula in Orion. He used a large reflect-
ing telescope of his own construction, which possessed
great light-grasping power owing to its large size in
proportion to its focal length. Following him, Dr.
Roberts, another amateur, made an extensive series
of photographs of nebula;, of which he published the
most interesting and striking. Many photographs
have since been taken at various observatories, either
with reflectors or refractors of short focus. A beau-
tiful series of photographs taken by Prof. Keeler
at the Lick Observatory, including all the remarkable
nebulas visible in that latitude, has recently been
published.
The nebula of Orion is perhaps the grandest object
the telescope reveals to us. Its brightest part covers
an area of the sky somewhat less than that covered
by the Sun. It cannot be less than 10 million times
the Sun's distance from us. The distance from one
side of the nebula to the opposite side is not less than
10 million million miles, or, comparing with the size
of the solar system, 4000 times as large as the distance
204 ASTRONOMY
from the Sun to Neptune. The tenuity of the nebula
must be of a far higher order than any vacua with
which we are acquainted, otherw-ise the mass would
produce very great velocities in the stars near it.
Some of the stars seen with it appear to be physically
connected with the nebula, and not to be merely in
the line of vision. This applies especially to four
stars forming a trapezium in its brightest part. It
was found by Sir W. Huggins that the spectra of
these stars contain a number of bright lines identical
with some in the nebula. They may have been
formed by the condensation of some of the gaseous
matter. The displacement of lines in the spectrum
shows the distance between the nebula and the Sun
to be increasing at a rate of 10 or n miles a second.
This apparent movement is nearly all due to the
movement of the Sun in the opposite direction.
There are indications of different velocities in different
parts of the nebula, but these are not greater than
one or two miles a second. Changes in the lumin-
osity of parts have been suspected, but have not been
certainly established. The source of this luminosity
(which is excessively small compared with that of the
Sun) is unexplained, but there is no reason to sup-
pose that the nebula is at a high temperature. Dia-
gram LXXX, from a photograph taken at Greenwich
with a 3O-inch reflector and an exposure of 2 h. 15 m.,
shows the general appearance of the nebula.
The forms of nebulas have been much better under-
STARS AND NEBULA 205
stood since photographs have been obtained. Some
are wholly irregular and diffuse, like that of Orion,
but several are ring-formed, and a very large number
are spiral. Prof. Keeler estimated that in the whole
sky there were 120,000 nebulae of spiral form within
Diag. LXXX. Orion Nebula.
easy reach of the light-grasping powers of the reflect-
ing telescope of the Lick Observatory.
Although the process is not fully understood, it
seems probable that stars have been evolved from
nebulae. The relationship of the stars in the Orion
nebula to the nebula itself and the forms of spiral
nebulae confirm the view that the long-continued
action of gravitation converts the nebulae into stars
206 ASTRONOMY
and stellar systems. The bright line spectra of nebulae
have therefore been taken as a starting-point in clas-
sifying the stars according to their order of develop-
ment. Classifications have been proposed by Huggins,
Vogel, Lockyer, and McClean, which differ in some
particulars, owing to the difficulty of interpreting
spectra. The following is given by Prof. Hale as the
one corresponding most closely with current views
Nebulae.
Helium stars.
Hydrogen stars.
Solar stars.
Titanium oxide and carbon stars/
Dark stars.
The Wolf-Rayet stars are probably in an early
stage of development.
We suppose, then, that a star begins as a nebulous
mass. This condenses and forms helium stars, like
those found in the centre of the Orion nebula. At
first only helium and hydrogen are seen in the spectra,
but gradually lines of oxygen, nitrogen, magnesium
and silicon are found. Next we come to stars, like
Sirius, in which the helium lines are not seen, but
where there are broad hydrogen lines, supposed to be
characteristic of very extensive atmospheres, as well as
fine metallic lines. The study of variable stars shows
that hydrogen stars are of much less density than the
Sun. It is probable that so far the stars have been
getting hotter, for more heat is obtained by contrac-
STARS AND NEBULAE 207
tion than is lost by radiation, as long as a star remains
gaseous. After the hydrogen stars, the order pro-
ceeds through stars like Procyon to Capella and
Arcturus, which resemble the Sun. The spectra of
these yellow stars is marked by the number of metallic
lines, the disappearance of all but the first five of the
broad hydrogen lines, and the prominence of two
calcium lines in the violet. Further, an absorbing
atmosphere, like the dusky veil round the Sun, cuts
off a large amount of the violet and blue light. Next
we come to the red stars, in which the absorbing
atmosphere has grown more intense and cuts off still
more of the blue light. The presence of compounds
with fluted spectra shows that these stars are of lower
temperature than the solar stars, and are declining
to the stage of dark stars. There are no doubt dif-
ferences in the evolution of different stars. A large
star will probably be longer in going through its
stages than a small one. Of the length of time occu-
pied we have no idea.
CHAPTER X
DOUBLE STARS AND CLUSTERS
SIR WILLIAM HERSCHEL is generally spoken of as
the founder of Sidereal Astronomy. He took for
his motto "Whatever shines should be observed,"
and constructed telescopes far surpassing in light-
grasping and penetrating power those of his pre-
decessors, with which he executed a most thorough
and minute exploration of the sky. Herschel was, in
addition, a philosopher who interpreted what he saw
with the consistent aim of obtaining as completely
as possible a rational description of the sidereal uni-
verse, but it is to his persistence and enterprise as an
explorer of the skies that the discovery of double stars
is due.
While making an examination of the sky for the
purpose of rinding some stars of measurable parallax,
he discovered that many stars were double, and in
1782 presented to the Royal Society a catalogue of 269
double stars. He supposed at the time that these
were only optically double, that is, were nearly in the
same line as seen from the Earth. His intention was
doubtless to see if in any cases a movement of the
brighter star relative to the fainter, such as would
arise from their different distances, could be discerned
208
DOUBLE STARS AND CLUSTERS
209
in the course of the year. He was, in fact, seeking
to determine the parallax of a star, in the way which
was successfully carried out by Bessel in 1831, and
which is described in Chapter VIII.
The observation of a double star will be understood
from Diagram LXXXI . If A and B are the two stars, the
distance AB between them
is measured, and also the
angle BAN, between the
line joining the stars and
the meridian through the
Diag. LXXXI.
star A. By 1803 Herschel
had sufficient evidence that
some of the stars he had
observed were not double
in appearance only, but
were real binary combinations of two stars, held
together by the bond of mutual attraction. The
bright star Castor first convinced Herschel of the
existence of double stars with orbital motion about
one another. In the space of 22 years the direction of
the line joining the stars had changed by more than
20. (Castor is easily seen to be double with a small
telescope; the distance between these two stars is
about 5"; both are bright, one being of mag. 2'y and
the other 3'y.) Herschel concluded that the stars
revolve round one another in 342 years. Similarly
he found for y Leonis a period of 1200 years, for 8
Serpentis 375 years, for e Bootis 1681, and for y
210 ASTRONOMY
Virginis 708 years. He also found that e Lyrae is a
double double star. Herschel's work was continued
by his son, and by Sir John South, but most of all by
Wilhelm Struve at Dorpat. Struve made measures
of all stars he knew to be double, and in addition
made a minute review of the heavens from the north
pole to 15 south of the equator. He examined
120,000 stars, and produced a great catalogue con-
taining 2640 double stars. Since Struve's time the
number of astronomers who have given attention to
the observation of double stars is considerable, and
has included some of exceptionally keen eyesight.
With the assistance of larger telescopes the scrutiny
of the stars has been pushed further, so that very faint
companions to bright stars have been discovered, and
many which with small telescopes appear to be single,
have been resolved into very close double stars.
Especially conspicuous is the work of Prof. Burnham
at various observatories in the United States, and of
his successors, Profs. Hussey and Aitken, at the Lick
Observatory.
During the time they have been under observation,
some double stars have made a complete revolution
about one another, and in many cases sufficient move-
ment has taken place for an accurate determination
of the period or time of revolution. The shortest
period as yet found is about 5^ years. There are a
considerable number whose periods are between 20 and
50 years, and a great many whose periods are hundreds
DOUBLE STARS AND CLUSTERS
211
of years. The orbit of Bootis, shown in Diagram
LXXXII and taken from a work by Mr. T. Lewis on
Diag. LXXXII.
the double stars observed by W. Struve, may be con-
sidered as that of a typical double star whose compo-
nents are fairly widely separated. The brighter star of
P 2
212 ASTRONOMY
the pair at A is of magnitude 47, and of yellow colour ;
the companion is of magnitude 6'6, and is purple.
The relative positions of the stars as seen by Herschel
in 1780 and 1802, by Struve in 1822, and subsequent
observers, are indicated by dots. These dots all lie on
an ellipse, but it is not an ellipse with A as focus,
for we see not the true orbit of the star about its
primary, but the projected orbit on a plane perpen-
dicular to the line joining the Earth and the star.
The true orbit may be determined from the apparent
one by calculation. In the case of Bootis the com-
plete revolution will be accomplished in about 137
years. The length of the major axis of the apparent
orbit is 9'6o", and of the minor axis S^i", and cal-
culation shows that the major axis of the true orbit is
io'66", the minor axis 8'53 /7 , and that the true orbit
is inclined at an angle of about 50 to the apparent
orbit.
When the distance of a double star from the Earth
is known, it is possible to determine the actual dis-
tance between the stars. Take, for example, the bright
star Sirius, which has a very faint companion. The
parallax of Sirius is known to be 0*37", and the semi-
major axis of the orbit of the companion around Sirius
is approximately 8'o". Construct a diagram (Dia-
gram LXXXIII) in which Q stands for the Sun and
S for Sirius, and let QS denote the distance of the
Sun from Sirius. Draw QE perpendicular to OS,
and make QE equal to the Earth's distance from the
DOUBLE STARS AND CLUSTERS
213
Sun on this scale. Similarly let SS 7 denote the semi-
major axis of the orbit of the companion about Sirius
on the same scale. Then
Diag. LXXXIII.
the angle ESQ = parallax of Sirius = Q"$f'\
and the angle SQS' = semi-major of orbit = 8 - o." J
From which it follows that SS' : QE = 8'o" : 0-37",
or that the semi-major axis of the orbit is : , or 22
3 /
times the Earth's distance from the Sun. Thus the
linear dimensions of the orbit of the faint companion
around Sirius are known.
Further, the combined mass of the bright star and
its companion can be compared with that of the Sun.
The attraction of the Sun causes the Earth to make
its revolution in one year. The companion of Sirius
takes 50 years to go round Sirius, and its mean dis-
tance from Sirius is 22 times that of the Earth from
the Sun. As we have seen in Chapter III (p. 52),
we can from these data find the sum of the masses of
Sirius and its companion. Calling them m and m',
214 ASTRONOMY
and that of the Sun M, we have the equation
m + m' /22\ 3 / i \ 2
~ ' = 4'3> or t " e sum * "* masse s is
4'3 times that of the Sun.
In the case of Sirius and a number of other double
stars it is possible to compare the masses of the
primary star and of its companion. This, however,
requires other observations than the relative move-
ments of companion and primary afforded by double
star measurements. In these measures the companion
is considered as describing an ellipse about its prim-
ary, whereas both the primary star and companion are
describing ellipses about their common centre of
gravity. Before the companion of Sirius was dis-
covered it was known to exist, because Sirius was seen
to have a slightly irregular movement in the sky. In
addition to its proper motion in a straight line, it was
seen to be describing a small ellipse in 50 years. In
1844 Bessel was convinced that the explanation of this
elliptic movement of Sirius was to be attributed to an
invisible but massive companion. In 1862 Mr. Alvan
G. Clark, while testing an object glass of 18 inches
aperture by examining the appearance of Sirius with
it, discovered this faint companion. It was only of
the tenth magnitude, and thus 16,000 times fainter
than Sirius, and at the time of discovery was 10"
distant. When the meridian observations which had
indicated the movement of Sirius about its centre of
gravity were investigated in 1864 by Dr. Auwers, it
DOUBLE STARS AND CLUSTERS 215
was found that the bright star described an ellipse
whose semi-major axis was 2'33". Thus in Diagram
LXXXIV, where S , ? ,
is Sirius, S' the ^
Diag. LXXXtV.
faint companion,
and G the centre of gravity, SG = 2'^" and SS'
8'oo", and therefore S'G = 5 "67". The mass of the
faint companion is therefore greater than that of
Sirius in the proportion of 5'6j" to 2*33", or about
2\ to i. Taking the total mass to be 4/3 times that of
the Sun, we see that Sirius itself is about 1*2 times the
mass of the Sun, and the dark, almost invisible, com-
panion is rather more than 3 times. In other cases
where it has been possible to compare the bright and
faint components of a double star, the faint component
has usually been found to be the more massive.
Spectroscopic Binaries. Sirius and Procyon were
shown to have invisible companions from their vari-
able motion on the face of the sky. In a large number of
cases stars which are apparently single have been shown
to be double by variations disclosed by the spectro-
scope in the velocity of the star to or from the Earth.
Let us consider the simplest case. Suppose there are
two stars, S and 5 (Diagram LXXXV), which are
describing circles about their centre of gravity, G, and
suppose the Earth to be in the same plane as their
orbit in the direction GE, but so far away that the
stars appear single in the largest telescope. When
the star S is at S lf S 2 , S 3 , S 4 , the companion will be
2l6
ASTRONOMY
at 5 X , s 2 , s 3 , s 4 , so that the line Ss always passes
through G. Further, for simplicity, let us suppose
that G is at rest relative to
ffc, the Earth. When the star
S is at S t it is moving
away from the Earth, and
the lines of its spectrum
will be shifted from their
normal position towards the
red end of the spectrum,
and from the amount of this
shift the velocity of S can
be determined. At the same
time the star s is at s 19
and moving towards the
Earth, the lines of its spec-
trum will be shifted towards the violet from their
normal positions by an amount which measures the
velocity of 5. When S is at S 3 , and 5 is at s 3 the con-
ditions will be reversed. At the intermediate points
when S is at S 2 or S 4 , and 5 at s 2 or s 4 , the stars
have no velocity to or from the Earth, and the lines
in their spectra will not be displaced from their normal
positions.
When the spectrum of a binary star which is seen
single in the telescope is photographed, the result is
the same as if the spectra of two separate stars
had been photographed on the same plate. It may
happen that S is a bright star and s a very faint one,
DOUBLE STARS AND CLUSTERS 217
in which case the spectrum of s will not be recorded.
Again, it is possible that S and 5 may be two stars
of nearly equal magnitude and similar spectra, in
which case, owing to the shift of the lines due to the
motion of the stars, lines in the spectra will sometimes
appear doubled. A third possibility is that S may be a
star giving an entirely different spectrum from s, in
which case two separate spectra are superposed. But
in all cases photographs of the spectrum of a binary
star, taken when the components are in different rela-
tive positions, will show displacements of the lines
due to the varying velocities of the stars in the direc-
tion of the Earth.
A large number of stars have proved to be spec-
troscopic binaries. Some have been discovered from
the composite character of their spectra, which
looked like the spectra of stars of two different types
on the same photograph. Others have been dis-
covered in the course of measurements of the positions
of lines in spectra made with the intention of deter-
mining the velocity of the star to or from the Earth.
The spectra obtained on different days have given
different results, and subsequent photographs have
shown the changes to be regular, and such as can be
accounted for by supposing the stars to be binaries.
The spectrum of Mizar (C Ursae Majoris), a bright
star of the Great Bear, was found by Miss Maury to
have the K line (due to calcium) double on two photo-
graphs taken at Harvard in 1887 and 1889, but
218 ASTRONOMY
single on other photographs. Examination of 72
photographs showed that the changes in the spectrum
occur at regular intervals, and were explicable if
Mizar consists of two stars which revolve round one
another in 104 days. Further, the relative velocity
of the two stars was found to be about 100 miles per
second. Assuming them to be of equal mass, and
that the plane in which they move passes through
the Earth, the two components are 140 million miles
apart, and their combined mass is 40 times that of
the Sun.
In 1890 Vogel found that Spica was a spectroscopic
binary. In this case the star consists of the bright
star we see and a dull but massive companion. The
displacements of the lines in its spectrum from their
normal positions are completely explained on the
assumption that Spica revolves about its companion
in 4 days approximately with a velocity of 57 miles
a second if the plane of the orbit passes through the
Earth. If the orbit is inclined to the direction joining
the Earth and star, as it is certain to be to a greater or
less extent, the velocity will be greater than 57 miles a
second, as the spectroscope only appreciates that part
of a star's velocity which is directed to or from it.
Another interesting spectroscopic binary is Capella.
In i goo Prof. Campbell at the Lick Observatory, and
Prof. Newall at Cambridge, independently found that
Capella consists of two stars, one like the Sun in
type of spectrum, and the other like Procyon. These
DOUBLE STARS AND CLUSTERS
219
two stars revolve about one another in a period of
104 days.
The following example, a Carinte, discovered by
Mr. Wright in the course of a Lick Observatory ex-
pedition to the southern hemisphere, is a fairly typical
case. From photographs of the spectrum of this star
on 25 nights the following velocities were found in
kilometers per sec. (i km. = f mile)
Date.
1904 Feb.
1505 Jan.
Feb.
Feb.
Mar.
1906 Mar.
1907 Jan.
Feb.
29.67
30.68
9.64
22.62
7.58
30-58
iS-79
19.81
21.76
25.81
26.79
2-75
5-77
Vel. Date.
+ 57
1907 Feb. 6:67
+ 33' 2
+ IO'O
19-73
Mar. 2.74
I *2
4-74
14.63
16.63
+ 39 'o
J 9-57
+ 3 1 ' 1
+ 44*4
+ 18-6
+ 31-2
23-53
24.58
Apr. 30.49
May 1.49
11.48
Vel.
2*O
1-9
4i '3
167
257
44 '3
5'2
40-8
28-8
20'4
+ 57
+ l6'2
From these figures the period during which these
fluctuations occur is found to be 6*744 days; the velo-
city of the centre of gravity of the system away from
the Sun is + 23*3 km. per sec. ; and the velocity of
the bright component of the star varies from o to
+ 43 km. per sec.
In the last few years a very large number of spec-
troscopic binaries have been discovered, especially
with the large telescopes of the Lick and Yerkes
Observatories, with their spectroscopes of great re-
220 ASTRONOMY
solving powers. In 1898 thirteen spectroscopic bi-
naries were known. The number discovered to the
end of 1905 was 140, and since that date the number
has been nearly doubled. Prof. Campbell found one
star in seven of those studied at the Lick Observatory
to be a spectroscopic binary. The larger proportion
of one in three was found by Prof. Frost at the Yerkes
Observatory in the particular class of stars he was
studying. In most cases the spectrum of only one
component is visible, so that these binary stars like
Sirius consist of a bright star with a dull but massive
companion.
Clusters. It has frequently happened in the course
of double star observations that one of the two com-
ponents has itself been found to be double. For
example, y Andromeda was found by Herschel to
consist of two stars of magnitudes 2'5 and 5*5 about
10" distant. Otto Struve found that the fainter com-
ponent, when examined with a very large telescope,
was itself a very close double star. In this way we
have become acquainted with systems consisting of
3 or 4 stars. But the sky contains groups of stars
on a much grander scale. The Pleiades are one of
the most familiar examples. In this collection of
stars six are bright enough to be seen by most
people with the naked eye, and six or seven more
are visible to persons of specially keen sight, while
a great many more are shown by an opera glass or
small telescope. It is found that the brighter stars
DOUBLE STARS AND CLUSTERS 221
among the Pleiades, and many of the fainter ones,
have the same proper motion of 7" a century. They
therefore form a group of stars moving together in
space, and are not a mere optical group because they
happen to lie nearly in line as seen from the Earth.
The brighter stars have similar spectra, and the whole
group is found by photographs taken with long
exposures to be involved in a faint nebula.
In Sir John Herschel's catalogue of nebulae in 1864
he includes no globular clusters of stars. In these
clusters the stars are
seen much nearer to-
gether than in the
Pleiades. With a
small telescope they
cannot always be
separated, and the
cluster might be
taken for a nebula ;
but with a larger
telescope they are
resolved into separ-
ate stars. Diagram
LXXXVI, from a
photograph with the
, . . Diag. LXXXVI. Cluster of Stars.
great refractor of the
Yerkes Observatory, taken by Prof. Ritchey, shows
the appearance of the cluster in Pegasus. The stars
are small and concentrated in the centre. The num-
222 ASTRONOMY
her of stars in some of these clusters have been
counted. In a photograph of the southern cluster
round w Centauri, Prof. Bailey found more than 5000
stars in a small area occupying about as much space
as the Sun or Moon in the sky. Till we know the
distance of the cluster it is impossible to say how far
the stars in it are apart.
A curious feature about the globular clusters of
stars is the large percentage of short period variables
(see Chapter XI). Thus in the cluster illustrated
above out of 500 stars 91 are variable.
In 1908 Prof. Boss pointed out that about 40 bright
stars in and near the constellation Taurus form a
small globular cluster, which is sufficiently near for us
to see inside, so to speak, and learn its dimensions.
Investigations of proper motions prove that these 40
bright stars, of magnitudes 4*0 to 6'5, are moving
towards one point in the sky. Diagram LXXXVII
shows the direction of motion, the length of the
arrows indicating the angular distance travelled in
50,000 years. Apparent motion towards one point
in the sky results from parallelism in the actual
paths of the stars. The amount of proper motion,
that is, projected angular motion on the face of the
sky, is known for each star, and for three of them
the velocity in the line of sight is also known. These
facts are sufficient to show that these 40 stars
are all moving in parallel directions towards a
point RA 6h. 52m.; Dec. +7 with a velocity of
DOUBLE STARS AND CLUSTERS
223
28^ miles a second, and to determine the distance
of each star from the Earth. The stars form a
cluster of roughly globular shape. The centre of
S/sr'- Stream in Taurus.
Diag. LXXXVII.
the cluster has a parallax of about o'O25", correspond-
ing to a distance of about 8 million times the Sun's
distance. The distance of outlying stars in the cluster
from one another is about 2 million times this dis-
tance, so that the cluster is packed about as loosely
as the Sun and its nearest stellar neighbours. The
cluster was nearest to the Sun about 800,000 years
ago, when it was at half its present distance. It is
moving rapidly away, and will gradually assume
the more compact appearance of a globular cluster,
which in 65 million years will be only 20' in diameter,
and consist of stars of Qth to I2th magnitude. Be-
sides these 40 stars, 50 fainter stars of magnitudes
224 ASTRONOMY
6' i to 7*5 probably belong to the cluster, and doubt-
less some still fainter ones will be discovered. To
confirm Prof. Boss's results, the velocities in the
line of sight of more stars in the cluster are being
determined at the Yerkes Observatory. The curious
fact has appeared that the stars are of Secchi's first
type (hydrogen) and that 8 out of the 14 examined
have proved to be spectroscopic binaries.
CHAPTER XI
VARIABLE STARS AND NEW STARS
Variable Stars. The discovery was made in 1596
by Fabricius that the star o Ceti varies in brightness.
Sometimes this star is easily visible to the naked eye,
but at other times it is as faint as the eighth or ninth
magnitude, and can only be seen with a telescope.
Other variable stars were gradually discovered, and
in 1844 Argelander published a catalogue giving
particulars of the 18 stars which were then known to be
variable and urged the importance of studying these
bodies in detail. A great deal of attention has been
given to variables since this date, and in recent times
the information acquired by studying the variation of
their light has been supplemented by that afforded by
the spectroscope. The number of stars known to be
variable has increased greatly, and in 1907 Prof.
Pickering of Harvard published a catalogue of 3748
of these bodies. He divides variable stars into five
classes, and though the distinction between them is
not absolute, this subdivision is rendered necessary
by the well-marked differences between them.
Eclipsing Stars. Algol or /? Persei is the best known
type of this class. Its changes of brightness are
Q 225
226
ASTRONOMY
regular and are repeated after a period of 2 days 20
hours 49 minutes.
For 2^ days the brightness of the star remains
constant (2^3 mag.); in 4^ hours it falls to 3*5 mag.,
and in the next 4^
hours returns to 2*3
mag. When at its
faintest Algol shines
tl
f Diag. LXXXVIII.
With Only one third of Light changes of Algol.
the light it has in its
brightest phase. These variations in magnitude are
shown graphically in Diagram LXXXVIII, from
which the magnitude at any time between January
3 d. 3 h. and January 5 d. 25 h., 1910, may be inferred.
Diag. LXXXIX.
Goodricke, who discovered the law of change in the
brightness of Algol, suggested that the star possesses
a dark companion, which periodically intervenes be-
tween Algol and the Earth and cuts off a part of the
light. Diagrams LXXXIX and XC illustrate exactly
how this occurs. In Diagram LXXXIX the observer
VARIABLE STARS AND NEW STARS 227
is nearly in the plane of the orbital motion of the t\vo
stars, as is really the case, while Diagram XC shows
the plan of the orbit. A is the bright star; B, C, D,
E, F, are the dark star in different positions. When
the dark star is at B, C or D part of the light from
A is intercepted.
In 1889 Prof. Vogel examined Algol spectroscopic-
ally, and completely established the fact that the varia-
tion of light is caused by a dark eclipsing satellite.
If the bright star Algol has a dark companion they
will revolve about their common centre of gravity.
After the dark star has passed in front it will be
moving away from the Earth and the bright star
towards the Earth, and the maximum velocity will be,
if the orbit is circular, one quarter of the entire period
of revolution, or 17 hours after the epochs of
minimum brightness. Similarly the maximum velo-
city of the bright star from the Earth should occur
17 hours before the epochs of minimum bright-
ness. The spectroscope confirmed these surmises,
and showed that 17 hours before mid-eclipse Algol
is moving towards the Sun with a velocity of 39
kilometres per second, and 17 hours after mid-eclipse
from the Sun with velocity 47 kilometres per second.
These figures show that Algol and its companion are
moving from the Sun with a .velocity of - - or 4
kilometres per second, and the velocity of Algol in its
orbit is - -or 43 kilometres per second, and, as
Q 2
228 ASTRONOMY
we have seen, the time of describing the orbit is 2 days
20 hours 49 minutes.
From the loss of light experienced at mid-eclipse,
the ratio of the diameters of the bright and dark stars
may be inferred. From the ratio of the period of the
eclipse to the period of revolution, the sum of the
radii of the stars can be compared with the distance
between their centres. Since the bright star is moving
43 kilometres or 28 miles a second and takes 2 days
20 hours 49 minutes, or nearly 250,000 seconds, to
complete its circle about the centre of gravity of the
two bodies, the radius of this circle w ? ill be rather more
than one million miles. It is necessary now to make
some assumption about the relative masses of these
two stars, and Vogel, taking them to be of equal
density, concludes that Algol is one million miles in
diameter or 1*2 times the size of the Sun, the com-
panion 800,000 miles, or about the size of the Sun, and
that the distance between the centres is 3,200,000 miles.
Between 30 and 40 variable stars resemble Algol.
The period of variation is generally short, less than
5 or 6 days, and the time of eclipse lasts for some
hours. The bright and dark star are very close together
in comparison with their diameters, as would naturally
be expected, for otherwise the chance of the Earth
being near enough to the plane of the orbit to witness
eclipses would be very small. A remarkable feature
in all these stars is their small mean density. In the
case of Algol, for example, this is not more than \
of the density of water.
VARIABLE STARS AND NEW STARS 229
Short-period Variables. - - The characteristic of the
variables whose periodic changes of brilliancy can be
explained by the revolution of a bright and dark star
around one another is the maintenance of the maxi-
mum brightness for a large part of the whole period.
The stars belonging to the second class change their
light continuously. Sometimes in a complete period
there are two maxima and two minima, sometimes
only one. The changes of brightness generally occur
in a space of less than 10 days and very rarely take
more than one month. At least 60 or 70 variables are
known to belong to this class. The three stars (3 Lyrae,
5 Cephei and C Geminorum may be taken as examples.
/3 Lyrae goes through its changes in 12^9 days, having
two maxima of magnitude 3'4, a primary minimum of
magnitude 4' 2, and a secondary one of magnitude 3*9.
Its four phases of increasing and decreasing bright-
ness are approximately equal. The variability of the
star has been known since
is difficult to interpret
1784. The spectrum
owing to the juxta-posi-
tion of bright and dark
lines and also on account
of its variability. The
changes which the spec-
trum undergoes have the
same period as the light- variation. Some of these
changes are explicable on the hypothesis that
two stars are revolving round each other. From
a very elaborate investigation of the variation of
Diag. XCI.
Light changes of /8 Lyrre.
2 3 o ASTRONOMY
magnitude and changes in the position of certain lines
in the spectrum observed by Prof. Belopolsky and Sir
N. Lockyer, Prof. Myers of Indiana has deduced that
the star consists of two large gaseous bodies very near
together which revolve round one another. They are
not quite spherical but owing to mutual gravitation
are spheroidal. The smaller is 2\ times as bright
as the larger and half as massive. The distance
between their centres is 50 million miles, and the orbit
they describe about one another is nearly circular.
As the Earth is nearly in the plane of the orbit, in
the course of a revolution first one body and then
the other is partly hidden and the dimensions given
are such as will account numerically for the changes
of brightness. The spectroscope shows the stars to
be gaseous, but Prof. Myers' figures give the astound-
ing result that the mean density of the system is a little
less than that of air.
S Cephei. The light curve of 8 Cephei is very
typical of short-period
variables. The period
of the light changes is 5
days 8 hours 47 minutes
40 seconds, but the time
taken for the brightness
to rise from the mini-
Diag. xcil. mum to the maximum
Light changes of 8 Cephei. . r
is much shorter than for
the fall. In 1894 tn i s star was shown by Belopolsky
*
VARIABLE STARS AND NEW STARS 231
to be a spectroscopic binary, whose changes in velocity
had the same period as the light changes. The
spectrum of only one component is shown. The star
is found to be moving in a very eccentric orbit, and if
it exhibited no variation of light would be set down
as a spectroscopic binary consisting of a bright and
dark star. But the changes of light cannot be ac-
counted for in this way, for it is found that the
minimum brightness occurs a day before the time
when the two stars are in line as seen from the Earth.
The light variation cannot, therefore, be explained as
due to an occultation of one star by another, and no
satisfactory explanation has been given.
C Geminorum. This star goes through its phases
in 10 days 3 hours 41 minutes 30 seconds. At its mini-
mum the magni-
tude is 4'5 and
at maximum 37.
The time during
which the bright-
ness increases is
almost equal to
the time during
Diag. XCIII.
Light changes of Geminorum.
which it decreases. Forty-four
photographs of the star's spectrum were taken at
the Lick Observatory between November 11, 1898
and February n, 1900. These showed that the star is
a spectroscopic binary, of which one component is
bright and the other dark. The changes of velocity
occur in the same period as the light changes.
232 ASTRONOMY
From the measures of velocity the orbit of the star
was determined, but as in the case of 8 Cephei the
time when the two stars are in line as seen from the
Earth does not coincide with the time when the bright-
ness is a minimum. The light variation does not
therefore result from an eclipse. Some peculiarities
in the velocities derived from the spectra suggest that
as the dark and bright body are very close together,
large tidal effects may be produced in the atmosphere
of the bright star, and that the explanation of the light
changes is to be looked for in causes of this nature.
In the variables of short period it is clear that we
are dealing with bodies of large size and small density.
There can be no doubt of their essentially binary
character. The two components appear to be very
close together and may in some cases be joined by a
neck. Possibly these variables present to us different
stages in the segmentation of nebulous matter which
is forming into two stars, the Algol class showing a
further stage of this development. Such a view is,
however, extremely speculative, as very little is known
of the dynamical conditions to which such nebulous
matter would be subject.
Long-period Variables. When a star is variable in
a short period of less than a month, we have seen
that the explanation is probably to be looked for in
the rotation of two very close bodies. There are a
large number of stars whose period of variability is
much longer. More than 300 are known whose
VARIABLE STARS AND NEW STARS 233
periods lie between 200 and 400 days, and a con-
siderable number beyond these limits. These are all
classified as variables of long period. The difference
in magnitude between these stars at their brightest
and faintest is often very great a difference of 5
magnitudes or a variation of light in the proportion
of 100 to i being not -at all unusual. Generally speak-
ing, the longer the period the greater the difference
between the extreme magnitudes. These stars do not
go through their variations with the same regularity
as the variables of short period. The brightness at
maximum varies from time to time, and the length
of the period is not exactly the same from each maxi-
mum to the next. Many of these stars are red or
reddish.
The most famous star of this class is o Ceti, or Mira
Ceti as it was called by Hevelius. In about 332
days it increases in brightness from below the ninth
magnitude to about the second and then diminishes
again. Its variations have been watched for 200
cycles, and its period has been seen to vary from 320
to 370 days, but no law has been discovered for these
changes. The greatest brightness the star attains also
varies considerably. In 1779 Herschel saw it rise to
magnitude 1*2; in 1868 it was only of magnitude 5'6
at maximum; in 1897 ^ reached the third and in 1905
the second magnitude. Similarly its brightness at
minimum has varied from 8'o mag. to 9*5 mag.
The spectrum of Mira Ceti has been studied by
234 ASTRONOMY
many astronomers. It consists of bright lines and
dark bands. The dark bands are those found in stars
of Secchi's third type, due to titanium oxide, while the
bright line spectrum contains lines due to hydrogen
and some metallic lines. The relative intensities of
the bright lines vary in different parts of the star's
cycle. There are no changes in the spectrum that
suggest orbital motion. It would seem that there are
periodically great outbursts of incandescence in the
star itself. The changes which occur in long-period
variables bear a resemblance to the periodic changes
in the amount of the Sun's area covered with spots.
The sun-spot period is long about 1 1 years and
irregular. Sun-spot and long-period variables show
the banded spectrum of titanium oxide. These sug-
gest that long-period variables may be stars which are
periodically largely covered by spots.
New Stars. Passing over another group of variable
stars in which the light fluctuates in an altogether
irregular manner we come to a very remarkable class
which bear some resemblance to variables of long
period. These are the ne-w stars. Hipparchus, Tycho
Brahe, and Kepler all witnessed with astonishment
the appearance of new stars in the sky. Two were seen
in the seventeenth century, and eight in the nineteenth,
while in this century two have been found, one by Dr.
Anderson at Edinburgh, and one photographically by
Prof. Turner at Oxford. The new stars from which
most has been learned are Nova Aurigae of 1892 and
VARIABLE STARS AND NEW STARS 235
Nova Persei of 1901, both of which were discovered
with the naked eye by the same amateur astronomer,
Dr. Anderson. Nova Persei has been observed
with larger telescopes and spectroscopes, but as far
as we know its history is closely like those of pre-
vious Novas. At discovery its magnitude was 2'8, or
about the brightness of the seven stars of the Great
Bear. The time of discovery was 2h. 40111. on the
morning of February 22. Twenty-eight hours previ-
ously Mr. Stanley Williams photographed the same
part of the sky, and although the photograph showed
stars fainter than the twelfth magnitude there was no
sign of a star in the position Nova Persei afterwards
occupied. Thus the light of the star had increased
at least 4000 times in 28 hours. Its brightness in-
creased for another day till it became 10 times as
bright as at the time of discovery. It then declined
till at the end of. February it was no brighter than on
February 22, at the end of 1901 it was of magnitude
7'o, and at the end of 1902 of magnitude io'o.
Before the star reached its maximum brightness its
spectrum was examined and found to be of the Orion
or helium type. The light from the star had passed
through an absorbing atmosphere of hydrogen and
helium. The next night its character had entirely
changed and consisted of bright lines associated with
dark lines on the side towards the violet. Some of
the bright lines were due to hydrogen and were in
the normal position, but the dark lines were shifted
236 ASTRONOMY
as much as if the absorbing atmosphere which pro-
duced them were approaching the Earth with a
velocity of 1000 miles a second. In addition a few
narrow lines due to sodium and calcium were dis-
placed slightly towards the red. The same displace-
ment was found later when the spectrum had changed,
and showed conclusively that the star was moving
from the Sun with a velocity of 5 miles per second.
The large displacements of the dark lines is most
easily explained on the assumption of a great explo-
sion by which hydrogen was driven away from the
star with great velocity. The spectrum of the star
changed still further till July when the chief nebular
line was seen, and in August and September it was
very similar to the spectrum of a planetary nebula.
Attempts were made to determine the parallax of the
star without success till in the autumn of 1901 Prof.
Max Wolf made the surprising discovery that the
star was surrounded by a nebula. Professors Ritchey
and Perrine of the Yerkes and Lick Observatories
obtained photographs by giving long exposures with
large reflecting telescopes. Two photographs taken a
fortnight apart showed the nebula to be moving. This
was clearly shown by comparing the position of the
nebula with the stars near it in two photographs taken
by Prof. Ritchey. Further photographs led to the
conclusion that the surrounding nebula had been
expanding continuously since the appearance of the
star. A very interesting explanation was given by
237
Prof Kapteyn. He postulated the existence in space
of nebulous matter, stationary and non-luminous.
This matter became visible to us by the reflection it
Diag. XCIV.
Nebula surrounding Nova Persei (Rilchey).
sent of the light from the Nova. As the light travel-
ling out from the star reached ever widening circles of
nebulous matter it illuminated them. More than this,
as we know that light travels 186,000 miles a second,
it was possible to infer the distance of the Nova from
the rate at which the luminous rings spread out. This
distance is found to be about 20 million times the
238 ASTRONOMY
distance of the Earth from the Sun, from which it fol-
lows that at its greatest brilliancy Nova Persei was
8000 times as bright as the Sun. By exposing a photo-
graphic plate on several nights for 36 hours alto-
gether in a little spectroscope fitted on to a large
telescope, Prof. Perrine was able to obtain the
spectrum of this faint nebula and found it to be
similar to the spectrum of the star in its early stages.
In this way it was demonstrated that the nebula shone
by reflected light, just as the identity of the lunar
and solar spectra could be used to prove that the
moon's light is reflected Sun-light.
Only a very hypothetical explanation can be given
of the phenomena of new stars. A collision between
two bodies is a natural supposition. But the spectro-
scopic observations do not point to two bodies after
the moment of collision. Apparently some conditions
have given rise to a great outburst of hydrogen and
helium gas from the interior of a star. The possibility
of such an outburst is remarkable whatever the excit-
ing cause may have been.
The appearance of such a bright new star as Nova
Persei is a very rare phenomenon. The photographs
of spectra taken at Harvard College revealed five
objects between 1893 and 1899 with the bright and
dark line spectrum characteristic of new stars. Prob-
ably new stars of small brilliancy are not infrequent
occurrences.
CHAPTER XII
THE: SIDEREAL UNIVERSE
WE have seen in previous chapters what varied
knowledge it is possible to acquire about the stars.
The distances of a few stars have been determined,
and the average distances of large numbers can be
approximately fixed. When the distances are known,
the velocities can be determined and the luminosities
of the stars compared with the Sun. By the study of
double stars we are enabled in some instances to deter-
mine the masses of stars, and from variable stars the
sizes and densities. The spectroscope has taught us
something of the chemistry of the stars, and of their
temperatures and physical conditions.
In these different ways the stars are shown to be
bodies like the Sun scattered in space at distances
apart comparable with 30 or 40 million million miles.
The Sun is the body with which we can best compare
them. Stars may be much bigger or smaller, denser
or much less dense, more or less luminous. Many are
double and some triple or quadruple. Planets may
circulate round some of them ; on this point, however,
we have no evidence, but only analogy for a guide.
Sidereal astronomy, as we have seen, is divided
239
2 4 o ASTRONOMY
into two branches. One of these concerns itself
with the physical state of the stars, and seeks to
describe completely these states in the different stages
of a star's history, and to follow the life of a star
through its whole course. The other branch of
sidereal astronomy is of a more geometrical character,
and is concerned to describe the universe as it now
is, to determine whether it is finite or infinite; if finite,
to determine its limits and the number of stars within
them ; if infinite, to peer as far as possible into its
infinity. These two departments cannot be kept
entirely separate, as it may, and does, happen that
stars of particular kinds or in a particular stage of
development have special geometrical relationships.
Hydrogen stars, for example, are further from the
Earth than those of solar type.
When the stars are looked at as a whole, the most
striking feature among them is the existence of the
Milky Way, which may be seen on a clear night in
winter reaching across the sky as a band of faint light.
It stretches right round the celestial sphere, dividing it
into equal parts. When examined with a telescope,
it is found to be full of stars. The illustration (Dia-
gram XCV) shows part of it as photographed by
Prof. Barnard, and brings out the remarkable features
of the dark rifts within it, or places void of stars.
The Milky Way thus seems to be not one but a
number of agglomerations of stars. It certainly con-
tains a vast number of faint stars. Does it also con-
THE SIDEREAL UNIVERSE
241
tain bright ones, or are the bright ones apparently in
it much nearer to the Sun and merely seen projected
against it ? An answer can be given to this question
by counting the number of bright stars in the dark
Diag. XCV.
Part of Milky Way (Barnanf).
rifts and comparing the result with the number in an
equal area where the faint stars are thick. In this way
it is found that a considerable number of bright stars
really belong to the galaxy.
242 ASTRONOMY
The physical characteristics of the stars show some
relationship to the Milky Way. Speaking generally,
the stars in it are blue, and the remarkable Wolf-
Rayet stars are wholly confined to it. New stars, too,
usually appear in the Milky Way.
When the number of stars of given magnitudes in
different parts of the sky is counted, it is found that
the density or number per square degree increases
with fair uniformity from the poles of the Milky Way
to the Milky Way itself. But this increase in density
is much more pronounced for the faint than for the
bright stars. If we take stars brighter than 5*5 mag.
there are on the average 4*63 in every 100 square
degrees near the pole of the Milky Way and 9'oy in
the Milky Way itself, or a proportion of i : i'g6. For
stars of magnitude 8'5 to g'5 the numbers are 235 and
595, and the proportion i : 2'53. For stars of magni-
tude u'5 to i2'5 the numbers are 3330 and 15,400,
and the proportion i : 4*62. The proportion increases
very rapidly for higher magnitudes. Moreover, the
numbers increase gradually as the Milky Way is
approached and do not suddenly alter, as if the Milky
Way were entirely distinct from the other stars.
When we consider proper motions, and these are
a fair index of the average distances of the stars, it
is found that stars of large proper motion are dis-
tributed pretty equally in all directions. Prof. New-
comb points out that the number of stars whose
proper motion is greater than 5" a century is no
THE SIDEREAL UNIVERSE 243
greater in the Milky Way than at a distance from it.
Now in a century the Sun moves a distance equal to
400 times its distance from the Earth, and will there-
fore produce a movement of 5" in a star whose parallax
is T^hr" or o'oi25", which corresponds to a distance of
16 million times the Sun's distance. The Milky Way
therefore lies beyond this limit. This is to be
taken as an example of the method of reasoning, as
the numerical result is very far less than the probable
distance of the Milky Way.
As the Milky Way divides the sky into equal parts,
the Sun is situated in its plane. We do not know-
how far it may be from the centre, for as yet the dis-
tance to the Galaxy in different directions has not been
determined. It would seem that the universe of stars
extends much further in the direction of the Milky
Way than in that perpendicular to it. Its boundary
is irregular, but nowhere nearer than 200 million
times the Sun's distance. Whether the agglomera-
tions which form the Milky Way are near this bound-
ary, or whether we see some stars which are quite
beyond them is as yet unknown. As far as we can
tell, the number of stars, though very great, is finite.
But there are some indications that light is absorbed
in its passage through space, and our conclusions
must be very guarded. We are obliged to say with
Laplace, "Ce que nous connaissons est pcu de chose,
ce que nous ignorons est immense."
INDEX
Aberration of light, 94-96
Achromatic object glass, 70
Algol, 225-228
Almagest, Ptolemy's, 28-29
Apse, 22
Calendar, 5
Cavendish experiment, 61-62
Chemistry of stars, 193-200; of
sun, 109-1 12
Chromosphere, sun's, 116-119
Circles, divided, 65-67, 77
Clocks, 65
Clusters of stars, 220-224
Copernican system, 30-37
Comets, 51, 149-157, 160-161
Corona, sun's, 119-121, 128
Declination, 63-64
Density, of earth, 61-62 ; of
sun, 101 ; of planet?, 133 ; of
Algol, 228 ; of ft Lyne, 230
Distance of moon, 26-28
of planets, 43
of stars, 170-179, 187-
190
of sun, 28, 85-99
Diurnal movement of stars,
9-13, 30
movement of sun, 2-4
rotation of earth, 30-
3i
Doppler's Principle, 124
Double stars, 208-215 ! spectro-
scopic, 215-220
Dusky layer round the sun,
113-114
Earth, density, 61-62 ; shape,
49 ; size, 26
Eccentricity of earth's orbit, 22
Eclipse of moon, 18-19, 26-27 ;
of sun, 17-18
Eclipsing stars, 225-228
Ecliptic, 1 5
Ellipse, 42, 52
Elliptic motion, 42, 46-47
Epicyclic movement, 21, 33
Equatorial mounting, 78-79
Equinoctial, 16
Eros, 91-93
Fixed stars, 9-13, 164-165
Galileo, 37-40, 45
Granulation of sun's surface,
114-115
Gravitation, 45-62, 98-99
Halley^s comet, 56-58
Heliometer, 81-82
Hipparchus, 21-25, 26-27
Hyperbola, 52
Jupiter, 38, 130, 132, 133, 135,
136, 144-146
Kepler's Laws, 42-44
Lens, 67
Light, aberration of, 94-96
245
246
INDEX
Light, velocity of, 93-94, 96-97
Luminosities of stars, 191-192
Magnitude, stellar, 166-168
Mars, 130, 133, 134-135
opposition of, 86-88,89-91
Mass, determination of, 52-53
of earth, 60-62
of planets, 132-133
of stars, 213-215, 228,
230
of sun, 101
Mercury, 34-35, 130, 131, 133,
134, 140
Meridian, 64
Meteors, 157-161
Metoris cycle, 8
Micrometer, 77, 80
Mi iky W 'ay, 240-243
Minor planets, 130-131
Month, 7-8
Moon, distance of, 26-28
eclipses of, 18-19, 26-27
features 0^37-38,1 46- 1 48
history of, 163
movement of, 7, 22-23,
58-60
phases of, 6
Motion in line of sight, 185-187
Movement of planets among the
stars, 19-21, 33-35
Nebulce, 201-207
Nebular hypothesis, 161-163
Neptune, 56, 130, 132, 133, 134,
139, Hi, H2
New stars, 234-238
Newton, 46-54, 69, 71
Number of stars, 168-170
Parabola, 52
Parallax, solar, 86-93
stellar, 170-179
Phases of the moon, 6-7
Precession of the equinoxes, 23-
25, 50-51
Principia, Newton's, 54
Prominences, solar, 116-119
Proper motions, stellar, 179-185
Ptolemy's Almagest, 28-29
Radiation, solar, 102-103
Reflecting telescope, 71-73
Refracting telescope, 67-7 1
Revolution of earth round sun,
31-33
Right ascension, 63
Rotation of earth on its axis,
30-31, 39
of planets, 133, 134
of sun, 39, 123-126
Saros, 19
Satellites, 134-136
Saturn, 130, 132, 133, 136-138,
141
Schehallien, attraction of, 60-6 1
Shape of earth, 25, 49
Sine of earth, 25-26
of planets, 131-132
of sun, loo-ioi
Solar chemistry, \ 09- 1 1 2
prominences, 116-119
radiation, 102-103
spectru m, 110-112
Spectra, different kinds of, 108,
109
of comets, 153, 157; of
nebulae, 201-202, 204;
of planets, 141, 142 ;
of stars, 194-200 ; of
sun, 110-112
Spectroheliograph, 121-122
Spectroscope, 106-109
Spectroscopic binaries, 2 1 5-220
Stars, names of, 165-166 ; cata-
logues of, 1 66 ; light of, 170,
191-192 ; magnitudes, 166-
INDEX
24?
Transit circle, 74-78
Types of stellar spectra, 195-200
Uranus, 130, 132, 133, 138, 139,
141, 142
1 68 ; distance of, 170-179,
187-190 ; velocities of, 190-
191 ; absolute luminosity, 191-
192 ; spectra of, 193-200
Sun, 100-128
Sun's corona, 119, 121-128
distance, 85-99 T , . ,, ...
heat, maintenance of, 103- Variable stars of long period,
232-234
Variable stars of short period,
225-232
Velocities of stars, 190-191
Velocity of solar system, 1 87
Venus, 34-35, 38, 130, 131, 133,
134, 139, 140, 141
transit of, 88-89
105
motion in space, 182-185
temperature, 105-106
spots, 39, H2, 115-116,
126-128
Stability of solar system, 5 5
Telescope, 37, 67-84
Temperature of planets, 139-141
of sun, 105-106 Zenith, 64
Tides, 49-50 Zodiac, 7-16
THE END
RICHARD CLAY & SONS, LIMITEP,
BREAD STREET HILL. E.G., AND
BUNGAY, SUFFOLK.
to
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