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wUh theas-lneh t ri m o pt «t WMMagUm. ins, JumM.

t,J^u.«tN.

AMERICAN 8UIENCE SEJtJES , V'.^.

ASTEONOMY

ron

SOUOOXjS ^IsTID OOIjXjBOBS

/ BY

SIMON "nEWCOMB, LL.D.,

auraiuiiraRD»(T aximoam ■PHmnis ams mautioai.

EDWARD S. HOLDEN, M.A.,

PHOVMBOB IN TBI V. 8, IIAVAIi OBRKBTATOBT.

\eVw ism .nV

NEW YORK
HENRY HOLT AND COMPANY

1879

{

HcNRT Holt & Co.

PRigg or JoHM A. Grat, Aot.,
]8 Jacob Strbbt.

KBW YORK.

I n

PREFACE.

The following work is designed principally for the use
of those who desire to pursue the study of Astronomy as a
branch of liberal education. To facilitate its use by stu-
dents of different grades, the subject-matter is divided into
two classes, distinguished by the size of the type. The
portions in large type form a complete course for the use
of those who desire only such a general knowledge of the
subject as can be acquired without the application of ad-
vanced mathematics. Sometimes, especially in the ear-
lier chapters, a knowledge of elementary trigonometry
and natural philosophy will be found necessary to the full
understanding of this course, but it is believed that it can
nearly all be mastered by one having at command only
those geometrical ideas which are familiar to most intelli-
gent students in our advanced schools.

The portions in small type comprise additions for the
use of those students who either desire a more detailed
and precise knowledge of the subject, or who intend to
make astronomy a special study. In this, &3 in the ele-
mentary course, the rule has been never to use more ad-
vanced mathematical methods than are necessary to the
development of the subject, but in some cases a knowl-
edge of Analytic Geometry, in others of the Differential
Oalculus, and in others of elementary Mechanics, is neces-

PREFAVB.

Biirily presupposed. The object aimed at has been to lay
u broad foundation for furtiier study rather than to at-
tempt the detailed presentation of any special branch.

As some students, especially in seminaries, may not de-
sire so extended a knowledge of the subject as that em-
braced in the course in large type, the following hints are
added for their benefit : Chapter I., on the relation of the
earth to the heavens, Chapter III., on tlie motion of the
earth, and the chapter o!i Chronology should, so far as pos-
sible, be mastered by all. The remaining parts of the course
may be left to the selection of the teacher or student.
Most persons will desire to know something of the tele-
scope (Chapter II.), of the arrangement of the solar system
(Chapter I V. , §§ 1-2, and Part II. , Chapter XL), of eclipses,
of the phases of the moon, of the physical constitution of
the sun (Part II., Chapter II.), and of the constellations
(Part III., Chapter I.). It is to be expected that all will
be interested in the subjects of the planets, comets, and
meteors, treated in Part II. , the study of which involves
no difficulty.

An acknowledgment is due to the managers of the
Clarendon Press, Oxford, who have allowed the use of a
number of electrotypes from Chambers's Descriptive
Astronomy. Messrs. Fauth & Co., instrument- makers, of
Washington, have also lent electrotypes of instruments,
and a few electrotypes have been kindly furnished by the
editors of the American Journal of Science and of the
Popular Science Monthly. The greater part of the illus-
trations have, however, been prepared expressly for the
work.

u i »Hi.- « »|]i.- ^

> been to lay
' than to at-

branch.
, may not de-

as that em-
ing hints are
elation of the
lotion of the
80 far as pos-
} of the conrso
r or student.
r of the tele-
e solar system
.), of eclipses,
onstitution of
constellations
d that all will

comets, and
hich involves

lagers of the
d the use of a
i Descriptive
»nt-makerB, of
instruments,
nished by the
<!e and of the
rt of the illus-
resslv for the

CONTENTS.

PART I.

Introductior .

CHAPTER I.

THB RBLATIOR OF THE EARTH TO THB HBAVENB.

The Enrth— The Diurntl Motion uid the Celestial Sphere — Corra-
■pondence of the Terrestrial and Celestial Spherea — The
Diurnal Motion in different Latitudes— Relation of Time to
the Sphere— Determination of Terrestrial Longitudes— Mathe-
matical Theory of the Celestial Sphere — Determination of
Latitudes on the Earth hj Astronomical Obsenrations—
PiralUx and Semidiameter 9

CHAPTER n.

ABTROHOiaCAL IHBTRTTHBim.

The Refracting Telescope-ReflectingTelesoopes— Chronometers
and Clocks— The Transit Instrument— Graduated Circles—
The Meridian Circle— The Equatorial— The Zenith Telescope
—The Sextant 58

CHAPTER in.

MOTION OF THB BABTH.

Ancient Ideas of the Planets— Annual Revolntlon of the Earth—
The Sun's apparent Path— OS-iqoity of the Ecliptic— The
Senwns »«

CHAPTER IV,

THB FI.A1TRTART KOTIONB.

Apparent and Real Motions of the Planets— GraTltation in the
Heavens— Kbflbr's Laws of Planetary Motion Ill

MMn

viii

aONTBNTS.

CHAPTER V.

UNITKRHAL OBAVITATIOH.

FAOB

NbwtoN'h L»w8of Motion— Froblema of QimvlUtlon—ReBultB of
Uravitation— ReiuarkB on the Theory of QraviUtion 181

CHAPTER VI.

THE MOTION AND ATTBACTION OF THK MOON.

The Mooii'b Motion and PhaBcB— The Sun'B disturbing Force-
Motion of the Moon's Nodes — Motion of the Perigee— Rotation
of the Moon— The Tides 16S

CHAPTER VII.

HCLIFSKS or THK BUN AND MOON.

The Earth's Shadow and Penumbra — EclipseB of the Moon —
Eclipses of the Bun — The Recurrence of Eclipses — Cliaracter
of EclipseB 168

CHAPTER Vra.

THE EARTH.

Mass and Density of the Eartli — Laws of Terrestrial Gravitation —
Figure and Magnitude of the Eartli — Change of Oravitj with
the Latitude — Motion of the Earth's Axis, or PreoesBion of the
Equinoxes 188

CHAPTER IX.

OBUBSTLAIi HBABURBKBNTfl OF XABS AND DIBTANOI.

The Celeatial Scale of Measurement— MeaaareB of the Solar
Parallax— Relative MaaBes of the Sun and Planets 218

CHAPTER X.

THE BBFBAOTION AND ABEBBATION OF LIGHT.

AtmoBpheric Refraction— Aberration uid the Motion of Light 284

CHAPTER XL
OHBONOIjOOT.

ABtronomical Measureb of Time — Formation of Oalendan —
DiviBion of the Daj — Remarks on improving the Calendar —
The Astronomical Ephemeris or Nautical Almanac. . , 245

FAOB

-ResultB of
>n 181

>ON.

ng Force —
B — Rotation
lt»

,he Moon —
—Character
168

ravitation —
(ravlty with
BMion of the
188

iTAlTCT.

the Solar
1 818

lOHT.

f Light 884

MendarB —
9 Calendar —

10. 845

V0NTENT8.

PART II.

TIIE SOLAR SYSTEM IN DETAIL

I.V

aiAPTEU I.

PAOB

Stbiicturk of the Solak System 267

CHAPTER II.

THE HUN.

General Sammarf— The PliotoHphere— Sun-Spots and Pacute—
The Sun'ii Chromospliere and Corona—Bources of the Sun'a
Heat 278

CHAPTER III.

THB IKTBRIOn VhKSVn.

Motions and Aspects —Aspect and RoUtion of Mercury — The
Aspect and supposed Rotation of Venus— Transits of Mercury
and Venus — Supposed intramercnrial Planets 810

CHAPTER IV.
The Moon 886

CHAPTER V.

THE PLANBT MAB8.

The Doscriotion of the Planet— Satellites of Mars 884

CHAPTER VI.
The Minor Planktb 840

CHAPTER VII.

JCFITBR AND HIS BATBI.LITB8.

The Planet Jupiter— The Satellites of Jupiter 848

CHAPTER VIII.

> BATTRN AND HIB BTBTBIC.

Gtoneral Description— The Rings of Saturn— Satellites of Satnm. . 8SS

llil

'ife;.. j --: -K-ffm^^p-.sv''.i

X VQHTKMti.

CHAPTER IX.
Tub PI.ANKT Ukaniis— BatuIIitM of Ursniu. UOa

CHAPTER X.
TiiK Pi.AMvr Nbitonb— Hatellitu of Neptune 800

CHAPTER XI.
Tub Phybioal Constitution of tub Plambts 870

CHAPTER XII.

MBTEORB.

Plionomena and Cauwa of Metoorn — Meteoric Skowera 870

CHAPTER XIII.

COMBTB.

Aipect of CometB— The Vaporous EnvelopeB— Tlie Physical Con-
stitution of Comets — Motion of Comets — Origin of Comets —
Remarkable Comets 888

PART III.

TIIE UNIVERSE AT LARGE.

Introddction *11

CHAPTER I.

THB OOnSTBLIiATIOIIB.

General Aspect of the Heavens— Magnitude of the BUre— The
Constellations and Names of the Stars— Deacriptlon of Con-
stellations—Numbering and Cataloguing the Stars 410

CHAPTER n.

VARIABT'B AKD TBHPOHABT BTAIW.

Stars Regularly Variable— Temporary or New SUrs—Theoiy of
Variable Stars **®

VONTKNTS. «^

(!HAPTKU III.

MIII.TII'I.K MTAIIX.

PAOl

Character of Doable »nd Multlj.k 8tar»-()rbll« ..f Binary KtarH. . 44M

CHAl'TKH IV.

MRBUL/K AND CI.IIMTKUC.

Dlncovory of Nebulie— (naMlflcatlon of Nebulas and Cluatera—
Htar Clu«teni-H|H)ttra of Nebula> and CluHtern-Dlstribuilon
of Nebul* and Cluatera on the Surface of tho Celestial

_ , „ 457

Sphere

CHAl'TEK V.

BPKCTRA or FIXKD ilTARB.

Charactera of Stellar Spectra— Motion of SUra In the Line of Sight. 4fl8

CHAPTEK VI.

MOTIONB AKD DIBTANCKB OF THR BTAR8.

Proper Motlona— Proper Motion of the Bun— Dbtances of the
Fixed Stan ^'^

CHAPTER VII.

CiOIIBTRUCTION 0» THH HBAVRHB *'^

CHAPTER Vlll.

COSMOOONT

Index «»

"'^jfi^'-Tavi'-'^"^-*'.'''^^'''-^"'^''"'""'^" •' ' '"^~~'-'''''^

' ;ieiiiW»;«W«»^«"IMlMratli')M

iiiiiiiiliilliiiiJiMii'HliW

ASTRONOMY,

INTRODUCTION.

AsTROKOMT {pKttrfp — a star, and ko'/ios — ^a law) ia the
science which has to do with the heavenly bodies, their
appearances, their nature, and the laws governing their
real and their apparent motions.

In approaching the study of th the most ancient of thd
sciences depending upon observation, it must be borne in
mind that its progress is most intimately connected with
that of the race, it having always been the basis of geog-
raphy and navigation, and the soul of chronology. Some
of the chief advances and discoveries in abstract mathe-
matics have been made in its service, and the methods
both of observation and analysis once peculiar to its prac-
tice now furnish the firm bases upon which rest that great
g^up of exact sciences which we call physics.

It is more important to the student that he should be-
come penetrated with the spirit of the methods of astron-
omy than that he should recollect its minntisa, and it is
most important that the knowledge which he may gain
from this or other books should be referred by him to its
true sources. For example, it will often be necepaiy to
speak of certain planes or circles, the ecliptic, the equa-
tor, the meridian, etc., and of the relation of the appa-
rent positions of stars and planets to them ; but his labor
will be useless if it has not succeeded in pving him a
precise notion of these circles and planes as they exist in

ASTRONOMT.

the sky, and not merely in the ligures of his text -book.
Above all, the study of this science, in which not a single
step coald have been taken Avithont careful and painstak-
ing observatioB' of the heavens, should lead its student
himself to attentively regard the phenomena daily and
hourly presented to him by the heavens.

Does the sun set daily in the same point of the hori-
zon ? Does a change of his own station afFect this and
other aspects of the sky 2 At what time does the full
moon rise ? Which way are the horns of the young
moon pointed ? These and a thousand other questions
are already answered by the observant eyes of the an-
cients, who discovered not only the existence, but the
motions, of the various planets, and gave special names to
no lees than fourscore stars. The modem pupil is more
richly equipped for observation than the ancient philoso-
pher. If one could have put a mere opera-glass in the
hands of Hipparohus the world need not have waited two
thousand years to know the nature of that early mystery,
the Milky Way, nor would it have required a Galilbo to
discover the phases of Venus and the spots on the sun.

From the earliest times the science has steadily progress-
ed by means of faithful observation and soimd reasoning
upon the data which observation gives. The advances in
our special knowledge of this science have made it con-
venient to regard it as divided into certain portions, whioh
it is often convenient to consider separately, although the
boundaries cannot be precisely fixed.

SphArioal and Praotiottl Astronomy. — ^First in logical
order we have the instruments and methods by which the
positions of the heavenly bodies are determined from obser-
vation, and by which geographical positions are also fixed.
The branch whidi treats of these is called spherical and
practical astronomy. Sf^erical astronomy provides the
mathematioal theory, mA practical astronomy (whioh is
almost as mudi an art as a soienoe) treats of the applioap
tion of this theory.

orHm ajt. i' j * ivJ^ t j|B Hj yy

DIVIBIONS OF TBE SUBJECT.

8 text book,
not a single
id painstak-
its Btudent
a daily and

of the hori-
fect this and
ioes the full
>f the young
ler questions
I of the an-
ice, but the
icial names to
pupil is more
sient philoso-
i-glass in the
ve waited two
sarly mystery,
a Gauleo to
on the sun.
idily progress-
imd reasoning
le advances in
made it con-
lortions, which
, although the

irst in logical
) by which the
ed from obser-

are ako fixed.

spherical and
r providas the
>my (which i»
of the appiioar

Theorttioal Astronomy deals with the laws of motion of
the celestial bodies as determined by repeated observiitiong
of their positions, and by the laws according Jo which they
ought to move under the influence of their'Inutual gravi-
tation. The purely mathematical part of the science, by
which the luws of the celestial motions are deduced from
the theory of gravitation alone, is also called Celestial
Jfechaniet, a term first applied by La Place in the title of
his great work JHecanique CeleHe.

OownloSil FhysiaB.— A third branch which has received
its greatest developments in quite recent times may be
called CosmiocH Physics. Physical astronomy might be
a better appellation, were it not sometimes applied to
celestial mechanics. This brandi treats of the physiqal
constitution and aspects of the heavenly bodies as investi-
gated with the telescope, the spectroscope, etc.

We thus have three great branches which run into each
other by insensible gradations, but under which a large
part of the astronomical research of the present day may
be included. In a work like the present, however, it
will not be advisable to follow strictly this order of sub-
jects ; wc shall rather strive to present the whole subject
in the order in which it can best be undentood. This
order will be somewhat like that in which the knowl-
edge has been actually acquired by the astroncnners of
different ages.

Owing to the frequency with which we hAve to use
terms expressing angular oieasnra, or ref anring to droles
on a sphere, it may be admissible, at the outset, to give
an idea of these terms, and to recapitulate some prop*
erties of the sphere.

Aniwler IbMaiea. — ^The unit of angular measure most
used for oonsidaiible ang^ is the degree, 840 of which
extend round the eiiele. The reader knows that it is 90"
tnuk the horiaon to the aodth, and that two objeele 180?
apart are diametrioally opposite. An idea of distanoes of

4 ASTttOItOMY.

a few degrees may l)e obtained by looking at the two Btars
which fonn the pointers in the constellation Urm Major
(the Dipper), soon to be described. These stars are 5°
apart. The angular diameters of the sun and moon are
each a little more than half a degree, or 30'.

An object subtending an angle of only one minute ap-
pears as a point rather than a disk, but is still plainly vis-
ible to the ordinary eye. Helmholtz finds that if two
minute points are nearer together than about 1' 12', no
eye can any longer distinguish them as two. If the ob-
jects are not plainly visible— if they are small stars, for
instance, they may have to be separated 3', 5', or even
10', to be seen as separate objects. Near the star a Lyra
are a pair of stars 3^' apart, which can be separated only
by very good eyes.

If the object bo nf>t a point, but a long line, it may be
seen by a gootl eye when its breadth snbtends an angle of
only a fraction of a minute ; the limit probably ranges
from 10' to 15'.

If the object lie much brighter than the background on
which it is seen, there is no limit below which it is neoes-
sarily invisible. Its visibility then depends solely on the
qnantity of light which it sends to the eye. It is not
likely that the brightest stars subtend an an^eofT^^ of

a second.

So long as the angle subtended by an object is nmU, we
may regard it as varying directly as the linear magnitude
of the body, and inversely as its distance from the ob-
server. A line seen perpendicularly snbtends an wo^
of 1° when it is a little less than 60 times its length dis-
tant from the observer (more exactly when it i» 67-8
lengths distant) ; an angle of 1' when it is 8488 lengths
distant, and of 1' when it is 206866 lengths distsnt.
These numbers are obtained by dividing the number of
degrees, minutes, and seoonds, respectively, in the cir-
cnmferenoe, by 2 x 814169966, the mtio of the droom^
ference of a circle to tlie radius.

»ii*li«<Ml

iie two Btara
7r»a Major
stare are 5°
d moon are

minute ap-
plainly vis-
that if two
1 1' 12', no
If the ob-
lU starB, for
5', or even
star a Lyra
parated only

B, it may be

an angle of

mbly ranges

ckground on
1 it is neoes-
lolely on the
I. It is not
fie of x^ of

t is small, we
tr magnitude
rom the ob-
nds an angle
to loigth dis-
m it is 67-8
8488l0DgibB
^gths cHittnt.
le number of
r, in the eir-
{ the dream-

CmCLEa OF THE spiimE. *

Oreat Cirele. of t.e 8phere.-In FJg^ 1 let^tho -^no
represent iW oi a ^Pj^' ^Id eti ^ These cir-
the two great circles AEBJ ^^^^ passing through the

from eveiy point of the eade -A it Ji .r.

^^ „ 4. «W»J^. w.* «* « ^ ^ the -me
fraoe between the pote. P « or r^ I-^^t repre«>i>to-

sphere.

SYMBOLS AND ABBREVIATIONS.

«IOH8 or THB PLAMRS, STC.

I or i

The Boa.
The Moon.
MefCBiy*
Veoot.
TheEuth.

i Man.

21 Jniriter.

« Sfttani.

S Uruiu.

^ Neptane.

The asteraidfl uedltttagnMied by a drele iBdodag n number. whl«h
number indicates the older of dlMsovenr, or by thdr BMneB, or br both.
fu^iHeeate '

UONB or THB womjko.

Spring
eigne.

T Ariee.
V Tanme.
n Gemini.
Sammer { t ® Ctacer.

it. Slhw.

Virgo.

Antamn
eigne.

Winter
rigns.

CIO. V3
(13. X

^ Libri
111 Sflorpina
t Sagittarina.
V3 Caprieorana.

Aqoariiuk
X Piaeeiw

AinDon.

6 Oonjanetioo, or having the ewae loafrltnde or right aaoearion.

a Qoadratore, or diflbring fK>° in " -

9 t^poaitioB, or difibring 180* la ■• '• «•

inmber,whldi
M,or by both,

llM.

iirt>ina
gitUriaa.
prieoraua.
lOAriiuk

AaTBONOMWAL SYMBOLS.

Q Ascending node.
n Descending node.
N. North. 8. South.
E. Bust. W. WlBt.

" Degree*.

' Minutes of uc

' Seconds of »rc.

*> Hours.

» Minutes of time.
. Seconds of time.

L. Mesn longitude of » body

g, Mesn nnoinsly.
f. True snomnly.

R^. or rt. Bight ascension.

Dec. or 6. Decllnstion.
r True senlth distance,
r Apparent «nith distance.
^Dirtance from the earth.
J Heliocentric longitude.
6, Heliocentric latitude.
X Oeocisffltrlclongltude.

a t4eooentric latitude.

2'o,^ Longitude of ascending

Undtationol orbit to the eclii..
tie.

a Mean anomaly. «>.

/[True anomaly. .„ » unit U. An8»»" ^'•»""" *""" ^

i: Mean sidereal motion in * unit «. ^g ^ ^^ ^^^

of time. L Distance from node, or argu

r, Radius vector. | ' ^ent for latitude.

^, Angle of e««'»t'*7y„„„ ,,i«, ! «. Altitude.
;:LoSgltude of perihelion C^"" | ^^i^.th.

'*^^"^' p. Earth'sBquatorlal radius.

familiar with It In reading the pans

occur : lAsttars. Rmms.

L.tt«n. VuMM. J, ^ Ku

A a Alpha

Y yC Oamma

E ( Bpsllon

ZCi »»•
H« »»•

e « Th«ta

li I«»

K « K»PP»,

j^ X Lambda

Mm Bfu

THE METRIC SYSTEM,

Thb metrle .y-tem of weight, and measure, being en>PW«i ««
J. volume, the following relations between the unit, of thl. .y.tem
mcl ;ied aid th«« of our oidiowy ou. will b. found conrenlent for
reference :

MRABURRS or LBMOTH.

1 kilometre = 1000 metres ^ 02187 mile.
1 metre = the unit = 89 87 inches

1 millimetre = TiAnr of a metre = 008987 Inch.

HKASUREB OF WEIGHT.

1 mlllier or tonneau = 1.000.000 gramme. = 8304-6 pounds.

!"•''-••"'-• -ther*""""': i^rg^nr

1 K^Lnme = W»» of a gramme = 001648 grain.

The fbllowing rough approximation, may be memoriied :

The kUometfe i. a little more than A of a mUe. but leM than | of

imile.
The mile i. lV\r Ulometies.
The kilogramme I. H pound..
The pound i. lew than half a kilogramme.

wing employed \n
mlU of this Kjtttm
and oonTenlent for

3187 mile.
7 incbeii.
8037 incli.

1204-6 pounds.
2 3046 pounds.
15-482 grains.
0- 01548 gntn.

aemoriied :

He, but Itm tliu | of

CHAPTER I.

,„K HK..T.O. -J„B^ -KT„ TO THB
$i 1. THB EABTH.

U considering the n^ladon of «;« -f^J^.tolTm^^
we iieceBearily l>egin r:f\'^l,t^\ChL:yXhJJ,

n'3eS*:f':;St;wn fact, will show th^ this
eih'l^u which we live is, at l east approxiuiately, >
Klobe whose dimensions are gigantic ^.hM^^^
when compared to onr ordinary aiid
daily ide«. of si«». If «^P«^^
Mveral ways known to he nearly |

that of a sphere. ,

I It haa been repeatedly circum-

navigated in various directions.

II Portions of its swrface, via-
ble from elevated positions in the

midst of extensive phihis or at sea,

Zoeu to be hounded by circles. T^Jl^^^

IWppemnce at all points of the j^TtS^^^:.
sorfw* Ta body i. a geometnca' f^,,^^^tSSlXi&^
attribute of a globufar form only. _ .

m Fortlier than this we know thrt «*»tui ""»"

geodetie surveys have agreed with this general wu

g (m aggg B j^y^:F'^''^g^^ ^WW^^' '*^ *'^^

^N*"*

ASTHONOMT.

More procisct reasonH will li« apparent later, but those will
be Buttioient to base our general considerations npon. Of
the aize of the earth we may form a rongh idea by the
time re(|uired to travel completely around it, which is
now about three months.

We find next that this globe Ih completely isolated
in space. It neither rests on any thing else, nor is it in
contact with any surrounding body. The most obvious
proof of this which presents itself is, that mankind have
visited nearly every part of its surface without finding
any such connection, and that the heavenly bodies seem
to perform complete circuits around it and under it with-
out meeting with any obstacles. The sun which rose to-
day is the same body as the setting sun of yestetrlay, but
it has been seen to move (apparently) about the earth
from east to west during the day, and it regulariy reap-
pears each morning. Moreover, if attentively watched,
it will be found to rise and set at different parts of the
horizon of any place at different times of the year, which
negatives the ancient lielief that its nocturnal joiirney was
made through a huge subterranean tunnel.

% 1. THS DZUBITAL KOnON AlTD THB CODUnTIAIi

PaisiDg now from the earth to the heavens, and vMwing
the son by day, or the stars by n^t, the first ]^ienomeiKm
whidi fMam our attention is that of the divmal motkm.

Wemwt here cantion the reader to carefnllj distin-
goiah between apparent and reed motions. For examine,
when the phenomena of the dinnuU motion are aet forth
as real visible motions, he must be prepared to ^um rab-
seqnentiy that this appearaneo^ which is obvioM to all, is
yet a oonseqnenoe of a real motion only to be detected by
reason. We shall first describe the dinmal motkm as it
appewn, and show that all the appearaaoes to » qieotator
at any one place may be re proao n lBd by 8a|i|Kiiii% the
earth to remain fixed in spaoe, and the wM* otnoave of

1
1
t
1
r
t
ii
li
t
si
n
I
si
t^
tl

HT
t(
s«
it
ii.
tl
tl

it t))om] will
I npon. Of
idoa by the
t, which is

ely isolftted
nor is it in
io8t obviooH
aikind have
ont finding
IxMlies seem
idor it with-
ich rose to-
fiterday, but
it the earth
ulariy reap-
)ly watched,
)art8 of the
year, which
joiirney was

andTWwing
dienomeiM»
tlmoikm.
folly diatiii-
Bxample,
re aet forth

lewninb-
ns toall,i8
d0t6otod by
motion as it

Aspeotator
iipoiog the

oeoeaTeof

TI/K DIURNAL MOTION.

the noavoiiH to turn abont it, and finally it will be shown
that we have reason to Iwlieve that tlio solid uarth itself
is in constant rotation while the heavens runmin immov-
ablo, pruHunting different portions in tnm to the obsorvor.
The motion in (piestSon is most obvious in the case of the
sun, which appears to make a daily circuit in the heavens,
rising in the vast, passing over toward the south, setting in
the west, and inovhig around under the earth until it
reaches the eastern horizon again. Observations of the stars
made through any one evening show that they also appear
to perform a similar circuit. Wliatevor stars we see near
the eastern horizon will be found constantly rising higher,
and moving toward the south, while those in the west
will be constantly setting. If we watch a star which is
rising at the same point of the horizon where the sun
rises, we shall find it to pursue nearly the same ooune in
the heavens through the night that the sun follows
through the day. Continued obaervations will show,
however, that there are some stars which do not let at all —
namely, those in the north. Instead of rising and letting,
they appear to perform a daily revolution around a point
in the heavens which in onr latitudes is neariy half way
between the senith and die northern horizon. Thla oen-
tral point i» called the pole of the heavens. Near it is
situated Polarity or the pole star. It may be recog-
nized by the Poinier»t two atars in the oonstelktion
Ur»a Mt^cTt famiHarly known aa TKe Dipper. These
stars are ahown in Fig. 8. If we wateh any star be-
tween the pole and the north horizon, we shall find
that instead of moving from east to west, aa the stars
generally appear to move, it really appears to move
toward tiie east ; but instead of oontinning its motion and
setting in the east, we shall find that it gradnally dUres
its course upward. If we could follow it for twenty-four
hours we should see it move upwards in the north-east, and
then pen over toward the west between the zenith ai^
the pole, then sink down in the north-west ; and on the

,TVi'/-*wrpjv..w*'j 3^'

Asrnnmmrr.

following night cnrvo itH couno onco nu.^o toward tho
east. The arc which it appears to deflcrilH) in a perfect
eircle, having tho pole in its centre. The farther ffom
the pole we go, the larger the circle which each star aeeina
to describe ; and when we get to a distance equal to that
between the pole and tho horizon, each star in its
rent passage below the pole just grazus 41h) horizon.

8.— rm APPABBMT DiniMAI. MonoM.

As a result of this apparent motion, each individual
constellation changes its configuration with respeot to the
horizon, that part which is highest when the oonstellatitm
is above the pole being lowest when below it. This is
shown in Figure 4, which represents a supposed omMtel-
lation at five different times oi the night.

Going farther still from the pole, tiie stars will dip be*

11-

THK DIURNAL MOTION.

toward the
I a porfeot
rther fi-om
1 star seeina
[ual to that
n its
izon.

indiTidnal
ipeoktothe
»tMteIlati(m
it. This is
led omistel-

Hrill dip be>

,„, the .,«ri.on anring a portion o^ ^ " C:^! t »t
,,„„.|,y „crc«>,ng ^''-«Jl,v„«,d on. hJ( Wow
r!l""'«» J[t;^S iirwlLn, «.d tUerob^ longer

Toni;::.! .Lt. i'* u. *» ^ »« -.'.. -^ -

Bets a little to the west of it.

% '- rl

NORTH
Fio. 4.

«nm, ♦«','^„'t^^ tSrfLTtoS but they J«
p,^t MvotaUon m 1^ "^^ jirtiac from «ch
Swerve iiiidi»nged Aeir """"^j, ^„^ «, wm-
Uher, tKth the «"»!*■<»> «« *7' '£?S are »WHe

»chMg. •ir.'JrJ the Se"'' the ide. thrt thM.
UrSttjrSrjTc^-neSl^^"-'^'-- ^

«rW".-flt.

ASTBONOMY.

apparent explanation, both of this and of the phenomena
of the diurnal motion, was offered by the conception of
the celestial sphere. The salient phenomena of the
heavens, from whatever point of the earth's surface they
might be viewed, were represented by supposing that the
globe of the earth was situated centrally within an im-
mensely larger hollow sphere of the heavens. The vis-
ible portion, or upper half of this hollow sphere, as seen
from any point, constituted the celestial vault, and the
whole sphere, with the stars which studded it, was called
the firmament. The stars were set in its interior surface,
or the firmament might be supposed to be of a perfectly
transparent crystal, and the stars might be situated in any
portion of its thickness. About one half of the sphere
could be seen from any point of the earth's surface, the
view of the other half being necessarily evt off by the
earth itself. This sphere was conceived to make a diurnal
revolution around an axis, necessarily a purely mathemat-
ical line, passing centrally through it and through the
earth. The ends of this axis were the poles. The situa-
tion of the north end, or north pole, was visible in north-
em latitudes, while the south pole was invisible, being
below the horizon. A navigator sailing south would so
change his horizon, owing to the sphericity of the earth,
that the location of the north pole would sink out of sight,
while that of the south pole would come into view.

It was clearly seen, even by the r' Jents, that the diur-
nal motion could be as well represented by supposing the
celestial sphere to be at rest, and the earth to ravolve
around this axis, as by supposing the sphere to revolve.
This doctrine of the earth's rotation was maintained by
several of the ancient astronomers, notably by Abistab-
oHus and Timoohabis. The opposite view, however, was
maintained by Ptolbmt, who could not con<»ive that the
earth could be endowed with such a rapid rotation with-
out disturbing the motion of bodies at its surface^ We
now know that Ptolbict was wrong, and his opponents <

THE CELESTIAL SPHERB.

phenomena
mception of
lena of the
surface they
ing that the
thin an ira-
B. The vis-
lere, as seen
alt, and the
, was called
rior surface,
a perfectly
lated in any

the sphere
surface, the

off by the
ke a diurnal
' mathemat-
hrongh the

The sitna-
le in north-
dble, being
h would so

the earth,
tut of sight,
idew.

It the diur-
pposing the
to revolve
to revolve,
intoined by
y Abistab*
>wev^r, was
!ve that the
sation with-
pface* We

opponents <

right. Still, so far as the apparent dinmal motion is con-
oerncd, it is indifferent whether we conceive the earth or
the heavens to be in motion. Sometimes the one concep-
tion, and sometimes the other, will make the phenomenA
the more clear. As a matter of fact, astronomers speak
of the sun rising and setting, just as others do, although
it is in reality the earth which turns. This is a form of
language which, being designed only to represent the ap-
pearances, need not lead us into error. .^ ^ , ,

The celestial sphere which we have described has long
ceased to figure in wrtronomy as a reaUty. We now know
that the celestial spaces are pmcticaUy perfectly void ;
that some of the heavenly bodies, which appear to l^ on
the surface of the oelertial sphere at equM dwtaneesfrom
the earth as a centre, are thousands, or even milhons of
times farther from the earth than others ; that there is no
material oonneetion betwefen them, and that the celestial
sphere itself ii» only a result of optical pewotive. But
the huiguage and the conception are stiU ret&i»4^ 1»cause
they afford the most dear and definite method of repre-
sentimr the directioBs of the heavenly bodies fiom the
obs«rw, wherever he may be situated. In this respect
it sema the same pwpose that the geometnc sphere
does in apherical trigono^netry. The stodeiit of this sci-
ence knows that there is reaUyno need of supposing a
sphere or a spherical trianj^e, because every spherical are
is only the representative of an angle between two lines
which emanate from the centre, one to each end of the
are, whae the angles of the triangle are only those of the
philies containing the three lines which are drawn to
Lh angle from the centre. Spherical trigonometry m,
therefore, in reaMty, only the trigonometry oi s^id
angles ; and the purpose of the sphere is only to afford a
convenient method of conceiving of such angles. In the
same way, althou^ the celestial sphere has no real ex-
istence, yet by eonoeiving of it a. a redity, and suppojng
eertain Unes of reference drawn upon it, we are enabled to

JWga»JM»»<i«!4i.!l,ttM!'.- ' . '" ? J? ,^'t>'"''^.' fl

A8TR0N0MT.

form an idea of tlie relative directions of the heavenly
bodies. We may conceive of it in two ways : firetly, as
having an infinite radius, in which case the centre of the
earth, or any point of its surface, may equally be supposed
to be in the centre of the celestial sphere ; or, secondly we
may suppose it to be finite, the observer carrying the wn-

Fio, 5 — aTARs nam oir thk CBuniAi. vbmhm.

tre with him wherever he goes. The iirat assumption wiU
probably l)e the one which it is best to adopt. The object
attained by each mode of representation is that of having
the observer always in the centre of the supposed sphere.
J*^. 5 will give the reader an idea of its apphcatjon. He
w supposed to be stationed in the centre, 0, ancl to have
Mwmd him the bodies py».,<, etc The sphere itself
temg supposed at an immense distance, outside of all
these bodies, we may suppose lines to be drown fiom
each of them directly away from the centre until they
waoh the sphere. The points PQBST, etc., in whieh

=s&

■ i-.i j * w<wiiw.jMij i |ii i wm

the heavenly
1^8 : firstly, as
centre of the
r be supposed
secondly, we
jring the oen-

imptifMi will
liie object
it of having
Bed sphere.
Mtlon. He
um) to have
phere itself
»ide of all
rawn itom
until they
!., in -wladi

THE CELESTIAL SPHERE.

these lines intersect the sphere, will represent the appa-
rent positions of the heavenly bodies as seen by the ob-
server at 0. If several of them, as those marked ttt^
are in the same direction from the observer, they will ap-
pear to be projected on the same point of the sphere.
Thus positions on the sphere represent simply the direc-
tions in which the bodies are seen, bnt have no direct re-
lations to the distance.

It was seen by the ancients that the earth was cmly a
point in comparison with the appfrent B|dtoi« of the fixed
stars. This was shown by the nniformity of the dinmal
motion ; if the earth had any sensible magnitnde in com-
parison with the sphere of the heavens, the son, or a star,
would seem to be nearer to the observer when it passed
the meridian, or any point near his zenith, than it wotild
when it was below the horizon, or nearly under his feet,
by a quantity equal to the diameter of the earth. Being
nearer to him, it would seem to move more rapidly when
above the horizon than when below,- and its apparent angular
dimensions would be greater in the zenith than in the
horizon. 4s a matter of fact, however, the most refined
observations do not show tlie slightest variation from
perfect uniformity, no matter what the point at which
the observer may stand. Therefore, observers all over
the earth are apparently equally near the stars at every
point of their apparent diurnal paths; wbence their
distance must be so great that in proportion to them the
diameter of the earth entirely vanishes. This aigoment
holds equally true whether we suppose the earth or tiie
heavens to revolvis, because the observer, carried around
by tlie rotating earth, will be brought nearer to those
stars which are over his head, and carried farther from
them when he is on the opposite side of the circre*in
which he moves.

Bajqxwe tht earth to be at 0, and the celestial sphere of the fixed
■taiato be represent^ in the figure by the circle NZ QSn, etc.
BuppoM N E8 W to reprewnt the plane of the hrriton of aome

A8TR0N0MT.

obwrrer on the ewth*s ■urfaoe.

He will then aee every thing oSmm
thie plane, and nothbg befow it
If NB 8 it hit etutem horizon,
■tan will •Ppear to rise atTarioiu
points, g, E, d, a, etc., and will
appear to describe, circles until
they attain their highest points
at A, Q, 0, h, etc., dnking into
the western horizon at t, W, /, «,
etc. These are facts of observa-
tion. The common aaiU of tliose
circles is P ^, and stars about P
(the pole) never set. The appa-
rent diurnal arc I m, for icatance,
represents the apparent wbit of
a eirmmpolor star.

ViQ. 9.

THS TSBBB8TBIAL

8. OOBBBSPOH DBNCB O F
AND OXIiBSTIAL

We have said that the direction of a heavenly body
from an observer, or, which is the same tiling, its ap-
^parent position, is defined by the point of the celestial
sphere on which it seems to be. This point is that in
which the straight line drawn from the observer to the
body, and continued forward indefinitdy, meets the celes-
tial sphere. Its position is fixed by reference to certain
fondamental circles supposed to be drawn on tiie sphere,
on the same plan by which longitude and latitude on the
earth are fixed. The system of thus defining terrestrial
positions by reference to the earth's equator, and to some,
prime meridian &om which we reckon the longitudes, is one
with whidi the reader may be supposed familiar. We shall
therefore commence with those eireles of the celestial
sphere which correspond to the meridians, parallels, etc,
onlthe earth.

First, we remark that if we consider the earth to be at
rest for a moment, every point on its surface is at the end
of a radius which, if extended, would toneh a correspond'-

..j i mmianii

I Wiaail B i l l B jBWM'IWIIW WI Iil i

m thing dboM
;huig bflfow it
Mttem horizon,
(riaeatTuioaa

etc., and will
« circles until
hiffheet points
, nnking into
nat*, r,/, e,
cts of obsenra-
o aada of these

stars about P
t. The appa-
I, for instance,
•rant orbit of

EtBffFBIAL

ivenly body
ling, its ap-
the celestial
It is that in
erverto the
)tB the oeles-
« to certain
the sphere,
itnde on the
g terrestrial
and to some
itddes, is one
v. We shall
the celestial
rallels, etc,

rth to beat
• at the end
oorrespondo

TBt OBLESTIAL AND TtBHtSTUAL BPBlBiSI. W
,„g point «pon A. ctatW •^J\^^":X

the MUth in dediied by » bm P~'"*„ " ;„ diraotlT np-
rf the e«th to th. ol«r™r, »d r*'"';j«,^^JJS;
,^ until it m«t. th. '»>»^'ifl*"r^^ wh^7h.

''*^''' wLthe oSTrverTon «ie eartVs equator.

^U «ee hi. zenith »«« -•y^^^^^h'^m d-criSi a
the earih revolve, on it. «-» .^» TT every point of
great circle around tlu. celestial »P^«^ •^"Y^^ „ ^e
^ch wiU be eqniOly dirtant 'TV^'fTm „y ^t

of the ewrth's equator ^e'^^Uj;*? ^^ ^ ' them,
conceive ihai iU !»««* «f ^ ««* jj S^ irbadf to the

called the «*•«« '''^'.^^TZIn^t^iT^ above a
to the terrestrial eqnator is t\«* ^J^'T^;"^; "tors lie
corresponduM^ point ofihela^The^two^^ ^^ ^^^

f^^'^^^tA^Sandtorr^ ^

belong, to both *~ ?T^^ ^^ from the eqnator

Now .appow that the ^^^^T^^Thavinir changed by
to 460 of north latitude. ^^^^""^^VX^SSon,
45-, the noiih polej^ now^be 46 *ove ^^ ^^

imMm^L'^-.^W.

ASTRONOMY.

sphere which Mrill be overywliere 45" distant from the
celestial equator. This cirde will thus correspond to the
parallel of 45° north upon the earth. If he goes to lati-
tude 60° north, he will see the pole at an elevation of 60°,
and his zenith will in the same way describe a circle which
will be everywhere 60° from the celestial equator, and 80°
from the pole. If he passes to the polo, the latter will
be directly over his head, and his zenith will not move at

FlO. 7.— TBBBnTRUIi AXD (ntUWIAI.

all. The celestial pole is simply the point inwiiioh the
earth's axis of rotation, if continued out in a straight line
of infinite length, would meet the celestial sphere. We
thus have a series of circles on the celestial spliere ooire-
sponding to the parallels of latitude upon the eartk.
Unfortunately the celestial element owresponding to
latitude on the earth is not called by that name, but by
that of dedmaUon. The d«dinaUon of a tkax is ^
distance north or south from the edestial equator, pre-

■■r

»nt from the
'espond to the
goes to kti-
ivation of 60",
a circle which
aator, and 80"
he latter will
1 not move at

in whioh the
a straight line
sphere. We
splbere oorre-
n the earth.
9ep<niding to
name, bnt by
a star is ^
eqiiator, pre-

and J7 e its equator. « " /"l" ..^m^imshH^^^

the VLw LF .^^f^rSrJ^ w jp"
finite di«t»ce thedlitMiM r^ r

the elevted pole. correspondence between

We have next to consider t^e cwrespu^ terrestrial me-
the celestial and ^^r\^^'Zfr the earth's snrf ace
ridian is ^ '^'^^'''^y^rSrotZ pole to the other,
in . north and sonA ^^"Z pole in every diiec-
Thesemeridiansdijerge from one F* ^^y

tion, and meet at the o^erjok^ ^ through « the
edled by A* "'"^T.^J ^Te mlridSwi of Washington.
,„eridian of ^^""^^^JZlllr^ as the intersection witli
E^ meridian may be <^f '^ ^^^ongh the axis of
jre«rth'ssnrf«»ofaplajeT^«J^^ ^les. Such a
Z earth, ««* *«tS^„S^ e^l hrnispherea, «.d
pl««, will cut the eaiAjntoJ^JJl^rth's surface Jong
L- \ of oonne be vertical y^V, " This phme is called
V^^ of its li»-^^*?'::^^y co?t.^^ng it 2^ t«
the Jlaneof the «»«"*"? '^^ve a celestial meridian

Teloestial sphere, T'J^^J^Zl precisely as we have
. oorwspondinp to each terrestrial one, p

JS^Ef

S^^l^yilK'lW'ii'e^'^^*-'^*^'^

ASTJtomifr.

circles of declination corresponding to parallels of latitnde
on the earth. But owing to the rotation of the earth, the
circle in which the plane of the meridian of any place in-
tersects the celestial sphere will be continnally moving
among the stars, so that there is no such permanent cor-
roapondence as in the case of the declinations. Thii
does not prevent us from conceiving imaginary meridiana
pawing from one pole of the heavens to the other pre-
cisely as the meridians on the earth do, only these me-
ridiang will be apparently in motion, owing to the rotation
of the earth. We may, in fact, conceive of two seta of
meridiana— one really at rest among the stars, but appa-
rently moving from east to west around the pole as the
rtara do, and the other the terrestrial meridians continued
to the celestial sphere, apparently at rest, but really in
inotion from west to east. The rektions of these me-
ridians will be best understood when we explain the in-
strnmonts and methods by which they are fixed, and by
which the positions of the stars in the heavens are deter-
mined. At present we will confine ourselves to the con-
sideration of the celestial meridians.

The reader will understand that these meridians pass
from one pole of the celestial sphere to the other, pre-
cisely as on the globe terrestrial meridians pass from one
pole to the other, and that being fixed among the stars,
they appear to turn around the imle as the stars appear to
do. As on the earth differences of longitude betwefo
different places are fixed by the differences between the
meridians of the two pkces, so in the heavens what eor-
responds to longitude is fixed by the differenoe between
the celestial meridians. This coordinate is, however, in
the heavens not caUed longitude, but righi Moeruion,
Let the student very thoroughly impres» upon his mind
this term— right ascension— which k ^Itngitnde on the
celestial sphere, and also the tenu i^riiavefbefore spoken
of— (JM^MMi^Mm— whieh u latitude on the celestial sphere.

In order to fix the right ascension of a hea^««ly bodyj

\hU of latitude
the earth, the
any pjgce in.
inally moving
)nnanent oor-
lations. Thig
larjr ineridiana
he other pre-
Inly these me-
» the rotation
f two aeta of
"*> but appa.
) pole as the
ana oontinaed
hut really in
of these rae-
fphiin the in-
<ixed, and by
ens are deter-
*8 to the con-

fierjdiana pass
le other, pi«.
MB from one
*>fir the Stan,
*« appear to
ade between
between the
>n8 what ow.
nee between
however, in

^ MMfWMn, ,

n his mind
ude on the
f<n« spoken
itialsphflve.
^••ly body,

niGirr ah(irnsion.

we must liave a first meridian to count from, precisely as
on the earth we count longitudes ^rom the meridian of
Greenwich or of Washington. L* 'ndiilerent wliat me-
ridian we take as the first one ; uat it is custouiary to
adopt the meridian of the vernal equinox. What the ver-
nal ef^uinox is will lie described hereafter : for our pres-
ent purposes, nothing more is necessary than to under-
stand that a certain meridian is arbitrarily taken. If noM'
we wish to fix the right ascension o^ a star, we have only
to imagine a meridian passing through it, and to deter-
mine the angle which this meridian makes with the meri-
dian of the vernal equinox, as measured from west to east
on the equator. That angle will be the right ascension of
a star. As already indicated, the declination of a star
will be its angular distance from the equator measured on
this meridian. Thus, the right ascension and declination
of a star fix its apparent position on the celestial sphere,
precisely as latitude and longitude fix the position of a
point on tlie surface of the jsarth.

To give precision to the ideas, we present a brief con-
densation of this snbjeet, with additional definitimis.

Let PZ^iT represent the oeleetial sphere of on ob-
server in the northern hemisphere, O being the position
of the earth. Pp is the oanaqf ike odesHal tphere^ or
the line about whieh the appwent dinmal orbits of the
stars and the actual revolution of the earth are performed.

The zenith, Z, is the point immediately above, the
nadir n, the point immediately below the observer.
The direction Zn is defined in practice by the position
freely assumed by the plnmb line.

The celettial Kmnzon is the plane perpendicular to the
line jc^ng the aenHA and nadir IfES W; or it is the
terrestrial horiion ocmtinued till it meets the oeleetial sphere.

The cdestial horiaon intersects the earth in the rational
AdfuwM, whieh pasaes through the earth's centre, and
whidi ia so called in distinction to the mmKe horiion^
whieh ia the plane tangent to the earth's surface at any

mg^:

14 ASTHoyoMY.

point. But, since the earth itself is considered as but »
point in comparison witli tlie celestial sphere, the rational
and sensible horizons mo considered as one and the same

circle on this sphere. . - .1

The oelettial poUm are the extremities of the (wis of m
ededial sphere P p, the nwth poU l«ing that one which
is above the horizon in the latitude of New \ork, in the

northern hemisphere. , . , . •*!.«-

The circles apparently described by the stars m their

diurnal orbits are called ptmMtU qf dedwatwn, KN ;

Fie. 0.— cnoun ov

that one whose plane passes through the centre of the
sphere being the «fo««»a/ eqwOWy or the tfumoaUalf

C W D.

The odeKliaSL tfuatar is then that pundlel of declination
which is a great drole of the celestial sphere.

The figure iUustawtes the phenomena which appear in
the heavens to an observer upon the earth. The stan
which Ue in the equator have their diurnal paths bisected
by the horizon, and are as long above the horiaon as b«l»W

>nsidored as but a
[pliere, tho rational
one and the same

of the ojtls of the

^ing that one which

New York, in tho

the Stan in their
\dedinatumy KN ;

\ the centre of the
or the tqmiMalMly

andlel of dedination

■phere.

nut which appeMr in

te earth. Th« itan

innud patiha bJMdted

the horiion as helaw

VIHCim OF TUi 1 1 Kit K. •

it ; tho8<t who8u diHtancu§ from tho \mAo {fnd<fr-'/ii*f"
are gn>uter than 90° will bu a Hliurtur tiniu nbuv«' tlit
rizon ; those whoso polar-distance* aru lues than i** li
longer time.

Tho circle iViT drawn aronnd tho pole Pm a centre
fo as to graze the horizon is called the circle iif perpetual
apparition^ liecauso stars situatKl within it never set.
The corresponding circle S U round tho south polo is
called tho circle qfperpetvMl disappearance, because stars
within it never rise above our horizon.

The groat circle passing throu«di the zenith and the
pole is the celettial meridian, NPZS. The meridian
intersects the Korixon in the meridian line, and the points
N and 8 are the north and touthpointg.

the prime vertical, £ZW,i» perpendicular to the meri-
dian line and to the horizon : its extremities in the hori-
zon are the ead and toettpointt.

The meridian plane is perpendienlar to the equator and
to the horizon, and therefore to their inteiMction. Hence
this intersection it the eatt and VMti line, which ia thus
determined by the inteneotion of the ]danei of the equator
and of the hn-imm.

The edUtudt of a htwrenly body ia ita apparent distance
above the horison, expreaaed in degreea, minutes, and
seconds of aro. hk the cenith the altitude is 90**, which
is the greatest poarible attitude.

If ^ be any hetTenly body, tho angle ZPA which the
oirde P A drawn from the pole to the body makes with
the meridian ia ealled the hour angle of the body. The
hour angle ia the angle through which the earth has ro-
tated on ita axis aince the body was on the meridian. It
is ao called becauae it measurea the time which has
elapaed linoe the paange of the body over the meri-
dian.

Thai diameter of the earth which ia coincident with the
Qonataat diraotion of the axis of the oekacial aphere is its
MM, and interaeots the earth in ita north and aouM poUz,

<t-<i^''-waggg j."

2rt

AHTUONOMY.

JOrWMBMKT LATI*

K 4. THl DXUBir AL MOTION IN
■ TUDE8.

As wo have ueon, ih celestial horizon of an observer
will change ita place on the celestial sphere as the observer
travels from place to place ou the sarfaco of the earth.
If he moves directly toward the north his zenith ^rill ii|>-
proach tho north polo, but as the zenith is not a visible
point, the motion will be naturally attributed to the pole,
which will seem to approach the point overhead. The
new apparent position of the pole will change the aspect
of the observer's sky, as the higher the pole appears above
the horizon the greater the circle of perpetual apparition,
and tlterefore the gi-eater the number of stars, wliich
never set.

If the observer is at the north pole his zenith and the
pole itself will coincide : half of the stars only will be vis-
ible, and these will never rise or set, but appear to nwve
around in circles parallel to the horizon. . The horijcon
and equator will coincide. The meridian will be indetw-
minate since Z and P coincide ; there will be no eMt and
west line, and no direction but south. The sphere in this
case is called a paraUd tphere.

WMSLMKT UlTI-

1 of an observer
V an the observer
iuo of the earth,
lia zenith '^11 )i|)-

is not a visible
voted to the pole,

overhead. The
change the aspect
ole appears above
)etnal apparition,

of stars, wliich

is zenith and the
rs only will be vis-
it appear to move
aa. . The horicon
an will be indetw-
will b« DO eaat and
The sphere in this

' .' ' ■ S 8'":V

DIUHNAL MOTION IN DIFFKHKNT LATITUDISS. 97

If itiHtuud of tnivt'Uiiig to the nortli the oltnerver shuiild
go toward tiie (Hiuatoi*, the nortli pole woiUd seem to ap-
proach iiiH horizon. Vt'hon he reached the (Hjuator Itoth
poles would be in the horizon, one north and the other
Honth. All the Btiirs in buccetwion would then be viHible,
and each would bo an equal time above and below the
horizon.

Fm. 11

The sphere in this case is called a righi (^here, because
the diurnal motion is at right angles to the horizon. If now
the observer travels southward from the equator, the south
pole will become elevated above his horizon, and in the
southern hemisphere appearances will be reproduced
whidi we have idready described for the northern, except
that the direction of the motion will, in one respect, be
di£Ferent. The heavenly bodies will still rise in tie east
and set in the west, but those near the equator will pass
north of the zenith instead of south of it, as in our lati-
tudes. The sun, instead of moving from left to right,
tliera moves from right to left. The bounding line be-
tween the two directions of motion is the equator, where
the snn culminates north of the zenith from Haroh till
September, and south of it from September till March.

If the observer travels west or east of hb first sta-
tic, his lenith will still remain at the same angular

ASTRONOMY.

distance from the north pole as before, and as the phe-
nomena caused by the earth's diurnal motion at any
place depend only upon the altitude of the elevated pole
at that place, these will not be changed except as to the
times of their occurrence. A star which appears to pass
through the zenith of his first station will also appear to
pass through the zenith of the second (since each star re-
mains at a constant angular distance from the pole), but
later in time, since it has to pass through the zenith of
every place between the two stations. The horizons of
the two stations will intercept difiEerent portions of the
celestial sphere at any one instant, but the earth's rotation
will present the same portions successively, and in the
same order, at both.

§ 6. BEI.ATI01T OF TIME TO THB 8FHEBB.

As in daily life we measure time aj the revolution of
the hands of a clock, so, in astronomy, we measure it by
the rotation of the earth, or the apparent revolution of
thf celestial sphere. Since the sphere seems to perform
one revolution, or 360° in 24 hours, it follows that it
moves through 16" in one hour, 1° in 4 minutes, 16' in
one minute of time, and 16* in one second of time.

The hour angle of a heavenly body counted toward the
west (see definition, p. 26) being the angle tlirough which
the sphere has revolved since the passage of the body over
the meridian, it follows that the time whidi has elapsed
eince that passage may be fonnd by dividing the hour
angle, expressed in degrees, minutes, and seconds of arc,
by 15, when the result will be the required interv^ ex-
pressed in hours, minutes, and seconds of timo. If we
know the time at which the body passed the meridian,
and add this interval to it, we sludl have the time corre-
sponding to the hoar angle. If we call it noon when
the sun passes the meridian, the hoar angle of the son
at any moment, divided by 16, gives the time since noon.
Me<m aolar time h onr ordinary time measured by the

SIDEREAL TIME.

i as the phe-
lotion at any
elevated pole
3ept as to thci
>pear8 to pass
ilso appear to
each star re-
the pole), but
the zenith of
e horizons of
)rtion8 of the
arth's rotation
y, and in the

8FHEBE.

I revolution of
measnre it by

revolution of
ns to perform
ollows that it
ninutes, 15' in
>f time.

ted toward the
tlirough whidi

the body over
'Ja has elapsed
ling the hour
leconds of arc,
id interval ez-

timo. If we
the meridian,
he time cone-
it noon when
^le of the sun
me since noon,
lasnred by the

«un, after allowing for certain inequalities hereafter de-

"1£re, however, an important remark is to be made^
Really ihe earth does not revolve on its axis m 24 of he
^ZnZ in ordinary life, but in about 4 minutes less than
^hirclre exactly in 23 hours 56 minutes 4.09 seconds )

If wei^te the exact time at which a star crosses the men-

i irorri-or setB, ordisappearsbehmd achunney or o^^^^

terr^trial object on one night, we shall find it to do tue

rXTnaS minutes 56 seconds earlier on the night follow-

thet^^ween two tr«»i.. of the «.n o^ «» »-
V. I. * K„ ♦!,«♦ between two transits of tne same siar.

rfter d.«ned), mi » .bout 8 'r""f',"XdMded into

r^r:-:s*^^-^brcwideai.to

24 tuureat nourvj ««* „.a«tiv like the common

JlTrate- that is, it gains about one second m sixminutes,

ASTRONOMT.

ten seconds in an hour, 3 minutes 56 seconds in a day,
two hours in a month, and 24 hours, or one day, in a year.
The hours of the sidereal day are counted forward from
to 24, instead of being divided into two groups of 12 each,
as in our civil reckoning of time. The face of the sidereal
clock is divided into 24 hours, and the hour hand
makes one revolution in this period instead of two. The
minutes and seconds are each counted forward from to
60, as in the common dock. Tho hands are set so as to
mark O*" 0" 0» at the moment when the vernal equinox
passes the meridian of the observer. Thus, the sidereal
time at any moment is simply the interval in hours, min-
utes, and seconds which has elapsed since the vernal equi-
nox was on the meridian. By multiplying this time by
16, we have the number of degrees, minutes, and seconds
through which the earth has turned since the transit of
the vernal equinox.

The sidereal time of onr common noon is given in the
astronomical ephemeris for every day of the year. It can
be found within ton or twelve minutes at any time by re-
membenng that on March 22d it is sidereal hours about
noon, on April 22d it is about 2 honro sidereal time at
noon, and so on through the year. Thus, by adding two
hours for each month, and 4 minutes for each day after
the 22d day last preceding, we have the sidereal time at
the noon we require. Adding to it the number of hours
since noon, and one minute more for ever fourth of a day
on account of the constant gain of the clock, we have the
sidereal time at any moment.

Eeam/ple. — Find the sidereal time on July 4th, 1881, at
4 o'clock A.1I. We have : i

h ■
June 22d, 3 months after March 22d ; tobe X S, 6
July 3d, 12 days after June 22d ; x 4, 48

4 A.M., 16 hours after noon, nearly | of a day, 16 3

This result is within a minute of the truth.

22 51

8IDSBBAL TIME.

ids in a day,
iay, in a year,
orward from
pe of 12 each,
)f the sidereal
e hour hand
of two. The
ard from to
e set so as to
emal equinox
}, the sidereal
n hours, min-
e vernal equi-
this time by
}, and seconds
the transit of

1 given in the
year. It can
y time by re-
) hours about
ereai time at
J adding two
ush day after
iereal time at
iberof hours
nrth of a day
we have the

4th, 1881, at

h ■

X S, 6
48

r, 16 8

22 61

Th« reader now understands that a sidereal dock is one

the Bun, but by ttat of 'f f^. J^",,^ , ki„„ the

'""TroX':^'*«WvX ^t'nSL We h.ve
poBtiont of the rt«re ^«^ J ;„„ „i ,ho rtars

now to .how how he fin^ the ng^ ^^ ^^ ___^_..

S'jr^nl^e.t.^f *i- ^-i.'-- «^-^

for the chapter on »»^'"«™- " . j„^ j, a^ed in an
a ™aU ttleaeop; ""^J* «^ ^ !» «xed, the tele-

power of the tele«.pe. ^* ".Srir^acay on the

»r'rs;te'rr^"^''--a^.

Suppose now in ^^ ^^ ^^^^ moment

mmBm

'''''^X!^tfi^t^r^^^»^^<>- of «.y rtar or
again. Then, *p^'***^™ *, y^enit ig about to reach

other heavenly ^y»^l^*^f,!i^t instrument at the
the meridian ; then directo the *«,""* ^^"^^ time,
point where it is about to cross, and notes ^ eMCt^

Shouts, minutes, and •^"^•;;r^J*'^^ti7yi^

"^^ tt te^'haft :4m ^.^n of^'^r^ de-
time by 16, he has tne ngni 'T; , ^^ j^ the trouble

SS.t^^oH'^n.w^lXtoex^i^.

|ij,uj; i i.,i

'I I i i.|ii| i

ASTRONOMY.

riglit ascensions of tlie heavenly bodies, not in degrees,
but in time. The circle is divided into 24 houre, like
the day, and these hours are divided into minutes and
seconds in the usual way. Then the right ascension of
a star is the same as the sidereal time at which it passes
tlie meridian.

The relation of arc to time, as angular measores, can be
readily remembered by noting that a minute or a second
of time is fifteen times as great as the corresponding de-
nomination in arc, while the hour is 15 times the degree.
The minute and second of time are denoted by the initial
letter of their names. So we have :

1" =16"
1"=16'
1*=15'

1"'=4»

l'=4»

1"=0'.0666.

Belation of Time and Longltade.— Considering our civil
time as depending on the sun, it will be seen that it is
noon at any and every place on the earth when the son
crosses the meridian of that place, or, to speak with more
precision, when the meridian of the places passeB under
the sun. In the lapse of 24 hours, the rotation of the
earth on its axis brings all its meridians under the sun in
succassion, or, which is the same thing, the sun appears to
pass in succession all the meridians of the earth. Henoe,
noon continually travels westward at the rate of 15* in an
hour, making the circuit of the earth in 24 houw. The
difference between the time of day, or local time as it is
called, at any two places, will be in proportion to the diflbr-
ence of longitude, amounting to one hour for eveiy 16
degrees of longitude, four minutes for every degree, and
so on. Vice versa, if at the same real moment of time
we can determine the local times at two different places,
the difference of these times, multiplied by 15, will give
the difference of longitude.

in degrees,

hours, like

minutes and

ascension of

ich it passes

'nres, can be
or a second

iponding de-
the degree.

>y the initial

=4">
'=4»

ring our civil
en that it is
hen the sun
k with more
PMses under
ttion of the
f the sun in
n appears to
'h. Hence,

GHANOB OF DA Y.

I)fl6«

in an

lours. The
t'm0 as it is
» the diflbr.
w eveiy 15
Iflgrae, and
nt of time
«nt phu»s,
', will give

Tlie longitudes of places are determined astronomically
on this principle. Astronomers are, however, in the
habit of expressing the longitude of places on the earth
like the right ascensions of the heavenly bodies, not in
degrees, but in hours. For instance, instead of saying
that Washington is 77" 3' west of Greenwich, we com-
monly say that it is 5 hours 8 minutes 12 seconds west,
meaning that when it is noon at Washington it is 5 hours
8 minutes 12 seconds after noon at Greenwich. This
course is adopted to prevent the trouble and confusion
which might arise from constantly having to change hours
into degrees, and the reverse.

A question frequently asked in this connection is.
Where does the day change ? It is, we will suppose, Sun-
day noon at Washington. That noon travels all the way
round the earth, and when it gets back to Washington
again it is Monday. Where or when did it change from
Sunday to Monday ? We answer, wherever people choose
to make the change, l^avigators make the change
occur in longitude 180° from Greenwich. As this meri-
dian lies in the Pacific Ocean, and scarcely meets any land
through its course, it is very convenient for this purpose.
If its use were universal, the day in question would be
Sunday to all the inhabitants east of this line, and Mon-
day to every one west of it. But in practice there have
been some deviations. As a general rule, on those islands
of the Pacific which are settled by men travelling east,
the day would at first be called Monday, even tiiough
they might cross the meridian of 180**. Indeed the Rus-
sian settlers carried their count into Alaska, so that when
our people took possession of that territory they found
that the inhabitants called the day Monday, when they
themselves called it Sunday. These deviations have, how-
ever, almost entirely disappeared, and with few exceptions
the day is changed by common consent in longitude ) ' '°
from Greenwich.

A8TR0N0MT.

g e. DETEBMnrATIOirS of TEBSB8TBIAL LONOI-

TUDES.

We have remarked that, owing to the rotation of the earth,
there is no such fixed correspondence between meridians on
the earth and aniong the stars as there is between latitude on
the earth and declination in the heavens. The observer
can always determine his latitude by finding the declination
of his zenith, but he cannot find his longitude from the
right ascension of his zenith with the same facility, be-
cause that right ascension is constantly changing. To deter-
mine the longitude of a place, the element of time as mea-
sured by the diurnal motion of the earth necessarily comes
in. Let us once more consider the plane of the meridian
of a place extended out to the celestial sphere so as to
mark out on the latter the celestial meridian of the place.
Consider two such places, Washington and San Francisco
for example ; then there will be two such celestial meri-
dians cutting the celestial sphere so as to make an angle of
about forty-five degrees with each other in this case. Let
the observer imagine himself at San Francisco. Then he
may conceive the meridian of Washington to be visible
on the celestial sphere, and to extend from the pole over
toward his south-east horizon so as to pass at a distance of
about forty-five degrees east of his own meridian. It
wonld appear to him to be at rest, although really both
his own meridian and that of Washington are moving in
consequence of the earth's rotation. Apparently the rtan
in their course will first pass the meridian of Washington,
and about three hours later will pass his own meridian.
Now it is evident that if he can determine the interval
which the star requires to pass from the meridiftn of Wash-
ington to that of his own place, he will at once have the
difference of longitude of the two places by simply turn-
ing the interval in time into degrees at the rate of fifteen
degrees to each hour.

Essentially the same idea may perhaps be more raa^ftiy
grasped by considering the star as apparently piassing over

LONOITUDE.

ion of the earth,
in meridians on
'een latitude on
The observer
the declination
|tude from the
e facility, be-
ing. To deter-
>f time as mea-
cessarily comes
f the meridian
>here so as to
I of the pkce.
San Francisco
celestial men-
kke an angle of
[this case. Let
^. Then he
n to be visible
I the pole over
It a distance of
meridian. It
arh really both
are moving in
rentlj the stars
f Washington,
own meridian.
« the interval
(Han of Wash-
once have the
Y simply tum-
nte of fifteen

more rea(|lly
f passmg over

gg-feiiiwa^saaajg

the snccessive terrestrial meridians on the surface of the
earth, the earth being now supposed for a moment to be
at rest. If we imagine a straight line drawn from the
centre of the earth to a star, this line will in the course of
twenty-four sidereal hours apparently make a complete
revolution, passing in succession the meridians of all the
places |)n the earth at the rate of fifteen degrees in an hour
of sidereal time. If, then, Washington and San Francisco
are forty-five degrees apart, any one star, no matter what
its declination, will require three sidereal hours to pass
from the meridian of Washington to that of San Francisco,
and the sun will require tluee gdar iiours for the same
passage.

Whichever idea we adopt, the result will be the same :
difference of longitude is measured by the time required
for a star to apparently pass from the meridian of one
place to that of another. There is yet another way of
defining what is in effect the same thing. The sidereal
time of any place at any instant being the same with the
right ascension of its meridian at that instant, it follows
that at any instant the sidereal times of the two places will
differ by the amount of the difference of longitude. For
instance : suppose that a star in hours right ascension is
crossing the meridian of Washington. Then it is hours
of local sidereal time at Washington. Three hours later
the star will have reached the meridian of San Francisco.
Then it will be C hours local sidereal time at San Fran-
cisco. Hence the difference of longitude of two places is
measured by the difference of their sidereal times at the
same ins^ At of absolute time. Instead of sidereal times,
we may equally well take mean times as measured by the
sun. It being noon when the snn crosses tiie meridian of
any place, and the snn requiring three hours to pass from
the meridian of Washington to that of San Francisco, it
follows that when it is noon at San Francisco it is three
o'olodc in the afternoon at Washington.*

* The dUtawnoe <rf kogitiide thus depends opon the anffular dU-
Uuu$^1tmtlrMmeHdiaiu, and not upon the motioa of a celestial body.

fiiSC

j£.m-

SSSE"

ABTRONOMT.

The whole problem of the determination of terrestrial
longitudes is thns reduced to one of these two : either
to find the moment of Greenwich or Washington time
corresponding to some moment of time at the place
which is tc bo determined, or to find the time required
for the sun or a star to move from the meridian of Green-
wich or Washington to that of the place. If it were
possible to fire a gun every day at Washington^ noon
which could be heard in an instant all over the earth,
then observers everywhere, with instruments to deter-
mine their local time by the sun or by thr: stars, would be
able at once to fix their longitudes by noting the hour,
minute, and second of local time at which the gun was
heard. As a matter of fact, the time of Washington noon
is daily sent by telegraph to many telegraph stations, and
an observer at any such station who knows his local time
can get a very close value of his longitude by observing the
local time of the arrival of this signal. Human ingenuity
has for several centuries been exercised in the effort to in-
vent some practical way of accomplishing the equivalent
of such a signal which could be used anywhere on the
earth. The British Government long had a standing offer
of a reward of ten thousand pounds to any person who
would discover a practical method of determining the lon-
gitude at sea with the necessary accuracy. This reward
was at length divided between a mathematician who con-
structed improved tables of the moon's motion and a
mechanician who invented an improved chronometer.
Before the invention of the telegraph the motion of the
moon and the transportation of ohronometen afforded
almost the only practicable and widely extended methods
of solving the problem in question. The invention of
the telegraph offered a third, far more perfect in its appli-

and hence the longitude of a place is the same whether ezprened as a
difference of two siderral times or of two solar times. Tab longitude
of Washington west from Greenwich is 5^ 8" or 77", and this Is. in UicX,
the ratio of the anguUr distance of tlie meridian of Washington frmn
that of Greenwich to 860° or 24^. It is thus phiin that the Iragitude is
the difference of the simultaneous local times, whether solar or sidereaL

kib

' wi&jjaMywMiMfefa#»rfi,^^^^

LONGITUDE BY CHRONOMETERS.

)f terrestrial
Itwo; either
fington time
ft tlie place
|me required
m of Green.

If it were
fngtoni' noon

the earth,
tfl to deter-
rs, would be
g the hour,
'he gun was
ington noon
itations, and
B local time
bserving the
tn ingenuity
effort to in-

> equivalent
Here on the
anding offer
person who
ing the Ion-
Phis reward
ui who con<
tion and a
uonometer.
tion of the
n afforded
id methods
vention of
n its appli.

nNwnedu •
lie longitude
>tais.infM3t.
ilagton frmn

> longitude is
rorddereaL

cation, but necessarily limited to places in telegraphic
communication with each other.

Longitude by Motion of the Moon. — When we de-
scribe the motion of the moon, we shall see that it moves
eastward among the stars at the rate of a)K)ut thirteen de-
grees per day, more or less. In other words, its right as-
cension is constantly increasing at the rate of a degree in
something less than two hours. If, then, its right ascension
can bo predicted in advance for each hour of Greenwich
or Washington time, an observer at any point of the
earth, by noting the local time at his station, when the
moon has any given right ascension, can thence determine
the corresponding moment of Greenwich time ; and hence,
from the difference of the local times, the longitude of his
place. The moon vrill thus serve the purpose of a sort of
clock running on Greenwich time, upon the face of which
any observer Mrith the proper appliances can read the
Greenwich hour. This method of determining longitudes
has its difficulties and drawbacks. The motion of the
moon is so slow that a very small change in its right ascen-
sion will produce a comparatively large one in the Green-
wich time deduced from it — about 27 times as great an
error in the deduced longitudes as exists in the determi-
nation of the moon's right ascension. With such instru-
ments as an observer can easily carry from place to place,
it is hardly possible to determine the moon's right ascen-
sion within five aeoonds of are ; and an error of this
amount will produce an error of nine seconds in the
Greenwich time, and henoe of two miles or more in his
deduced longitude. Besides, the mathematical processes
of dedndng from an observed right-ascension of the moon
the corresponding Greenwich time are, under ordinary
oircumstances, too troublesome and laborious to make this
method of value to the navigator.

Tmnaportfttioii of Ghxonometers. — ^The transportation
of ohronometera affords a simple and convenient method
of obtaining the time of the standard meridian at any
moment. The observer sets his chronometer as nearly as

ASTnONOMT.

possible on Greenwich or Washington time, and deter-
mines its correction and rate. This he can do at any sta-
tion of which the longitude is correctly known, and at
which the local time can be determined. Then, wherever
he travels, he can read the time of his standard meridian
from the face of his chronometer at any moment, and
compare it with the local time determined with his transit
instrument or sextant. The principal error to which this
method is subject arises from the necessary uncertainty in
the rate of even the best chronometers. This is the
method almost universally used at sea where the object is
simply to get an approximate knowledge of the ship's
position.

The accuracy can, however, be increased by carrying a
large number of chronometers, or by repeating the de-
termination a number of times, and this method is often
employed for fixing the longitudes of seaports, etc.
Between the years 1848 and 1855, great numbers of chro-
nometers were transported on the Cunard steamers plying
between Boston and Liverpool, to determine the difference
of longitude between Greenwich and the Cambridge Ob-
servatory, Massachusetts. At Liverpool the chronometers
were carefnily compared with Greenwich time at a >ocal
observatory — ^that is, the astronomer at Liverpool found
the error of the chronometer on its arrival in the ship,
and then again when the ship was about to sail. When
the chronometer reached Boston, in like manner its error
on Cambridge time was determined, and the det«inination
was repeated when the ship was about to return. Having
a number of such determinations made alternately on the
two sides of the Atlantic, the rates of the cfaronometers
could be determined for each double voyage, and thus the
error on Greenwich time could be calculated for the mo-
ment of each Cambridge comparison, and the moment of
Cambridge time for each Greenwich xiomparison.

Longitade by the Bectrio Tdegzmph. — ^As soon as the
electric telegraph was introdaced it was seen by American

"OMns

mmm^fimi^^ l mk^M'^-^^^''

|e, and deter-
lo at any sta-
liown, and at
pen, wherever
lard meridian
inonient, and
|ith Lis transit
to which this
incertaintj in
This is the
the object is
>f the ship's

by carrying a
ftting the de-
ithod is often
seaports, etc.
ibers of chro-
iamers plying
the difference
unbridge Ob-
chronometers
ime at a .'ocal
erpool found
in the ship,
saiL When
mer its error
letennination
rn. Having
utely on the
shronometers
and thus the
for the mo-
> moment of
ion.

i soon as the
y American

LOyOITUDE BT TBLEORAPn. ••

astronomers that wo here had a method of determining
longitudes wliicli for rapidity and convenience would
supersede all others. The first application of this method
was mode in 1844 between Washington and Baltimore,
under the direction of the late Admiral Charles Wilkes,
U. 8. N. During the next two years the method was intro-
duced into the Coast Survey, and the difference of longitude
between New York, Philadelphia, and Washington was
thus determined, and since that time this method has had
wide extension not only in the United States, but between
America and Europe, in Europe itself, in the East and West
Indies, and South America. The principle of the method
is extremely simple. Each place, of which the difference of
time (or longitude) is to be determined, is furnished with a
transit instrument, a clock and a chronograph ; instruments
described in the next chapter. Each clock is placed in
galvanic communication not only with its own chronograph,
but if necessary is so connected with the telegraph wires
that it can record its own beat upon a chronograph at the
other station. The observer, looking into the telescope
and noting the crossing of the stars over the meridian,
can, by his signals, record the instant of transit both on his
own chronograph and on that of the other station. The
plan of making a determination between Philadelphia and
Washington, for instance, was essentially this : When
some previously selected star reached the meridian at Phil-
adelphia, the observer pointed his transit upon it, and as
it crossed the wires, recorded the signal of time not only
on his own ohron<^praph, but on that at Washington.
About eight minutes afterward the star reached the
meridian at Washington, and there the observer recorded
its transit both on his own chronograph and oa that at
Philadelphia. The interval between the transit over the
two places, as measured by either sidereal clock, at once
gave the difference- of longitude. If the record was in-
stantaneous at the two stations, this interval ought to be
the same, whether read off the Phihtdelphia or the Wash-

'to ARTHOiTOMY.

ington chronogrupli. It was found, however, tliat there
wan a difleronce of a Binall fraction of a second, ariHing
from the fact tliat electricity re(£uired an interval of time,
minute but yet appreciable, to puss between the two
cities. The PhiUdelphia record was a little too late in
being recorded at Washinj^ton, and the Washington one a
little too late in being recorded at Philadelphia. We
may illustrate this by an example as follows :

Suppose £ to Ih3 a station one degree of longitude eaat
of another station, W ; and that at each station there is a
clock exactly regulated to the time of its own place, in
which case the clock at E will l)e of course four minutes
fast of the clock at W ; let us also suppose that a signal
takes ft quarter of a second to pass from one station to the
other :

Then if the obgerver at E sends a nignal to W at exactly

noon by his clock 12'' O" COO

It will be received at W at * n*" 66"> 0'.25

Showing an apparent difference of time of S" fiiCTS

Then if the observer at W sends a signal at noon by his

dock la* 0" COO

It will be received at E at 12'' 4"" 0".a6

Showing an apparent difference of time of 4" 0*.25

One half the sum of these differences is four minutes»
which is exactly the difference of time, or one degree of
longitude ; and one half their difference is twenty-live
hundredths of a second, the time taken by the electric im-
pulse to traverse the wire and telegraph instruments.

This is technically called the "wave and armature
time."

We have seen that if a signal could be made at Wash-
ington noon, and observed by an observer anywhere sit-
uated who knew the local time of hia station, his longi-
tude would thus become known. This principle is often
employed in methods of determining longitude other than
those named. For example, the instant of the banning

that there
Olid, ariHiiig
•vul of time,
ton tlio two
too lato in
ington ono a
slphia. We

ngitudo eaat
>ii there ig a
vn place, in
oar minutes
lat a signal
tttion to tlie

la* o-o-.oo

.ll*>86">0'.a5

S" 59'.76

la'o-'O'.oo
la"- 4- c.aa

i-O-.M

ur minutegf

le degree of

twenty-liye

electric iin-

ments.

d armature

le at Wash-
ywhere dt-
, his long!-
pie is often
I other than
9 beginning

TUKOttY OF THM bVUKHK.

.„. .nOuM, of an «=Up» of .... -J" *^*:^ --"^^J
.v.rfm.tlv dotln to p lenoineiion. it this w ooiwrvwu j
wo obirve™, and these in.t«iU noted by each in the
Wal ttieo? his station, then the difference of thej«
W S (subject to small correction, due U, pa«Uax,
etc.) will bo the difference of longitude of the two aw

^'^Tho satellites of Jupiter suffer ecUpaes frequently, and
the cCuw^rand wihington times of theje phenomena
a^ ooZZa and set down in the Nautical Almanac Ob-

L'vatSon- of these at any -^*!<>V'L*tf S'rl^^^^^^^^
ence of longitude between tlus rtation and ^^'''^'''V'J
wlington^ As, however, they require a larger tele-
ZeTnd a higher magnifying power than can Ik, used at
t^rtWB meth^ is not a practical one for navigators.

8 7. ItATHBIATIOAL Iggg OP THB 0«L«TIAL

In thU •xplanatKm «' »'« » tX%*ir7nt*i^^^^^^^^^^
the heavenly bodies to «*«>«• «°*of the rSlor is necesgarlly pre-
Ipherlcal trUnometry on the ~^^ „, f^^on

gUpposed. >• 8«i«'!l'5?i*lolJtrrclroWs u follow. :

thi sphere i«refen*dto axed pgntoor^^^^^ U Uken as a bwis,

A M»"«nt»ie:!r* S^S"u.. b<SVl?t« angular dUUnce from
„d the first S;«^'"J*»T«i,rI, S is taken^ the fundwnenUl
this circle. When the •^•^'^^"rf^ called Latitude ; on the
circle, this dlrta«je J^^JJjJjjJJJ^J^i Declination. If

't'^^^^^^I^^S^ScircXe thedUUnceiajMll^
thehodaonls tAen MiMran«™ »bovethe horison.

AUituds. Altltoda to «»J^*^oBDOsite sides of the circle, dis-
todiBti^^VHA^^^^^J'^^Mj positive quantltie^
tance.onoMsldeawrv2J " "^"^ ^ ^ the equator the
«Bd on the otiwr •«• " "^iSiion the upper side, are considered
north •«•, and »« *f •J.J'JgJ'SIhe hoK Ito altitude U ne«-
8S»'2d S^ZSHi^i^^^ of U.e earthB equator Is. in
•S^^ lKSd£5f^"d2& another elided «nl«i
or'^dJL^ffSS^-reSiU The lund«n.nUl circle I.

dfAiM lU jojinon . ri ^^ poMUon on • -k!"-? -

lines, wWch

• ■ are lu

ccHyrdl*

ASTRONOMY.

cTery where W from its positiTe pole, P. Hence, if A is tlie position

of a star or other point on tlie
sphere, and we put

tf, its declination or altitude.
= aA.

p, its polar or senith distance
=PA, we shall have

or.

p = 90"— d.

Fio. la.

If the star is south of the
fundamental circle, at B for ex-
ample, d being negative p will ex-
ceed 00°. This quantity p may
range from zero at the one pole
to 180° at the other, and will al-

T» i. «« ♦».:« * ^ u . V'^^ ^ algebraically positive.

It is on this account to be preferred to S, though less frequently

II. The second co-ordinate required to fix a position on the celes-
tial or terrestrial sphere is longitude, riffht ateetuion, or azimuth, ac-
cording to tiie fundamental plane adopted. It is expressed by the
position of the great circle or meridian P A a P which passes
wirough the position from one pole to the other, at right angles to
the fundamental circle. An arbitrary point, F for instance, is chosen
on this latter circle, and the longitude is the angle Va'inm this
point to the intersection of the meridUn or vertical circle passing
through the object. We may also consider it as the angle V/* 3
which the circle passing through the object makes with the circle
P V, because this angle is equal
to Va. The angle is commonly
counted from V toward the right,
and from 0° round to 860', so as
to avoid using negative angles.
If the observer is stationed in
the centre of the sphere, with his
head toward the positive pole P,
the positive direction should be
from right to left around the
sphere. When the horiion is
taken as the fundamental circle
or plane, this secondary co-ordi-
nate is called the arimiah, and
should be counted from the soutii
point toward east, or from the
north point toward west, but is
commonly counted the other way. It may be defined as the ancnlar
distance of the vertical circle passing through the object from the
south point of the horiion.

litti

A is the position
er point on the
put

on or altitude,

zenith distance
have

= 90°,
r-6.

s south of the
cle, at B for ex-
Bgativep will ex-
quantity p may
at the one pole
her, and will al-
aically positive,
less frequently

n on the celes-
or azimuth, ac-
pressed by the
which passes
right angles to
tance, is chosen
Va, from this
I circle passing
le angle VPA
with the circle

THEORY OF THE BPHERS.

The fto«ran!/fe of a sUr is measured by the interral which has

r, the sidereal time, v.n k.-«

a, the right ascension of the object, we shall have

Hour angle, A = t — «.

Tt will be neeatiTe before the object has passed the meridian, and
\- n-^S^? It differs from right ascension only m the point
r'''-hVcni^eckonSandThe '^direction which 'is conrifoed
Sive The ghTa^eSon is measured toward the east from a
Suthe yernal equinox) which is fixed among the stars^.while the
C angle S mewured toward the west from the mendmnof the
Er^er, which meridian is consUntly in motion, owing to the

•*m'h^t"xt to show the trigonome^icri relations which subsist
between Se hour angle, decUnation, altitude, and aaimuth. Let

as the angular
>bject from ttie

Fm.l4

Pig. 14 be a view of the celestial hemiaphere which is above tiie
hraixon, as seen from the eaat Wetiienhave:

HER F, the horiaon.

P, the pole.

Z, the lenith of the observer.

ir Jf Z P JJ; the meridian of the observer.

P Ji; the latitude of the observer, which call f.

?C'S.1Litf S£»«»*.-' = •«• - ■^'"«»"-

Ta,i\M altitude, which call a,
za,i\» aenitii diataooa = W" - «•
MZS, itoaaimuth, = 180' -anrie 8 Z P.
Z P ^ its hour an^e, which call *.

The spherical triangle Z P -8, of which the angles are formed by

ASTRONOMY.

the xenith, the pole, and the star, is the fundamental triangle of our
problem. The latter, as commonly solved, may be put into two forms.

I. Givi-n the latitude of the place, the declination or polar dis-
tance of the star, and its hour angle, to find its altitude and azimuth.

We have, by spherical trigonometry, considering the angles and
sides of the triangle Z P 8 :

con Z S = coB PZcoB PS + sin P Z sin PS cos P.
Bin ZS coa Z = sia PZ eoa PS — coA PZ sin PS cos P.
sin ZSain Z = Bin PS sin P.

By the above definitions,

Z S=90° — a, (a being the altitude of the star).

PZ=90° — ^, (^ being the latitude of the place).

PS = 90' — d, (6 being the declination of the star, + when north).

P = h, the hour angla

Z = 180° — t, (2 being the azimuth).

Making these substitutions, the equation becomes :

sin a = sin f sin 4 + coa f cos 4 cos A.
COR a cos • = — COB ik sin ^ + sin f coa ' cos A.
cos a sin • = cos J sin A.

From these equations sin a and cos a may be obtained separately,
and, if the computation is correct, they wul give thi> i.. <3 val'je of a.
If the altitude only is wanted, it mayv.1be obiaim 1 f > t*>e first
equation alone, which may be transformed in Tarioua . xy^ ained

in works on trigonometry.

II. Given the latitude of the place, the deelination of a star, and
its altitude above the hwison, to find its hour ande and (if its right
ascension is known) the sidereal timi when it liaa the given altitude.

We find from the first of the above equations.

cosA =

sin a — 'lin ^ sin dl.

or we may use :

sin'iA = i

cos ^ 008 i

COS (f — «t) — sin o

cos ^ 000 4

Having thus found A, we have

Sidereal time s= A + cr,

a being the star's right ascension, and the hour angle A being changed
into time by dividing by 16.

ni. An interesting form of this last problem arises when we sup-
pose a sa 0, which is the same thii^; as supposing the star to be in

tal triangle of our
tit into two forms.

ion or polar dis-
,ude and aumuth.
ig the angles and

1 P S cos P.
\PScmP.

ir, + when north).

6 cos h.

tabled separately,
It, b. .aval'jeof a.
1 1 r > ♦»•« arst
» . < xit^'vined

Ion of a star, and
e and (if its right
the given altitude.

le A being ebanged

iseswhenwe au

ABlRONOMr.

the horizon, and therefore Xo be rising or setting ^s • t'blj

time between its "«"«. *""':* P^Ji^s interval is caUed the $emir
tween this passage and its setting. This mtervai « c~.

diurnal are, and by doubling it ^^^— ^

we have the time between the
rising and setting of the star or
other object Putting a = in
the preceding expression for cos
h we find for the semi diurnal
arc A,

_ wn ^ sin j
CCS ft — — -^ ^ cos S

= — tan ^ tan d,

and the arc during which the
sUr is above the horiion is 2 *.

Prom this formula may be

deduced at once many of the ^bbbi^^^^^^^^

results given in the preceding j.^ IB.— cpm um umtM mro-

S6Ction8. HAIi ABC&

(I). At the poles f = ,^' ^^ r _ »„ftnitv But the cosine of
tan * = infinity, and thw^JJw cm A ^^ ^« ^^ ^„^

an angle can never be g'«'*«' .IS" "^^L' e^ . gjr »rthe pole can
of A which fulfite the condition. Hence, a siar at w» i~

neither rise nor set . _ ao ♦.n a = whence cos A = 0,

. <'>in^* *;«T^ iXihaterer beT *TO. brinj a semicircum.
{e^nSrAVhia7en\?'boj£*rh.lf the time above the hori«.n to

^e t^aL-SiSu^tTeJielirve^h^^^^

tude of the observer. Here we except *« I^|«; ^'^^.S *. ^tuok

Und

tand

Ig the star

ire aup-
to be in

«••* = " SSI "■ tan (90° - f)
wbMi<tapo«ltiT«,oos»tan«8»tlTe,andA>W,»»?' *"«

A8TR0N0MT.

negative i, cos h is positive, A < 90% 2 A < 180°. Hence, in north-
em latitudes, a northern sUr is more than half of the time above the
horizon, and a soi'them star loss. In the southern hemisphere, f and
tan f are negative, and the case is reversed. ^

(6). If, in the preceding case, the declination of a body is supposed
constant and north, then the greater we make ♦ the greater the nega-
tive value of cos h and the greater h itself will be. Considering, m
succession, the cases of north and south declination and north and
south latitude, we readily see that the farther we go to the north on
the earth, the longer bodies of north declination remam above the
horiioD, and the more quickly those of south declination set. In the
southern hemisphere Uie reverse is true. Thus, in the month of
June, when the sun is north of the equator, the dnys are shortest
near the aoath pole, and contiDually increase in length as we go north.

Examples.

(1). On April », 1879, at Washington, the altitude of Rigel above
the west hmuon was observed to be 12° 26'. Ite position was :

Right ascension = S" 8- 44'-27 = a.
Declination = - 8° 20' 86' = «.
The latitude of Washington is + 88° 58' 89' = *.
What was Uie hour angle of the star, and the sidereal time of ob-
servation f

lgBina= 9-882478

lg8in#= 9-797879
lgsind= - 9- 161681

— Ig sin ^ sin S = 8-959560

-sin*sin.J= 0-091109
sina= 0-215020

sin a - sin f sin il = 0806129

Igcos^ =
Igoos o =

IgCOSf 008 d =

Ig (ain a — sin ^ sin d, =
Igcos A =

* -I- 1« =
sidereal time =

9-891151
9-995879

9-886580
9-486905

9-599875 ,

66° 84' 88'
4^ 26'* 18'.90
6* 8-44'.2T
»k85» 2'.47

(2) Had the star been observed at the same altitude in the east,
iriut would have been the sidereal timet
Ans. a-A = 0k4a-8«*.07.

DBTBRMINATION OF LATITUDE.

Hence, in north-
the time ftbove the
hemisphere, f and

i body ifl supposed
) greater the nega-
I. Cmisidering, in
on and north and
go to the north on
I remain above ths
ination set. In the
, in the month of
dnys are shortest
^h as we go north.

ude of Rigel above
position was :

= a.

iidereal time of ob-

J8'
18'.90

a'.47

altitude in the east,

(8). At what sidereal time does Rigel rise, and at what sidereal
time does it set in the latitude of Washington f
- tg« - -9-906728
tgd = - 9166801

cos h =

A =

* -5- 15 =

a ^

- 9 078029

88^ 12' 19"
6h 82'» 49*.27
5k 8»'44'.27

rises 23'' 8»" aS'.OO
sets 10<' 41"' 88*.fi4

(4). What is the greatest altitude of Rigel above the horicon of
Washington, and what is its greatest depression below it r Ans.
Altitude=4a' 46' 45" ; depression =89° 26' 67'.

(6). What is the greatest altitude of a ater OD the equator in the
meridian of Washington f Ans. 51° •' 81". _

(6). The ddcllnatron of the pointer in the Great Bear whioh is
nearest the pole is 62' 80' N., at what altitude does it pass abow
the pole at Washington, and at what altitude does it pass below it V
Ans. 66° 88' 89' above the pole, and 11" 28' »9' when below it.

(7). If the declination of a star is 00° N., what length of sidereal
time is it above the horiaon of Washington and what length below it
during its apparent diurnal drauitf Ans. Above, ai** 68"* ; below.
2'' S".

§ 8. DETBBMIFATION OF lATTFUDBS ON THE
BABTH BY ASTBONOlCKSAIi OBSBBVATIONB.

Latitude fivm eireumpolor Uan.— In Pig. 16 let Z represent the
zenith of the place of observation, P the pole, and MPZ it the me-
ridian, the observer bring at the
centre of the sphere. Suppose
.Sand iS* to be the two points
at which a oircumpolar atar
' crosses the meridian in the d*-
scription of its q>pannt diurnal
cn-bit Then, since P is midway
between 8 and S",
ZS + ZB „„ .^

or.

Z+Z'

= W-f.

If, then, we can measure tiie dia-
tances Z and Z, we have

Z4-Z^

Fie. 16.

whidi seeree to determine f. The diataooes ZmA iF can be m«M-

, ,. .KS5^-

fc "

^SSy

A8TnoyoMr.

l! !

nred by the meridian circle or the sextant— both of which instru-
ments are descrilied in the next chapter — and the latitude in then
known. Z and Z" must be freed from tlie effects of refraction. In
this method no previous knowledge of the star's declination is re-
quired, provided it remains constant lietween the upper and lower
transit, which is the case for fixed stars.

Latitude by Oiroum-ienith Obaerratioiui If two stars

8 and S*, whose declinations 6 and A' are known, cross the meridian,
one north and the other south of the xenith, at zenith distances Z 8

and ZS', which call Z and Z', and
if wo have measured Z and Z, we
can from such measures find the
latitude ; for ^ = d + Z and « =
<' — Z", whence

f = i((d + d') + (z-2r)].

It will be noted that in this meth-
od the ktitude depends simply
upon the mean of two declinations
which ean be determined before-
hand, and only requires the diff'er-
meg of Moith distances to be ac-
curately measured, while the aln
solute values of these are unknown. In this oonslsts its capital ad-
vantage. This is the method invented by Oapt. Amdrrw Talcott,
U.S.A., and now universally adopted in America in Add astronomy,
in the practice of the Coast Survey, etc.

Latitude liy a Single Altitude of a Star. — In the triangle
ZPS(Vig. 14)thesidesareZP=iK)''~f;P5=90'' — a; Z8 =
Z = 90" — ri ; ZP8 = A = the hour angle. If we can measure at
any known sidereal time the altitude a of the star iS, and if we
further know the right ascension, a, and the declination, <i, of the
body (to be derived from the Nftutical Ahnanac or a catalogue uf
•tan), than w« have fron the tritngle

riofassinasind-l-cosacosdcosA;
or, idoM

taeS-' a; da f ^tin a tin 6 + CM a en 6 co» (9 — a),

firaoi whidi wa €M1 obtain *. It to to be noted that in a ptoce whose
latitode if) to known, this observatimi will determine 9, the side-
rsal time, ■• explained in tha last sectiim; if the sun is observed,
t to aimiily tiia solar tiua.

Latftnde tar a Meridian Altttnde.— If the alUtode of the
body to obaMTcd on tha iMridiKD and south of the lenith, the aqua-
tton above beeonas, since h^O'm thto case,

idnfssin«sin4<fcosacos4,
which u evidently the simplast method of obtaining f fram a

or.

tSf.

m^.Mi0^^mmm^^f^^m^^

l>oth of which instru-
«] the latitude in then
ict8 of refraction. In
tar's declination is re-
the upper and lower

btions.— If two stars
rn, cross the meridian,
it zenith distances Z 8
hich call Z and Z', and
measured Z and Z, we
ich measures find the
Dr f = i + Z and « =
ence

i + d') + (z-2r)].

9ted that in this meth-
tud« depends simply
san of two declinations
be determined before-
nly requires the diff'er-
th distances to be ac-
wmred, while the ab-
oonalsts its capital ad-
ipt. Amdrrw Talcovt,
icain Add astronomy,

Har. — In the triangle
?S=90' — 6i Zti =
If we can measure at
the star <t;, and if we
i declination, «i, of the
nac or a catalogue uf

I cos A;

08 d cos (0 — a),

that in a place whoae
cletermine 9, the side-
the sun is obaerred,

f the altitude of the
the lenith, the equa-

-a + S,
kining f fram a

PARALLAX.

ured altitude of a body of known declination. The last motliod is
that commonly used at sea, the altitude iMiing measured by the sex-
tant. The student can deduce the formula for a northern altitude.

% 0. PABALLAX AND 8EMIDIAMBTEB.

An observation of the apparent poeition of a heavenly
body can give only the direcUon in which it lies from the
station occupied by the observer without any direct indi-
cation of the distance. It is evident that two observers
stationed in different parts of the earth will not see such

tody in the same direction. In Fig. 18, let ^ be a sta-

Fia 18.-«ABAU.AZ.

tion on the earth, P a planet, Z' the zenith of S, and the
outer arc a part of the celestial sphere. An observation
of the apparent right ascension and declination of /* taken
from the station 1^ will give us an apparent position P*.
A similar observation at 8' will give an apparent position
P", while if seen from the centre of the earth the appar-
ent position would be P,. The angles P* P P, and
P* P P,^ which represent the differences of direction, are
called parallaaes. It is clear that the parallax of a body
depends upon its distance from the earth, being greater
the nearer it is to the earth.

The word parallaaB having several distinct applications,
we shall give them in order, commeudug with the most
general signification.

ASTRONOMT.

(1.) In itflmoHt general acceptation, parallax in tlio difTor-
encu between the diroctionH of a l)ody m neeii from two
different standpoints. This difference is evidently equal
to the angle made between two lines, one drawn from each
point of observation to the body. Thus in Fig. 18 the
difference between the direction of the body P as seen
from C and from S' is equal to the angle P' P P^, and this
again is equal to its opposite angle SPG. This angle is,
however, the angle between the two points C and S as
seen from P : we may therefore refer this most general
deiinition of parallax to the body itself, and define parallax
as the angle subtended by the line between two stations as
seen from a heavenly body.

(2.) In a more restricted sense, one of the two stations is
supposed to be some centre of position from which we
imagine the body to be viewed, and the paralkx is the
difference between the direction of the body from this
centre and its direction from some other point. Thus
the parallax of which we have just spoken is the differ-
ence between the direction of the body as seen from the
centre of the earth G and from a point on its surface as S.
If the observer at any station on the earth determines
the exact direction of a body, the parallax of which we
speak is the correction to be applied to that direction in
order to reduce it to what it would have been had the ob-
servation been made at the centre of the earth. Obser-
vations made at different points on the earth's surface are
compared by reducing them all to the centre of the earth.

We may also suppose the point ^7 to be the sun and the
circle /^ 4^ to be the earth's orbit around it. The paral-
lax will then be the difference between the directions of
the body as seen from the earth and from the sun. This
is termed the anmud paraUatt, because, owing to the an-
nual revolution of the earth, it goes through its period
in a year, always supposing the body observed to be at
rest.

(3.) A yet more restricted parallax is the horizontal

lax iR t,he diffor-
Hceti from two
ovidoutly equal
rewn from each
in Fig. 18 the
ody P as seen
'PP,, and this
This angle is,
its C and S as
is most general
1 define parallax
two stations as

B two stations is
From which we
paralUx is the
XKly from this
r point. Thus
nis the difFer-
seen from the
its surface as S.
rth determines
c of which we
lat direction in
Ben had the ob-
earth. Obser-
•h's surface are
re of the earth.
;he sun and the
t. The paral-
e directions of
the sun. This
ving to the an-
>ugh its period
served to be at

the hmzoniai

pahallax.

pavaJlm of a hoavo.ilj IkkIj. The parallax first doserilwl
"1 the last pairugmpli varies with the jKwition of tlio ob-
■erveron the surface of the earth, and lias its greatest
value when the body is seen in the horizon of the ob-
server, as may be seen by an inspection of Fig. 19 in
which the angle GPS attains its maximum when the Hne
18 IS tangent to the earth's surface, in which case P
will appear in the horizon of the observer at 8.

IV.— HmunniTAi. pAkaixax

The horizontal parallax depends upon the distance of a
body m the followmg manner: In the triangle C P 8.
nght-angled at S, we have S ^ ^ ^.

C8^GPmiCP8.
If, then, we put

p, the radius of the earth G8\
JS^the distance of the body P from the centre of the

»r, the angle 8P G, or the horizontal parallax,
we shall have,

sin n'

P = r sin >r; r

i« It wf Tf" *' '''** P^'^^^y «P^«"«J' the quantity p
^^tabsolute y con^nt for aU parts of thi earth, «7ito
greatest value w usually taken as tiiat to which 4e hori-

r^ nt' "^ ^ ^^«"^- This greatest value fa' «
we shall hereafter see, the radius of the equator, a^d h"

VS**"

53 ARTRONOMT.

corresponding valnc of tho parallax 18 thcroforo called the
eqmiton'd /wrhontaf jMUuUfito).

When the diatanco /• of the Ixxly i» known, tho wpxa-
tonal horizontal parallax can bo found by the firet of the
above equationa ; when tho paralUx can be obBerved, the
distance r is found from the second equation. IIow this
is done will be described in treating the subject of celes-
tial measurement. . . , . ^ , ii„.

It is easily seen that the equatorial horizontal parallax,
or the angle CPS^i'^ the same as the anguUr seim-
diameter of the earth seen from the object P. In fact,
if we draw the Une PST tangent to «io earth at ^, he
angle 5 P 5' will be the apparent angular diameter of tlie
earth as seen from i>, and wiU also be donblo the angle
CP8 The apparent semi-diameter of a heavenly body
is therefore given by the same f ormute as the pindlax
its own radius being substituted for that of the earth. If

we put,
p, the radius of the body in linear measure ;
r, the distance of its centre from the observer, expressed

in the same measure ; ^w.,„«r •

«, its anguhir semi-diameter, as seen by the observer ,

we shall have,

. . P

sm « = -•

If we measu^ tbe semi-diameter «, and know the dis-
tance, r, the radius of the body will be

p = r rin «.
Generally tlie angnkr semi-diameters of the heavenly
bod^r.^L small that they may be considered the same
^Wr^nl We may theref o.^ say that the apparent
Tn^Sr diameter of a heavenly body varies inversely as
its distance.

oforo called the

own, the cqua-
the first of the
e observed, the
ion. IIow thia
iibject of celea-

izontal parallax,
anffular semi-
set P. In fact,
earth at S', the
diameter of the
onblo the angle
a heavenly body
as the parallax,
if the earth. If

lure ;

server, expressed

the observer ;

kd know the dis-

i of the heavenly
isidered the same
th^the apparent
aries inversely as

CHAPTER II.

ASTRONOMICAL INSTRUMENTa
§ 1. THE EBFEAOmrO TBLBSOOPB.

In explaining the theory and use of the refracting tele-
scope, we shall assume that the reader is acquainted with
the fundamental principles of the refraction and disper-
sion of light, so that the simple enumeration of them
will recall them to his mind. These principles, so far
as we have occasion to refer to them, are, that when
a ray of light passing through a vacuum enters a trans-
parent medium, it is refracted or bent from its course
in a direction toward a line perpendicular to the sur-
face at the point where the ray enters ; that this bend-
ing follows a certain law known as the law of sines ;
that when a pencil of rays emanating from a luminous
point falls nearly perpendicularly upon a convex lens,
the rays, after passing through it, all converge toward a
point on the other side called a focus : that light is com-
pounded of rays of various degrees of refrangibiUty, so
that, when thus refracted, the component rays pursue
slightly different courses, and in passing through a lens
come to slightly dififerent foci ; and finally, that the ap-
parent angular ma^itude subtended by an object when
viewed from any point is inversely proportional to its
distance.*

• More exactly. In the cam of a globe, the sine of the angle Is in-
venely as the diatanoe of the object, aa shown on the preceding page.

64 AHTRONOMY.

We ■hall tint doscrilM) tho toloncopo in its siniplMt
^H^^B form, showing the principluH upon whidi
^^^^^1 its action depends, leaving out of considora-
^^^^^1 tion tlie defects of aberration which retpiiro
^l^^^l special devices in order to avoid them. In
^^^^^1 the simplest fonn in which we can conceive
^^^^^1 ^ of a telescope, it consists of two lenses of
^^^^H § unequal focal lengths. The puqKMBo of one
^^^^^H ° of these lenses (called the of^ectivc, or object
^^^^M I gkua) is to bring the rays of light from a
^^^^H i distant object at which the telescope is
^^^^H ° pointed, to a focus and there to form an
^^^^H ^ image of the object. The purpose of the
^^^^H M other lens (called the eye-piece) is to view
^^^^H I this object, or, more precisely, to form an-
^^^^^1 other enlarged image of it on the retina of
^^^^^1 ^ tho

^^^^H § The figure gives a representation of the
^^^^H I course of one pencil of the rays which go to
^^^^H S fonn the image ^ 7' of an object / li after
^^^^H & passing through the objective 0'. The
" pencil chosen is that composed of all the
rays emanating from / which can possibly
[ „ fall on tho objective 0'. All these are,
^^^^1 2 by the action of the objective, concentrated
^^^^H 2 at the point T. In the same way each point
^^^^H g of the image out of the optical axis A B
^^^^H % emits an oblique pencil of diverging rays
^^^^H '. which are made to converge to some point
^^^^1^. of the image by the lens. The image of
^^^^H£ the point B of the object is the point A of
^^^^H the image. We must conceive the image of
^^^^H any object in the focus of any lens (or
^^^^H mirror) to be formed by separate bundles
^^^^H of riiya as in the figure. The image thus
HHlB formed Inicomcs, in its turn, an object to
be viewed by the eye-piece. After the rays meet to form

MAUNIFYIlfU PVWh'Il VF TKI.K8G0PK.

in ito ninipleflt
»luit upon which
mi of conaidera-
)n which recjuiro
iivoid them. In
wo can concoivo
of two lunacH of
e pur]K)8o of one
hjective^ or cijeot
of light from a
the telescope is
lere to form an
3 purpose of the
•piece) is to view
jely, to form an-
on the retina of

Mentation of the
rays which go to
object / B after
jtivc 0'. The
ipoeed of all the
liich can poflBibly
'. All these are,
;iye, concentrated
lie way each point
optical axis A B
)f diverging rays
irge to some point
The image of
ig the point A of
leive the image of

of any lens (or
separate bundles

The image thus
iim, an object to
rays meet to form

the imago (»f an object, as at /, thoy continue on tlioir
course, diverging from /' as if the latter wore a material
object reflecting the light. There is, however, this excep-
tion : that the rays, insteiwl of diverging in every direction,
only fonn a small cone having its vertex at /', and having
its angle equal io O F C The reason of this is that
only those rays which pass through the objective can form
the image, and thoy must continue on their course in
straight lines after forming the image. This image can
now bo viewed by a lens, or even by the unassisted eye, if
the observer places himself behind it in the direction A^
so that the pencil of rays shall enter his eye. For the pres-
ent we may consider the eye-piece as a simple lens of
short focus nice a common hand-magnifier, a more com-
plete description l>« ng given later.

Magnifying Fow«r.— To unc^orstand the manner in
which the telescope magnifies, we remark that if an eye at
the object-glass could view the image, it would appear of
the saine size as the actual objt^ct, the iii^ge and the object
subtending the same angle, but lyinc^ » opposite direc-
tion. This angular magnitude beih^ ihe same, whatever
the focal distance at which • > ^ tmage is former', it follows
that the size of the inuige vf ties iirectly as thu local length
of the object-ghus. But when we view an object with a
lens of small focal distance, its apparent magnitude is thr;
same as if it were seen at that focal distance. Consequently
the apparent angular magnitude will be inversely as the
focal distance of the leuF Hence the focal image as
seen with the eye-pioce will appear lai^r than it would
when viewed from the objective, in the ratio of the focal
distance of the objective to that of the eye-piece. But we
have said that, seen through the objective, the image and
the real object subtend the same angle. Hence the angu-
lar magnifyi^T power is equal to the focal distance of the
objective, dir h-] by that of the eye-piece. If we simply
turn the telescope end for end, the objective becomes the
eye-piece and the latter the objective. The ratio is in-

ASTRONOMY.

verted, and the object is diminished in size in tl:o same
ratio that it is increased when viewed in the ordinary
way. If we should form a telescope of two lenses of
equal focal length, by placing them at double their focal
distance, it would not magnify at all.

The image formed by a convex lens, being upside
down, and appearing in the same position when viewed
with the eye-piece, it follows that the telescope, when
constructed in the simplest manner, shows all objects in-
verted, or upside down, and right side left. This is the
case with all refracting telescopes made for astronomical
uses.

Light-gathering Power.— It is not merely by magnify-
ing that the telescope assists the vision, but also by in-
creasing the quantity of light which reaches the eye from
the object at which we look. Indeed, should we view an
object through an instrument which magnified, but did
not increase the amount of light received by the eye, it is
evident that the brilliancy would be diminished in propor-
tion as the surface of the object was enlarged, since a con-
stant amount of light would be spread over an increased
surface ; and thus, unless the light were faint, the object
might become so darkened as to be less plainly seen tlian
with the naked eye. How the telescope increases the
quantity of light will be seen by considering that when the
unaided eye looks at any object, the retina can only re-
ceive so many rays as fall upon the pupil of the eye. By
the use of the telescope, it is evident that ac many rays
can be brought to the retina as fall on the entire object-
glass. Tlie pupil of the human eye, in its normal state,
has a diameter of about one fifth of an inch ; and by the
use of the telescope it is virtually increased in surface in
the ratio of the square of the diameter of the objective to
the square of one fifth of an inch. Thus, with a two-mch
aperture to our telescope, the number of rays collected is
one Imndred times as great as the number collected with
the naked eye. ,

ze in tlio Batne
the ordinary
two lenses of
ible their focal

being upside
when viewed
elescope, when
all objects in-
t. This is the
or astronomical

sly by magnify-
but also by in-
hs the eye from
uld we view an
!;niiied, but did
by the eye, it is
shed in propor-
:ed, since a con-
er an increased
faint, the object
lainly seen tiian
e increases the
g that when the
na can only re-
»f the eye. By
t ac many rays
le entire object-
B normal state,
ch ; and by the
d in surface in
th& objective to
with a two-inch
ays collected is
r collected with

POWER OF TELESCOPE.
"With a 5-inch object-glass, the ratio is

(( in (< (t (( (( ((

n ii^g (( <t (( (( ((

i( 20 " '' " " "

(( 26 " '* *' ** **

625 to 1

2,500 to 1

5,625 to 1

10,000 to 1

16,900 to 1

When a minute object, like a star, is viewed, it is
necessary that a certain number of rays should fall on the
retina in order that the star may be visible at all. It is
therefore plain that the use of the telescope enables an
observer to see much fainter stars than he could detect
with the naked eye, and also to see faint objects much
better than by unaided vision alone. Thus, with a 26-
inch telracope we may see stars so minute that it would
require many thousands to be visible to the unaided eye.

An important remark is, however, to be made here,
inspecting Fig. 20 we see that the cone of rays passing
through the objiBct-glass converges to a focus, then diverges
at the same angle in order to pass through the e/e-piece.
After this passaga the rays emerge from the eye-piece
parallel, as shown in Fig. 22. It is evident that the
diameter of this cylinder of parallel rays, or '* emergent
pencil," as it is called, is less than the diameter of the
object-glass, in the same ratio that the focal length of the
eye-piece is less than that of the object-glass. For the
central ray //'is the common axis of two cones, A 1' and
r Cfj having the same angle, and equal, in length to
the respective focal distances of the glasses. But this
ratio is alsb the nutgnifying power. Hence the diameter
of the emergent pencil of rays is found by dividing the
diameter of the object-glass by the magnifying power.
Now it is clear that if the magnifying power is so small
that this emergent pencil is larger than the pupil of the
eye, all the light which falls on the object-glass cannot
enter the pupil. This will be the case whenever the
magnifying power is less than five for every inch of
aperture of the glass. If, for example, the observer should

ASTBONOMT.

look through a twelve-inch telescope with an eye-piece
so large that the magnifying power was only 30, the
emergent pencil would be two fifths of an inch in diam-
eter, and only so much of the light could enter the pupil
as fell on the central six inches of the object-glass.
Practically, therefore, the observer would only be using a
six-inch telescope, all the light which fell outside of the
six-inch circle being lost. In order, therefore, that he
may get the advantage of all his object-glass, he must use
a magnifying power at least five times the diameter of his
objective in inches.

When the magnifying power is carried beyond this
limit, the action of a telescope will depend partly on the
nature of the object one is looking at. Viewing a star,
the increase of power will give no increase of light, and
therefore no increase in the apparent brightness of the
star. If one is looking at an object having a sensible
surface, as the moon, or a planet, the light coming
from a given portion of the surface will be spread over a
larger portion of the retina, as the magnifying power
is increased. All magnifying must then be gained at
the expense of the apparent illumination of the surface.
Whether this loss of illumination is important or not will
depend entirely on how much light is to spare. In a
general way we may say that the moon and all the plan-
ets nearer than Saturn are so brilliantly illuminated by
the sun that the magnifying power can be carried many
times above the limit without any loss in the distinctness
of vision.

The Telescope in Meaaurement. — A telescope is gen-
erally thought of only as an instrument to assist the eye
by its magnifying and light-gathering power in the man-
ner we have described. But it has a very important
additional function in astronomical measurements by en-
abling the astronomer to point at a celestial object with a
certainty and accuracy otherwise unattainable. This func-
tion of the telescope was not recognized for mon than

USE OF TELBSCOPK

ith an eye-piece
as only 30, the
m inch in diam-
. enter the pupil
the object-glass.

I only be using a

II outside of the
lerefore, that he
^ass, he must use
} diameter of his

ed beyond this
id partly on the
Viewing a star,
se of light, and
rightness of the
Eiving a sensible
e light coming
be spread over a
ignifying power
in be gained at
of the surface,
rtant or not will
to spare. In a
uid all the plan-
illuminated by
)e carried many
the distinctness

elescope is gen-
to assist the eye
wer in the man-
very important
arements by en-
ial object with a
t>le. This fonc-
l for more thaa

^^m^^m

half a century after its invention, and after a long and
rather acrimonious contest between two schools of astron-
omers. Until the middle of the seventeenth century,
when an astronomer wished to determine the altitude of a
celestial object, or to measure the angular distance be-
tween two stars, he was obliged to point his quadrant or
other measuring instrument at the object by means of
' * pinnules. ' ' These served the same purpose as the sights
on a rifle. In using them, however, a difliculty arose.
It was impossible for the observer to have distinct vision
both of the object and of the pinnules at the same time,
because when the eye was focused on either pinnule, or
on the object, it was necessarily out of focus for the
others. The only way to diminish this diflSculty was to
lengthen the arm on which the pinnules were fastened so
that the latter should be as far apart as possible. Thus
Tycho Bbahe, before the year 1600, had measuring in-
struments very much larger than any in use at the pres-
ent time. But this plan only diminished the difficulty and
could not entirely 't)bviate it, because to be manageable
the instrument must not be very large.

About 1670 the English and French astronomers found
that by simply inserting fine threads or wires exactly in
the focus of the telescope, and then pointing it at the ob-
ject, the image of that object formed in the focus could be
made to coincide irith the threads, so that the observer
could see the two exactly superimposed upon each other.
"When thus brought into coincidence, it was known that
the point of the object on which the wires were set was in
a straight line passing through the wires, and through the
centre of the object-glass. So exactly could such a pointr
ing be made, that if the telescope did not magnify at all
(the eye-piece and object-glass being of equal focal length),
a very important advance would still be made in the ac-
curacy of astronomical measurements. This line, passing
oentrally through the telescope, we call the line of col-
Umatim of the telescope, A Bin Fig. 20. If we have

sifiEBisiasjc;;

IfSJ^WftffS

flO

A8TB0N0MT.

any way of determining it we at once realize the idea ex-
pressed in the opening chapter of this book, of a pencil ex-
tended in a definite direction from the earth to the heav-
ens. If the observer simply sets his telescope in a fixed
position, looks through it and notices what stars pass along
the threads in the eye-piece, he knows that those stars all
lie in the line of collimation of his telescope at that instant.
By the diurnal motion, a pencil-mark, as it were, is thus
being made in the heavens, the direction of which can be
determ'ned with far greater precision than by any meas-
urements with the unaided eye. The direction of this line
of collimation can be determined by methods which we
need not now describe in detail.

The Aohromatio Telescope. — The simple form of tele-
scope which we have described is rather a geometrical
conception than an actual instrument. Only the earli-
est instruments of this class were made with so few as two
lenses. Galileo's telescope was not made in the form
which we have described, for instead of two convex lenses
having a common focus, the eye-piece was concave, and
was placed at the proper distance inside of the focus of the
objective. This form of instrument is still used in opera-
glasses, but is objectionable in large instruments, owing to
the smallness of the field of view. The use of two con-
vex lenses was, we believe, first proposed by Eepleb.
Although telescopes of this simple form were wonderful
instruments in their day, yet they would not now be re-
garded as serving any of the purposes of such an instru-
ment, owing to the aberrations with which a single lens is
effected. We know that when ordinary light passes
through a simple lens it is partially decomposed, the differ-
ent rays coming to a focus at different distances. The
focus for red rays is most distant from the object-glass,
and that for violet rays the nearest to it. Thus arises
the ohromatio aberration, of a lens. But this is not all.
Even if the light is but of a single degree of refrangi-
bility, if the surfaces of our lens are spherical, the rays

ize the idea ex-
, of a pencil ex-
■th to the hear-
scope in a fixed
stars pass along
it those stars all
B at that instant,
it were, is thus
>f which can be
in by any meas-
tion of this line
ithods which we

le form of tele-
r a geometrical
Only the earli-
th so few as two
ide in the form
leo convex lenses
as concave, and
' the focus of the
11 used in opera-
Lments, owing to
use of two con-
led by Kepleb.
were wonderful
not now be re^
such an instru-
li a single lens is
17 light passes
)0fled, the differ-
distances. The
the object-glass,
it. Thus arises
t this is not all.
;ree of refrangi-
herical, the rays

A CHROMA TIO OBJECT- GLASS.

wliich pass near the edge will come to a shorter focus
than those which pass near the centre. Thus arises
spherical aherratian. This aberration might be avoided
if lenses could be ground with a proper gradation of
curvature from the centre to the circumference. Prac-
tically, however, this is impossible ; the deviation from
imiform sphericity, which an optician can produce, is too
small to neutralize the defect.

Of these two defects, the chromatic aberration is much
the more serious ; and no way of avoiding it was known
until the latter part of the last century. The fact had,
indeed, been recognized by mathematicians and physicists,
that if two glasses could bo found having very different
ratios of refractive to dispersive powers,* the defect could
be cured by combining lenses made of these different
kinds of glass. But this idea was not realized until the
time of DoLLOND, an English optician who lived during
the last century. This artist found that a concave lens of
flint glaj98 could be combined with a convex lens of crown of
double the curvature in such a manner that the dispersive
powers of the two lenses should neutralize each other, being
equal and acting in opposite di-
rections. But the crown glass
having the greater refractive
power, owing to its greater cur-
vature, the rays would be brought
to a focus without dispersion.
Such is the construction of the
achromatic objective. As now
made, the outer or crown glass lens is double convex ; tlie
inner or flint one is generally nearly plano-concave.
Fig. 31 shows ihe section of such an objective as made
by Alvan Glabk & Sons, the inner curves of the crown
and flint being nearly equal.

* By the r^fraelitie power of a glass is meant its power of bending the
rays out of thefar ooane, so as to bring them tn a focus. By its d^pvr-
«iw potter is meant its power (rf separating tlie colors so as to form a
Vectnun, or to produce chromatic aberration.

iiiiiiiriii

Fio.

21.— flBonoN or oBntoT-
ahim.

ms.:-^^

aX-^

mmm

ASTRONOMY.

A great advantage of the achromatic objective is that it
may be made to correct the spherical as well as the chro-
matic aberration. This is effected by giving the proper
curvature to the various surfaces, and by making such
slight deviations from perfect sphericity that rays passing
through all parts of the glass shall come to the same focus.

The Secondary Speotrum. — It ia now known that the
chromatic aberration of an objective cannot be perfectly
corrected with any combination of glasses yet discovered.
In the best telescopes the brightest rays of the spectrum,
which are the yellow and green ones, are all brought to
the same focus, but the red and bine ones reach a focus
a little farther from the objective, and the violet ones a
focus still farther. Hence, if we look at a bright star
through a large telescope, it will be seen surrounded by a
blue or violet light. If we push the eye-piece in a little
the enlarged image of the star will be yellow in the centre
and purple around the border. This separation of colors
by a pair of lenses is called a secondary spectrum.

Bye-Pleoe.— In the skeleton form of telescope before
described the eye-piece as well as the objective was con-
sidered as consisting of but a single lens. But with such
an eye-piece vision is imperfect, except in the centre of
the field, from the fact that the image does not throw
rays in every direction, but only in straight lines away
from the objective. Hence, the rays from near the edges
of the focal image fall on or near the edge of the eye-
piece, whence arises distortion of the image formed on
the retina, and loss of light. To remedy this difficulty a
lens is inserted at or very near the place where the focal
image is formed, for the purpose of throwmg the different
pencils of rays which emanate from the several parts of
the image toward the axis of the telescope, so that they
shall all paos nearly through the centre of the eye lens pro-
per. These two lenses i>re together called the eye-piece.
There are some small differences of detail in the con-
struction of eye-pieces, but the general principle is the

TUEOnr OF OBJBXfT-OLASS.

ictive is that it
11 as the chro-
ng the proper

making Bnch
it rays passing
he same focus.
noMOi that the
)t be perfectly
yet discovered.
' the spectrum,
> all brought to
s reach a focus
le violet ones a
t a bright star
arrounded by a
piece in a little
w in the centre
ration of colors
iotntm.

elescope before
jective was con-
But with such
1 the centre of
loes not throw
ght lines away
L near the edges
Jge of the eye-
lage formed on
this difficulty a
gvhere the focal
ug the different
several parts of
36, so that they
the eye lens pro-

the eye-piece.
»il in the con-
principle is die

same in all. The two recognized classes are tlio posi-
tive and negative, the former being those in which the
imago is formed before the light reaches the field lens ; the
negative those in wlilch it is fonned between the lenses.

The figure shows the positive eye-pieco drawn accurately to scale.
/ is one of the converging; pencils from the object-glass which
forms one point (/) of the focal image / a. This image is viewed
by the Jlela lent F of the eye-piece as a real object, and the shaded
pencil between F and E shows the course of these rays after de-
viation by F. If there were no eye-lmu E an eye properly placed
beyond F would see an ima^ at /' a'. The eye-lens E receives the
pencil of rays, and deviates it to the observer's eye placed at such a
point that the whole incident pencil will pass through the pupil
and fall on the retina, and thus be effective. As we saw in the

22.— BBcnoR or a vaarmt BTR-pmnL

figure of the refracting telescope, ever; point of the object producet

a pencil similar to /, and the whole surfaces of the lensea F

and E are covered with rays. All of these pencils paasinK through

the pupil ^ to make up the retinal image. This image u refemd

by the mind to the distance of distinct vision (about ten inches),

and the image A I" represents the dimension of the final image

A F'
relative to the image a / as fonned by the objective and — y ^

evidently the nujipiif ving power of this particular eye-piece used
in combination with this particular objective.

More Eicaot Theory of the Ol^jeotive For the benefit of the

reader who wishes a more precise knowledge of the optical princi-

Sles on which the action of the objective or other system of lenses
epends, we present the following geometrical theory of the sub-
ject. This theory ft not rigidly exact, but is sufficiently so for all
ordinary computations of we focal lengths and sizes of image in
the usual combinations of lenses.

A8TR0N0MY.

Oentrea of Oonyenenoe and Divergenoe.—Siinpoge A B, Fig.
28, to be a IcnH or commnation of lonscs on which the light falls from
the left hand and passes through to the right. Suppose rays parallel
to 7? P to fall on every part of the first surface of tnc glass. After
passing through it they are all supposed to converge nearly or ex-
actly to the same point If. Among all these rays there is one, and
one only, the course of which, after emerging from the glass at Q,
will be parallel to its original direction It P. Let li P Qlf be this
central ray, which will \hs completely determined by the direction
from which it comes. Next, let m take a ray coming from another
direction m 8 P, Among all the rays parallel to 8 P, let us take
that one which, after emerging from the glass at 7*, moves in a line
parallel to its original direction. Continuing the process, let u>
suppose isolated rays coming from all parts of a distant object sub-
ject to the single condition that the course of each, after passing
through the glus or system of glasses, shall be parallel to its original
course. These rays we may call cmtml rayt. They have this re-
markable property, pointed out by Oauw: that they all converge

Fig. 38.

toward a single point, i*, in coming to the gloss, and diverge from
another point, i*, after passing through the last lens. These points
were termed by Gacbs " Hauptpunkte," or principal points. But
they will probably be better understood if we call the first one the
centre of convergence, and the second the centre of divergence.
It must not be understood that the central rays necessarily pass
through these centres. If one of them lies outside the first or lost
refracting surface, then the central rays must actually pass through
it. But if they lie between the surfaces, they will be fixed by the
continuation of the straight line in which the rays move, the latter
being refracted out of their course by passing through the surface,
and thus avoiding the points in question. If the lens or system of
lenses be turned around, or if the light passes through them in an
opposite direction, the centre of oonveigence in the first case be-
comes the centre of divergence in the second, and mee verta. The
necessity of this will be clearly seen by reflecting that a return ray
of light will always keep on the course of the original ray in the
opposite direction.

liinpoBe A B, Fig.
ic light falls from
iposc rays parallel
the glass. After
rge nearly or ex-
tnere is one, and
n the glass at Q,
R P Q li' he Mh
{ by the direction
ling from another
SP, let us take
T, moves in a line
he process, let us
istant object sub-
ich, after passing
illcl to its original
hey have this re-
they all converge

and diverge from
lens. These points
cipal points. But
11 the first one the
tre of divergence.
j» necessarily pass
ide the first or last
dually pass through
rill be fixed by the
lys move, the latter
irough the surface,
le lens or system of
hrough them in an
n the first case be-
tnd mce verta. The
ig that a return ray
I original ray in the

riiKOBY OF oBJBcr-aLAaa.

The figure represents a plano-convex lenn with light falling on
the convex side. In this case the centre of convergence will be
the convex surface, and that of divergence inside the glass

aliout one third or two fifths of the way from the convex to the
plane surface, the positions varying with the refractive index of the
glass. In a double convex lens, both points will lie inside the glass,
while if a glass is concave on one side and convex on the other,
< ne of the points will be outside the glass on the concave side. It
nust be remembered that the positions of these centres of conver-
gance and divergence depend solely on the form and size of the
lenses and their refractive indices, and do not refer in any way to
the distances of the objects whose images the^ form.

Tht principal properties of a lens or objocti^ c, by which the size
of imageb «re determined, are as follows : Since the angle 9 P B!
made by the u>erging rays is equal U> RP 8, made by the con-
verging ones, it fo;Ws, that if a lens form the image of an object,
the size of the image will be to that of the object as their respec-
tive distances from the cei:t<«« of convergence and divergence. In
other words, the object seen from the centre of convergence P will
be of the same angular magnitude as the image seen from the
centre of divergence P*.

By eotyugaU fon of a lens or system of lenses we mean a puIi- of
points such that if rays diverge from the one, they will converge to
the other. Hence if an object is in one of a pair of such foci, the
image will be formed in the ot)i«r.

By the rtfraOMt powr of a lens or combination of lenses, we
mean its influence in refracting parallel rays to a focus which we
may measure by the recipiocai of its focal distaoce or 1 -i-f. Thus,
the power of a piece of plain glass is 0, because it cannot bring
rays to a focus at alL The power of a convex lens is positive, while
that of a concave lens is negative. In the latter case, it will be
remembered by the student of optics that the virtual focus is on
the same side of the lens from which the rays proceed. It is to
be noted that when we speak of the focal distance of a lens, we
mean the distance from the centre of diveq^nce to the focus for
])arallel rays. In astronomical language this focus is called the
stelhir focus, being that for celestial objects, all of which we may
regard as infinitely distant. If, now, we put

p, the power of the lens ;

/, its stellar focal distance ;

fy the distance of an object from the centre of convergence ; .

/', the distance of its image from the centre of divergence ; then
the equation which determines/ will be

1 1 1

f^f'-f-^'

or.

f- ffL. .

/' = >^.

f-f

From these equations may be found the focal length, having the
distance at which the image of an object is formed, or viee verta.

?*?»*«

wfsMTfmi'^m**- ,

ASTRONOMY.

8 9. BSFLEOTDfO TXLBBOOPBS.

Ar wo liavo Been, the most enential part of a rafraeting
teluHcopo is the objective, which brings all the incident
rays from an object tu one focus, forming there an image
of tba object. In reflecting telescopes (reflectors) the
objective is a m^ror of speculum metal or silvered glass
ground tQ the shape of a paraboloid. The figure shoMnt
the action of such a mirroi on a bundle of parallel rays,
which, after impinging on it, are brought by reflection tu
one focus F. The image formed at this focus may be
viewed with an eye-piece, as in the case of the refracting
telescope.

The eye-pieces used with such a mirror are of the kinds
already described. In the figure the eye-piece would

FlO. 84.— CONCAVS MIRBOR rORMINO AK IMAOC

have to be placed to the right of the point F, and the
observer's head would thus interfere with the incident
light. Various devices have been proposed to remedy this
inconvenience, of which we will ifaiiffribe the two most
common.

Hm Vewtonieii IMeecope. — In this form the rays of
light reflected from the mirror are made to fall on a small
plane mirror placed diagonally just before they reach the
principal focus. The rays are thus reflected out laterally
through an opening in the telescope tube, and are there
brought to a focus, and the image formed at the point
marked by a heavy white line in Fig. 25, instead of at
the point inside the telescope marked by a dotted line.

)PES.

t of a rofracting

nil the incident

there an image

(reflectors) the

>r silvered glass

10 figure showt

)f parallel rays,

by reflection to

I focus may be

f the refracting

are of the kinds
)ye-piece would

K IMAOB.

oint F, and the
ith the inddeDt
d to remedy this
le fhe two most

ytm the rays of
bo fall on a small
■e they reach the
ted out laterally
le, and are there
led at the point
i5, instead of at
»y a dotted line.

RKFLKCTtNO TSLBBGOPKS.

This focal image is then examined by means of an or-
dinary eye-piece, the head of the observer being outside
of the telescope tube.

Tills device is the invention of Sir Isaac Nkwton.

HBWTONIAN TBLBSCOPB.

FiOw M.

CAflERnRAINTAN TKI^BSCOTB.

Tlie Oalisegr&iman Teietiooi>e. — In this form a second-
ary convex mirror is piaced in the tube of the telescope

'-~«.sSB^PIB««WB'"-

r.8

AHTHONOMr.

abont three ■ 'tii« ,jf Uie wiiy from the hirge HptMtuiutn
to the fociiH. The riiyH, after l>eing roHeetetl from the
largo 8))ecuhiin, fall oa this mirror befoit) reaching the
focus, and are reHected back again to the Bpvculuni ; an
opening is made in the centre of the latter to lot the ravs
imm through. The position and curvature of the secondary
mirror are adjusted so that the focus shall be formed just
after passing through the opening in the speculum.

In this telescope the obsurvet stands behind or under
the speculum, and, with the oyo-pieco, looks through the
opening in the centre, in the direction of the object.
This form of reflector is much more convenient in use
than the Newtonian, in using which the observer has to
be near the top of the tube.

This form was devised by Cabrkorain in 1672.

Tho advantages of reflectors are found in their cheap-
ness, and in the fact that, supposing the mirrors perfect in
tigure, all the rays of the spectrum are brought to one
focus. Thus the reflector is suitable for spectroscopic or
]>hotographic researches without any change from its or-
dinary fonn. This is not true of the refractor, since the
rays by which we now photograph (the blue and violet
rays) are, in that instrument, owing to the secondary
spectrum, brought to a focus slightly different from that
of the yellow and adjacent rays by moans of which we

060*

Beflectors have been made as large as six feet in aper-
ture, the greatest being that of Lord Robse, but those
which have been most successful have hardly ever been
larger than two or three feet. The smallest satellite of
Satntm {Minuu) was discovered by Sir Wiujam Hersohel
with a four-foot speculum, but all the other satellites dis-
covered by him were seen with mirrors of about eighteen
inches in aperture. With these the vast majority of his
faint nebnlsB were also discovered.

The satellites of Neptune and TTrantts were discovered
by Lassell with a two-foot speculum, and much of the

nKFLKcrmn TKijjsropfss.

largo Rpecuium
leotud from tlio
m reaching the
J spvculuin ; an
ir to lot the rava
of the secondary
i Im) formed just
tpeculum.
behind or nndor
x>k8 through the
I of tho object,
mveniont in uro
) observer has to

in 1672.

in their chcap-
nirrors perfect in
brought to one
spectroscopic or
mge from its or-
f ractor, since the
) blue and violet
o the secondary
ferent from that
lans of which we

\ six feet in aper-
RosBE, but those
hardly ever been
allest satellite of
II4.IAM Hersohel
ther satellites dis-
at about eighteen
t majority of his

» were discovered
and much of the

work of Lord Rohhk has boon doiio with liitt throo-foot
mirror, iuHtead of liiw (Hilobmtod nix foot oin\

From tho tinu) of Nkwton till (luito rccontly it wa«
usual to make tho largo mirror or objoj-tivo out of Bpcu-
Inni motal, a brilliant alloy liublo to tanuHh. Whon tho
mirror was onco tiirnishod through cxjKWuro to tho
woathor, it could bo ronowod only by a proccBS of jwlish-
ing almost equivalent to figuring and polishing tho mirror
anew. Consequontly, in such a speculum, after the cor-
rect f jrtn and polish wore attained, there was groat diffi-
culty in preserving them. In rocont years this difficulty
has been largely ovorcomo in two ways : first, by im-
provements in the composition of the alloy, by which its
liability to tarnish under exposure is greatly diminished,
and, secondly, by a plan proposed by Foucault, which
C(m8ist8 in making, onco for all, a mirror of ghws which
will always retain its good figure, and depositing upon it a
thin film of silver which may be removed and restored
Mrith little labor as often as it becomes tarnished.

In this way, one important defect in the reflector has
been avoided. Another great defect has been less success-
fully treated. It is not a pntcess of exceeding difficulty
to give to the reflecting surface of either metal or glass
the correct parabolic shape by which the incident raya are
brought accurately to one focus. But to maintain this
shape constantly when the mirror is mounted in a tube,
and when this tube is directed in succession to various
parts of the sky, is a mechanical problem of extreme diffi-
culty. However the mirror may be supported, all the
unsupported points tend by their weight to sag away from
the proper position. "Wben the mirror is pointed near
the horizon, this effect of flexure is quite different from
what it is when pointed near the zenith.

As long as the mirror is small (not greater than eight to
twelve inches in diameter), it is foimd easy to support it
so that these variations in the strains of flexure have little
practical effect. As we increase its diameter up to 48 or

mmm

AaTRONOMT.

72 inches, the effect of flexure rapidly increases, and
special devices have to he used to couuterhalaiice the
injury done to the shape of the mirror.

§ 3. CHBONOMETEBS AND CLOCKS.

In Chapter I., § 5, wo described how the right ascen.
sions of the heavenly bodies are measured by the times
of their transits over the meridian, this quantity increas-
ing by a minute of arc in four seconds of time. In order
to determine it with all required accuracy, it is necessary
that the time-pieces with wliich it is measured shall go
with the greatest possible precision. There is no great
difficulty in making astronomical measures to a second
of arc, and a star, by its diurnal motion, passes over this
space in one fifteenth of a second of time. It is there-
fore desirable that the astronomical clock shall not vary
from a uniform rate more than a few hundredths of a
second in the course of a day. It is not, however,
necessary that it should be perfectly correct ; it may go
too fast or too slow without detracting from its char-
acter for accuracy, if the intervals of time which it
tellfl off—hours, minutes, or seconds— are always of ex-
actly the same length, or, iu other words, if it gains or
loses exactly the same amount every hour and every day.

The time-piecos used in astronomical observation are
the chronometer and the clock.

The chronmnMer is merely a very perfect time-piece
with a balance-wheel so constructed that changes of tem-
perature have the least possible effect upon the time of its
oscillation. Such a balance is called a eom^pematum bal-
ance.

The ordinary house clock goes faster in cold than in
warm weather, because the pendulum rod shortens under
the influence of cold. This effect is such that the clocl
will gain about one second a day for every fall of 3° Cent.
{ft" A Fahr.) in the temperature, supposing the pendulum

THE ASTRONOMICAL CLOCK.

increases, and
iterbalanco the

[jOCKB.

:ho right ascen.
d by the times
uantity increas-
time. In order
•, it is necessary
lasured shall go
ere is no great
■£S to a second
passes over this
e. It is there-
c shall not vary
lundredths of a
not, however,
rect ; it may go
from its char-
time which it
3 always of ex-
3, if it gains or
and every day.
observation are

rfect time-piece
changes of tem-
1 the time of its
vr^^ensaMon bal-

in cold than in
i shortens under
li that the clocE
rfaUof 3°0ent.
g the pendulnm

rod to be of iron. Such changes of rate would be entirely
inadmissible in a clock used for iistronomical purposes.
The astronomical 'Jock is therefore provided with a com-
pensation pendulum, by which the disturbing effects of
changes of temperature are avoided.

There are two forms now in use, the Harrison (grid-
iron) and the mercurial. In the gridiron pendulum the
rod is composed in part of a number
of parallel bars of steel and brass,
so connected together that while the
expansion of the steel bars produced
by an increase of temperature tends
to depress the hob of the pendulum,
the greater expansion of the brass bars
tends to raise it. When the total
lengths of the steel and brass bars
have been properly Jidjusted a nearly
perfect compensation occurs, and the
centre of oscillation remains, at a con-
stant distance from the point of sus-
pension. The rate of the clock, so
far as it depends on the length of the
pendulum, will therefore be constant.

In the mercniial pendulum the
weight which f onus the bob is a
cylindric glass vessel nearly filled
with mercury. With an increase of temperature the steel
suspension rod lengthens, thus throwing the centre of
osdllation away from the point of suspension ; at the
same time the expanding mercury rises in the cylinder,
and tends therefore to raise the centre of oscillation.
When the lengdi of the rod and the dimensions of the
cylinder of mercury are properly proportioned, the centre
of osdllation is kept at a constant distance from the point
of suspension. Other methods of making tiiis compensa-
tion have been used, but these are the two in most gen-
eral use for astronomical clot-.ks.

Pig. 27.— oRroiRON

■vmmmmmmmmimiitmiiM

ABTBONOMT.

Ill

The Mtreetion of a chronometer (or clock) is the quantity of time
(expressed in hours, minutes, seconds, and decimals of a second)
which it is necessary to add algebraically to the indication of the
hands, in order that the sum may be the correct time. Thus, if at
sidereal 0\ May 18, at New York, a sidereal clock or chronometer
indicates 23'' 58"' 20* -7, itc correction is + 1»' 89'. 8 ; if af.O'' (siderwl
noon), of May 17, its correction was + 1"' 88- -8, its daily rate or the
change of its correction in a sidereal day is + 1*0: in other words,
this clock is loring 1" daily.

For clock Blow the sign of the eorreetion is + ;
«' '' fast " " " " " '8 — ;
" " gaining " " " " rate

loting

18 — 5

is + .

A clock or chronometer may be well compensated for temperature,
and yet its rate may be gaining or losing on the time it is intended
to keep : it is not even necessary that the rate should be small (ex-
cept that a small rate is practically convenient), provided only that
it IS constant. It is continually necessary to compute the clock cor-
rection at a given tims from its known correction at some other time,
and its known rate. If for some definite instant we denote the time
as shown by the clock (technically "the clock-face") by 2', the true
time by T and the clock correction by a T, we have

T = T + A r, and

i,T = r - T.

In alt obserratories and at sea observations are made daily to de-
termine A T. At the instant of the observation the time T is noted
by the clock; from the data of the observation the time r is com-
puted. If these agree, the clock is correct. If they differ, ATia
found from the above equations.

If by observation we have found

A 7» = the clock correction at a clock-time 7»,
A 7* = the clock correction at a clock-time T,
ST =: the clock rate in a unit of time,

we have

Ar= AT, + d2'(5P-7',)

where T — T, must be expressed in days, hours, etc., according as
dr is the rate in one day, one hour, etc. :,,.-,. .

When, therefore, the clock correction A T. and rate ST have been
determined for a certain instont, T., we can deduce the true time
from the clock-face 2* at any other Instant by the equation r = T
. AT* + dr(7'— !•)• " ^^ dock correction has been deter-
mined at two different ttmes, T. and T to be A T. and A T, the rate
is inferred from the equation

6T.

AT- Ag>

the quantity of time
nmals of a second)
:he indication of the
t time. Thus, if at
Dck or chronometer
'•8; if aiO'' (sidereal
, its daily rate or the
*-0: in other words,

■ion is + ;

is — ;

I is — ;

is + .

ited for temperature,
le time it is intended
should be small (ex-
), provided only that
»mpute the clock cor-
n at some other time,
it we denote the time
ace") by 2\ the true
have

are made daily to de-
>n the time T is noted
a ths time T is com-
If they differ, LTxs

;k-time T»,
ck-time 7,
me,

ITS, etc., according as

md rate ^ 7 have been
deduce the true time
the equation 7* = 7
ction has been deter-
, T» and A T, the rate

THE ASTRONOMICAL CLOCK,

These equations apply only so long as we can regard the rate as
comtnnt. As observations can bo made only in clear weather, it is
plain that during periods of overcast sky wc must depend on these
equations for our knowledge of 7" — i.e., the true time at a clock-
time T.

The intervals between the determination of the clock correction
should be small, since even with the best clocks and chronometers
too much dependence must not be placed upon the rate. The follow-
ing example from Cbauvemet's Astronomy will illustrate the practi-
cal processes :

" Example. — At sidereal noon, May 5, the correction of a sidereal
clock is— 16"' 47'0; at sidereal noon, May 12, it is — 16'" IS'-SO;
what is the sidereal time on May 25, when the clock-face is 11" 13'"
12" -6, supposing the rate to be uniform ?

May 5, correction = — IB"" 47'. 30
" 12 , " = -16"' 13' . 50

7 days' rate =r+ 83' "50
dT= + 4'.829.

Taking then as our starting-point T^ = May 12, O**, we have for the
interval to T= May 25, ll"- 13'« 12'-6, T- To = W^ W 13'" 12"e
= 18''-467. Hence we have

Ar.,= - 16»l'}«-60
dT(T— To)= + 1" fi'OS

AT= - 15" 8'-47

T=n*' 18'»J2;^^60

7»= 10^ SS" 4'. 13

But in this example the rate is obtained for one true sidereal day,
while the unit of the interval 18''-467 is a sidereal day as shovn by
the clock. The proper interval with which to compute the n\te in
this case is W 10^ 68" 4* 18= 18'' -457, with which we find

AT»= — Id" IS'. 50

6Ty 18-457= + 1- 4' 98

A 7* = — IS" 8'. 52

T = 11'' 18"' 12' -60

7*- 10'' 68" 4* 08

This repetition wVl 'ot rendered unnece^^sary by always giving the rcte
in a vntt of the ek>A. Thus, suppose that on June 8, at 4" 11*" 12'-86
by the clock, we have found the correctiori + 2*" 10* 14; and on
June 4, at W ^7*" 49*. 89 we L.* .^ fo>jnd tba correction -i- 2"' 10<-89 ;
the rate in cm iuiw of the eloek will be

iiT =

-^9••7S

84'11'M

rr = t- 0'-2868."

■■M

.U:, -^

74 ASTRONOMY.

I 4. THE TRANSIT INSTBUMENT.

The meridian transit instrument, or briefly the " tran-
sit," is used to observe the transits of the heavenly bodieg.

Fig. 28.— a tiukbit ihstbiimbnt.

and from the times of these transits as read from the
clock to determine either the corrections of the clock or
the right ascension of the observed body, as explained in
Chapter I., §5.

[TMENT.

briefly the " traii-
3 heavenly bodies.

BNT.

18 read from the
nB of the clock or
y, as explained in

THE TnANSIT INaTRUMENT. tS

It has two general forms, one (Fig. 28) for use in fixed
observatories and one (Fig. 29) for nse in the fiekl

It consists essentially of a telescope TT TFiir 28^
mounted on an axis F Fat right angle's to it ^ ^' ^

Pig. 29.-P011TABLE transit mSTRlWKNT.

The ends of this axis terrainate in accurately cvlindrio^l
Bteel pivots which re«t in metallic bearing FfTI.^
like the letter Y, and hence called the f, ' *^

iWi^aB Bit j w i iff iw Maw ''

AaTltONOMT.

These are fastened to two pillars of stone, l)rick, or
iron. Two counterpoises W W are connected with the
axis as in the plutc, so as to take a largo portion of the
weight of the axis and telescope from the Ys, and thus to
diniinish the friction npon these and to render the rota-
tion about V V more eaay and regular. In the ordinary
use of the transit, the line F F is placed accurately level
and perpendicular to the meridian, or in the east and west
line. To effect this *' adjustment," there are two sets of
adjusting screws, by which the ends of F F in the Ys may
be moved either up and down or north and south. The
plate gives the form of transit used in permanent observa-
tories, and shows the observing chair G^ the reversing car-
riage R, and the level L. Tl arms of the latter have
Y'b, which can be placed over the pivots F F.

The line of coUiination of the transit telescope is the
line drawn through the centre of the objective perpendic-
ular to the rotation axis V V.

The reticle is a network of fine spider lines placed in
the focus of the objective.

In Fig. 30 the circle represents the field of view of a
transit as seen through the eye-piece. The seven ver-
tical Unes, I, II, III, IV, V, VI,
VII, are seven fine spider lines
tightly stretched acroes a metal plate
or diaphragm, and so adjusted as to
be perpendicular to the direction of
a star's apparent diurnal motion.
This metal plate can be moved right
and left by five screws. Tb' hori-
zontal wires, guide-wires, a and h,
mark the centre of the field. The
field iii Illuminated at night by a lamp at the end of the
axis which shinep through the hollow interior of the lat-
ter, and causes the field to appear bright. The wires are
dark against a bright ground. The line of sight is a line
joining the centre of the objective and the central one, IV,
of the seven vertical wires.

TUH TRANSIT INSTUUMKNT.

me, brick, or
ictcd with tlio
)ortiou of the
8, and thus to
inder the rota-
;n the ordinary
iccurately level
e east and west
are two sets of
In the Ys may
id south. The
lanent observa-
s reversing car-
the latter have
VV.

elescope is the
jtive perpendic-

lines placed in

Id of view of a
The seven ver-

II, IV, V, yi,

no spider lines
08B a metal plate
10 adjusted as to
the direction of
diurnal motion.
1 be moved right
«wfc. Tb' hori-
i-vn/reB, a and b,
the field. The
, the end of the
iterior of the lat-
. The wires are
of »ight is a line
B central one, IV,

The whole transit is in adjustment when, first, the axis
V V is horizontal ; second, when it lies east and west ;
and third, when the line of sight and the line of collinia-
tion coincide. When these conditions are fulfilled the
line of sight intersects the celestial sphere in the meridian
of the place, and when T T\9, rotated about V V the line
of sight marks out the meridian on the sphere.

In practico the three adjustments are not exactly made, since it is
impossible to effect them with mathematical precision. The errors
of each of them are first made as small as is convenient, and are then
determined and allowed for.

To find the error of level, we place on the pivots a fine level (shown
in position in the figure of the portable transit), and determine how
much higher one pivot is than the other in terms of the divisions
marked on the level tube. Such a level is shown in Fig. 4 of plate
85, page 86. The value of one of these divisions in seconds of arc
can be determined by knowing the length I of the whole level and
the number n of divisions through which the bubble will run when
one end is raised one hundredth of an inch.

If I is the length of the level in inches or the radius of the circle
in which either end of the level moves when it is raised, then as
the radius of any circle is equal to 57° • 296, 3437' • 75 or 206,264" • 8,
we have in thui particular circle one inch = 206, 264" -8 -s- I;
0-01 inch = 2(0^264 -8 -4- 100 Z = a certain arc in seconds, say a".
That is, n divisions = a", or one division d = a" -i- n.

The error of eoUimation can be found by pointing the telescope
at a distant mark whose image is brought to the middle wire. The
telescope (with the axis) is then lifted bodily from the Ys and re-
placed so that the axis V Fis reversed end for end. The telescope is
again pointed to the distant mark. If this is still on the middle
thread the line of sight and the line of eoUimation coincide. If not,
the reticle must be moved bodily west or east until these conditions
are fultiUed after repeated reversals.

To find the error of mimuth or the departure of the direction of
VV from an east and west line, we must observe the transits of
two btars of different declinations d and <S, and right ascensions a
and a'. Suppose the clock to be running correctly — that is, with no
rate — and tne sidereal times of transit of the two stars over the mid>
die thread to be and 0'. If — 6' = « — «', »hea the mid4lc wii»
is in the meridian and the azimuth is zero. For if the nziinvitli
was not zero, but the west end of the axis w«us tou far south, for
example, the line of sight would fall eant <«l the meridian for a
south stifkr, and further and further cast tK ftirthcH !«>wth the star
was. Hence if the two stars have widel> tliff(ro»t detlinationa 6
and <5', then the star furthest south would lom* ]>ioportion»toly
sooner to the middle wire than the otlK''t :««Ki U — 0' wowkl be
different from a — u'. The amount of irM» diSereBC« give!> a

MMMMI

A8TR0N0MT.

means of deducing tho deviation oi A A from an east and west
tine. In a similar way the effect of a given error of level on the
time of the transit of a star of declination 6 is found.

Methods of Obaerving with the Transit Instrument.—
We ]i.)ve »o far asHUiiicd tliat the time of a star's transit
over the middle tliread was known, or could be noted.
It is neccHsary to speak more in detail of how it is noted.
When tho telescope is pointed to any star the earth's
diurnal motion will carry the image of the star slowly
across the field of view of the telescope (which is kept
fixed), as before explained. As it crosses each of the
threads, the time at which it is exactly on the thread is
noted from the clock, which must be near the transit.

The mean of these times gives the time at which this
star was on the middle thread, the threads being at equal
intervals ; or on the " mean thread," if, as is the case in
practice, they are at unequal intervals.

if it were possible for an astronomer to note the exact
instant of the transit of a star over a thread, it is plain
that one thread would be sufficient ; but, as all estima-
tions of this time are, from the very natifre of the case,
but approximations, several threads are inserted in order
that the accidental errors of estimations may be eliminated
as far as possible. Five, or at most seven, threads are
sufficient for this purpose. In the
figure of the reticle of a transit instru-
ment the star (the plimet Vemta in this
ciise) may enter on the right hand in the
figure, and may be supposed to cross
each of the wires, the time of its tran-
sit over each of them, or over a suffi-
cient number, being noted. The
method of noting this time may be best
understood by referring to the next figure. Suppose that
the line in the middle of Fig. 32 is one of the transit-
threads, and that the star is passing from the right hand
of the figure toward the left ; if it in on this wire at an

Pio. 81.

THE TRANSIT HfSTRVMENT.

%n east and west
)r of level on the
d.

Instrument.—
a star's transit
>uld be noted,
ow it is noted,
tar the earth's
le star slowly
which is kept
38 each of the

the thread is
the transit.

at which this

being at equal

18 is the case in

note the ^Must
■ead, it is plain
r, as all estima-
te of the case,
iserted in order
\y be eliminated
en, threads are
rpose. In the
a transit instra-
et Ventw in this
■ight hand in the
pposed to cross
time of its tran-
or over a suffi-
noted. The
ime may be best
. Suppose that
of the transit-
the right hand
this wire at an

Fie. 82.

exact second by the clock (which is always near the ob-
server, beating seconds audibly), this second must be writ-
ten down as the time of the transit over this thread. As
a rule, however, the transit cannot occur on the exact
beat of the clock, but at the seventeenth second (for exam-
ple) the star may be on the right of the wire, say at a ;
while at the eighteenth second
it will have passed this wire and
may be at h. If the distance of
a from the wire is six tenths of
the distance a 5, then the time
of transit is to be recorded as —
hours — minutes (to be taken
from the clock-face), and seven-
teen and ^x tenths seconds ; and in this way the transit
over each wire is observed. This is the method of " eye-
and-ear" observation, the basis of such work as we have
described, and it is so called from the part which both the
eye and the ear play in the appreciation of intervals of time.
The ear catches the beat of the clock, the eye fixes the place
of the sti r at <z ; at the next beat of the clock, the eye fixes
the star at ft, and subdivides the space a b into tenths, at
the same time appreciating the ratio which the distance
from the thread to a bears to the distance a h. This is
recorded as above. This method, which is still used in
many observatories, was introduced by the celebrated
Bbadlet, astronomer royal of England in 1750, and per-
fected by Maskeltme, his successor. A practiced observer
can note the time within a tenth of a second in three cases
out of four.

There is yet another method now in common use,
which it is necessary to understand. This is called the
American or chronographic method, and consists, in the
present practice, in the use of a sheet of a paper wound
about and fastened to a horizontal cylindrical barrel,
which is caused to revolve by machinery once in one min-
ute of time. A pen of glass which will make a continu-

^*mmtm

riitiWiiiiirntwimiWT'iiillMlili • Ifirti I n imii

tttmlm

,U.ni

AHTliONOMr.

ouB lino is allowed to rest on the pajxir, and to this jien a
continuous motion of translation in the direction of the
length of the cylinder is given. Now, if the pen is allow-
ed to mark, it is evident that it will trace on the paper an
endless spiral line. An electric current is caused to run
through tlio ("iV/serving clock, through a key which is held
in the observer's hand and through an electro-magnet
connected with the pen.

A simple device enables the clock every second to give
a slight lateral motion to the pen, which lasts about a
thirtieth ol a second. Thus every second is automatically
marked by the clock on the chronograph paper. The ob-
server also has the power to make a signal by his key
(easily distinguished from the clock-signal by its different
length), which is likewise permanently registered on the
sheet. In this way, after the chronograph is in motion,
the observer has merely to notice the instant at which the
star is <m the thread, and to press the key at that moment.
At any subsequent time, he must mark some hour, min-
ute, and second, taken from the clock, on the sheet at its
appropriate place, and the translation of the spaces on
the sheet into times may be done at leisure.

% 6. OaADXTATED OIBOItBS.

Koarly every datum in practical astronomy depends
either directly or indirectly upon the measure of an angle.
To make the necessary measures, it is customary to em-
ploy what are called graduated or divided circles. These
are made of metal, as light and yet as rigid as possible,
and they have at their circumferences a narrow flat band
of silver, gold, or platinum on which fine radial lines
called " divisions" are cut by a " dividing engine" at
regular and equal intervals. These intervals may be
of 10', 5', or 2', according to the size of the circle
and the degree of accuracy desired. The narrow band
is called the divided limb, and the circle is said to be di-

•'Hr

riiK vhmNfhm.

d to thi8 jien a
irection of the
le pen is allow-
in the paper an
caused to mn
y whicli is held
electro-magnet

second to give

lasts about a
is automatically
aper. The ob-
nal by his key

by its different
;istered on the
h. is in motion,
nt at which the
at that moment.
>me hour, min-
the sheet at its

the spaces on

momy depends
ure of an angle,
istomary to em-
circles.. These
^d as possible,
arrow flat band
ine radial lines
ling engine" at
terTftIs may be
5 of the circle
le narrow band
> said to be di-

Fio. 88.

vided to 10', r»', y'. The separate diviBJons are numbered
consecutively from 0" to 30(>^ or from 0" to 1)0°, etc. The
graduated circle has an axiH at itH centre, and to this may
be attached the telescope by whicli to view tlie pointti
whose angiilar distance is to be dcteriuiued.

To this centre is also attached an arm wliicli revolves
with it, and by its motion past a certain nuinbur of divi-
sions on the circle, determines the angle through which the
centre has been rotated. This arm is called the index
arm, and it usually carries a vernier on its extremity,
by means of which the spaces on
the graduated circle are subdivided.
The reaijimj of the circle when the
index a ' in any position is the

number 'agrees, minutes, and

seconds w cH correspond to that po-
sition ; when the index arm is in an-
other position there is a different
reading, and the differences of the two
readings S' — <S", S* — S*, S*—S* are the angles through
which the index arm has turned.

The process of measuring the angle between the objects
by means of a divided circle consists then of pointing the
telescope at the first object and reading the position of the
index arm, and then turning the telescope (the index
arm turning with it) until it points at the second object,
and again reading tlie position of the index arm. The
difference of these readings is the angle sought.

To facilitate the determination of the exact reading of
the circle, we have to employ special devices, as the
vernier and the reading microscope.

The Vernier.— In Fig. 34, M JV ia a portion of the
divided limb of a graduated circle ; Ci) is the index arm
which revolves with the telescope about the centre of the
circle. The end ah of CD k also a part of a circle con-
centric with Mlf^, and it is divided into n parts or divi-
sions. The length of these n parts is so chosen that it is

mumm

i, '

AHTRONOMY.

tltc BUiiio UH thut of {a — 1) purta on tliu divided limb M N
or tho roversc.

The first stroke a is tlio zero of tho vernier, and the
reading is always determined by tl»o position of this zero
or pointer. If this hiwa revolved past exactly twenty di-
visions of tho eircle, then the angle to be measured is
20 X d, d being tho value of one division on the limb
(iV M) in arc.

FlO. 84.— THR VKRNIKR.

Gall the angular value of one division on the vernier d'\

n — \ 1

(n — l)d = n-d', or d' = d,BLndd—d'=-df

d — d' is called the least count of the vernier which is one
n*"* part of a circle division.

If the zero a does not fall exactly on a division on the
circle, but is at some other point (as in the figtire), for ex-
ample between two divisions whose numbers are P and
{P + 1), the whole reading of the circle in this position is
P X d+ the fraction of a division from P to a.

If the m"" division of the vernier is in the prolongation
of a division on the limb, then this fraction Pa k m

ridiid limb J/ JV

vernier, and the
tiun of this zero
ictiy twenty di-
bu ineaAiired is
on on the limb

n the vernier d'\

dd-d'=-d;
n '

lier which is one

, division on the

e figtire), for ex-

bers are P and

n this position is

Ptoa.

the prolongation

EMStion Pa h m

msm

mmm

..^...

IMAGE EVALUATION
TEST TARGET (MT-3)

i/..

1.0

1.1

11.25

Ui|2£ 121

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lu Ui2 12.2
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23 WIST MAIN STRUT

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CIHM/ICMH

Microfiche

Series.

CIHIVI/ICIVIH
Collection de
microfiches.

Canadian institute for Historicai iVIicroreproductions / institut Canadian de microreproductions historiques

TUE MERIDIAN CIRCLE.

(d - d') =--d. In the figure n = 10, and as the 4th

division is almost exactly in coincidence, m = 4, so that

the whole reading of the circle isPxd + j^'d. Ifdia

10', for example, and if the division P is numbered 297°
40', then this reading would be 297° 44', the least count
being 1', and so in other cases. If the zero had started from
the reading 280° 20', it must have moved past 17* 24',
and this is the angle which has been measured.

§ 6. THE MERIDIAN CIBCLE.

The meridian circle is a combination of the transit in-
strument with a graduated circle fastened to its axis and
moving with it. The meridian circle made by Repsold
for the United States Naval Academy at Annapolis is
shown in the figure. It has two circles, c c and c' c', finely
divided on their sides. The graduation of each circle is
viewed by four microscopes, two of which, H B, are
shown in the cut. The microscopes are 90° apart. The
cut shows also the hanging level L Z, by which the
error of level of the axis AAia found.

The instrument can be used as a transit to determine
right ascensions, as before described. It can be also used
to measure declinations in the following way. If the tele-
scope is pointed to the nadir, a certain division of the cir-
cles, as If, is under the first microscope. If it is pointed
to the pole, the reading will change by the angular distance
between the nadir and the pole, or by 90° + ^, ^ being
the latitude of the place (supposed to be known). 'The
polar reading P is thus known when the nadir reading
If is found. If the telescope is then pointed to various
stars of unknown polar distances, p', p'\p"', etc., as they
successively cross the meridian, and if the circle readings
for these stars are P', P", P"', etc., it follows that
p' = P'-P ; p" = P'-P; p'" = P"' - P, etc.

pt.

A8TR0N0MY.

Pig. 35.— the MunmiAw cmciJi.

BCOpi

that

tre(
the
plact
inicr
form
Just
crosf
whic
is d
the <
slidi
grad
cout
bein
and
itb:
If

cide
ber
sion
U
oftl
non
this
sere
plm
circ
■woi
are
utc(

din
the

(«)
circ
poll
1
be
abi
tun
of
thii
Wl
seei
Th(
sioi
obi

THE MEUIDIAN CIJiCLE.

To determino the readings P, P', P', etc., wo use the micro-
Bcopea li, B, etc. The observer, after having set the telescope so
that one of the stars shall cross the field of view exactly at its cen-
tre (which may be here marked by a single horizontal thread in
the reticle), goes to each of the microscopes in succession and
places his eye at A (see Pig. 1, page 86). He sees in the field of the
microscope the image of the divisions of the graduated scale (Fig. 2)
formed at D (Fig. 1), the common focus of the lenses A and C.
Just at that focus is placed a notched scale (Pig. 2) and two
crossed spider lines. These lines are fixed to a sliding frame a a,
which can be moved by turning the graduated head F. This head
is divided usually into sixty parts, each of which is 1 ' of arc on
the circle, one whole revolution of the head serving to move the
sliding frame a o, and its crossed wires through 60" or 1' on the
graduated circle. The notched scale is not movable, but serves to
count the number of complete revolutions made by the screw, there
being one notch for each revolution. The index i (Pig. 2) is fixed,
and serves to count the number of parts of F which are carried past
it by the revolution of this head.

If on setting the crossed threads at the centre of the motion of
F and looking into the microscope, a division on the circle coin-
ci'des with the cross, the reading of the circle Pis the exact num-
ber of degrees and minutes corresponding to that particular divi-
sion on the divided circle.

Usually, however, the cross has been apparently earned pait one
of the exact divisions of the circle by a certain quantity, which is
now to be measured and added to the reading corresponding to
this adjacent division. This measure can be made by turning the
screw back say four revolutions (measured on the notched scale)
plus 37-3 parts rmeasured by the index t). If the division of the
circle in question was 179° 50', for example, the complete reading
would be in this case 179' 50' + 4' 87''. 3 or 179° 64' 87". 3. Such
a reading is made by each microscope, and the mean of the min-
utes and seconds from all four taken as the circle reading.

We now know how to obtain the readings of our circle when
directed to any point. We require some zero of referencej as
the nadir reading (N), the polar reading (P), the equator reading,
(Q\ or the zenith reading (Z)- Any one of these being known, the
circle readings for any stars as P. P', P", etc., can be turned into
polar distances p', p", p'", etc.

The nadir reading (N) is the zero commonly employed. It can
be determined by pointing the telescope vertically downward at
a basin of mercury placed immediately beneath the instrument, and
turning the whole instrument about the axis until the middle wire
of the reticle seen directly exactly coincides with the in ^e of
this wire seen by reflection from the surface of the quicksilver.
When this is the case, the telescope is vertical, as can be easily
seen, and the nadir reading may be found from the circles.
The meridian circle thus serves to determine both the ripht ascen-
sion and declination of a given star at the same culmination. Zone
observations are made with it by clamping the telescope in one

ASTRONOMY.

nfti.

n«.s

Ti]|.4.

FlO. 36.— RKADINa MICR08C0PK, MICROMETEK AND LKVKt.

dlr
its
larj

pri
of
to
ell
inf
eai
ap
cei
eie
ot]
wt
mi
th
ax
(tl
hx

ei1
te
fo

kc
a>
al

ti(
rij
si:

ni
te

THE EQUATOJtIAL.

direction, and observing succossively the stars wliich ^ass through
its field of view. It is by this rapid method of observing that the
largest catalogues of stars have been formed.

§ 7. THE EQUATORIAL.

To complete the enumeration and description of the
principal instruments of jistronomy, we require an account
of the eqtiatorial. This terra, properly speaking, refers
to a form of mounting, but it is commonly used to in-
clude both mounting and telescope. In this class of
instruments the object to be attained is in general the
easy finding and following of any celestial object whose
apparent place in the heavens is known by its right as-
cension and declination. The equatorial mounting con-
sists essentially of a pair of aaes at right angles to each
other. One of these S N (the jpolar oasis) is directed to-
ward the elevated pole of the heavens, and it therefore
makes an angle with the horizon equal to the latitude of
the place (p. 21). This axis can be turned about its own
axial line. On one extremity it carries another axis Z D
(the declination <m»), which is fixed at right angles to it,
but which can again be rotated about its axial line.

To this last axis a telescope is attached, which may
either be a reflector or a refractor. It is plain that such a
telescope may be directed to any point of the heavens ;
for we can rotate the declination axis until the telescope
points to any given polar distance or declination. Then,
keeping the telescope fixed in respect to the declination
axis, we can rotate the whole instrument as one mass
about the polar axis until the telescope points to any por-
tion of the parallel of declination defined by the given
right ascension or hour-angle. Fig. 37 is an equatorial of
six-inch aperture which can be moved from place to place.

If we point such a telescope to a star when it is rising
(doing this by rotating the telescope first about its decli-
nation axis, and then about the polar axis), and fix the
telescope in this position, we can, by simply rotating the

VKIi,

ASlJiONOMr.

FlO. 37.— BQUATORIAL TELEBCOPE IHIIHTED TOWAHD THE POI-E.

;

rilK MWROMKTRR.

whole apparatus on the polar axis, cause the telescope to
trace out on the celestial sphere the apparent diurnal path
which tliis star will appear to follow from rising to set-
ting. In such telescopes a driving-clock is so arranged
that it can turn the telescope round the polar axis at the
same rate at which the earth itself turns about its own axis
of rotation, but in a contrary direction. Hence such a
telescope once pointed at a star will continue to point at it
as long as the driving-clock is in operation, thus enabling
the astronomer to observe it at his leisure.

I I lli

POIiE.

FlO. 88.— MKABCBQMBHT OF F08ITION-ANGLB.

Every equatonal telescope intended for making exact measures
has a JUar micrometer, which is precisely the same in principle as
the reading microscope in Fig. 3, page 86, except that its two wires
are parallel.

A figure of this instrument is given in Pig. ? v cce 86. One of
the wires is fixed and the other is movable by > ha screw. To
measure the distance apart, of two objects A and B, wire 1 (the
fixed wire) is placed on A and wire 2 (movable by the screw) is
placed on B. The number of revolutions and parts of a revolution
of the screw is noted, say 10' -267 ; then wires 1 and 2 are placed
in coincidence, and this zero-reading noted, say 5' -143. The dis-
tance A B is equal to 5'- 124. Placing wires 1 and 2 a known num-
ber of revolutions apart, we may observe the transits of a star in the
equator over them ; and from the interval of time required for this
star to move over say fifty revolutions, the value of one revolution

AaTRONOMT.

is known, and can alwavs bo used to turn distances measured in
revolutions to distances in time or arc.

By the filar micrometer we can determine the distance Hput in
seconds of arc of any two stars A and B. To completely nx the
relative position of A and B, wo require not only this distance, but
also the angle which the line A B mulces with some fixed direction
in space. We assume as the fixed direction that of the meridian
passing through A, Suppose in Fig. 88 A and £ to be two
stars visible in the field of the equatorial. The clock-work
is detached, and by the diurnal motion of the earth the two
stars will cross the field slowly in the direction of the parallel of
declination passing through A, or in the direction of the arrow in
the figure from E. to W., east to west. The filar micrometer is con-
structed so that it can be rotated bodily about the axis of the tele-
scope, and a graduated circle measures the amount of this rotation.
The micrometer is then rotated until the star A will pass along
one of its wires. This wire marks the direction of the parallel.
The wire perpendicular to this is then in the meridian of the star.

The pontion angle of B with respect to ^1 is theh the angle which
A B makes with the meridian A N passing through A toward the
north. It is zero when B is north of A, 90* when B is east, IHO
when B is south, and 270° when B is west of A. Knowing p, the
position angle (NAB in the figure), and i (A B) the distance of B,
we can findthe difference of right ascension (A a), and the differ-
ence of declination (hi) ot B from A by the formulte,

Aa = < sin |>; A6=s$ cotp.

Conversely knowing Aa and Ad, we can deduce « and p from
these formulae. The angle p is measured while the clock-work
keeps the star A in the centre of the field.

§ 8. THX ZnnTH TBLB800PE.

The accompanying figure givn a view of the zenith telescope in
the form in wuich it is used by the United States Coast Survey. It
consists of a vertical pillar which supports two T$. In these
rests the horizontal axis of the instrument which carries the tele-
scope at one end, and a counterpoise at the other. The whole in-
strument can revolve 180° in azimuth about this pillar. The tele-
scope has a micrometer at its eye-end, and it also carries a divided
circle provided with a fine level. A second level is provided,
whose use is to make the rotation axis horizontal. The peculiar
features of the zenith telescope are the divided circle and its at-
tached level. The level is, as shown in the cut, in the plane of
motion of the telescope (usually the plane of the meridian), and it
can be independently rotated on the axis of the divided circle, and
set by means of it to any angle with the optical axis of the telescope.
The circle is divided from zero (0°) at its lowest point to 90° in
each direction, and is firmly attached to the telescope tube, and
moves with it.

By setting the vernier or index-arm of the circle to any degree
and minute as a, and clamping it there (the level moving with it).

THE ZKNirU TKLEtiUOPK.

d in

rt in

the
, but
ction
idian

two
work

two
lei of
9W in
I con-
I tele-
ttion.
ilong
rallel.
}tar.
which
d the
, 180
p, the
of B,
differ-

> from
L-work

Qope in
rey. It
1 these
le tele-
liole in-
he tele-
divided
ovided,
peculiar
[its at-
tlane of
I, and it
cle, and
lescope.
;o 90° in
ibe, and

y degree
with it),

-rtiiiijiljli

PlO. 89.— THE ZBNITH TELBBCOPE.

AsTn(tm)MY.

niul then rntatiiiK thn tclcscono and tho whnlo NyMtuin nlioiit tliu
horizontal axis until tlie bub1>lc of the level ix in tho contro of tlu;
lovcl-tubo, tho axiH of the tolcHcopcH will bo directed to the zenith
diHtance a. The filar micromotor \* ho adjusted that a motion of itit
Hcrow moMurcB differences of zenith distance. Tho uhc of tho ze-
nith telescope is for determining tho latitude by Talcott'h
method. The theory of this operation has been already given on
irngo 48. A description of tho actual process of observation will
illustrate the excellences of this method.

Two stars, A and B, are selected beforehand (from Star Cata-
logues), which culminate, A south of the zenith of tho nluce of ob-
servation, B north of it. They are chosen ot nearly eijual zenith dis-
tances f* and £*, and so that $* — {* is less than tho breadth of tho
field of view. Their right ascensions are also chosen so as to bo alwut
the same. The circle is then set to the mean zenith distance of the
two stars, and the telescope is pointed so that the bubble is nearly in
the middle of the level. Suppose the right ascension of A is the
smaller, it will then culminate first. The telescope is then turned
to the south. As A passes near the centre of the field its distance
from the centre is measured by the micromotor. Tho level and
micrometer are read, the whole instrument is revolved 180", and
star B is observ«}d in the same way.

By these operations wo have determined the difference of tho
zenith distances of two stars whoso declinations d* and <)■ uro
known. But tp being the latitude,

^ = (J* -f. 4* and ^ = d" — {", whence

^ = !(<)* + ')•) + 1 ({* - «").

The first term of this is known ; tho second is measured ; so that
each pair of stars so observed gives a value of tho latitude which
depends on the measure of n very small arc with the micrometer,
and UN this arc can be measured with great precision, the exactness
of the determination of the latitude is equally great.

hnruim
plane <
This
the in(
which
E is a
Hv it a
silverec
plane c

g 8. THE SEXTAnr.

Tho sextant is a portable instrument by which tho altitude!^
of celestial bodies or tho angular distances between them mny
bo measured. It is used chiefly by navigators for determining the
latitude and the local time of the position uf tho ship. Knowing
the local time, and com]}aring it with a chronometer regulated on
Greenwich time, the longitude becomes known and the snip's place
is fixed.

It consists of the arc of a divided circle urually 00° in extent,
whence the name. This arc is in fact divided into 120 equal parts,
each marked as a degree, and these are again divided into smaller
spaces, so that by means of the vernier at the end of tho index-arm
M San arc of 10" (usually) may be read.

The index-arm M 8 carries the ind«e-ghu» M, which is a silvered
plane mirror set perpendicular to the plane of the divided arc. The

(and t\
second
to be re
telosco{
the sex
one dir

Tho
which
thelaat

TIIK SRXTANi: W

hnrixim-iihiM m is nlt<(» n pliino mirror flxp«l |M!rpcn<lic>ilttr to tint
i»lun<> oif tlio «livi(lf(l <-inU'.

TliiH liiHt kIiihh Im 11x1(1 in poHitixn, wliilii (lie llrnt rcvolvcH with
the index-unn. Tlu! horizon-gliws in divided into two piirtH, «»f
wJiich the lower one is Bilvered, the vippcr Imlf beinjr tran»i»«rent.
E iH II tcleBCope of low power i>ointu(l toward the horizon-gluiw.
Hy it any object to which it Ih directed can Iw seen through tlic un-
Bilvcrcd half of the horizon-glawH. Any other object in the f«anio
pUnu can be brought into the same field by rotating the indpx-arm

FfO. 40. — THB BKXTAHT.

(and the index-glass with it), so that a beam of light from this
second object shall strike the index-glass at the proper angle, there
to be reflected to the horizon-glass, and again reflected down the
telescope E. Thus the images of any two objects in the plane of
the sextant may be brought together in. the telescope by viewing
one directly, and the other by reflection.

The principle upon which the sextant depends is the following,
which IS proved in optical works. The artgle between theftnt and
the latt directum of a ray which hat suffered two rejUetiont in the tame

ASTRONOMY.

plans M equal to tt^^s the angle whkh tTu two reflecting mrfaeea make

with each other. . . , , , a *».;„ ,o„ Sa i.tr

In the figure S A is the ray incident upon -4, and this ray is by

reflection brought to the direction BE The theorem declares

that the angle BE Sis equal to twice D C B, or tvice the angle of

theiairrors, since BO mAD Care perpendicular to Band ^. To
measure the altitude of a star (or the sun) at sea, the sextant is held
in the hand, and the telescope is pointed to the sea-honzon, which
appears like a definite line. The index-arm is then moved until
the reflected image of the sun or of the star coincidcB with the

Fie. 43.— ABTIVTCIAL HOBOOK.

imaee of the sea-horizon seen directly. When this occurs the tune
isto be D ied from a chronometer. If a star is observed, the reaa-
injr of the divided limb gives the altitude directly; if it is the
sun or moon which has been observed, the lower limb of these is
brought to coincide with the horizon, and the altitude of the centre

is found
Almanac

The an
ured by j
tant abou
vided arc
the indes
star's imi

On shn
tho obsei
hffrigon, '
liquid, a
surface if
a A, fror
in the di
ing E A
to an eye
With a »
angle 8
and if A
all celest
will equi
half the i

i mahe

y isby
eclarea
ngle of

A. To
: is held
, which
id until
nth the

THE 8KXTANT.

is found by applying the semi-diameter as found Jn the Nautical
Almanac to the observed altitude ol the limb.

The angular distance apart of a star and the moon can be meas-
ured by pointing the telescope at the star, revolving the whole sex-
tant about the sight-line of the telescope until the plane of the di-
vided arc passes through both star and moon, and then by moving
the index-arm until the reflected moon is just in contact with the
star's image seen directly.

On shore the horizon is broken up by buildings, trees, etc., and
tho observer is therefore obliged to have recourse to an artificial
harum, which consists usually of the reflecting surface of some
liquid, as mercury, contained in a small vessel A, whose upper
surface is necessarily parallel to the horizon DAG. A ray of light
8 A, from a star at 8, incident on the mercury at A, will be reflected
in the direction A E, making the angle 8AG= A 8' (A 8^ be-
ing E A produced), and the reflected image of the star will appear
to an eye at £ as far below the horizon as the real star is above it.
With a sextant whose index and horizon-masses are at /and H, the
angle 8 E 8 may be measured ; but aES = 8AS — A8E,
ana it A E'vi exceedingly small as compared with ^ i8, as it is for
all celestial bodies, the angle A 8 Emaj be weglected, and 8 B 8'
will equal 8 A 8', or double the altitude of the object : hence one
half the reading of the instrument will give the apparent altitude.

the time
the read-
it is the
these is
he centre

\ii

'■'I

§1.

CHAPTER III.

MOTION OF THE EARTH.
ANCIENT IDEAS OF THE PLANETS.

It was obBerved by the ancients that while the great

mass of the stars maintained their positions relatively to

Lh other not only during each diurnal revolution, but

^nth after month and year after year, the«, were vi«.

bleto them seven l^eavenly bodi^ which ch^gedth^r

positions relatively to the starB and to «««'5^^f «^. J^,^

Siey called planets or wandenng stars. Still calbng the

apmi^t crystalline vault in which the sters seem to

^^ the celestial sphere, and imagining it as at rest,

^wt found that the seven planets performed a y^

slow revolution around the sphere from west to e.«t

L periods ranging from one month in the case of the

mooTto thirtyVars in that of m^n. 1* w- eviden

that these bodies could not be «o"«^«'«'l. ^^ ^* ^ not
same solid sphere with the stars, because tW could^no
then change their positions among the stars. Vanous
w^s of acfounting for their motions were therefore pro-
xJed One of the earliest conceptions is associated with
rnameofPvTHAOOKAS. He is said to have taugM t^t

each of the seven planets had its ^^/P^^^^^^^^t^j
concentric with that of the fixed stars, and that these
len hoUow spheres each performed its own revolution,
Se^ndently of theothers. Thisideaof anumber of con-
3c solid^heres was, however, apparently given up

without

argumci

close ex

tent wit

being »

perfect i

by the

The latl

move so

it was (

nearer \

were en

fixed in

use — th(

space or

These

lowed, \

rightly <

stars. ]

most slo

distance

case of J

We n

the eart!

scope ha

themseh

ably grei

surface I

pared wi

stars. 1

tem, it if

its sever

them thi

following

to be eij

in the o

bodies a

STB.

the great
atively to
ution, but
were visi-
iged their
r. These
ailing the
I seem to
18 at rest,
id a very
t to east,
ase of the
ras evident
set in the

could not
. Various
•efore pro-
ciated with
taught that
iside of and

that these
revolution,
iber of con-
f given up

THE SOLAR SYSTEM.

without any one having taken tlie trouble to refute it by
argument. Although at first sight plausible enough, a
close examination would show it to be entirely inconsis-
tent with the observed facts. The idea of the fixed stars
being set in a solid sphere was, indeed, in seemingly
perfect accord with their diurnal revolution as observed
by the naked eye. But it was not so with the planets.
The latter, after continued observation, were found to
move sometimes backward and sometimes forward ; and
it was quite evident that at certain periods they were
nearer the earth than at other periods. These motions
were entirely inconsistent with the theory that they were
fixed in solid spheres. Still the old language continued in
use — the word sphere meaning, not a soUd body, but the
space or region within which the planet moved.

These several conceptions, as well as those which fol-
lowed, were all steps toward the tnith. The planets were
rightly considered as bodies nearer to us than the fixed
stars. It was also rightly judged that those which moved
most slowly were the most distant, and thus their order of
distance from the earth was correctly given, except in the
case of Mercury and Venus.

We now know that these seven planets, together with
the earth, and a number of other bodies which the tele-
scope has made known to us, form a family or system by
themselves, the dimensions of which, although inconceiv-
ably greater than any which we have to deai with at the
surface of the earth, are quite insignificant when com-
pared with the distance which separates us from the fixed
stars. The sun being the great central body of this sys-
tem, it is called the Solar System. It is to the motions of
its several bodies and the consequences which flow from
them that the a oention of the reader is directed in the
following chapters. We premise that there are now known
to be eight lai^ planets, of which the earth is the third
in the order of distance from the sun, and that these
bodies all perform a regular revolution around the son.

■

98 ASTRONOMY.

Mercnry, the nearest, performs its revolution in three
montlis ; Neptune, the farthest, in 164 yea".

First n importance to us, among the heavenly boU es
which we see from the earth, stands the sun, the supporter
rS and motion upon theearth. At fi«t«ghUUm^
seem curious that the sun and seemmg stars like Ma/rs
and^a Cm should have been classified together as plajete
bv the ancients, while the fixed stars were considered as
forming anoth;r class. That the ancients were acute

Z^f to do this tends to impr^ m wHh a favorable
sense of the scientific character of their mteUect To any
but the most careful theorists and observers, the star-like
pknete if we may call them so, would never have seemed
rSng in the Ime class with the sun but rather m

hat of tie stars ; especially when it ^^^^^^^^ '^' '^^
were never visible at the same time with the sun. iJut
Srthe times of which we liave any histenc r^rd
there were men who saw that, in a motion from west to
rramong the fixed stars, these several ^^^ ^^^^J
common character, which was more ««««^*^^.2;^ ^^^^
of the universe than were their immense diforences of

aspect and lustre, striking tl^o^g^^.J^'fl^^-^ ,„_
It must, however, be remembered ^^^^J^^^^
consider the sun as a planet. We have /no^^^f *^« "^
dent system by making the sun and the earth /jhaage
llrso that the latterl now regarded as one of theei^t
wTiknets, while the former has taken the place of the
e^Kfientral body of the system In consequence
oUhe revolntion of the planets romid Jbe "an «ach of
them seems to perform a corresponding circuit m the
htvenriund Se celestial sphere, when viewed from
any other phmet or from the earth.
§ 2. AMlfUAL EBVOLTJTIOM OF THE BABTH.
To an observer on the earth, the sun seems to pe^o^f
Jua^volution among the stars a fact v.hich has b^n
Wn from the earUest ages. We now know that this

is due
sun.
tion oi
directe
it and
which
In ]
of the

fixed
tent, 1
AB
numb
15 dn
called
exten
the p

MOTION OF TBE BARTB.

is due to the annual revolution of the earth round the
Bun. It is to the nature and eflfects of this annual revolu-
tion of the earth that the attention of the reader is now
directed. Our first lesson is to show the relations between
it and the corresponding apparent revolution of the sun,
which is its counterpart.

In Fig. 43, let S represent the sun, ABC D the orbit
of the earth around it, and EFQIl tlie sphere of the

Fia. 43.— BRVOLCTioN or thb earth.

fixed stars. This sphere, being supposed infinitely dis*
tent, must be considered as infinitely larger than the circle
A B G D. Suppose now that 1, 2, 3, 4, 5, 6 are a
number of consecutive positions of the earth. The line
\S drawn from the sun to the earth in the first position is
called the radius vector of the earth. Suppose this line
extended infinitely so as to meet the celestial sphere in
the point V. It is evident that to an observer on the

tofO.

jQO ASTRONOMY.

y ;^Tr«:'aLtI »« .Sana so„„. in other
Will ^PP"" , rnvolves around the sun, the latter

-''itr=rre^;r.:'r>rt-,. .o.a

described. „„„„„i mvolntion of the

Let us now study the apparent ^^^'^'^Xe i^ult of
«„n produced in the way just mentioned. One result

TUE aUN'B APPARENT PATH.

101

>liere
2, it
other
latter
Btars,

inrould
xactly
i from
dly in
t that
ng the
irately

rse de-
ited by
iiity in
eat cir-
pear to
ndiffer-
iptic is
the po-
eferred.
letry, it
a think-
ceive of
ical line
perpen-
Rgure is
iects the
c. This
Ets an ex-
j, owing
hereafter

on of the
result of

this motion is probably familiar to every reader, in the
different constellations whicli are seen at different times of
the year. Let lis take, for example, the bright star Aide-
baran, wliicli, on a winter evening, we may see north-
west of Orion. Near the end of February this star crosses
the meridian about six o'clock in the evening, and sets
about midnight. If we watch it night after night through
the months of March and April, we shall find that it is far-
ther and farther toward the west on each successive even-
ing at the same hour. By the end of April we sliall bare-
ly be able to see it about the close of the evening twilight.
At the end of May it will be so close to the sun as to be
entirely invisible. This showa. that during the months we
have been watching it, the sun has been approaching the
star from the west. If in July we watch the eastern
horizon in the early morning, we shall see this star rising
before the sun. The sun lias therefore passed by the
star, and is now east of it. At the end of November we
will find it rising at sunset and setting at ennrise. The
sun is therefore directly, opposite the star. During the
winter months it approaches it again from the west, and
passes it about the end of May, as before. Any other
star south of the zenith shows a similar change, since the
relative positions of the stars do not vary.

§ 3. THE SUV'S AFPASEirF PATH.

It is evident that if the apparent path of the sun lay in
the equator, it would, during the entire year, rise exactly
in the east and set in the west, and would always cross
the meridian at the same altitude. The days would
always be twelve hours long, for the same reason that a
star in the equator is always twelve hours above the hori-
zon and twelve hours below it. But we know that this
is not the case, the sun being sometimes north of the
equator and sometimes south of it, and therefore having
a motion in declination. To understand this motion.

XOa ASriiONOMY.

8unix«e that on March 19th, 1879, the Bun had been
observed with a meridian circle and a Biderca,! clock at the
moment of transit over the meridian of Wa«hnigton. Its
position would have been found to bo this :
Eight Ascension, 23" 55™ 23' ; Declination, 0" 30' south.

Had the observation been repeated on the 20th and
following days, the results would have been :

March 20, R. Ascen. 23" 59™ 2'; Dec. 0° 6' South.
2 J u 0" 2™ 40"; " 0° 17' North.

22' " 0" C™ 19* ; " 0° 41' North.

Fio.

44.— THB BOH CROfltniO THB BQUATOB.

If we lay these positions down on a chart, we shall find
them to be as in Fig. 44, the centre of the sun being
south of the equator in the first two positions, and north
of it in the last two. Joining the successive positions by
a line, we shall have a small portion of the apparent path
of the sun on the celestial sphere, or, in other words, a
small part of the ecliptic. ^v. * *i.

It is clear from the observations and the figure that the
sun crossed the equator between six and seven o'clock on
the afternoon of March 20th, and therefore that the equa-
tor and ecliptic intersect at the point where the sun was at
that hour. This point is called the verrud e^mnox, the

TUB SUN'S APPAUKNT PATH.

been

it the

Itg

louth.
1 and

ith.
rth.
•rth.

ai find
being
i north
ions by
nt path
^ords, a

;hat the
lock on
le eqna-
i was at
UKC, the

first word indicating the eeason,
cxpreflscs the equality of the
nights and days which occurs
when the sun is on the equator.
It will be remembered that this
equinox is the point from wliich
right ascensions are counted in
the heavens in the same way
that longitudes on the earth are
counted from Greenwich or
Washington. The sidereal
clock is therefore so set that
the hands shall read hours
minutes seconds at the
moment when the vernal equi-
nox crosses the meridian.

Continuing our observations
of the sun's apparent course for fe
c:v m/inflia fiTtm Mftnth 20th ^

while the second

six months from March 20th
till September 23d, we should
find it to be as in llg. 45. It
will be seen that Fig. 44 cor-
responds to the right-hand end
of 45, but is on a much larger
scale. The sun, moving along
the great circle of the ecliptic,
will reach its greatest northern
declination about June 2l8t.
This point is indicated on the
figure as 90° from the vernal
equinox, and is called the sum-
iner solstice. The sun's right
ascension is then six hours, and
its declination 23i° north.

The course of the sun now
inclines toward the south, and
it again crosses the equator about September Sad at

104

ASTRONOMY.

a point diametrically opposito the vernal equinox. In
virtue of the theorem of spherical trigonometry that all
great circles intersect each other in two opposite points,
the ecliptic and equator intersect at the two opposite equi-
noxes. The equinox which the sun crosses on September
22d is called the autumnal equinox.

During the six months from Septemher to March the
sun's course is a counterpart of that from March to Sep-
tember, except that it hes south of the equator. It at-
tains its greatest south declination about December 22d,
in right ascension 18 hours, and south declination 234°.
This point is called the winter soUtice. It then begins to
incline its course toward the north, reaching the vernal
equinox again on March 20th, 1880.

The two equinoxes and the two solstices may be re-
garded as the four cardinal points of the sun's apparent
annual circuit around the heavens. Its passage through
these points is determined by measuring its altitude or
declination from day to day with a meridian circle. Since
in our latitude greater altitudes correspond to greater
declinations, it follows that the summer solstice occurs on
the day when the altitude of the sun is greatest, and the
winter solstice on that when it is least. The mean of
these altitudes is that of the equator, and may therefore
be found by subtracting the latitude of the place from
90°. The time when the sun reaches this altitude going
north marks the vernal equinox, and that when it reaches
it going south marks the autumnal equinox.

These passages of the sun through the cardinal points
have been the subjects of asti-onomical observation from
the earliest ages on account of their relations to the change
of the seasons. An ingenious method of finding the time
when the sun reached the equinoxes was used by the as-
tronomers of Alexandria about the beginning of our era.
In the great Alexandrian Museum, a large ring or wheel
was set up parallel to the plane of the equator— in other
words, it was so fixed that a star at the pole would shine

'_^X^

THE ZODIAC.

106

»x. In
that all
points,
te equi-
ptumber

ircli the
to Sep-
, It at-
)6r 22d,
on 234°.
)eginB to
e vernal

y be re-
apparent

through
itude or
I. Since
I greater
xscnrs on

and the
mean of
therefore
ace from
ide going
it reaches

al points
tion from
le change
; the time
by the as-
f our era.
or wheel
—in other
)uld shine

perpendicularly on the wheel. Evidently its plane if
extended must have passed through the cast and west
points of the horizon, while its inclination to the vertical
was equal to the latitude of the place, which was not far
from 30°. When the sun reached the equator going north
or south, and shone upon this wheel, its lower edge would
be exactly covered by the shadow of the upper edge ;
whereas in any other position the sun would shine upon
the lower inner edge. Thus the time at which the sun
reached the equinox could be determined, at least to a
fraction of a day. By the more exact methods of modem
times, it can be determined within less than a minute.

It will bo seen that this method of determining the an-
nual apparent course of the sun by its declination or alti-
tude is entirely independent of its relation to the fixed
stars ; and it could be equally well applied if no stars
were ever visible. There are, therefore, two entirely dis-
tinct ways of finding when the sun or the earth has com-
pleted its apparent circuit around the celestial sphere ;
the one by the transit instrument and sidereal clocV, which
show when the sun returns to the same position among
the stars, the other by the measurement of altitude, which
shows when it returns to the same equinox. By the for-
mer method, already described, we conclude that it has
completed an annual circuit when it returns to the same
star ; by the latter when it returns to the same equinox.
These two methods will give slightly different results for
the length of the year, for a reason to bo hereafter
described. •

The Zodiac and its Diviaioiia. — The zodiac is a belt
in the heavens, commonly considered as extending some 8°
on each side of the ecliptic, and therefore about 16° wide.
The planets known to the ancients are always seen within
this belt. At a very early age the zodiac was mapped out
into twelve signs known as the signs of the zodiac^ the
names p£ which have been handed down to the present
time. Each of these signs was supposed to be the seat of

loe

AsmoNimr.

■«»»>

a conftoUation after whicli it wa« calUui Oommcncmg
it the vorruvl ciuinox, tho tt«t thirty dogrc«8 through
whchtroHun i,La,orth« region a.no..g the «tar8 m
whic it wa8 ou.ul during tlie m<mth following, wan
Ta^lod the In ArieM. The next thirty degrees w.« called
SJT The nanicB of all the twelve «gnB u. the^
proper order, with the approximate time of the buu « en-
tering upon each, are a» follow :

Arieti, the Ram,
Taurus, the Bull,
Gemmh the Twins,
Camer, the Crab,
Leo, the Lion,
F//yw, the Virgin,
Libra, the Balance,
Scorpin4t, the Scorpion,
Sagittarius, the Archer,
Capricornm, the Goat,
yljMartt**, the Wator-l)earer,
Pi»ce«, the Fishes,

March 20.
April 20.
May 20.
Juno 21.
Julv 22.

August 22.
Septemlwr 22.
October 23.
Noveml)er 23.
December 21.
January 20.
February 19.

Each of these signs coincides roughly with a conste a-
tion in the heavens ; and thus there are twelve constella-
tions called by the names of these signs, but the signs and
the constellations no longer correspond. Although the sun
now crosses the equator and enters the m^r^ Anes on the
20th of March, he does not reach the comteUatwn Anes
nntil nearly a month later. This arises from the preces-
sion of the equinoxes, to be fxplained hereafter.

§ 4. OBLIQUITY OP THE BCLIPTIO.

We have already stated that when the sun is at the
Bommer solstice, it is about 23*° north of the equator,
and when at the winter solstice, about 23i° south. This
Bhow. that the ecliptic and equator make an angle
of about 23i° with each other. This angle ifl caUed

the
v«r

ol>H(

suit
the
mui
will
tim
abo
sevi
the

BCV

tw^t

son

tor

isp!

is s

cell

vei

hal

isp

soi

fai

lat

is,

in
Tl
o\

onuqvirr of riiK Kvuprra.

107

incing
rough
aro in
, waH
callod
I their
i'b eu-

•nstella-
»nBtella-
gns and
the Bun
I on the
m Aries
preces-

8 at the
equator,
li. This
kU angle
IB called

the obliquity of (lie ocliptit , iirid its dotonnination ia
very siinpk'. It is onlv necesBary to find by repeated
oiwervation tin tiun's greato«t north declination at the
eutnnier Bolstice, and its greatest south declination at
the winter aolstice. Either of these decliimtions, which
must bo equal if the olworvations are accurately made,
will give the obliquity of the ecliptic. It has iMjen con-
tinually diminishing from the earliest ages at a rate of
about half a Becond a year, or, more exactly, about forty-
seven seconds in a century. This diminution is due to
the gravitating forces of the planets, and will continue for
several thousand yearn to come. It will not, however, go
on indefinitely, but the obliquity will only oscillate be-
tween comparatively narrow limits.

The relation of the obliquity of the ecliptic to the Bea-
Bons is quite obvious. When the sun is north of the equa-
tor, it culminates at a higher altitude in the northern hem-
isphere, and more than half of ita apparent diurnal course
is above the horizon, as explained in the chapter on the
celestial sphere. Hepce we have the heats of summer.
In the southern hemisphere, of course, the case is re-
veraeu : when the sun is in north declination, less than
half of his diurnal course is above the horizon in that hem-
isphere. Therefore this situation of the sun corresponds
to summer in the northern hemisphere, and winter in the
southern one. In exactly the same way, when the sun is
far south of the equator, the days are shorter in the north-
em hemisphere and longer in the southern hemisphere.
It is therefore winter in thft former and summer in the
latter. If the equator and the ecliptic coincided— that
is, if the sun moved along the equator— there would
be no such thing as a difference of seasons, because the
sun would always rise exactly in the east and set exactly
in the west, and always culminate at the same altitude.
The days would always be twelve hours long the world
over. This is the case with the planet Jupiter.
In the preceding paragraphs, we have explained the

108

ASTRONOMY.

apparent annual circuit of the sun relative to the equator,
and shown how the seasons depend upon this circuit. In
order that the student may clearly grasp the entire subject,
it is necessary to show the relation of these apparent move-
ments to the actual movement of the earth around the

sun.

To understand the relation of the equator to the eclip-
tic, we must remember that the celestial pole and the
celestial equator have really no reference whatever to the
heavens, but depend solely on the direction of the earth s
axis of rotation. The pole of the heavens is nothing
more than that point of the celestial sphere toward which
the earth's axis points. If the direction of this axis
changes, the position of the celestial pole among the stars
will change also ; though to an observer on the earth,
unconscious of the change, it would seem a& if the starry
sphere moved while the pole remained at rest. Again, the
celestial equator being merely the great circle in which the
pkne of the earth's equator, extended out to infimty in
every direction, cuts the celestial sphere, any change in
the direction of the pole of the earth necessarily changes
the position of the equator among the stars. Now the
positions of the celestial pole and the celestial equator
among the stars seem to remain unchanged throughout
the year. (There is, indeed, a minute change, but it does
not affect our present reasoning.) This shows th•^t, as
the earth revolves around the sun, its axis is constantly
directed toward nearly the same pohit of the celestial
sphere.

§ 5. THE 8EA80IV8.

The conclusions to which we are thus led respecting
the real revolution of the earth are shown in Fig. 46.
Here S represents the sun, with the orbit of the earth
surrounding it, but viewed nearly edgeways so as to be
much foreshortened. ABGD are the four cardina
positions of the earth which correspond to the cardinal

poll
In<
nor

san

it i

Ag
the
inc
]
sur
noi
dai
son
an|
wi
the
thi
ilh
m(

gl«
pe

ator,
In
ject,
love-
l the

jclip-
the

the
irth'a
thing
vhich
> axis

1 stars
sarth,
starry
a, the
ihthe
ity in
ige in
langes
w the
juator
ighout
t does
•\t, as
itantly
ilestial

tecting
ig. 46.
i earth
I to be
ardinal
ordinal

THE SEASONS.

109

points of the apparent path of the sun ah*eady described.
In each figure of the earth J/'S is the axis, iT being its
north and S its south pole. Since this axis points in the

FlO. 46.— CAV8B8 OF THK 8BA80NB.

same direction relative to the stars during an entire' year,
it follows that the different lines N S Are all parallel.
Again, since the equator does not coincide with the ecliptic,
these lines are not perpendicular to the ecliptic, but are
inclined from this perpendicular by 23i°.

Now, consider the earth as at ^ ; here it is seen that the
sun shines more on the southern hemisphere than on the
northern ; a region of 23^° around the north pole is in
darkness, while in the corresponding region around the
south pole the sun shines all day. The five circles at right
angles to the earth's axis are the parallels of latitude around
wMch each region on the surface of the earth is carried by
the diurnal rotation of the latter on its axis. It will be seen
that in the northern hemisphere less than half of these are
illuminated by the sun, and in the jiouthern hemisphere
more than half. This corresponds to our winter solstice.

When the earth reaches -ff, its axis JVS is at right an-
gles to the line drawn to the sun, so that the latter shines
perpendicularly on the equator, the plane of which passes
through it. The diurnal circles on the earth are one half

A8TB0N0MT.

illuminated and one half in darkness. This position cor-
responds to the vemal equinox. ^ a *^

At G the case is exactly the reverse of that at A, the
sun shining more on the northern hemisphere than on the
southern one. North of the equator more than half the
diurnal circles are in the illuminated hemisphere, and south
of it less Here then we have winter in the southern and
summer in the northern hemisphere. The sun is above a
region 23i° north of the equator, so that this position cor-
responds to our summer solstice.

At D the earth's axis is once more at right angles to a
line drawn to the sun. The latter therefore shines upon
the equator, and we have the autumnal equinox.

In whatever position we suppose the earth, the Une A JV,
continued indefinitely, meets the celestiad sphere at its
north pole, while the middle or equatorial circle of the
earth, continued indefinitely in every direction, marks out
the celestial equator in the heavens. At first sight it might
seem that, owing to the motion of the earth through so
vast a circuit, the positions of the celestial pole ^d equa-
tor must change in consequence of this motion. We might
say that, in reaUty , the pole of the earth describes a circle in
the celestial sphere of the same size as the earth's orbit.
But this sphere being infinitely distant, the circle thus de-
scribed appears to us as a point, and thus the pole of the
heavens seems to preserve its position among the stars
through the whole course of the year. Again, we may
suppose the equator to have a slight annual motion among
the stars from the same cause. But for the same reason
this motion is nothing when seen from the earth. On the
other hand, the slightest change in the direotim of the
axis SIf wUl change, the apparent position of the pole
among the stars by an angle equal to that change of direc-
tion. We may thus consider the position of the celestial
pole as independent of the position of the earth in its
orbit, and dependent entirely on the direction in which
the axis of the earth points.

tic
of
ex
diJ

ri|

til

si
C

ai
al
t<
tl
b
o

cor-

thc
1 the
: the
ionth
I and
jve a
1 cor-

to a
upon

SJV,
Eit its
f the
C8 ont
[night
igh so
equa-
tnight
vie in
orbit,
osde-
>f the
I stars
e may
unong
reason
)n the
of the
o pole
direc-
elestial
in its
which

CELESTIAL LATITUDE AND LONGITUDE 111

If this axis were perpendicular to the plane of the eclip-
tic, it is evident that the sun would always lie in the plane
of the equator, and there would be no change of seasons
except such slight ones as might result from the small
differences in the distance of the earth at different seasons.

§ e. CELESTIAL LATTTUDB AND LONQITUDB.

Besides "the circles of reference described in the first
chapter, still another systfem is used in which the ecliptic
is taken as the fundamental plane. Since the motion of
the earth around the sun takes place, by definition, in the
plane of the ecliptic, and the motions of the planets very
near that plane, it is frequently more convenient to refer
the positions of the planets to the plane of the ecliptic than
to that of the equator. The co-ordinates of a heavenly
body thus referred are called its celestial Utituds and
hmgitude. To show the relation of these co-ordinates to
right asocmsion and declination, we give a figiwe showing
both co-ordmates at the same time, as marked on the
celestial sphere. This figure is supposed to be the celes-
tial sphere, having the solar system in its centre. The
direction /> ^ is that of the axis of the earth ; IJ\& the
ecliptic, or the great circle in which the plane of the
earth's orbit intersects the celestial sphere. The point in
which these two circles cross is marked 0^, and is the ver-
nal equinox from which the right ascension and the longi-
tude are both counted.

The horizontal and vertical circles show how right ascen-
sion and declination are counted in the manner described in
Chapter I. As the right ascension is counted all the way
around the equator from (^ to 24S so longitude is counted
alon ,' the ecliptic from the point 0^, or the vernal equinox,
toward J in degrees. The whole circuit measuring 360",
this dlhtance will carry us all the way round. Thus if a
body ^ in the ecUptic, its longitude is simply the number
o^'i^ees from the vernal equinox to its position, meas-
lllif !n the direction from / toward J. If it does not lie

112

A8TR0N0MY.

SipSo ffle»gth of thi. i«rpe«dicukr,me«oredm
^, i» cUedX W«. of .ho IfJy. f'f ™y^
««^l. nr south whUe the distance of the foot of the per
™^.S^f*m r vomal eqainox i. called '■^^'-f^-

botoTof the Botar «T»tem, retatively to the smi, by their
^"X^taat«d«. lU«.intheecUptiewehave .

FlO. 47.— CIBCUCB OF THE BPHBBB.

plane more nearly fixed than that of the equator On^e
Ler hand, it is more convenient totepreeent ^ po«Uon
of aU the heavenly bodies ae Been from the ««^^y *^
right ascensions and declinations, because we ««»o* «T;
rJhriongitudes and latitudes <^%^;\r^f^
observe right ascension and decimation. If we wisn w
dSn/the longitude and l^tjude of a^y as -n
from the centre of the earth, we have to fi«*/»f ^^«j^^
ascension and decUnation by observation, and then cbm^
Sr^nMitities to longitude and htitude by tngonometn-
oal formnlsB.

priB
nitii
core
rate
ter,
pki
the
uia'

•

iut(
g
iirsi
tha
the
whi
mo
mo
alw
cer
1
pec
boc
sun
pla

we
the
iin
^ be
per-
ude.
the
heir
vea

)nthe
wition
^ their
meas-
riOAly
rifih to
B seen
I right
shauge
unetri-

CHAPTER IV.

THE PLANETARY MOTIONS.

§ 1. APPABEnr Ain> beal Monovs of the

FLAITETS.

DeflnitioiiB. — The solar system, as wo now know it, com-
prises so vast a number of bodies of various orders of mag-
nitude and distance, and subjected to so many seemingly
complex motions, that we must consider its parts sepa-
rately. Our attention will therefore, in the present chap-
ter, be particularly directed to the motions of the great
planets, which we may consider as forming, in some sort,
the fundamental bodies of the system. These bodies
may, with respect to their apparent motions, be divided
into three classes.

Speaking, for the present, of the sun as a planet, the
first class comprises the »un and moon. We have seen
that if, upon a star chart, we mark down the positions of
the sun day by day, they will all fall into a regular circle
which marks out the ecliptic. The monthly course of the
moon is found to be of the same nature, although its
motion is by no means uniform in a month, yet it is
always toward the east, and always along or very near a
certain great circle.

The second class comprises Venus and Mereury. The
peculiarity exhibited by the apparent motion of these
bodies is, that it is an oscillating one on each side «, ? the
sun. If we watch for the appearance of one of theae
planets after sunset from evening to evening, we shall find

ABTR0N0M7.

it to appear above the western horizon. Night after night
wiUW arther and farther from the sun untU it attems
ar^Sr maximum distance; then it^llappearter^^^^
to the sun again, and for a while to be lost m its rays.
A f^w Zs ISer it will reappear to the west of the ^n,
fnd ther^^ter be visible in the eastern horizon before
Bunrise In the case of Mercury, the time reqmred for
oneT»mplete oscillation back and forth is about four
Zt?^7and in the case of Venus more than a year and

* m third class comprises Jfor«, Jupit^, and Saturn as
weU ^a ^at num Jof planets not visible to the na^ed
Tye Thfgeneral or average motion of these planets i
X'ard the% a complete revolution i- «^« J^^^^
Bphere being performed in times ranging from two years
ZZ Z^e^Mars to 164 years in that of Neptnn..
But instead of moving uniformly forward, they^m to
have a swinging motion ; first, they move forward or
towIrJ Zlt 'through a pretty long arc tb- backw^^
or westward through a short one, then forward through
a J^r one, etc. It is only by the excess of the longer
aiTS the shorter ones that the circuit of the heavens

^'S'general motion of the sun, moon, and planets
among the stars being tcJward the east the motion inth^^
diredlon is called direct; whereas the occasional short
Z&Z toward the west are called retro^. During
the periods between direct and retrograde motion, the
pknete will for a short time appear stationaiy. ^^^

The planets Venm and Mercury are said to be at great-
est ^atUm when at their greatest «^"g^;.J«^^^^™
the sun The elongation which occurs with the planet
J^tTihe sun, andXrefore visible in the -estei. hon-
zon after sunset, is called the eastern elongation, the other

^T^^irslid to be in conjunction with the smi when
it is in the same direction, or when, as it seems to pass by

the B
oppo.
tion-
apla
sun,
yond
Ai
knov
and \
cent!
plant
inFi

in tl
whi<
fari

ight
tains
itum
rays.
Bun,
afore
i for
four
r and

m as

laEked

lets is

lestial

years

■kune.

em to

a-d or

kward

rough

longer

eavens

planets
in this
short
During
in, the

igreat-
se from
planet
m hori-
le other

n when
pass by

ARRANGEMENT OF THE PLANETS.

116

the sun, it approaches nearest to it. It is said to be in
apposition to the sun when exactly in the opposite direc-
tion — rising when the snn sets, and vi^ie vecsa. If, when
a planet is in conjunction, it is between the earth and the
sun, the conjunction is said to be an inferior one ; if be-
yond the snn, it is said to be tniperior.

Arrangements and Motions of the Planets. — We now
know that the sun is the real centre of the solar system,
and that the planets proper all revolve around it as the
centre of motion. The order of the five innermost large
planets, or the relative positions of their orbits, are shown
in Fig. 48. These orbits are all nearly, but not exactly,

48. — ORBIT8 OF THB PLANETS.

in the same plane. The planets JUercury and Venits
which, as seen from the earth, never appear to recede very
far from the sun, are in reality those which revolve inside

,,„ ASTKONOMr.

llo

, , -♦I, The Dlanets of the third clasB,
the orbit of the earth. ?^* Pn^auces from the «un,
which perform tl^«y^;j-^„^^^^^^^^^ and ai.;nore
are what we now call the J^ "*\ t*. ^f these, the or-
aietantfj^the^mH^-^^^^ telescopic planets

bits of Mars, Jujnter, ana a ^ ^^^

are shown in t^>« ^f ^^f ^* Jurvisible to'^the naked
Samr>., the farthest P^»"«* ^Ll telescopic planets,
eye, and ^^ J^^^;^jteX^l ^'^^ ^^^^^
On the scale of l?ig. *» ^"« Wnallv, the moon is a

^ore than two feet m diameter. ^^Z.U. ^^^.^e, and

The farther »?!»««* i^^*^^^ '^e go frJm tbe sun,
is its orbital motion. TW ^^ f^, ^he double reason
the periods of revolution are ^«J««'^;^**J^ribe and moves
that the planet has a larger orbit o de^"^^^.^^ ^^ ^^^

xnonj slowly in it« orbit, f^^^^^^^^^trognide motion
outerplanetsthattheoccasiomaapp««ntreirog

li Jplanets is du. - -y^r<^^W a pU,
We first remark that the ^Pl^j^^ , ^^ li^e joining
as seen from the «^%» *^^^t Z to be continued
the earth and planet. S^I^^lt tbe celestial sphere,
onward to infinity, so as to ^^J^^^^J^J^efined by the
the apparent motion of t^l^P^''?* ^^temcte the sphere,
motion of the point ^^^^^f ^^^^^^^^^^^ dir^t ; if
If this motion is toward the east, it wiu oe
toward the west, retrograde. g

^ V"/^X*JV ': Cu^clTve "^Itioi^ of the earth
poee ^i^^ff^cDEF ^ ^« corresponding posi-
in its orbit, wAABtVJ;^ Tt must be remembered that
tions of ^-- - fXTi^Tnti^cTnnection, we do
irmiraf alir dl^ction in space, but a direction

aronr
down
diroc
inovt
earth
beini
evidi
great
sun I
totl

the
dir
the
H
pel
inj
eai
is

ItJ

lird cla8B,
i the Bun,

are jnore
se, the or-
lic planets
Iter comes
the naked
ic planets.
I would be

moon is a
sentro, and
an.
inude that

outside that

I, the Blower
9m the sun,
)uble reason
} and moves
lotion of the
grade motion

ring Fig- 49-
of a planet,
i line joining
be continued
cstial sphere,
efined by the
its the sphere,
be direct ; if

pUnet. Sup-
riB of the earth
spending posi-
membered that
inection, we do
but a direction

APPABBNT MOTIONS OF TlIK PLANKTS. 117

around the sphere. In the figure wc are supposed U <k
•lown upon the planetary orbitH from the north, anu a
direction west is, tlien, that in which the ImudH of a watch
move, while east is in the opposite direction. When the
earth is at // the planet is seen at A. The Ime JIA
being supposed tangent to the orbit of the planet, it is
evident from geometrical considerations that this is the
Kreatest angle which the planet can ever make with the
sun as seen from the earth. This, therefore, corresponds
to the greatest eastern elongation.

When the earth has reached /the planet is at B, and is
therefore near the direction IB. The line has turned in a
direction opposite that of the hands of a watch, and cuts
the celestial sphere at a point farther east than the line
ffA did. Hence the motion of the planet during this
period has been direct ; but the direction of the sun hav-
ing changed also in consequence of the advance of the
earth, the angular distance between the sun and the planet
is less than before.

While the earth is passing from / to K, the planet

118

ASTRONOHr.

pasHuH from li to C. The distance B C ox(!«odH / A', be-
cause the planet niovet) faster than the earth. The line
joining the earth and planet, therefore, cuts the celestial
sphere at a point farther west than it did l)eforo, and
therefore the direction of the apparent motion is retro-
grade. At G the planet is in inferior conjunction. The
retrograde motion still continues imtil the earth reaches Z,
and the planet />, when it 1>ecomcs stationary. After-
ward it is direct until the two bodies again come into the
relative positions I Ji.

Let U8 next snpposo that the inner orbit A B CD EF
represents that of the earth, and the outer one that of a
superior planet, Moth ior instance. We may consider
O QPJitohe the celestial sphere, only it should be infi-
nitely distant. While the earth is n «yving from ^ to ^ the
planet moves from II to 7. This ^ni. tion is direct, the di-
rection OQP li being from west to east. While tlie earth
is moving from B to D, the planet Is moving from / to
Z ; the former motion l)eing the more rapid, the earth
now passes by the planet as it were, and the line conjoin-
ing tiiem turns in the same direction as the hands of a
watch. Therefore, during this time the planet seenu* to
describe the arc P Q' in the celestial sphere in the direction
opposite to its actuai orbital motion. The lines Z D and
MEixe supposed to be parallel. The planet is then really
stationary, even though as drawn it would seem to have a
forward motion, owing to the distance of these two lines,
yet, on the infinite sphere, this distance appears as a
point. From the point M the motion is direct until the
two bodies once more reach the relative positions B I.
When the planet is at JT and the earth at C, the former is
in opposition. Hence the retrograde motion of the supe-
rior planets always takes place near opposition.

Theory of Bpioy<des. — The ancient astronomers repre-
sented this oscillating motion of the planets in a way which
was in a certain sense correct. The only error they made
was, in attributing the oscillation to a motion of the planet

API

instead of

really cans

the nteans

tion of the

celebrated

motions w

Ulcus. C

seen by tl

sented by

circle or «

with a rei

then the

f erence c

true one

epicycle

the sun,

cumferei

from tht

plain thi

motion.

Itisi

motion

pear to

which 1

is uncoi

appear

shown

and^

the obi

imagin

Suppo

the pi

rest, s

have

imagi
thep

APPARBNT MOTIONS OF TIIK PLANKTH.

119

1DEF
at of a
ionsider
be infi-
o R the
the di.
le earth
m /to
e eartJi
Jonjoin-
^ds of a
senifi to
irection
'/>and
D really
have a
o lines,
rs as a
itil the
wJ?/
pmer is
3 sope-

repre-

whioh

made

planet

insteatl of a motion of the earth around the sun, whiclk
really causes it. But their theory was, notwithstanding,
tlie means of leading Cupeuniuus and others to the percep-
tion of the true nature of the motion. We allude to the
celebrated theory of epicycles, by which the planetary
motions were always represented before the time of Copkk-
NiciTB. Complicated though these motions were, it was
seen by the ancient astronomers that they could be repre-
sented by a combination of two motions. First, a small
circle or epicycle was supposed to move around the earth
with a regular, though not uniform, forward motion, and
then the planet was supposed to move around the oircnm-
ference of this circle. The relation of this theory to the
true one was this. The regular forward motion of the
epicycle represents the real motion of the planet aronnd
the sun, while the motion of the planet aronnd the cir-
cumference of the epicycle is an apparent one arising
from the revolution of the earth around the snn. To ex-
plain this we must understand some of the laws of relative
motion.

It is familiarly known tl)at if an observer in unconscious
motion looks upon an object at rest, the object will ap-
pear to him to move in a direction opposite that in
which he moves. As a result of this law, if the observer
is unconsciously describing a circle, an object at rest will
appear to him to describe a circle of equaJ size. This is
shown by the following figure. Let 8 represent the sun,
and A B CDBF the orbit of the earth. T^ us suppose
the observer on the earth carried around in this orbit, but
imagining himself at rest at 8^ the centre of motion.
Suppose he keeps observing the direction and distance of
the planet P, which for the present we suppose to be at
rest, since it is only the apparent motion that we shall,
have to consider. When the observer is at ^ he really
sees the planet in a direction and distuioe A P, but
imagining himself at 8 he thinks he sees the planet at
the point a determined by drawing a line Sa parallel and

120

ASTHONOMV.

equal to A P. A* he pam-H from A to B the planet
will wjeui to him to move in the opiKwite ilirection fr(»m

A to b, the point h Injiiig deter-
mined by drawing Sb equal and
parallel to B P. As ho reeedes
from the planet through the arc
BCDy the planet seems to re-
cede from him through hcd\
and while he moves from loft to
right through DE the planet
seeniB to move from right to left
through D E. Finally, as he ap-
proaches the planet through the
arc EFA the planet seems to
approach him through EFA,
and when he returns to A the
pUnet will appear at ^, as in the
beginning. Thus the planet,
though really at rest, will seem
to him to move over the circle
ahcdef corresponding to that
iu which the obser^'er himself is

carried around the sun.

Tlie planet being really in motion, it is evident that
the combined effect of the real motion of the planet and
the apparent motion around the circle a J o <; «/ will bo
represented by carrying the centre of this circle P along
th.> true orbit of the planet. The motion of the earth
being more rapid than that of an outer planet, it follows
that the apparent motion of the phmet through a J is more
rapid than the real motion of P along the orbit. Hence
in this part of the orbit the movement of the planet wUl be
retrograde. In every other part it will be direct, because
the progressive motion of P will at least overoome, some-
times be added to, the apparent motion around the circle.
In the ancient astronomy the apparent small circle
ahcdef was called the epieyde.

flm ri
I lero
ifH rei
the t
forwt
tion
earth

In
wo hi
by II
really
to de
of iti
tho a
that
of itf
incoi
all tl
was,
was 1
mov<
bratc
the I
of m
real
in 01
part,
poset
Thej

Tl
ineqi
to b<

•I
quity
Buppc
idled

UNEQUAL MOTION OF THE PLANETS.

121

I planet
>ii fr<»iii
ij tlotur-
[ual iind

recedos

the arc
8 to ro-
ll hed\
w loft to
) planet
t to left
u ho ap-
)Ug1l tlio
iOoinB to

EFA,
o A the
as in the

planet,
nil seem
he circle

to that
litnBelf is

dent that
lanot and
f will bo
) P along
the earth
it follows
h is more
. Hence
let will be
t, because
ne, some-
he circle.

lall circle
t

In the ciiHo of \\\v innor planets Mernnnf and Vtrnm
\\w rbliition of tlie epiiiyelo to the tr.io orlnt Ih reverHed.
Here the epieyelic motion ih tliiit of the plunet annind
ifH real orbit— that is, the true orliit of the plunot around
tho sun was itself taken for the epicycle, while the
forward motion was really duo to tho apparent revolu-
tion of tho sun produced by tho aimual motion of tho
earth.

In tho preceding descriptions of tho planetary motions
wo have spoken of them all as eircukr. But it was found
by Ilii'J'ARcnus * that none of tho planetary motions were
really unifonn. Studying tho motion of the sun in order
to determine tho length of tho year, ho observed tho times
of its passage through tho equinoxes and solstices with all
tho accuracy which his instruments pennitted. He found
that it was several days longer in passing through one half
of its course than through tho other. This was apparently
incompatible with tho favorite thcoiy of tho ancients that
all tho celestial motions were circular and uniform. It
was, however, accounted for by supposing that the earth
was not in the centre 6f tho circle around which tho sun
moved, but a little to one side. Thus arose the cele-
brated theory of tho eccentric. Careful observations of
the planets showed that they also had similar inequalities
of motion. The centre of the epicycle around which the
real planet was carried was found to move more rapidly
in one part of the orbit, and more slowly in the opposite
part. Thus the circles in which the planets were sup-
posed to move were not truly centred upon the earth.
They were therefore called eccentrics.

This theory accounted in a rough way for the observed
inequalities. It is evident that if the earth was supposed
to be displaced toward one side of the orbit of the planet,

* HnTAi{CHi7B was one of thie most celebrated astronomers of anti-
quity, being frequently spoken of as the father of the science. He is
supposed to have made most of his observations at Rhodes, and flour-
hdied about one hundred and fifty years before the Christian era.

iiu Ti

♦

522 ASTRONOMY.

the latter wonkl seem to move more rapidly when nearest
the earth than when farther fron. it. 1^ wa. not untd ^e
time of KE..LEK that the eccentric w;ifl shown to be
caTable of accounting for the real motion ; and it ,s his
discoveries which we are next to descnbe.

§ 2. KBPLBB'S LAWS OF PLAJTETARY MOTION.

The direction of the sun, or its longitude, can be deter-
mined from day to day by direct observation If we
could also observe its distance on each day, we should, by
laying down the distances and directions on a large piece
7paper, through a whole year, be able to trace the curve
Sthe earth describes in its annual course, this cour^
C^g, SB already shown, the counterpart of the appa^^t
L of the sun. A rough determination of *ae rela-
tive distances of the sun at difierent times of the year may
be made by measuring the sun's apparent angular diame-
ter, becaJe this diameter varies inversely aa Je distan^
of the object observed. Such measur^ would show that
the diameier waa at a maximum of 32' 36' on January 1st,
Ind a"a minimum of 31' 32" on July 1st of every y«.^
The difference, 64% is, in round numbers, A tbe mean
diameter-that is, the earth is nearer the sun onjmu^j
1st than on July Ist by about ^ We may consider ^
as A greater than the mean on the one date, and ^ less
TntheSer. This is therefore the actual displacement
of the sun from the centre of the earth s orbit.

Again, observations of the apparent daaly motion of
thT^ among the stars, corresponding to the real dady
'IZoi the'earth round the sun, show t^s motion^o be .
least about July Ist, when it amounts to 57 12 _ 34d^ ,
and greatest about January 1st, when it a^^^^ t°
«1 ' ir = 3671'. The difference, 239', is, m round num-
bers A the mean motion, so that the range of variation
M; proportion to the mean, double what it is in the c^
p L diBtences. If the actual velocity of the earth m its

pou]
was
pose

m 01
in lo
half
long
eartl
ingi
attril
the t
bit-
centi
the (
greal
A]
tion :
radi',
rouni
pose,
and
day t
of it
and I

geom
the a:
are ir

KEPLER'S Laws.

Idd

jarest
il the
ae iu-
is his

[ON.

deter-
[f wo
Id, by

piece

curve
course
parent
3 rela-
armay
diame-
istance
»w that
ary iBt,

y y«ar.

Q mean
fanuary
sider it
L^less
icement

)tion of
al daily
on to be ^
= 3432',
rants to
nd num-
variation
the case
rth in its

orbit were niiiforin, tlie apparent angular motion round
tlie sun would be inversely as its distance from the sun.
Actually, however, the angidar motion, as given above, is
inversely as the square of the distance from the sun, be-
cause (1 + ^V)' = 1 + tV very nearly. The actual ve-
locity of the earth is therefore greater the nearer it is to
the sun.

On the ancient theory of the eccentric circle, as pro-
pounded by IIippAKcnus, the actual motion of the earth
was supposed to be uniform, and it was necessary to sup-
pose the displacement of the sun (or, on the ancient theo-
ry, of the earth) from the "ontre to be ^ its mean distance,
in order to account for the observed changes in the motion
in longitude. We now know that, in round numbers, one
half the inequality of the apparent motion of the sun in
longitude arises from the variations in the distance of the
earth from it, and one half from the earth's actually mov-
ing with a greater velocity as it comes nearer the sun. By
attributing the whole inequality to a variation of distance,
the ancient astronomers made the eccentricity of the or-
bit—that is, the distance of the sun from the geometrical
centre of the orbit (or, as they supposed, the distance of
the earth from the centi-e of the sun's orbit) — twice as
great as it really was.

An immediate consequence of these facts of observa-
tion is Kepleb's second law of planetary motion, that the
radii vectored drawn from the sun to a planet revolving
round it, sweep over equal areas in equal times. Sup-
pose, in Fig. 51, that /.S' represents the position of the sun,
and that the earth, or a planet, in a unit of time, say a
day or a week, moves from P, to P,. At another part
of its orbit it moves from P to P, in the same time,
and at a third part from P. to P.. Then the areas
SP,P,, SPP„ SP,P, will all be equal. A Kttle
geometrical consideration will, in fact, make it clear that
the areas of the triangles are equal when the angles at S
are inversely as the square of the radii vectores, SP, etc.,

*^-

1^4

ASTBONOMT.

.„ee t„e exprcion ,. the - "V^^™^'" '" *" *"°
angle at S w very anaU « J angle * X ^ J

O pi *

Fig. 51.— law of areas.

1„ the ttoe of K...« *-> ™-™J*.Cr^^ctd!

.un'B '»P'l»%*'r''''r J™£'3> S the earth around
ing method of deternnmng the l«ttt o ^^ ^^^

thl »m could 7'\''»^:^;tol^edhyTTOHoBKi■>.^
motions of the planet ^ar.,^*^ ^^^ ^ ,

that Keplee was led to his ceieore j^ ^

motion. He found that "» P^^^J";^^ „p^«>nt the

,r^y elreular orb^ho«-7C*^ ejeu^tions and

„h<«rvat.ons. Jf^' ;™f ™ t numher of hypothes^
the triil aud rejection ot a p« ^^^ ^^^^^

he was led to the eondusion .«'»' «« ^^ j^ the analo-
toanelU^. having *e™-^^Jtl^; attthe planets,
gieaof nature led *»*« ™'°"°r„ „f the same chM,
L earth i»«<^V "'°'^„ twX ™ led to enunciate

S*C^- "^ -"^" ^"^""^ "'°"°-

,hich were as follow: ,^ ^ „ „ . .^. „.., Ok,

^ 7ve the area mentioned above.

KEPLER' 8 LAWS.

195

I. Eachplanet moves around the sun in an ellipse, hav-
ing the sun in one of its fad.

II. The radius vector joining each planet toith the
sun, moves over equal areas in equal times.

To these be afterward added another showing the rela-
tion between the times of revolution of the separate
planets.

III. The square of the tim^ of revolution of each
planet is proportional to the cube of its mean distance
from, the sun.

These three laws comprise a complete theory of plan-
etary motion, so far as the main features of the motion are
concerned. There are, indeed, small vai-iations from
these laws of Keplkh, but the laws are so nearly correct
that they are always cmijloyed by astronomers as the basis
of their theorios.

Mathematioal Theory of the Elliptio Motion. — The
laws of Kkpleb lead to problems of such mathematical
elegance that we give a brief synopsis of the most impor-
tant elements of the theory. A knowledge of the ele-
ments of analytic geoUietry is necessary to understand it.

Let us put :

a, the semi-major axis of the ellipse in which the pUuut moTflt.
In the figure, if (7 is the centre of the el-
lipse, and <9 the focus in which the sun is
situated, then <i = A 0= On.

08
e, the eccentricity of the ellipse = — .

IT, the longitude of the perihelion,- rep>
resented by the angle n 8E, B being the
direction of the vernal equinox from
which longitudes are counted.

n, the mean angular motion of the
planet round the sun in a unit of time.
The actual motion being variable, the
mean motion is found by dividing the As. 01.

circumference = 860° by the time of revolution.

T, the time of revolution.

Tj the distance of the planet from the sun, or its radius vector, a
variable quantity.

I. The first remark we have to make is that the Mij^ieiUu of the

126 ASTIiONOMY.

the ellipse we have :

8B = Bemi-major axis = a,

BC= semi minor axis = a V 1 — «',
or 5 = a (1 - i «') nearly, when e is very small.

very nearly, so that flattening of the orbit is only about ^ or .02
of the major axis. , j^ j ^jjid^ ^ = .093 ;

B^t""! -loirs tff'i«tE.^»l"« of tl,, orbit U only

a ,cry cioso approxnmtion to the true lorm o.^ I ' ^,

It 1. Jnl, leceuar, to »"PP°?° *? ""°jrof tl • Scentricit, loto
re?Sto'o?rS.'rS.?er»S?"™„pre«„t«ioo o. the

-t' •^,C.X£°o<'t!!iVS:ot .™m «io .- "
and the greatest distance is

Kefleb : Q

vector during such unit ^i^" *^* J^rfg ggcond law. Therefore,

jj»"!'^fi5tcto;?r.t:^'ri'?s%hoh, .r» oj^th.

dh^ which i. . »• V T^-?.. The time re,m»a to do th«i 1»

. 1» ll,i. formula , n,pr»env. Iho r«io of the ciroumfereoee of the
circle to its diameter.

mg
alB(

KEPLER'S LA WS.

1»7

ing called T, the area swept over with the areolar velocity 4CU
t\ao\GT. Therefore

J C 2' = IT a' ^\ — e' ;

2irfl*Vf — e»
= j5

The .luantity 2 t hero represents 860% or the whole circumference,

called M. Therefore

2ir

and , -.

C = a*n Vl - e\

This value of being substituted in the expression for 8, wc have

a' rt Vl -"? *^

^= is

IV By Kepleh's third law r is proportioned to a" ; that is,
IL is a constant for all the planets. The numerical value of this

and a for the earth will both be unity, and the ratio ^ will there-
fore be unity for all the planets. Therefore
a» = 2" ; o = r*.

i^vc^r ATS-trhricrrormined with very great pre-
"^V °To find the position of a planet we must kno^^t^e epoch at
M^ Wn^irolllfte^^^^^^

Se';s;s^he%a£/Thi^^^^

^Ssltiorof the planet at this time wc shall have

Area of sector PSk _ _r
]\fcaof ^hoie ellipse T

(1).

128

ASTRONOMY.

The times r and T being both given, the problem is "^uced to
t. Jt of c^tUng a given area of the ellipse by a line drawn from the
V^„« to some point of its circumference to be found. This is
ISn as Slkk'8 problem, and may be solved by analytic geom-

TiO. 68.

the ratio of i> P to D i*, or of « to b. Hence,

Area GPB : area OP'S = b:a.

n * «,«« nvn- ftnffle P" B x i a», taking the unit radius
as?Se unU of'^fgulaJ^lllsfre!' Hence, putting « for the angle
pf G Bvre have

Area CPB = - area CP* 5 = J « S «
a

(2).

Again, theareaof the trianglcOPSisequaltoibaseC^f x al-
titudePD. AlsoPD = ^-P'AandP'i>= CP' sin « = «sm«.

Wherefore,

tri)

an(

It (

or,

PD = &sin

(8).

KSPLBR'8 LAWS.

1S9

By the first principles of conic sections, C 8, the base of the
triangle, is equal to a «. Hence

Area CP8 = iabeMau,

and, from (3) and (8),

Area SPB = Jo ft (« — «Bin «).

Substituting in equation (1) tliis value of the sector area, and
IT a 6 for the area of the ellipse, we have

tt — g sin w _ jr
3^;^ ~ 2"

or.

u — « sin u = 2 T -^.

Prom this equation the unknown angle « « ^^*^^:V'^
equation being*a transcendental one, this ««"»"«» ^,^°°«f^"?L
but it may be rapidly done by successive approximation, or the
value of u may be developed in an infinite series.

Next we wi^h to expreiTthepositionof *£« P»"'«*i.^J^^Si?,K
by its radius vector -8 P and the angle B 8 ^,^,^|«f *7"^'^''"
vMtor makes with the major axis of the orbit. Let us put

r, the radius vector SP,

/' the angle B 3P, called the true anomaly.

Then . „^

r sin/ = P2> = ft sin « (Equation 8),

rcos/=8D=CD- 08= P cosu - ae = a(coiu-e),

from which r and r can both be determined. By taking the square
I^^oTtiS^sums ohhe squares, they give, by suUable reducbon and
putting ft' = a' (1 - «'),

r = a (1 — « cos u),
and, by dividing the first by the second,

ft sin «

tan/ =

a (cos M — «)

Vl — g' sin M
cos u- e

Prtttog, „ before, . for the longtad. of th. peritaUon, th.tr..

'°t'°T;s'.X''^woVS°rpT::iKuti;..,.o th. ..upuc,

180

ASTRONOMY.

the inclination of the orbit to the ecliptic has to be taken into ac-
counf The orbits of the several large planets do not lie in the
Smc plane, but are inclined to each other, and to the ecliptic, by
tft^ous imkll anirles. A table giving the values of these angles
;rb"e g™en her&r, from whi?h it^ill be seen that the orbu o
Mereurv^haA the greatest inclination, amounting to 7 , and that of
f/mSe least, teing only 40'. The reduction of the position of
tlHw to «;« ecliptic fs a problem of spherical trigonometry,
the solution of which need not be discussed here.

fun

whi

feal

rea<

trat

fiho

cov

teBl

abi

Ion

tig

iB<

foi

Bci

i'- 1

gr(
th(
tb
ex
tis

&
in

nto ac-
) in the
jtic, by
angles
orbit of
that of
ition of
ometry,

CHAPTER V.

UNIVERSAL GRAVITATION.
§ 1. NEWTON'S LAWS OP MOTION.

The eBtablishment of the theory of universal gravitation
furnishes one of the best examples of scientific method
which is to be found. We shall describe its leadmg
features, less for the purpose of making known to the
reader the technical nature of the process than for illus-
trating the true theory of scientific investigation, and
Bhowing that such investigation has for its object the dis-
covery of what we may call generalized facts. The real
test of progress is found in our constantly increased
abiUty to foresee either the course of nature or the eSects
of any accidental or artificial combination of causes. So
long as prediction is not possible, the desires of the mves-
tiinTtor remain unsatisfied. When certainty of prediction
is once attained, and the laws on which the prediction is
founded are stated in their simplest form, the work of
science is complete. , .

The whole process of scientific generalization consists in
grouping facts, new and old, under such general laws that
they are seen to be the result of those laws, combined with
those relations in space and time which we may suppose to
exist among the material objects investigated It ib essen-
tial to such generalization that a single law shall suffice for
grouping and predicting several distinct facts. A law
invented simply to account for an isolated fact, however

'.'If'

ASTBONOMY.

general, cannot be regarded in gcienco as n law of nature.
It may, indued, bo true, Imt its truth caniiut lie proved
until it is shown that eeverol distinct facts can he accounted
for by it better than by any other law. The reader will
call to mind the old fable which represented the earth as
suppoi'ted on the back of a tortoise, but totally forgot that
the support of the tortoise needed to be accounted for as
much as that of the earth.

To tlie pre-Newtonian astronomers, the phenomena of the
geometrical laws of planetary motion, which we have just
described, formed a group of facts having no connection
with any thing on the earth. Tlie epicycles of Hippakciiits
and Ptolkmv were u truly scientilic conception, in that they
explained the seemingly erratic motions of the planets by
a single simple law. In the heliocentric theory of Coper-
MiODS this law was still further simplified by dispensing in
great part with the epicycle, and replacing the latter by a
motion of tho earth around the sun, of the same nature
with the motions of the planets. But Copebnicds had no
way of accounting for, or even of describing with rigor-
ous accuracy, the small deviations in the motions of the
planets around the sun. In this respect he made no real
advance upon the ideas of the ancients.

Kepleb, in his discoveries, made a great advance
in representing the motions of all the planets by a
single set of simple and easily understood geometrical
laws. Had the planets followed his laws exactly, the
theory of planetary motion would have been substiuitially
complete. Still, further progress was desired for two
reasons. In the first place, the laws of Keplkr did not
perfectly represent all the planetary motions. When ob-
servations of the greatest accuracy were made, it was found
that the planets deviated by small amounts from the ellipse
of Kepler. Some small emendations to the motions com-
puted on the elliptic theory were therefore necessary.
Had this requirement been fulfilled, still another step
would have been desirable — namely, that of connecting the

n
c
1

tl
1

V
Ci

1«
f<

it
f«
n
tl

t
t
ii
I

LAWS OF MOTION.

188

turo.
oved
intc<l
•will

til U8

; that
ior as

jfthe

5 just

jctiou

KCII178

ttboy
Bts by

loPKB-

ing in
r by a
nature
lad no
rigor-
of the
10 real

ivance
by a
letrical
ly, the
mtially
or two
did not
ben ob-
£ found
s ellipse
as com-
cessary.
ler step
ting the

motions of the planets with motion upon the earth, and
reducing them to the same laws.

Notwithstanding the great step which Kepi/kr made in
describing the celestial motions, ho unveiled none of the
great mystery in which they were enshrouded. This mys-
tery was then, to all appearance, impenetrable, becaiwc
not the slightest likeness could be perceived between the
celestial motions and motions on the surface of the earth.
The difficulty was recognized by the older philosophers in
the division of motions into " forced " and " natural.
The latter, they conceived, went on perpetually from the
very nature of things, while the former always tended to
cease. So when Kepler said that observation showed tfej>
law of planetary motion to be that around the circum-
ference of an ellipse, as asserted in his law, he said all that
it seemed possible to learn, supposing the statement per-
fectly exact. And it was all that could he learned from the
mere study of the planetary motions. In order to connect
these motions with those on the earth, the next step wm to
study the laws of force and motion here around us. Sm-
gukr though it may appear, the ideas of the ancients on
this subject were far more erroneous than then- concep-
tions of the motions of the planets. We might ahnost say
that before the time of Galileo scarcely a single correct
idea of the laws of motion was generally entertained by
men of learning. There were, indeed, one or two who in
this respect were far ahead of their age. Leonardo da
Vinci, the celebrated painter, was noted in this respect.
But the correct ideas entertained by him did not seem to
make any headway in the world until the early part of
the seventeenth century. Among those who, before the
time of Newton, prepared the way for the theory in
question, Galileo, Hutghbns, and Hooke are entitled to
especial mention. As, however, we cannot develop the
history of this subject, we must pass at once to the gen-
eral laws of motion Ldd down by Newton. These were
three in number.

184

A8TR0N0M7.

Law First : Jl^jery body preserves its stats qf rest or (ff
un'tform motion in a right Htm, tnUens it is compelled to
change that state by forces impressed thereon.

It waft foimorly eiipposcd that a XwAy acted on by no
forco tended to come to rest. Here lay one of the great-
est difflcultioB which the predecessors of Newton found,
in accounting for tlie motion of the planets. The idea
that the sun in some way caused these motions was enter-
tained from the earliest times. Even I*T0LBMr had a
vague idea of a forco which was always directed toward
the centre of the earth, or, which was to him the same
thing, toward the centre of the universe, and which not
.only caused heavy bodies to fall, bat bound the whole nni-
versfl together. Kepleb, again, distinctly aifiims the ex-
istence of a gravitating force by which the sun acts on the
planets ; but he supposed that the sun nmst also exercise
an impulsive forward force to keep the planets in motion.
The reason of this incorrect idea was, of course, that all
bodies in motion on the surface of the earth had practically
come to rest. But what was not clearly seen before the
time of Kewton, or at least before Gald^eo, was, that this
arose from the inevitable resisting forces which act upon
all moving bodies around us.

Law Second : The aU&raUon of motion is ewr propor-
tional to ike mooing force impressed, and is made in the
direction qf the right line in which that force acts.

The first law might be conddered as a particular case of
this second one arising when the force is supposed to van-
ish. The accuracy of both laws can be proved only by
very carefully conducted experiments. They are now
considered as mathematically proved.

Law Third : Toevery action there isahoays qfy)08ed an
equal reaction / or the mtitual actions of two bodies "wpon
each other are always equal, and in opposite directions.

That is, if a body A acts in any way upon a body B,
B will exert a force exactly equal on ^ in the opposite
direction.

lat

tlu

la/u

OR]

seal
con
obv
cull
in a
peri
fort
ive

circ!

law

fOH

low
cen
bits
sun
mol
the

witl
will

rest or cf
TmpeUed to

I on by no
' the j^roat-
rTON found,
The idea
J was ontor-
KMY liad a
jted toward
n the same
I which not
a whole nni-
litns the ox-
I acts on the
ilso exercise
B in motion,
irso, that all
d practically
1 before the
iras, that this
ich act upon

everjtropor-
made in the
e acts.

icular case of
posed to van-
oved only by
'hey are now

</8 opposed cm,
bodies tipon
e directions,
m a body B,
the opposite

OliA VITATION OF TUK PLANKT8.

180

These laws onco established, it l>ocame possible to calcu-
late the motion of any body or system of bodies when oncu
the forces which act on them wore known, and, vice versa,
to define what forces were re<^uisite to produce any given
motion. The question which presented ifaself to the mind
of Newton and his contemporaries was this : Under what
lo^ (if force will planets move round the sun in accord-
ance with Kepi.kr'b laws t

The laws of central forces had been discovered by IIuy-
OHENS some time before Newton commenced his re-
searches, aad there was one result of them which, taken in
connection with Kbpleb'b third law of motion, was so
obvious that no mathematician could have had much diffi-
culty in perceiving it. Supposing a body to move around
in a circle, and putting R the radius of the circle, T the
period of revolution, IIuyoiiens showed that the centrifugal
force of the body, or, which is the same thing, the attract-
ive force toward the centre which would keep it in the

circle, was proportional to ^. But by Kepler's third

law 7" is proportional to I^. Therefore this centripetal

R 1

force is proportional to -^j, that is, to -^. Thus it fol-
lowed immediately from Kepler's third law, that the
central force which would keep the planets in their or-
bits was inversely as the square of the distance from the
sun, supposing each orbit to be circular. The first law of
motion once completely understood, it was evident that
the planet needed no force impelling it forward to keep
up its motion, but that, once started, it would keep on
forever.

The next step was to solve the problem, what law of
force will make a planet describe an ellipse around the
sun, having the latter in one of its foci ? Or, supposing
a planet to move rotmd the sun, the latter attracting it
with a force inversely as the square of the distance ; what
will be the form of the orbit of the planet if it is not cir-

is.

■4 — '-

136 AamONOMT.

cnlar ? A solution of cither of these problems was beyond
ArpowetoTmathematicians before the time o Newton ;
Ind^ttaremained uncertain whether the planets uh>v-
wlder the influence of the sun's gravxtation would or
wouW not describe elUpses. Unable at first, to reach a
raJSLtory solution, Newton attacked the problem m

:Sw Section, sUng f-\*^« n-^n^ll^tinl
the sun, but of the earth, as explained m the following

section.

§ 2. OBAVTPATION IN THE HEAVENS.

The reader is probably familiar with the story of N ew-
J^ and the falling apple. Although it has «o authonta-
TeToundation, if is strikingly illustrative of the method
by wWch New;,k first reached a solution of the problem.
fi,e course of reasoning by which he ascended from gra^v-
itetion on the earth to the celestial motions was as f^^ .
We see that there is a force acting all over the earth by
which all bodies are drawn toward its centre This force
S f^ar to every one from his infancy, and is property
^ed gravitation. It extends without sensible diminut^n
TtheTops not only of the highest braidings, but of the
highest mountains. How much higher does it extend?
my should it not extend to the moon ? If it does, the
moon would tend to drop toward the earth, ]ust as a stone
^Zvm from the hand drops. As the moon moves romid
Sr^th in her monthly cou«e, there -ust be some ^rce
drawing her toward the earth ; else, by the first law of
motionfshe wouldflyentirely away in a straight hue. Why
Zuld not the force which makes the apple fall be the
^ioL which keeps her in her orbit ? To answer tlus
^^ion,itwasnotonTynece8sarytocalcuktethemten«ty

of the firce which would keep the moon herself in her
orbit but to compare it with the intensity of gravity at the
S's surface. & long been know, that ^e distanc^^
of the moon was about sixty radu of the earth. If this

for©
then
the I
teen
were

The

GliA VITATION OF THE PLANETS.

137

5yond

fTON ;

mov-
ald or
aach a
>in in
aot of
owing

: New-

horita-

nethod

oblem.

a grav-

jllows :

arthby

is force

•roperly

linution

of the
extend ?
oes, the

a stone
» round
ne force
; law of
a. Why
I be the
iwer this
intensity
f in her
ty at the

distance

If this

force diminished as the inverse square of the distance,
then, at the moon, it would be only ^^ as great as at
the surface of the earth. On the earth a body falls six-
teen feet in a second. If, then, the theory of gravitation
were correct, the moon ought to fall toward the earth
^^-^ of this amount, or about ^ of en inch in a second.
The moon being in motion, if we imagine it moving ui a
straight line at the beginning of any second, it ought to
be drawn away from that Une -^ of an inch at the end of
the second. When the calculation was made with the
correct distance of the moon, it was found to agree ex-
actly with this result of theory. Thus it was shown that
the force which holds the moon in lier orbit is the same
which makes the stone fall, only diminished as the inverse
square of the distance from the centre of the earth.*

As it appeared that the central forces, both toward the
sun and toward the earth, varied inversely as the squares
of the distances, Newton proceeded to attack the mathe-
matical problems involved in a more systematic way than
any of his predecessors had done. Kepler's second law
showed that the line drawn from the planet to the sun
will describe equal areas in equal times. Newton showed
that this could not be true, imless the force which held
the planet was directed toward the sun. We have already
stated that the third law showed that the force was in-
versely as the square of the distance, and thus agreed ex-
actly with the theory of gravitation. It only remained to

* It is a remarkable fact in the history of science that Newton
would have reached this result twenty yec\rs sooner than he did, had
he not been misled by adopting an erroneous v alue of the earth's diame-
ter. His first attempt to compute the earth's gravitation at the distance
of the moon was made in 1665, when he was only twenty-three year« of
age. At that time he supposed that a degree on the earth's surface was
sixty statute miles, and was in consequence led to erroneous results by
supposing the earth to be smaller and the moon nearer than they really
were. He therefore did not make public his ideas ; but twenty years
later he learned from the measures of Picabd in Prance what the true
diameter of the earth was, when he repeated his calculation with
entire success.

tiC-S'jBfW"

paMP

I:
I

i!;

138

ASTRONOMY.

consider the results of the first law, that of the elliptic
motion. After long and laborious efforts, Nkavton was
enabled to demonstrate rigorously that this law also re-
sulted from the law of the inverse square, and could result
from no other. Thus all mystery disappeared from the
celestial motions ; and planets were shown to be simply
heavy bodies moving according to the same laws tliat were
acting here around us, only under very different circum-
stances. All three of Kepler's laws were embraced in
the single law of gravitation toward the sun. The sun
attracts the planets as the earth attracts bodies here
around us.

Mutual Action of the Flanets. — It remained to extend
and prove the theory by considering the attractions of the
planets themselves. i3y Newton's third law of motion,
each planet must attract the sun with a force equal to that
which the sun exerts upon the planet. The moon also
must attract the earth as much as the earth attracts the
moon. Such being the case, it must be highly probable
that the planets attract each other. If so, Kepler's laws
can only be an approximation to the truth. The sun,
being immensely more massive than any of the planets,
overpowers their attraction upon each other, and makes
the law of elliptic motion very nearly true. But still the
comparatively small attraction of the planets must cause
some deviations. Now, deviations from the pure elliptic
motion were known to exist in the case of several of the
planets, notably in that of the moon, which, if gravitation
were universal, must move under the influence of the com-
bined atti'action of the earth and of the sun. Newton,
therefore, attacked the complicated problem of the deter-
mination of the motion of the moon under the combined
action of these two forces. He showed in a general way
that its deviations would be of the same nature as those
shown by observation. But the complete solution of the
problem, which required the answer to bo expressed iu
numbers, was beyond his power.

othJ

ticlj
sul

" ''''^^ tiUHBT'"

ATTRACTION OF GRAVITATION.

139

sUiptic
)N was
Iso re-
l result
)m the
simply
at were
jircum-
aced in
'he sun
iS here

extend
18 of the
motion,
1 to that
oon also
•acts the
probable
sr's laws
Che sun,

planets,
id makes

still the
tist cause
re elliptic
•al of the
ravitation

the com-
Newton,
the deter-
combined
mend way
I as those
ion of the
pressed in

Gravitation Besides in each Particle of Matter. — Still
another question arose. Were these mutually attractive
forces resident in the centres of the several bodies attracted,
or in each particle of the matter composing them ? New-
ton showed that the latter must be the case, because the
smallest bodies, as well as the largest, tended to fall
toward the earth, thus showing an equal gravitation in
every separate part. The question then arose : what
would be the action of the earth upon a body if the
body was attracted— not toward the centre of the earth
alone, but toward every particle of matter in the earth 'i
It was shown by a quite simple mathematical demonstra-
tion that if a planet were on the surface of the earth or
outside of it, it would be attracted with the same force^as
if the whole mass of the earth were concentrated in ite
centre. Putting together the various residts thus arrived
at, Newton was able to formulate his great law of uni-
versal gravitation in these comprehensive words : *' Every
particle of matter m the immeree at^acta every other
particle with a f&rce directly as the masses of the two
particles, and vrwersely as the square of the distance
which separates them.^^

To show the nature of the attractive forces among
these various particles, let us represent by m and m' the
masses of two attracting bodies. We may conceive the
body w to bo composed of m particles, and the other
body to be composed of m' particles. Let us conceive that
each particle of the one body attracts eadi particle of the

other with a force -, . Then every particle of m will be

r
attracted by each of the m' particles of the other, and
therefore the total attractive force on each of these m par-
ticles will be 'i Each of the m particles being cquaUy
subject to this attraction, the total attractive force between

the two bodies will be

turn

When a given force acts

ASTRONOMY.

„po„ a body. H will pK^oce 1-.™>"„K ^

be ^« ; and couvcrBely the accelerating force acting on the
body m will be represented by the fraction -^.

§ 3. PBOBLEMB OP QBAVITATIOW.

The problem solved by I. K^^^^
eBt genemlity, was ^^^^.^^^^^^H^^^^^^ and

are given are P^J^.^ ^^ "^'^ ^^^ u^ ^ motion under
with certain velocities. W hat wm ^ ^

the influence of t^-r mutual gravi^^aU^j J^^^^^^

tive motiondcH. -^-^^J^jf^^^^^^ of g^avit;
will each revolve around tneir commv/ o

^l^hpe, aainthecaseof planetaiT-^^^^

ever, the illative velocity «^«^^^^*^^S,g ^„nd the
bodies will separate f^-J^^^^j^f^^^^^
common centre of,g^«;f f /^"^X^ in the case where
These curves are found o be ^™^'^ hj^^bolas when
the velocity is exac^^ at *^ ^^tr^urvrmay be de-
the velocity exceeds it. ^J^LZ^^ the two bodies
scribed, the common centre of g^a^ «* ^^ ^^^^^
will be in the focus of the curve ^^^^^^^^^^^.^^
to two bodies, the problem admits of a perfectly ngo

mathematical solution. rv^Hem of planetary

Having succeeded in solvi^he p^bl^ of p^,^ J

motion for the case of *7« ^^'.HfieTa rimilar solu-
temporaries very natumlly desired to effee^a «nn

mimber of Iwdies , ana nav ug ^^^

two bodies, it was necessary next to try tnai

•HI

larger the
lal to the
the body
jcts on the
lotion, will

iiig on the

in its great-
the masses
Bctions, and
otion under
I their rela-
mount, they
B of gravity
3. If, how-
mit, the two
around the
ite branches.
J case where
erbolas when
may be de-
etwo bodies
en restricted
jctly rigorous

of planetary
and his con-
i similar solu-
em of motion
;ion of a great
in the case of
that of three.

PROBLEMS OF GRAVITATION.

141

Thus arose the celebrated problem of three bodies. It is
fonnd that no rigorous and general solution of this problem
is possible. The curves described by the several bodies
would, in general, be so complex as to defy mathematical
definition. But in the special case of motions in the solar
system, the problem admits of being solved by approxima-
tion with any required degree of accuracy. The princi-
ples involved in this system of approximation may be com-
pared to those involved in extracting the square root of
any number which is not an exact square ; 2 for instance.
The square root of 2 cannot be exactly expressed either
by a decimal or vulgar fraction ; but by incretaing the
number of figures it can be expressed to any required limit
of approximation. Thus, the vulgar fractions |, |J, fH,
etc., are fractions which approach more and more to the
required quantity ; and by using larger numbers the errors
of such fraction may be made as small as we please. So, in
using decimals, we diminish the error by one tenth for eve-
ry decimal we add, but never reduce it to zero. A process
of the same nature, but immensely more complicated, has
to be used in computing the motions of the planets from
then- mutual gravitation. The possibility of such an ap-
proximation arises from the fact that the planetary orbits
are nearly circular, and that their masses are very small
compared with that of the sun. The first approximation
is that of motion in an ellipse. In this way the motion of
a planet through several revolutions can nearly always be
predicted within a small fraction of a degree, though it
may wander widely in the course of centuries. Then sup-
pose each planet to move in a known ellipse ; their mutual
attraction at each point of their respective orbits can be
expressed by algebraic f ormulie. In constructing these
formulsB, the orbits are first supposed to be circular ; and
afterward account is taken by several successive steps of
the eccentricity. Having thus found approximately their
action on each other, the deviations from the pure eUiptic
motion produced by this action may be approximately cal-

• r-

1 1

149

ASTROIfOMT.

ciliated. This being done, tlic motionfl will bo more exact-
ly duteriiiinod, and the niutnal action can be niui'e exactly
calcnlated. Thus, the process can be carried on step by
step to any degree of precision ; but an enormous amount
of calculation \& necessary to satisfy the requirements of
modern times with respect to precision.* As a general
rule, every successive step in the approximation is much
more laborious than all the preceding ones.

To understand the principle of astronomical investiga*
tion into the motion of the planets, the distinction be-
tween observed and theoretical motions must be borne in
mind. When the astronomer with his meridian circle de-
termines the position of a planet on the celestial sphere,
that position is an obseiTcd one. When ho calculates it, for
the same instant, from theory, or from tables founded on
tlie theory, the result will be a calculated or theoretical
position. The two are to be regarded as separate, no mat-
ter if they should be exactly the same in reality, because
they have an entii*ely different origin. But it must be re-
membered that no position can be calculated from theory
alone independent of observation, because all soimd theory
requires some data to start with, which observation alone
can furnish. In the case of planetary motions, these data
are the elements of the planetary orbit already described,
or, which amounts to the same tiling, the velocity and di-
rection of the motion of the planet as well as its mass at
some given time. If these quantities were once given
with mathematical precision, it would be possible, from the
theory of gravitation alone, without recourse to observa-
tion, to predict the motions of the Janets day by day
and generation after generation with an^ required degree
of precision, always supposing that they are subjected to no
influence except their mutual gravitation according to the
law of Newton. But it is impossible to determine the
elements or the velocities without recourse to observation ;

* In the works of the great mathematicians on this subject, algcbruic
formolee extending tlmraj^ many pages are sometimns given.

and
for 1
then
mus
mat]
obse
than
obsei
80 tr
their
W
mer]
he cc
aseri
futur
he de
he mi
termi
oretic
will «
the d
may I
throu
its pi
some
comn
omer
havin
struci
toler
possilj
latioi
tirelj
only
vices I
way
table

--"T--t -'—--■-'•■•

PROBLEMS OF GRAVITATION.

143

exact-
exactly

step by
amount

leuts of
general

is much

ivestiga-
ition be-
borne in
jirclo dc-
, sphere,
tes it, for
anded on
leoretical
, no mat-
, because
ast be re-
im theory
Qd theory
ion alone
these data
iescribed,
ty and di-
itB mass at
nee given
I, from the
) observa-
ly by day
■ed degree
sctedtono
ling to the
ermine the
^servation ;

|ect, algebraic
ren.

and however correctly they may seeiiiingly be (letcriiiineil
for the time being, subHcquent obscrvatiouH alwiiyH bIiow
them to have been more or less in error. The reader
must understand that no astronomical observation can be
mathematically exact. Both the instruments and the
observer are subjected to influences which prevent more
than an approximation being attained from any one
observation. The great art of the astronomer consists in
80 treating and " bining his observations as to eliminate
their err. , anu ». • a result as near the > ' at possible.
When, by thus bumbining his observati.,-*, the astrono-
mer has obtained the elements of the planet's motion which
he considers to be near the truth, he calculates from them
a series of positions of the planet from day to day in the
future, to be compared with subsequent observations. If
he desires his work to be more pennanent in its nature,
he may construct tables by which the position can be de-
termined at any future time. Having thus a series of the-
oretical or calculated places of the planet, he, or others,
will compare his predictioas with observation, and from
the differences deduce corrections to his elements. We
may say in a rough way that if a planet has been observed
through a certain number of years, it is possible to calculate
its place for an equal number of years in advance with
some approach to precision. Accurate observations are
commonly supposed to conamence with Beadley, Astron-
omer Eoyal of England in 1750. A century and a quarter
having elapsed since that time, it is now possible to con-
struct tables of the planets, which we may expect to be
tolerably accurate, until the year 2000. But this is a
possibility rather than a reality. The amount of calcu-
lation required for such work is so immense as to be en-
tirely beyond the power of any one person, and hence it is
only when a mathematician is able to command the ser-
vices of others, or when several mathematicians in some
way combine for an object, that the best astronomical
tables can hereafter be constructed.

AaTRONOMT.

% 4. RESULTS OP GRAVITATION.

From what we have said, it wiU Ihj Been that the problem
of the motions of the planets under the influence of grav-
itation has caUed forth all the skill of the mathematicians
who have attacked it. They actually find themselves able
to reach a solution, which, so far as the mathematics of the
subject are concerned, may be true for many centuries, but
not a solution which shall be true for all time Among
those who have brought the solution so near to perfec-
tion, La Place is entitled to the firstrank, although there
are others, especiaUy La Gbangk, who are fully worthy o
L named aloVg with him. It will be of interest to state
the general results reached by these and other mathema-

^'''mcall to mind that but for the attraction of the
planets upon each other, every planet would move around
the sun hi an invariable ellipse, according to Kbplebs
laws The deviations from this elliptic motion proved
bv their mutual attraction are called perturhaiiom. When
they were investigated, it was found that they were of two
claies, wliich were denominated respectively perwdtc
perturbatiom mi seGular variations.

The periodic pert^bations consist of oscillations depend-
ent upon the mutual positions of the ^ets, and there-
fore of comparatively short period. Whenever after a
number of revolutions, two planets return to the same
nosition in their orbits, the periodic perturbations are of
^e same amount so far as these two planets are concerned.
They may therefore be algebraically expressed ««. depend-
ent upon the longitude of the two planets, the d«t™;^>ng
one and the disturbed one. For instance, the jwrturba-
tions of the earth produced by the action of M^cury
depend on the longitude of the earth and on that of Jfjr-
eZ. Those produced by the attraction of ^^^ /e-
pS upon the longitude of the earth and on that of
Vervus, and so on.

seni

the
Let
ano
the
one
lim
mo
son

RESULTS OF OBAVITATIOir.

145

problem
of grav-
naticians
Ives able
cs of the
iries, but
Among
) perfec-
igh there
<rorthy to
it to state
uathema-

•n of the
ire around
Kbplbb's
produced
18. When
ere of two
• periodic

18 depend-
md there-
er, after a

the same
)n8 are of
concerned,
as depend-
disturbing
» perturba-
l Mercury
lat of Mer-

Vemu de-
ou that of

The sefitil^r perturbations, or secular variations as they
are commonly called, consist of slow changes in the forms
and positions of the several orbits. It is found that the
perihelia of all the orbits are slowly changing their ap-
parent directions from the sun ; that the eccentricities of
some are increasing and of others diminishing ; and that
the positions of the orbits are also changing.

One of the first questions which arose in reference to
these secular variations was, will they go on indefinitely ?
If they should, they would evidently end in the subversion
of the solar system and the destruction of all life upon the
earth. The orbits of the earth and planets would, in the
course of ages, become so eccentric, that, approaching
near the sun at one time and receding far away from it at
another, the variations of temperature would be destruc-
tive to life. This problem was first solved by La Gbanob.
He showed that the changes could not go on forever, but
that each eccentricity would always be confined between
two quite narrow limits. His results may be expressed
by a very simple geometrical construction. Let 8 repre-
sent the sun situated iu the focus of the ellipse in which

the planet moves, and let C be the centre of the ellipse.
Let a straight line SB emanate from the sun to B,
another line pass from BtoD, and so on ; the number of
these lines being equal to that of the planets, and the last
one terminating in C, the centre of the ellipse. Then the
line S B will be moving around the sun with a very slow
motion ; B D will move around B with a slow motion
somewhat different, and so each one will revolve in the

146

AHTRONOMY.

same manner until wo micl. the lino which carncs on its
end the centre oi the ellipne. The«o m..tH.n« are «<> «low
that Bi.me of them rciuire tenn of thonsaiu h, and otherH
hundreds of thoiiBands of years to perform the revolution.
By the combined motion of them all, the centre of the
ellipse deBcribcH a somewhat irregular curve. It i8 ov»
dent, however, that the distance of the centre froin the
sun ian never be greater than the mm of these revolving
lines Now this distance shown the eccentricity of the
ellipse, which is equal to half the difference between the
greatest and least distances of the planet from the sun.
The perihelion being in the direction 6'.^, on the opposite
Bide of the sun from C, it is evident that the motion of
(7 will carry the perihelion with it. It is found m this
way that the eccentricity of the earth's orbit has been
diminishing for about eighteen thousand years, and will
continue to diminish for twenty-five thousand years to
come, when it will be more neariy circular than any orbit
of our system now is. But before becoming quite circu-
lar, the eccentricity will begin te increase again, and so go
on oscillating indefinitely.

Seoular Aooeleration of the Moon.— Another remark-
able result reached by mathematical research is that of the
acceleration of the moon's motion. More than a century
ago it was found, by comparing the ancient and modern
Nervations of the moon, that the ktter moved around the
earth at a slightly greater rate than she did m ancient
times. The existence of this acceleration was a source of
groat perplexity to La Geanob and La Place, because
Lv thought that they had demonstrated mathematically
that the attraction could not have accelerated or retarded
the mean motion of the moon. But on continuing his m-
vestigation, La Place found that there was one cause
which he omitted to take account of-namely, the secular
diminution in the eccentricity of the earth « orbit ^^
which we have just spoken. He found that this change
in the eccentricity would slightly alter the action of the

ACt'KI.KHATlON Ot TUB MOON.

arrics on itB
are «<> slow
and other»
revolution,
mtro of the
It 18 ovi
re from the
BO revolving
icity of the
between the
oni the sun.
the opposite
le motion of
)und in this
tit has been
ars, and will
ind years to
tan any orbit
5 quite circu-
in, and so go

;her remark-
is that of the
an a century
and modem
;d around the
id in ancient
as a source of
.ACE, because
lathematically
d or retarded
inning his in-
ras one cause
[y, the secular
;h'B orbit, of
it this change
action of the

Bun upon the moon, and that this alteration of action
would l>e such that so long as the eccentricity grew
smaller, the motion of the moon would continue to be ac-
celerated. Computing the moon's acceleration, he found it
to be e(iual to ten seconds into the square of the numlxsr
of centuries, the law being the same m tliat for the motion
of a falling body. That is, while in one century she would
1)6 ten seconds ahead of the place she would have occupied
had her mean motion l)een uniform, she would, in two
centuries, be forty seconds ahead, in three centuries ninety
seconds, and so on ; and during the two thousand years
which have elapsed since the observations of Hipi'archus,
the acceleration would be mote than a degree. It has re-
cently been found that La Place's calculation was not com-
plete, and that with the more exact motliods of recent times
the real acceleration computed from the theory of gravita-
tion is only about six seconds. The observations of ancient
eclipses, however, compared with our modem tables, show
an acceleration greater than this ; but owing to the rade
and doubtful character of nearly all the ancient data, there
is some doubt about the exact amount. From the most
celebrated total eclipses of the sun, an acceleration of about
twelve seconds is deduced, while the observations of
Ptolemy and the Arabian astronomers indicate only eight
or nine seconds. Tliere is thus an apparent discrepancy
between theory and observation, the latter giving a larger
value to the acceleration. This diflEerence is now accounted
for by supposing that the motion of the earth on its axis
is retarded— that is, that the day is gradually growing
longer. From the modem theory of friction, it is found
that the motion of the ocean under the influence of the
moon's attraction which causes the tides, must be accom-
panied with some friction, and that this friction must re-
tard the earth's rotation. There is, however, no way of
determining the amount of this retardation unless we
assume that it causes the observed discrepancy between
the theoretical and observed accelerations of the moon.

■r-"

148

AHTUoNoMir.

Tlow tliis uffwt in imnhKHMl will ho won hy ruflvcting that
if thu (liiy iHrontinuully growing longiti' without our know-
ing it, uiir obflorvutions of tlic nuMin, whicli wu niuy H(ip|M)M!
to bo madu at noon, for oxanijtlo, will l)c couHtantly niado a
little later, becauHO the interval from one noon to another
will be continually growing a little longer. The moon con-
tinually moving forward, the ol)6orvation will place her fur-
ther and further ahead than she would have been observed
had there l)een no retardation of the time of noon. If in
the course of ages our noon-dials get to l)e an hour too
late, wr nliould find the moon ahead of her calculated place
by one hour's motion, or about a degree. The present
theory of acceleration is, therefore, that the moon is really
accelerated al)out six seconds in a century, and that the
motion of the earth on its axis is gradually diminishing
at such a rate as to produce an apparent additional ac-
celeration which may range from two to six seconds.

§ 5. REKABKS ON THE THEORY OF OBAVITA-

TIOK.

The real nature of the great discovery of Newton is so
frequently misunderstood that a little attention may be
given to its elucidation. Gravitation is frequently spoken
of as if it were a theory of Newton's, and very generally
received by astronomers, but still linble to be idtimately
rejected as a great many other theories have beeu. Not
infrequently people of greater or less intelligence are
found making great efforts to prove it erroneous. Every
prominent scientific institution in the world frequently
receives essays having this object in view. Now, the fact
is that Newton did not discover any new force, but only
showed that the motions of the heavens could be accounted
for by a force which we all know to exist. Gravitation
(Latin graviteu — weight, heaviness) is, properly speaking,
tlio force which makes all bodies here at the surface of the
earth tend to fall downward ; and if any one wishes to

in,

itta

foi

tht

gra

doi

is.

exp

as I

thai

line

dev

tioE

on(!

it is

con|

for

unil

witi

oui

HKALITY OF OllAVITATIoy.

14i)

cting tliat
nir know-

tly made a
to another
moon con-
co her f ur-
m observed
)on. Hin
in hour too
dated place
'he present
on is really
id that the
dhninishing
ditional ac-
icouds.

OBAVTPA-

Jewton is BO
tion may be
lently spoken
ery generally
)e ^dtimately
B beeu. Not
elligence are
eouB. Every
Id frequently
Kow, the fact
orce, but only
dbe accounted
Gravitation
)erly speaking,
5 surface of the
one wishes to

Htibvort the theory of gravitation, he uiust l)Ogin by prov-
ing tliftt this force does not exist. This no one would
think of doing. What Nkwton did was to show that
this force, which, before his time, had been recognized
only as acting on the surface of the earth, really extended
to the heavens, and that it resided not only in the earth
itself, but in the heavenly bodies also, and in each particle
of matter, however situated. To put the matter in a terse
form, what Nkwton discovered was not (/ra/oitatian, but
the nniversality of gravitation.

It may bo inquired, is the induction which supposes
gravitation universal so complete iis to be entirely beyond
doubt ? We reply that within the solar /stem it certainly
is. The laws of motion as established by observation and
experiment at the surface of the earth nmst be considered
as mathematically certain. Now, it is an ooserved fact
that tha planets in their motions deviate from ^a-aight
lines in a certain way. By the first law of motion, such
deviation can be protluced caly by a force ; and the dire,
tion and intensity of this force admit of being ilcnlated
once that the motion is determined. When thus < siho lated,
it is found to be exactly represented by one great force
constantly directed toward the sun, and smaller subsidiary
forces directed toward the several planets. Therefore,
no fact in nature is more firmly estabhshed than is that of
universal gravitation, as laid down by Newton, at least
within the solar system.

We shall find, in describing double stars, that gravita-
tion is also found to act between the components of a great
number of such stars. It is certain, therefore, that at
least some stars gravitate toward each other, as the bodies
of the solar system do ; but the distance which separates
most of the stars from each othe" rani from our sun is so
immense that no evidence of gravitation between them
has yet been given by observation. Still, that they do
gravitate according to New ■Jj's law can hardly be seri-
ously doubted by any one v ho understands the subject.

160

ASTBONOMT.

The reader may now be supposed to see the absurdity of
supposing that the theory of gravitation can ever be sub-
verted. It is not, however, absurd to suppose that it may
yet be shown to be tlie result of some more general law.
Attempts to do this are made from time to time by iiM:n
of a philosophic spirit ; but thus far no theory of the sub-
ject having the sUghtest probability in its favor lias been

propounded. i • •

Perhaps one of the most celebrated of these theories is
that of George Lewis Le Sage, a Swiss physicist of the
last century. He supposed an infinite number of ultra-
mundane corpuscles, of transcendent minuteness and veloc-
ity, traversing space in straight lines in all tUrections. A
smgle body placed in the midst of such an ocean of mov-
ing corpuscles would remain at rest, sino« it would be equal-
ly impelled in overy direction. But two bodies would ad-
vance toward each other, because each of them would
screen the other from these corpuscles moving in the
straight line joining their centres, and there would be a
slight excess of corpuscles acting on that side of each
body which was turned away from the other.*

One of the commonest conceptions to account for grav-
itation is that of a fluid, or ether, extending through all
space, which is supposed to be animated by certain vibra-
tions, and forms a vehicle, as it were, for the transmission
of gravitation. This and all other theories of the kind
are subject to the fatal objection of proposing complicated
systems to account for the most simple and elementary
facts. If, indeed, such systems were otherwise known to
exist, and if it could be shown that they really would
produce the effect of gravitation, they would be entitled
to recei»tion. But since they have been imagined only to
account for gravitation iteolf, and since there is no proof
of their existence except that of accounting for it, they

* Reference may be made to nn article on the kinetic theories of
gravitation by William B. Taylor, in the Smithsonian Report for
1876.

p I fi

CAU8B OP GRAVITATION.

VSi

dity of
be sub-
it may
•al law.

I)y \VA:Xi

ho sitb-
asbeen

iories is
; of the
f ultra-
d veloc-
m&. A
of mov-
e equal -
[)uld ad-
i would
in the
aid be a
of each

'or grav-
ough all
in vibra-
ismission
;he kind
iplicated
smentary
mown to
ly would
entitled
d only to
no proof
• it, they

theories of
Report for

are not entitled to any weight whatever. In the present
state of science, we are justified in regarding gravitation as
an ultimate principle of mattfcv, incapable of alteration by
any transformation to which matter can be subjected.
The most careful experiments show that no chemical pro-
cess to which matter can be subjected either increases or
diminishes its gravitating principles in the slightest degree.
We cannot therefore see how this principle can ever be
referred to any more general cause.

CHAPTER VI.

THE MOTIONS AND ATTRACTION OF THE MOON.

Each of the planets, except Mercury and Vmua, is at-
tended by one or more satellites, or moms as they are some-
times familiarly called. These objects revolve around their
several planets in nearly circular orbits, accompanying them
in their revolutions around the sun. Their distances from
their planets are very small compared with the distances
of the latter from each other and from the sun. Iheir
magnitudes also are very small compared with those of the
planets around which they revolve. Where there are
several satellites revolving around a planet, the whole of
thflse bodies forms a small system similar to the solar sys-
'^ in arrangement. Considering each system by itself,
the satellites revolve around their central planets or
" primaries," in nearly circular orbits, much as the planete
revolve around the sun. But each system is carried around
the sun without any serious derangement of the motion
of its several bodies among themselves.

Our earth has a single satellite accompanjang it in this
way, the familiar moon. It revolves around the earth m
a little less than a month. The nature, causes and con-
sequences of this motion form the subject of the present
chapter.

§ 1.

THE MOOW'B MOTIONS AHD PHASES.

That the moon performs a monthly circuit in the heav-
ens is a fact with which we are all familiar from child-
hood. At certain times we see her newly emerged from

MOTION OF THE MOON.

168

OON.

is at-
8ome-
1 their
r them
B from
stances
Their
of the
jre are
lole of
lar sys-
r itself,
lets <»•
planets
around
motion

in this
earth in
nd con-
present

lie heav-
n child-
ed from

the snn's rays in the western twilight, and then we call
her the new moon. On each succeeding evening, we see
her further to the east, so that in two weeks she is oppo-
site the sun, rising in the east as he sets in the west.
Continuing her course two weeks more, she has approached
the sun on the other side, or from the west, and is once
more lost in his rays. At the end of twenty-nine or thirty
days, we see her again emerging as new moon, and her cir-
cuit is complete. It is, however, to be remembered
that the sun hsis been apparently moving toward the east
among the stars during the whole month, so that during
the interval from one new moon to the next the moon has
to make a complete circuit relatively to the stars, and
move forward some 30° further to overtake the sun. The
revolution of the moon among the stars is perfonned in
about 27i days,* so that if we observe when the moon is
very near some star, we shall find her in the same position
relative to the star at the end of this interval.

The motion of the moon in this circuit differs from the
appareni motions of the planets in being always forward.
We have seen that the planets, though, on the whole, mov-
ing directly, or toward the east, are affected with an ap-
parent retrograde motion at certain intervals, owing to the
motion of the earth around the sun. But the earth is the
real centre of the moon's motion, and carries the moon
along with it in its annual revolution around the styi. To
fonn a correct idea of the real motion of these three
bodies, we must imagine the earth performing its circuit
around the sun in one year, and carrying with it the moon,
which makes a revolution around it in 27 days, at a distance
only about ^^ that of the sun.

In Fig. 55 suppose S to represent the sun, the large
circle to represent the orbit of the earth around it, E to
bie some position of the earth, and the dotted circle to rep-
resent the orbit of the moon around the earth. We must

* More exactly. 27* 82166.

154

A8TR0N0MT.

imagine the latter to carry this circle with it in its an-
nual course around the sun. Suppose that when the earth
is at ^ the moon is at M. Then if the earth move to

El in 27^ (lays, the moon
will have made a complete
revolution relative to the
stars — that is, it will be at
M„ the line E^ J/, being par-
allel to EM. But new
moon will not have arrived
again because the sun is not
in the same direction as lie-
fore. The moon must move
through the additional arc
Jf, EM^, and a little more,
owing to the continual ad-
vance of the earth, before it
will again 1)6 new moon.
Phasea of the Moon. — The moon being a non-luminous
body shines only by reflecting the light falling on her
from some other body. The principal source of light is
the sun. Since the moon is spherical in shape, the sun
can illuminate one half her surface. The appearance of
the moon varies according to the amount of her illumi-
nated hemisphere which is turned toward the earth, as
can bf seen by studying Fig. 56. Here the central
globe is the earth ; the circle around it represents the orbit
of the moon. TLo rays of the sun fall on both earth and
moon from the right, the distance of the sun being, on the
scale of the flgure, some 30 feet. Eight positions of the
moon are shown around the orbit at A, E, C, etc., and
the right-hand hemisphere of the moon is illuminated in
each position. Outside these eight positions are eight
others showing how the moon looks as seen from the earth
in each position.

At .4 it is " new moon," the moon being nearly
between the earth and the sun. Its dark hemisphere

PHASES OF THE MOON.

155

its an-
B earth
lOve to

moon
iinplete
to the

be at
ng par-
it new
arrived
n is not
n as be-
st move
inal arc
B more,
raal ad-
jefore it
oon.
iiminous

on her
: light is

the sun
trance of
r illumi-
earth, as
! central
the orbit
iarth and
g, on the
ns of the
etc., and
inated in
are eight
the earth

ig nearly
emisphore

is then turned toward the earth, so that it is entirely
invisible.

At ^'the observer on the earth sees about a fourth of
the illuminated hemisphere, which looks like a crescent,
as shown in the outside figure. In this position a great
deal of light is reflected from the earth to the moon, ren-
dering the dark part of the latter visible b} a gray light.

Vis. cm.

"old moon in

This appearance is sometimes called the
the new moon's arms.''

At C the moon is said to be in hrr '* first quarter," and
one half l»er illmninated hemisphere is visible.

At O three fourths of the illuminated hemisphere is
visible, and at B the whole of it. The latter position, when
the moon is opposite the sun, is called '* full moon."

After this, at H, 2>, F^ the same appearances are re-
peated in the reversed order, the position D being called
the "last quarter."

156

ASTRONOMY.

The four principal phases of the moon are, New
mo^!" " Fi4 quarter," " Full moon," " Last quarter,
which occur in regt.lar and unending succession, at mter-
vals of between 7 and 8 days.

§2. THE SUN'S DISTURBmO FOBOB.

The distances of the sun and planets being so immensely
great compared with that of the moon, their attraction
STn the JLrth and the moon is at all times very neariy
Zal. Now it is an elementary principle of mechan cs
th^if two bodies are acted upon by equal and paraM
forces no matter how great these forces may be, the
bo2 will move relatively to each other as if those orces
did not act at all, though of course the absolute moUon of
each will be different from what it otherwise would be.
If we calculate the absolute attraction of the sun «pon the
moon we shall find it to be about twice as great as that of
r^rtZ tea-, although it is situated at 400 tim^ the
distance, its mass is al^out 330,000 times as great as that of
the earth, and if we divide this mass by the square of the
distance 400 we have 2 as the quotient. ,.n,„.,^

To those unacquainted with mechanics, the difficulty
often suggests itself that the sun ought to draw the moon
away f i^m the earth entirely. But we are to remember
that thesun attracts the earth in the same way that it at-
tracts tSe moon, so that the difference between the sun s
attraction on the moon and on the earth is only a smaU
fraction of the attraction between the earth and the moon

As a consequence of these forces, the moon moves around
the earth nearly as if neither of them were attracted by

•In this comparison of the attractive forces of the sun "poiLthe
moon and upon the earth, the reader will remember that we are 8p«.k-
Sr^JSf the a6«««te force, but of what is called the '^'^'^l^"'^'
which is properly the ratio of the absolute force to the mass of he
SatrST The earth haying 80 times the mass of the moon the
s^sltf course attract it with 80 Umes tlfe ateolute force in order
to produce the same motion, or the same accelerating force.

SUN'H ATTRACTION ON MOON.

1B7

the sun — that is, nearly in an ellipse, having the earth in
its focus. But there is always a small difference between
the attractive forces of the sun upon the moon and upon the
earth, and this difference constitutes a disturbing force
which makes the moon deviate from the elliptic orbit
which it would otherwise describe, and, in fact, keeps the
ellipse which it approxhnately describes in a state of con-
stant change.

A more precise idea of the manner in which the sun disturbs the
motion of the moon around the earth majr be gathered from
Fig. 57. Here 8 represents the sun, and the circle F Q ^ JV repre-
sents the orbit of the moon. First suppose the moon at N, the posi-
tion corresponding to new moon. Then the moon, being nearer to
the sun than the earth is, will be attracted more powerfully by it
than the earth is. It will therefore be drawn away from the earth,
or the action of the sup will tend to separate the two bodies.

Pig. 67.

Next suppobo the anon at ^the position corresponding to full
moon. Here the action of the sun upon the earth will bo more

Sowerful than upon the moon, and the earth will in consecjOence be
rawn away from the moon. In this position also the effect of the
disturbing force is to separate the two bodies. If, on the other
hand, the moon is near the first quarter or near Q, the sun will exert
a nearly equal attraction on both bodies ; and ince the lines of at-
traction E S and Q 8 then convergt' toward 8, it follows that there
will be a tendency to bring the two bodies together. The same
will evidently be true at the third quarter. Hence the influence of
the disturbing force changes back and forth twice in the course of
each lunar month.

The disturbing force in question may be constructed for any po-
sition of the moon in iia orbit in the following way, which is be-
lieved to be due to Mr. R. A. Pkoctok : Let 3f be the position of
the moon ; let us represent the sun's attraction upon it by the line
M 8, and let us investigate what line will represent the sun's attrac-
tion upon the earth on the same scale. From Jf drop the perpen-

Ui )1

15g A8TR0N0M7.

have,

Attrmctionon tmrth _ SM

Attraction on moon S E '
We have taken the line 8 M it-elf to represent the attraction on
the moon, so that we have

Attraction on moon = 8M.
Multiplying the two equations member by member, we And,

Attraction on earth = S Ji x ^-gi-

The line S Af is nearly equal to 8 P, so that we may take for an
approximation to the required line.

8F
'8'E

= 8P^

SP*

{SP+PEf

_ =zSP

(}^8P)

the last equation being obtained by the binomial theorm. But
the fraction ^ is so small, being less than ^, that lU p«we«
above the first will be small enough to be neglected. 8o we shall
have for the required hne,

ap—^EP.

MOON'S N0DK8.

160

, This
re shall

the bodies together at the quarten. Conaeauentlv, upon the whole,
the tendency of the sun's attraction is to diminish the attraction of
the earth upon the moon.

ction on

«1,

le for an

rm.

But

bs powers
} we shall

equal to 2
ae scale be
;h we seek
»f the sun
I. If then
le opporite
will repre-
omposition

mple nuin-
lie moon is
■bing force
the moon.

KAnUiBIf
ich tends
}ay the line
ly from the
hich draws

g 8. MOnOCT OF THS MOOirS NODSI.

Among tho changt« which the snn's attraction produces
in the moon's orbit, Oiat which interests ns most is the
constant variation in the pUne of the orbit. This plane
is indicated by tho path which Xu'^ moon seems to describe
in its circuit around the celestial sphere. Simple naked
eye estimates of the moon's position, continued during a
month, would show that her path was always quite near
the ecliptic, l)ecause it would be evident to the eye that,
like the sun, she was much farther north while passing
from the vernal to the autumnal equinox than while de-
scribing the other half of her circuit from the autumnal
to the vernal equinox. It would be seen that, like the
sun, she was farthest north in about six hours of right as-
cension, and farthest south when in about eighteen hours
of right ascension.

To map out the path with greater precision, we have to
observe the position of the moon from night to night with
a meridian circle. We thus lay down her course among
the stars in the same manner that we have formerly shown
it possible to lay down the sun's path, or the ecliptic. It
is thus found that the path of the moon may be considered
as a great circle, making an angle of 5° with the ecliptic,
and crossing the ecliptic at this small angle at two oppo-
site points of the heavens. These points are called the
moon's nodea. The point at which she passes from the
south to the north of the ecliptic is called the ascending
node; that in which she passes from the north to the
south is the descending node. To illustrate the motion of
the moon near the node, the dotted line a a may be taken
as showing the path of the moon, while the circles show
her position at successive intervals of one hour as she is ap-
proaching her ascending node. Position number 9 is exactly

IfiO

ABTnOirOMT.

end
wo
bIio
the

at the node. H we
continue following her
course in this way for
a week, wo should find
that she had moved
about 90°, and attained
her greatest north lati-
tude at 5° from the
ecliptic. At the
of another week,
should find that
had returned to
ecliptic and crossed it
at her descending node.
At the end of the third
week very nearly, we
should find that she had
made three fourths the
circuit of the heavens,
and was now in her
greatest south latitude,
being 5° south of the
ecliptic. At the end
of six or seven days
more, we should again
find her crossing the
ecliptic at her ascend-
ing node as before. We
may thus conceive of
four cardinal points of
the moon's orbit, 90°
apart, marked by the
two nodes and the two
points of greatest north
and south latitude.

Motion of the Nodes.
—A remarkable prop-

f we
g licr
ly for
dliml
iioved
tallied
h lati-
n the
end
k, wo
dX she
the
SBcd it
r node,
e third
ly, wo
iho had
ths tho
Qavons,
in hor
ititudo,

of the
he end
m days
Id again
ing the
ascond-
)re. We
seive of
oints of
bit, 90°

by the
the two
est north
nde.

lo Nodes.
>le prop-

MOONS NO DBS.

161

orty of these points is tliat they are not Hxed, btit are uoiu
Btantly moving. The general motion ia a little irregnlar,
but, leaving out small irregularities, it is constantly toward
the west. Thus returning to our watch of the course of
the moon, we should find that, at her next return to the
ascending node, she would not describe the lino a a as
before, but the line hh nbuut one fourth of a diameter
north of it. She would therefore reach the ecliptic more
than 1^° west of the preceding point of crossing, and her
(tther cardinal points would be found 1^° farther west as
she went around. On her noxt return she would dcscribo
the lino CO, then tho line dd, etc., indefinitely, each line
l)eing farther toward the west. The figure shows the
paths in five consecutive returns to tho node.

A lapse of nine years will bring the descending node
around to the place which was before occupied by the
ascending node, and thus wo shall have the moon crossing
at a small inclination toward the south, as shown in the
figure.

A complete revolution of the nodes takes place in 18.6
years. After the lapse of this period, the motion is re-
peated in tlie same manner.

One consequence of this motion is that the moon, after
leaving a node, reaches the saTue node again sooner than
she completes her true circuit in the heavens. How much
sooner is readily computed from the fact that tho retro-
grade motion of the node amounts to 1° 26' 31' daring
the period that tho moon is returning to it. It takes the
moon about two hours and a half (more exactly O**. 10944)
to move through this distance ; consequently, comparing
with the sidereal period already given, we find that the
return of the moon to her node takes place in 27''. 82166
— O"*. 10944 = 27*. 21222. This time will be important to
us in considering the recurrence of eclipses.

In Fig. 59 is illustrated the effeot of these changes in
the jwBition of the moon's orbit upon lior motion rela-

leu

ASTRONOMY.

tivo to the equator. E hero ropre«enU the vernal and
uve lo mn «H ^ ^j^^ autunnml eqninox, situated

180° apart. In March, 1876,
the moon's aucending node cor-
responded with the vernal equi-
nox, and her descending node
with the autumnal one. Conse-
quently she was 6° north of the
ecliptic when in six hours of
right ascension or near the mid-
dle of the figure. Since the
ecliptic is 23r north of the
equator at this point, the moon at-
tained a maximum declination of
284°; she therefore passed nearer
the zenith when in six hours
of right ascension than at any
other time during the eighteen
years' period. In the language
of the almanac, " the moon ran
high." Of course when at her
greatest distance south of the
equator, in the other half of her
orbit, she attained a correspond-
ing south declination, and cul-
minated at a lower altitude than
she had for eighteen years. In
1886 the nodes will change places,
and the orbit will deviate from
the equator less than at any other
time during the eighteen years.
In 1880 the descending node will
be in six hours of right ascension,
and the greatest angular distance

of the moon from the equator

will be nearly equal to that of the sun.

*a(K7i=-iw^

PKHiailK OF TIIK MOON.

183

ftl and
it dated

1876,
lo cor-
I eqni-
; node
Conso-
of the
mre of
le inid-
ice the
of the
toon at-
ition of
i nearer
t hours

at any
)ighteen
angaage
oon ran
I at her

of the
If of her
respond-
and cul-
ude than
ears. In
^ places,
ate from
any other
en years,
node will
ascension,
\r distance
e equator

^ 4. MOTION OF THB FIBIOBB.

If the sun uxurtod no disturbing force on the moon, the
latter would move round the earth in an oUipse according
to Kki'lek's laws. But the difference of the sun's attrac-
tion on the earth and on the moon, though only a small
fraction uf the earth's attractive force on the moon, is yet
so great as to produce deviations from the elliptic motion
very much greater than occur in the motions of the planets.
It also produces rapid changes in the elliptic orbit. The
most remarkable of these changes are the progressive
motion of the nodus just described and a corresponding
motion of the pcrigoo. Referring to Fig. 62, which illus-
trated the elliptic orbit of a planet, let us suppose it to
represent the orbit of the moon. 8 will then represent
the earth instead of the sun, and n will be the Xxmax per-
igee, or the point of the orbit nearest the earth. But,
instead of remaining nearly fixed, as do the orbits of the
planets, the lunar orbit itself may be considered as making
a revolution round the earth in about nine years, in the
same direction as the moon itself. Hence if we note the
longitude of the moon's perigee at any time, and again
two or three years later, wo shall find the two positions
quite different. If we wait four years and a half, we shall
find the perigee in directly the opposite point of the
heavens.

The eccentricity of the moon's orbit is about 0.056, and
in consequence the moon is about 6° ahead of its mean
place when 90° past the perigee, and about the same dis-
tance behind when half way from apogee to perigee.

The disturbing action of the sun produces a great num-
ber of other inequalities, of which the largest are the
eoectian and the variation. Tlie former is more than a
degree, and the latter not much lees. The formulee by
which they are expressed belong to Celestial Mechanics,
and the reader who desires to study them is referred to
works on that subject.

1U4

ASTRONOMY.

§ 5. EOTATION OP THE MOON.

The moon rotates on her axis in the same time and in
the same direction in which she revolves around tlie earth.
In consequence she always presents very nearly the same
face to the earth.* There is indeed a small oscillation
called the libt-ation of the moon, arising from the fact that
her rotation on her axis is uniform, while her revolution
around the earth is not uniform. In consequence of
this we sometimes see a little of her farther hemisphere
first on one side and then on the other, but the greater
part of this hemisphere is forever hidden from human

The axis of rotation of the moon is inclmed to the
ecliptic about 1° 29'. It is remarkable that this axis
changes its direction in a way corresponding exactly to
the motion of the nodes of the moon's orbit. Let us sup-
pose a line passing through the centre of the earth per-
pendicular to the plane of the moon's orbit. In conse-
quence of the inclination of the orbit to the ecUptic, this
line will point 5° from the pole of the ecliptic. Then,
suppose another line parallel to the moon's axis of rota-
tion. This line will intersect the celestial sphere 1° 29'
from the pole of the ecliptic, and on the opposite side
from the pole of the moon's orbit, so that it will bo 6i°
from the latter. As one pole revolves around the
pole of the ecliptic in 18.6 years, the other wiU do the
same, always keeping the same position relative to the
first.

• This conclusion is often a pons aaiwrum, to some who conceive
that, if the swne face of the moon ia always presented to the earth, she
cannot rotate at all. The difficulty arises from a misunderstaudmg of
the difference between a relative and an absolute rotation. It is true
that she does not rotate relatively to the line drawn from the earth to
hef centre, but she must rotate relative to a fixed line, or a line drawn
to a fixed star.

line and in
i the earth,
y the same
oscillation
le fact that
• revolution
equence of
hemisphere
the greater
■om human

ned to the
it this axis
5 exactly to
Let us sup-
) earth per-
In conse-
jcliptic, this
itic. Then,
xie of rota-
Aero 1° 29'
pposite side
; will bo 6i°
around the
will do the
ative to the

who conceive
a the earth, she
iderstauding of
tion. It is true
}m the earth to
w a line drawn

THE TIDES.

105

§ 6. THE TIDES.

The ebb and flow of the tides are produced by the un-
equal attraction of the sun and moon on different parts of
the earth, arising from the fact that, owing to the magni-
tude of the earth, some parts of it are nearer these attracting
bodies than others, and are therefore more strongly at-
tracted. To understand the nature of the tide-producing
force, we must recall the principle of mechanics already
cited, that if two neighboring bodies are acted on by
equal and- parallel accelerating forces, their motion rel-
ative to each other wiil not be altered, because both will
move equally under the influence of the forces. When
the forces are slightly different, either in magnitude or
direction or both, the relative motion of the two bodies
will depend on this difference alone. Since the stin and
moon attract those parts of the earth which are nearest
them more powerfully than those which are remote, there
arises an inequality which produces a motion in the
waters of the ocean. As the earth revolves on its axis,
different parts of it are brought in in succession under the
moon. Thus a motion is produced in the ocean which
goes through its rise and fall according to the apparent
position of the moon. This is called the tidal wme.

The tide-producing force of the sun and moon is so nearly like
the disturbing force of the sun upon the motion of the moon around
the earth that nearly the same explanation will apply to both. iiCt
us then refer again to Pig. 57. and suppose i to represent the
centre of the earth, the circle FQNxU circumference, M a par-
tide of waver on the earth's surface, and 8 either the sun or the

"^The entire earth being rigid, each part of it will move under the
influence of the moon's attraction as if the whole were concen-
trated at its centre. But the attraction of the moon «pon the
Darticle M, being different from its mean attraction on the earth, will
ffi to m^ke it move differently from the earth. , The *o«e wtadi
causes this difference of motion, as already explained, ^llJe'«P«-
sented by the line MA. It is true that this same distuibing force is
Tcting ujon that portion of the solid earth at if as well, as upon t e
water But the elwth cannot yield on account of its ngidity ; the

166

ASTnONOMT.

water therefore tends to flow along the earth's surface from M
toward N. There is therefore a residual force tending to make the
water higher at N than at M.

If we suppose the particle M to be near F, then the point A will
be to the left of F. The water will therefore be drawn in an oppo-
site direction or toward F. There will therefore also be a force
tending to make the water accumulate around F. As the disturb-
ing force of the sun tends to cause the earth and moon to separate
both at new and full moon, so the tidal force of the sun and
moon upon the earth tends to make the waters accumulate both at
M and F. More exactly, the force in question tends to draw the
earth out into the form of a prolate ellipsoid, having its longest
axis in the direction of the attracting boay. As the earth rotates
on its axis, each particle of the ocean is, in the course of a day,
brought in to the four positions N Q F R, or into some positions
corresponding to these. Thus, the tide-producing force changes
back and forth twice in the course of a lunar day. (By a lunar day
we mean the interval between two successive passages of the moon
acrosdthe meridian, which is, on the average, about 24** 48".) If the
waters could yield immediately to this force, we should always have
high tide at ^and JVand low tides at Q and R. But there are two
causes which prevent tliis.

1. Owing to the inertia of the water, the force must act some
time before the full amount of motion is produced, and this motion,
once attained, will continue after the force has ceased to act.
Again, the waters will continue to accumulate as Icng as th^re is
any motion in the required direction. The result of this would be
high tides at Q and R and low tides at F and N, if the ocean
covered the earih and were perfectly free to move. That is, high
tides would then be six hours after the moon crossed the meridian.

2. The principal cause, however, which interferes with the
regularity of the motion is the obstruction of islands and continents
to the free motion of the water. These deflect the tidal wave from
its course in so many different ways, that it is hardly possible to
trace the relation between the attraction of the moon and the mo-
tion of the tide ; the time of high and low tide must therefore be
found by observing at each point along the coast. By comparing
these times through a series of years, a very accurate idea of the
motion of the tidal wave can bo obtained.

Such observations have been made over our Atlantic and Pacific
coasts by the Coast Survey and over most of the coasts of Europe,
by the countries occupying them. Unfortunately the tides cannot
be observed away from the land, and heace little is known of the
coarse of the tidal wave over the ocean.

We have remarked that both the sun and moon exert a
tide-producing force. ^^That of the sun is aI>out ^ of that
of the moon, ^^tloew and full moon the two forces are
united, and 4;he actual force is equal to their sum

first
thej
a hi
and
new
tide
the
duct
moo
aftei
est 8
new
tion,
threi
uallj
T]
lems
seve:
less I
plan!
wlii(
at d
tum
havt
sofi
tidei
whi(
give
cons
give
obse
are
the
cffe<

THK TIDEa.

167

ace from M
to make tlie

point A will
. in an oppo-

be a force
the disturb-
n to separate
;he sun and
ilate both at
to draw the
; its longest
earth rotates
rse of a day,
ime positions
)rce changes
Y a lunar day

of the moon
48-".) If the
. always have
there are two

ust act some

1 this motion,
lased to act.
(ig as there is
his would be
if the ocean
That is, high
le meridian,
res with the
ad continents
al wave from
ly possible to

and the mo-
t therefore be
3y comparing
te idea of the

ic and Pacific
its of Europe,
I tides cannot
kaown of the

iQon exert a
it ^ of that
forces are
ir sum. At

first and last quarter, when the two bodies arc 90° apart,
tliey act in opposite directions, tlie sun tending to produce
a high tide where the moon tends to produce a low one,
and vice versa'. The result of this is that near the time of
new and full moon we have what are known as the spring
tides, and near the quarters what are called neap tides. If
the tides were always proportional to the force which pro-
duces them, the spring tides would be highest at full
moon, but the tidal wave tends to go on for some time
after the force which produces it ceases. Hence the high-
est spring tides are not reached until two or three days after
new and full moon. Again, owing to the effect of fric-
tion, the neap tides continue to be less and less for two or
three days after the first and last quarters, when the grad-
ually increasing force again has time to make itself felt.

The theory of the tides offers very complicated prob-
lems, which have taxed the powers of mathematicians for
several generations. These problems are in their elements
less simple than those presented by the motion? of the
planets, owinj* to the number of disturbing circumstances
which enter into them. The various depths of the ocean
at different points, the friction of the water, its momen-
tum when it is once in motion, the effect of the eoast-lines,
have all to be taken into account. These quantities are
so far from being exactly known that the theory of the
tides can be expressed onl^ by some general principles
which do not suffice to enable u^ *o prfK?;''t them for any
given place. From observation, howevor, it is easy to
construct tables showing exactly what tid* c corrsspond 1,o
given positions of the sun and moor, at any norl where tlie
observations are made. With such tables th j ebb and flew
are predicted for the benefit of all who *re interested, but
the results may be a little uneert r'n on acccuui < f the
effect of the winds upon the motion ov the wat'^r.

CHAPTER VII.

ECLIPSES OF THE SUN AND MOON

Eclipses are a class of phenomena arising from the
shadow of one body being cast upon another, and tlius
wholly or partially obscuring it. In an eclipse of the sun,
the shadow of the moon sweeps over the earth, and the
sun is wholly or partially obscured to observers on that
part of the earth where the shadow falls. In an eclipse of
the moon, the latter enters the shadow of the earth, and is
wholly or partially obscured in consequence of being de-
prived of some or all its borrowed light. The satellites
of other planets are from time to time eclipsed in the
same way by entering the shadows of their primaries ;
among these the satellites of Jupiter are objects whose
eclipses may be observed with great regularity.

g 1. THE EABTH'S SHADOW AND PENUHBBA.

In Fig. 60 let 8 represent the sun and E the earth.
Draw straight lines, DB Fand D' W, each tivngent
to the sun and the earth. The two bodies being supposed
spherical, these lines will be the intersections of a cone
with the plane of the paper, and may be taken to repre-
sent that cone. It is evident that the cone B VB' will
be the outline of the shadow of the earth, and that within
this cone no direct sunlight can penetrate. It is therefore
called the earth's shadow cone.

Let us also draw the lines D' B P and D B' P' to rep-
resent the other cone tangent tc '^e sun and earth. It is

thei
the

So if

1 =

the ci

r =

R =

P =
8,t

we ha

But h

Hence

The
tlic rei
byobsi

THE EARTH'S SHADOW.

169

)0N

I from the
r, and tlius
of the sun,
th, and the
ere on that
in eclipse of
larth, and is
•f being de-
he satellites
psed in the
primaries ;
jects whose

BnTHBBA.

i* the earth.
!ach timgent
ng supposed
IS of a cone
on to repre-
B VB' will
1 that within
; ia therefore

3' P' to rep-
earth. It is

then evident that within the region V B P and V B' P'
the light of the sun will be piirtially but not entirely cut
off.

Pig. 60.— form op sitadow.

DimmmoM of Shadow. —Let us investigate the distance E Ffrom
the centre of tlie earth to the vertex of the shadow. Tlie triangles
V E B and V 8 D axe similar, having a right angle at B and at D.
Hence,

VE: En = VS:SD= ES:(81}-EBy.

So if we put

l—VE, the length of the shadow measured from the centre of
the earth.
r = ES, the radius vector of the earth,
R=8 D, the radius of the sun.
p = EB, the radius of the earth,

8, the angular semi-diameter of the sun as seen front the earth,
ir, the horizontal parallax of the sun,

we have

l=z VE=z

ES X EB

rp
8D - EB~ R^-P

But hy the theory of parallaxes (Chapter I., § 7),

p = r sin TT

£ = r sin 8
Henco,

1 =

sin ^' — sm rr

The mean value of the sun's angular semi-diameter, from which
the real value never differs by more than the sixtieth part, is found
by observations to be altout 16' 0' = 960", while the mean value of ir

iro

ASTRONOMY.

is about 8" ■ 8. We find sin 8-An rr = • 00461, and -^^^--^j^-
I - 217 Wc tliercforo conclude that tiic mean lengtli of

'"• S h™ "(Srfflt on. BXtieth l™ .tan the .new in D».m-

earth's centre it ^ill be equal to (l - ?,)p. for this formula gives
the radius p when z = 0, and the dian.eter /*ro when ^ = / as it
should.*

§ 2. ECLIPSES OP THE MOOW.

The mean distance of the moon from the eavtli is about
60 radii of the latter, while, as we have jnst Been, the
length EVoi the earth's ahadow is 217 radu ot the earth.
Hete when the moon passes through the shadow she does
BO at a point Iobs than three tenths of tl»e way froin
E to F. The radius of the shadow here will be HVT
of the radius E B oi the earth, a q.antity which we read-
ily find to be about 4600 kilometres. The radius of the
moon being 1736 kilometres, it will be f tl'^ly.f^.^^'Xi
by the shadow when it passes through it withni 28b4
kilometres of the axis i? Fof the shadow. If its least dis-
tance from the axis exceed this amount, a portion ot the
lunar globe will be outside the limits B F of the shadow
cone, and will thoiofonj receive a portion of the direct
light of the sun. If ♦ae least distance of the centre of the
nfoon .^rom the uxis of the shadow is greater than the
sum of the radii of the moon and the shadow-that is,
greater than 6336 kilomf.t ea-tho mooa will not enter tlic
* It will bo noted that this expression is not. rigorouslv spf^klnp, the

greater than K B.

" — ~... rtjUMl

^1 :: i M4j:-^?- ' ^-.-.. ' ^

ECLTPsm or rnK moon.

tri

*( — sin fl-
n Icngtii of
; ill roiiiul
nean radius
n the figure
li from the
,n in Decem-

the distance
e from the

rmula gives

1 2 = / as it

•til is about
b seen, the
[ the eartli.
)W she does
way from

ch we read-
idius of the
^ enveloped
vithin 2864
its least dis-
rtion of the
the shadow
t the direct
jcntro of the
er than the
ow— that is,
lot enter the

y spottklng, the
from a point on
measured in a
iieter woiiltl be
Duld be a little

shadow at all, and there will be no ellipse proper, thongh
the brilliancy of the moon must be diminished wherever
sho is within the pennmbral region.

When an eclipse of the moon occnrs, the phases are laid
down in the almanac in the following manner : Supposing
the moon to be moving aronnd the earth from below np-
ward, its advancing edge first meets the boundary B' P'
of the penumbra. The time of this occurrence is given in
the almanac as that of " moon entering penumbra." A
small portion of the sunlight is then cut off from the ad-
vancing edge of the moon, and this amount constantly in-
creases until the edge reaches the boundary B' V of the
shadow. It is curious, however, that the eye can scarcely
detect any diminution in the brilliancy of the moon ifntil
she lias almost touched the boundary of the shadow. The
observer must not therefore expect to detect the coming
eclipse until very nearly the time given in the almanac as
that of " moon entering shadow." As this happens, the
advancing portion of the lunar disk will be entirely lost to
view, as if it were cut off by a rather ill-defined line. It
takes the moon about an hour to move over a distance
equal to her own diameter, so that if the eclipse is nearly
central the whole moon will be immersed in the shadow
about an hour after she firt strikes it. This is the time of
beginning of total eclipse. So long as only a moderate
portion of the moon's disk is in the shadow, that portion
will be entirely invisible, but if the eclipse becomes total
the whole disk of the moon will nearly always bo plainly
visible, shining with a red coppery light. This is owing to
the refraction of the sun's rays by the lower strata of the
earth's atmosphere. Wo shall see hereafter that if a ray of
light D B passes from tlie sun to the earth, so as just to
graze the latter, it is bent by refraction more than a de-
gree out of its course, so that at the distance of the moon
the whole shattow is filled with this refracted liglit. An
observer on the mo<m would, during a total edijisc of tW
later, see the earth surrounded by a ring of light, and riiis

172

AsrnoNOMr.

ring would appear red, oving to the absorption of the blue
and green rays by the earth's atmosphere, just as the sun
seeins red when setting.

The moon nuiy remain enveloped in the shadow of the
earth during a period ranging from a few minutes to nearly
two hours, according to the distance at which she passes
from the axis of the shadow and the velocity of her angu-
lar motion. When she leaves the shadow, the phases
which wo have described occur in reverse order.

It very often happens that the moon passes through the
penumbra of the earth without touching the shadow at all.
No notice is taken of these passages in our almanacs, be-
cause, as akeady stated, the diminution of light is scarcely
perceptible unless the moon at least grazes the edge of the
shadow.

§ 8. EC5LIPSBS OP THE SUN.

In Fig. 57 we may suppose B I^ B' to represent the
moon as well as the earth. The geometrical theory of the
shadow will remain the same, though the length of the
shadow will be much less. We may regard the mean
semi-diameter of the sun as seen from the moon, and its
mean parallax, as being the same for the mOon as for the
earth. Therefore in the formula which gives the length
of the moon's shadow the denominator will retain the
same value, while in the numerator we must substitute the
radius of the moon for that of the earth. The radius ot
the moon is about 1736 kilometres, or 1080 miles. Multi-
plving this by 217, as before, we find the mean length ot
[he moon's shadow to be 377,000 kilometres, or 235,000
miles. This is very nearly the same with the distance ot
the moon from the earth when she is in conjunction with
the sun. We therefore conclude that when the moon
passes between the earth and the sun, the former will be
very near the vertex V of the shadow. As a matter of
fact an observer on the earth's surf ace will sometimes pass

THE MOON'S SItAlJOW.

178

the blue
the 8un

V of tho
:o nearly
lie paABCB
er aiigu-
3 phases

ongh the
>w at all.
nacs, be-
} scarcely
gc of the

csent the
>ry of the
;th of the
the mean
tn, and its
as for the
bhe length
retain the
stitute the
3 radius of
8. Multi-
length of
,r 235,00()
distance of
iction with
the moon
ner will be
. matter of
Btimes pass

through the region O VC\ and sometimes on the other
side of F.

Now, in Fig. ♦•0, still supposing 7? E Ji' to he the
moon, let us draw the lines /> />" /" and JJ' li P tan-
gent to i)othtlie n»oon and the sun, but crossing each other
between these bodies at h. It is evident that outside the
space P li B' P' an observer will see the whole sun, no
part of the m(x»n being projected ujwn it ; while within
this space the sun will be more or less obscured. The
whole obscured space may bo divided into three regiotis, in
each of which the character of the phenomenon is differ-
ent from what it is in the others.

Firstly, we have the region B VB' fonning the shadow
cone proper. Here the sunlight is entirely cut off by the
moon, and darkness is therefore complete, except so far as
light may enter by refraction or reflection. To an observer
at V the moon would exactly cover the sun, the two
bodies being apparently tangent to each other all around.

Secondly, we have the conical region to the right of V
between the lines B Fand B' V continued. In this
region the moon is seen wholly projected upon the sun,
the visible portion of the latter presenting the form of a
ring of light around the moon. This ring of light will be
wider in proportion to the apparent diameter of the sun,
the farther out we go, because the moon will appear
smaller than the sun, and its angular diameter will dimin-
ish in a more rapid ratio than that of the sun. This
region is that of annular eclipse, because the sun will pre-
sent the appearance of an annulus or ring of light around

the moon.

Thirdly, we have the region PB VandP'B V, which
we notice is connected, extending around the interior cone.
An observer hero would see the moon partly projected
upon the sun, and therefore a certain part of the sun's
light would be cut off. Along the inner boundary B V
and B' V the obscuration of the sun will be complete,
but the amount of sunlight will gradually increase out to

174

AtiTRONOMY.

tliu outer boiimlary B /' Ji' 7", wliorc tlio whole sun is
vi8il>lu. This region uf pai-'jiil obseuration is culluil the
jtcnumbra.

To sliow more clearly t'iic phenomena of solar c('li|iHo,
we jircseiit another figure reprcsi-iiting the pentimhra of

Fio. fll.— noiTRB or hhadow por MxnvhAit bclifbb.

tlie moon tlirown upon the earth.* The outer of the two
circles S represents the limb of the sun. The exterior tan-
gents which mark the boundary of the shadow cross each
other at F before reaching the earth. The earth being
a little beyond the vertex of the shadow, there can be no
total ccli^)se. In this case an observer in the penumbral
region, C or D Oy will see the moon partly projected on
the sun, v/hile if ho chance to be sitnated at O he will see
an annular eclipse. To show how this is, we draw dotted
lines from O tangent to the moon. The angle bolAoen
these lines represents the apparent diameter of the moon
as seen from the earth. Continuing them to the sun, they
show the apparent diameter of the moon as projected upon
the sun. It will be seen that in the case supposed, when

* Tt will In; noted that nil the HgiircH of eclipses nrc necessarily drawn
very much out of proportion. Really the sun is 400 times the distance
of the moon, whicli again is 00 times the radius of the earth. But it
would lie entirely impossible to draw a figure of this proportion ; wi
are therefore obliged to represent the earth as larger than the sun, ani
the moon as nearly half way between the earth and sun.

th
th
th
sic

rei

in
ec

ili .lJ i a *i HiM.j. i | I IA< I

~Z}.

O 8UT1 IB

tllud the

• C('li|)HO.
iuil>ra uf

E0LIP8B8 OF TUh' HUN.

175

the vortex of the shadow is hotweon the earth and moon,
tlie hitter will neccHsarily apjHjar sniallcr tlian the rjui, and
the observer will see a portion of the solar disk on all
sides of the moon, as shown in Fig. (52.

If the moon were a little nearer the eaith than it is rep-
resented in the figure, its shadow would reach the earth

nn.

>f the two
ten or tan-
cross each
firth being
can be no
pcnumbral
ojected on
[le will see
•aw dotted
i bfct*veen
the moon
5 sun, they
icted upon
ised, when

iHarily drawn
the distance
kfth. But it
portion ; we
the sun, and

FlO. 62.— DARK BOOT OF MOON nUMECTBD OH SUN DORINU AN
ANNOLAR ECLIP8B.

in the neighljorhood of O. We should then liave a total
eclipse at each point of the earth on which it fell. It will
be seen, however, that a total or annular eclipse of the sun
is visible only on a very small portion of the earth's sur-
face, because the distance of the moon changes so little
that the earth can never be far from the vertex Fof the
shadow. As the moon moves around the earth fi-om west
to east, its shadow, wliether the eclipse be total or annu-
lar, moves in the same direction. The diameter of the
shadow at the surface of the earth ranges from zero to 150
miles. It therefore sweeps along a belt of the earth's sur-
face of that breadth, in the same direction in which the
<jartli is rotating. The velocity of the moon relative to
the earth being 3400 kilometres per hour, the shadow
would pass along with this velocity if the earth did not ro-
tate, but owing to the earth's rotation the velocity rektive

176

AtiTliUiSOM Y.

to |H»int« on itH Hiirftwo riiiiy raiif^c from 2000 to 3400
kiloMictivH (1200 to 2100 mih'H).

The ruiuler will readily umlc!r«tiiiKl tliiit in (trder to hoc
a total wlipHU an olmciver iiiUHt station liin»»ell' hcforo-
haiid at m\\w point of the carth'H HuriWo over which the
Hhadow is to paHH. These points ai-e ^'enerally ealr,ulate»l
Home years in ailvanee, in the iwtronomieal ephemerides,
with as inueh precision as the tables of the celestial mo-
tions admit of.

It will ho seen that a partial eclipse of the sun may Im)
visible from a much larger jwrtioii of the earth's surfaco
than a tt>tal or annular one. The space CD (Kig. «!) over
^vhi(;h the penumbra extends is generally of about one hull
the diameter of the earth. Roughly speaking, a partni!
eelipso of the su); may sweep over a ]M>rtion of the earth's
surface ranging from zero to perhaps one fifth or one sixth

of the whole.

There are really more eclipses of the eun than «)f tlie
moon. A year never passes without at least two of the
fonner, and sometimes five or six, while there are rarely
mon than two eclipses of the moon, an«l in many years
now: ;Af all. But at any one place more eclipses of the moon
vill ,c seen than of the sun. The reason of this is that
an eclipse of the moon is visible over the entire hemi-
sphere of the earth on which the moon is shining, and aa it
lasts several hours, observers who are not in this hemi-
sphere at the beginning of the eclipse may, by the earth's i-o-
tation, be brought into it before it ends. Thus the eclipse
will be seen over more than half the earth's surface. But,
as we have just seen, each eclipse of the sun can be seen
over oidy so small a fraction of the earth's surface as to
more than compensate for the greater absolute frequency
of solar eclipses.

It will be seen that in order to have either a total or ari«^
nular eclipse visible upon the earth, the line joining the
centres of the sun and moon, being continued, must
strike the earth. To an observer on this line, the centres

>il_

to 3400

ler to Hcc
I' hcforo-
vliich tliu

'illcllliltctl

,!ineri(loH,
Htial ino-

■2

w may bo
'h Hurfttco
, ISl) over
t onu liuit'

u parttu)
lio eartli'^

une eixth

lan of tlic
wo of the
are rarely
lany years
: the moon
^hig is that
tiro hemi-
r, and as it
this heini-
earth'sro-
tho eclipse
face. But,
;an be seen
irfaco as to
! frequency

total or art*-'
joining the
lued, must
the centres

i^igjjaftioua i iawm

^em^^m^mymMMuj.. ' -^.-^- f>#''rm ->f .^ .-,'f..^^.,Ai..m L.i'i^.:. . r ,... .,). .■ r ; ?'g^'tP#H!#Piy'^S^' '"'

._J

CIHM/ICMH

Series.

CIHM/ICMH
Collection de
microfiches.

Canadian Instituta for HIatorical Microraproductiona / Inatftut Canadian da microraproductiona hiatoriquaa

BEGURRENOK OF EGLlPSBa.

177

of the two bodies will seem to coincide. An eclipse in
which this occurs is called a central one, whether it be
total or annular. The accompanying figure will perhajis
aid in giving a clear idea of the plienoinena of eclipses of
both sun and moon.

FlO. 63.^COMPARI80N OV SHADOW AND PKNimBRA OF EARTH AKD
MOON. A IS THE POSITION OP TUB MOON DUBINO A BOLAK, B DCB-
INO A LUNAR ECLIPSE.

§ 4. THX BXOUBBHNCE OF aOUPSES.

If the orbit of the moon around the earth were in or
near the same plane with that of the latter around the sun
— that is, in or near the plane of the ecliptic — It will be
readily seen that there would be an eclipse of the sun at
every new moon, and an eclipse of the moon at every
full moon. But owing to the inchnation of the moon's
orbit, described in the last chapter, the shadow and
penumbra of the moon commonly pass above or below the
earth at the time of new moon, while the moon, at her
full, commonly passes above or below the shadow of the
earth. It is only when at the moment of new or full moon
the moon is near its node that an eclipse can occur.

The question now arises, how near must the moon be to
its node in order that an eclipse may occur ? It is found
by a trigonometrical computation that if, at the moment
of new moon, the moon is more than 18° '6 from its
node, no eclipse of the sun is possible, while if it is less
&aa 18** • 7 an eclipse is certain. Between these limits an
ecUpse auLj occur or fail aocording to the respeotiye dis-
taaocB of tiie snn and moon from tibe earth. Half way be-
tw«en these limits, or say 16** from the node, it is an even

ASTRONOMY.

uhance that an eclipBe will occur ; toward the lower limit
(13° -7) the chances increase to certainty; toward the
upper one (18° • 6) they diminish to zero. The correspond-
ing limits for an eclipse of the moon are 9° and 12^° — that
is, if at the moment of full moon the distance of the
moon from her node is greater than Vi^^ no eclipse can
occur, while if the distance is less than 9° an eclipse is cer-
tain. Wo may put the mean limit at 11°. Since, in the
long run, new and full moon will occur equally at all dis-
tances from the node, there will be, on the average, sixteen
eclipses of the sun to eleven of the moon, or nearly fifty per
cent more.

Fra. 64.— mutntias Imiar cdipM at diUMeiit dMuow ftrom ttw nod*. The dark
circle* ar« Ike earth's ahadow, tiia ceatre of whieh Is alwajrs in the ecliptie AB. The
moon's orbit is represented ^jOD. At (3> the eelipso is central and total, at J'Uls
partial, and at K there is baieljr an ecUpse.

tut an illustration of these computatioiM, let us investigatQ the lim-
its within which a central eclipse of the sun^ total or annular, can
occur. To allow of such an eclipse, it is oTident, from an inspec-
tion of Fig. 61 or 68 that the actual distance of the moon from
the plane of the ecliptic must be less than the earth's racUus,
because the line joining the centres of the sun and earth always lies
in this plane. This distance must, therefore, be leaa than 6870 kilo-
m«trea- The mean distance of the moon being 884,000 kilometres,
the sine of the latitude at this limit is jfUHi mi<1 ^^ Utitude itself
is 57'. The formula for the latitude u, by sjdwrical trigonometry,

rin latitude = sin • sin «,

» being the inclination of the moon's orbit (5* 80, ud « the distance
of the moon from the node. The value of sin < is ncA far fmn A.
while, in a rough calcuhtion, we may suppose the comnaratively
small angles « and the latitude to be tlM mow as theb miiQs. We
may, therefore, suppose

tt=rll latitDdesB t^'.

BEVURttENOE OF ECLIPSES.

179

ird the lower limit
iinty ; toward thu

The correspond-
9" and 12^°— that
[6 distance of the
2^** no eclipse can

an eclipse is oer-
1°. Since, in the

equally at all dis-
he average, sixteen
I, or nearly fifty per

■ fhmittMiiod*. Tiiedirk
jrt In the ecllptie AB. Ttta
OMUml andtoUl, at JTUU

ua invettigatQ the lim-
, total or wmular, can
idnit, from an iii8pec>
Be of the moon Iram
a the earth's radius,
I and earth always lies
te less than «870]dlo-
ig 884,000 kilometns,
and the latitude itself
iherical trigonometry,

80, and « the distance
a < is not far f mn A,
MS the ooapnntiTely
e as their uaes. We

We therefore conclude that if, at the moment of new moon, the
distance of the moon from the node is less than 101° there will be
a central eclipsr, of the sun, and if greater than this there will not be
such an •«lip«o. The eclipse limit may range half a degree or more
on each side of this mean value, owing to the varying distance of
the moon from the earth. Inside cf 10 a central eclipse may be re-
garded as certain, and outside of 11° as impossible.

If the direction of the moon's nodes from the centre of
the earth were invariable, eclipses could occur only at the
two opposite months of tlie year when the sun had nearly
the same longitude as one node. For instance, if the lon-
gitudes of the two opposite nodes were respectively 54'^
and 234°, then, since the sun must be within 12° of the
node to allow of an eclipse of the moon, its longitude
would have to be either between 42° and 66°, or between
222° and 246°. But the sun is within the first of these re-
gions only in the month of May, and within the second only
during the month of November. Hence lunar eclipses
could then occur only during the months of May and No-
vember, and the same would hold true of central eclipses
of the sun. Small partial eclipses of the latter might be
seen occasionally a day or two from the beginnings or ends
of the above months, but they would be very small and
quite rare. Now, the nodes o " the moon's orbit were act-
ually in the above directions in the year 1873. Hence
during that year eclipses occurred only in May and No-
vember. We may call these months the seasons of eclipses
for 1873.

But it was explained in the last chapter that there is a
refaoigrade motion of the moon's nodes amounting to 19^°
in a year. The nodes thus move back to meet the sun in
its annual revolution, and th meeting occurs about 20 days
eariiw every year than it did the year before. The re-
salt is that tibe season of eclipses is constantly shifting, so
that each season ranges throngfaout the'whole year in 18*6
yean. Tor instance, the season oorreeponding to that of
November, 1873, had moved baok to July and August in

180

ASTRONOMY.

1878, and will wicur in May, 1882, while that of May,
1873, will bo shifting back to November in 1882.

It may bo intoreBting to illuBti-ato this by giving the
days in which the sun is in conjunction with the nodes of
the moon's orbit during several years.

AKCuding Node.

1879. January 24.

1880. January 6.

1880. December 18.

1881. November 30.

1882. November 12.

1883. October 25.

1884. Octobers.

DeiicondlDg Mode.

1879. July 17.

1880. Jime27.

1881. June 8.

1882. May 20.

1883. May 1.

1884. April 12.

1885. March 25.

During these years, eclipses of the moon can occur only
within 11 or 12 days of these dates, and eclipses of the
sun only within 15 or 16 days.

In consequence of the motion of the moon's node, three
varying angles come into play in considering the occur-
rence of an eclipse, the longitude of the node, that of the
sun, and that of the moon. We may, however, simplify
the matter by referring the directions of the sun and
moon, not to any fixed line, but to the node — t&at is, we
may count the longitudes of these bodies from the node
instead of from the vernal equinox. We have seen in the
last chapter that one revolution of the moon relatively to
the node is accomplished, on the average, in 27 • 21222
days. If we calculate the time required for the sun to re-
turn to the node, we shall find it to be 346 • 6201 days.

Now, let US suppose the sun and moon to start out
together from a node. At the end of 346 '6201 days the
sun, having apparently performed nearly an entire rev-
olution around the celestial sphere, will again be at the
same node, which has moved back to meet it. But the
moon will not be there. It will, during the interval, have
passed the node 12 times, and the 18th paasage will not
occur for a week. The same thing will be tme for

BECUBRENVB OF ECL/P8E8.

181

ilo that of May,

ill 1882.

lis by giving tho

iritli tlio nodes of

mdlng Node.

July 17.
June 27.
June 8.
May 20.
May 1.
April 12.
Marcli 25.

in can occur oitly
1 eclipses of tho

oon's node, three
lering the occur-
node, that of the
lowever, simplify
of the sun and
lode — that is, we
fl from the node
have seen in the
loon relatively to
ige, in 27-21222
for the sun to re-
^•6201 days.
lOon to start out
16-6201 days the
y an entire rev-
i again be at the
leet it. But the
he interval, have
paamge will not
lill be true for

IS successive returns of the sun to the node ; we shall
not lind the moon there at the same time with the sun ;
she will always have passed a little sooner or a little later.
But at the 10th return of the sun and the 24:2d of the
moon, the two bodies will be in conjunction within half
a degree of the node. Wo iind from the preceding
periods that

242 returns of the moon to the node require 6585 - 357 days.

19 ♦' " sun " " " 6585-780 "

The two IxMlies will therefore pass the node within 10
hours of each other. This conjunction of the sun and
moon will be the 223d new moon after that from which
wo started. Now, one lunation (that is, the interval
between two consecutive new moons) is, in the mean,
29-530588 days ; 223 lunations therefore require 6585-32
days. The new moon, therefore, occurs a little before the
bodies reach the node, the distance from the latter being
that over which the moon moves in 0*-036, or the sun in
0^-i59. We readily find this distance to be 28' of arc,
somewhat less than the apparent semidiameter of either
body. This would be the smallest distance from either
node at which any new moon would occur during the
whole period. The next nearest approaches would have
occurred at the 35th and 47th lunations respectively.
The 36th new moon would have occurred about 6° before
the two bodies arrived at the node from which we started,
and the 47th about 1^° past the opposite node. No other
new moon would occur so near a node before the 223d
one, which, as we have just seen, would occur 0" 28'
west of the node. This period of 223 new moons, or 18
years 11 days, was called the Saras by the ancient astron-
omers.

It will be seen that in the preoedinff calcnlalioiu we taftre aMumed
the ran aad moon to more uniformly, so that the aucceuive new
moon's occurred at equal intervals of 29 -680588 days, and at equal
angular distances around the ecliptic. In fact, however, the month-
ly uuqnslities in the motioa at the moon cause deviatiomi from lier

182

AaTRONOMY.

mean motion which amount to six doffroei in either direction, while
the annual inequality in the motion of the sun in lonsitiide is nearly
two degrees. Consequently, our conclusions respecting the point at
which new moon occurs may be astray by eight degrees, owing to
these inequalities.

But there is a remarkable feature connected with the Saros which
greatly reduces these inequalities. It is that this period of 6585}
days corresponds very nearly to an integral number of revolutions
both of the eartli round the sun, and of the lunar perigee around
the earth. Hence the inequalities both of the moon and of the
sun will be nearly the same at the beginning and the end of a Saros.
In fact, ttSSfil days is about 18 years and 11 days, in which time
the earth will have made 18 revolutions, and about 11° on the
10th revolution. The longitude of the sun will therefore be about
11° greater than at the Mginning of the period. Again, in the
same perio<l the moon's perigee will have made two revolutions,
and will have advanced 18° 88' on the third revolution. The sun
and moon being 11° further advanced in longitude, the conjunction
will fall at the same distance from the lunar perigee within two or
three degrees. Without going through the details of the calcula-
tion, we uiay say as the result of this remarkable coincidence that
the time of the 228d lunation will not generally be accelerated or
retarded more than half an hour, thou^ those of the intermediate
lunations will sometimes deviate more than half a day. Also that
the distance west of the node at which the new moon occurs will
not generally differ from its mean value, 28' by more than 20'.

In the preceding explanation, we have eapposed the snn
and moon to start ont together from one of the nodes of
the moon^s orbit. It is evident, however, that we might
have supposed them to start from any given distance east
or west of the node, and should then at the end of the 223d
lunation find them together again at nearly that distance
from the node. For instance, on the 6th day of May,
1864, at seven o'clock in the evening, Washington time,
new moon occurred with the sun and moon 2° 26' west of
the descending node of the moon's orbit. Counting for-
ward 223 lunations, we arrive at the 16th day of May,
1882, when we find the new moon to occur 3° 20' west of
the same node. Since the character of the eclipse depends
principally upon the relative position of the sun, the moon,
and the node, the result to which we are led may be stated
as follows :

Let us note the time of the middle of any eclipse.

RKVURRBNGB OF B0LIP8B8.

188

either diroction, while
I in lonffitude is nearly
respecting the point at
ght degrees, owing to

with the Saros which
t this period of 658S1
number of revolutions

lunar perigee around
the moon and of the
md the end of a Saros.

days, in which time
and about 11° on the
rill therefore be about
leriod. Again, in the
nade two revolutions,

revolution. The sun
itttde, the conjunction
perigee within two or
oetaiTs of the calcula-
kable coincidence that
rally be accelerated or
ose of the intermediate
half u day. Also that
new moon occurs will
by more than 30'.

ve supposed the snn
)ne of the nodes of
ever, that we might
given distance east
theendof the22dd
learly that distance
B 5th day of May,
, Washington time,
noon S** 35' west of
'bit. Counting for-
16th day of Hay,
>ccur 3° 20' west of
' the eclipse depends
the sun, the moon,
« led may be stated

die of any eclipse.

whotlior of the buii or of the moon. Tliuii let lis go for-
ward 0585 dayu, 7 hours, 42 minuluH, nnd wo shall find
unothor cclipsu very Hiniilar to the tirst. Iludnced to years,
the interval will be 18 years and 10 or 11 days, according
as a 2Utli day of February intervenes four or live times
during the interval. This Iwing true of every eclipse, it
follows that if we record all the eclipses which occur dur-
ing a ])eriod of 18 years, we shall find a new set to begin
over again. If the period were an integral number of
(lays, each eclipse of the new set would be visible in the
same regions of the earth as the old one, but since there is
a fraction of nearly 8 hours over the round imniber of
days, the earth will be one third of a revolution further
advanced before any eclipse of the new set begins. Each
eclipse of the new set will therefore occur about one third
of the way round the world, or 120° in longitude west of
the region in which the old one occurred. The recur-
rence will not take place near the same region until the end
of three periods, or 54yeanB ; and then, since there is a
slight deviation in the series, owing to each new or full
moon occurring a little further west from the node, the
fourth eclipse, though near the same region, will not
necessarily be similar in all its particulars. For example,
if it be a total eclipse of the sun, the path of the shadow
may be a thousand miles distant from the path of 54 years
previously.

As a recent example of the Saros, we may cite some
total eclipses of the ' '.* well known in recent times ; for
instance :

1842, July 8th, l** a.m., total eclipse observed in
Europe ;

1860, July 18th, 9^ a.m., total eclipse in, America and
Spain ;

1878, Jnly 39th, 4^ p.m., one visible in Texas, Col-
orado, and on the coast of Alaska.

A yet more reuuurkable series of total edipsee of the

184

AStTttONOMT.

mn uro those of thoyeiirB 1850, 1808, 188<), utc, tho dates
and regions 1)eing :

1850, August 7tli, 4'' I'.M., in tlie Pacific Ocean ;

18«8, August 17tli, 12'' I'.M., in India;

1880, August 2»th, 8'' a.m., in tho Central Atlantic
< )cean and Southern Africa ;

iyo4, Septeud)er Uth, noon, in South America.

This scries is remarkable for the long duration of total-
ity, aiaouuting to some six minutes.

Let lis now consider a series of ecliiHies recurring at i-eg-
ular intervals of 18 years and 11 days. Since every suc-
cessive recurrence of such an eclipse throws the conjunc-
tion 28' further toward tho west of the node, the conjunc-
tion must, in process of time, take place so far back from
tho node that no eclipse will occur, and the series will end.
For the same reason there must be a commencement to
the series, the first eclipse being east of the node. A new
eclijjse thus entering will at first be a very small one, but
will be larger at every recurrence in each Saros. If it is
an eclipse of the moon, it will be total from its 18th until
its 36th recurrence. There will then be about 18 partial
eclipses, each of which will bo smaller than the kst, when
they will fail entirely, the conjunction taking place so far
from the node that the moon does not touch the earth's
shadow. The whole interval of time over which a series
of lunar eclipBCS thus extend will be about 48 periods, or
865 years.

When a series of solar eclipses begins, the penumbra of
the finst will just graze the earth not far from one of the
poles. There will then be, on the average, 1 1 or 12 partial
eclipses of the sun, each lai^r than the preceding one,
occurring at regular intervals of one Saros. Then the
central line, whether it be that of a total or annular
eclipse, will begin to touch the earth, and we shall have a
series of 40 or 50 central edipBes. The central line will
strike near one pole in the first part of the MRW ; in the
equatorial regions about the middle of tlie aoriet, Mid will

VtlAUAGTKIlH OF MHJI'SKS.

185

SB, utc, thu datu8

itic Ocuuii ;

Ouiitrul Atliiiitic

Aiiiurica.
durutiun uf tuta]-

i rufurriiig at ivg-
8incti every buc-
row8 the coiijuuu-
tude, the coiiji.iic-
) so far back from
he 8erio8 will end.
ioinmeucemeiit to
the node. A new
cry gniall one, but
ch Sarofl. If it is
^rom its 13th until
10 about 18 partial
ban the last, when
Aking place so far
touch the earth's
iver which a series
>out 48 periods, or

, the penumbra of
■ from one of the
^, llor 12 partial
he preceding one,
Sarofl. Then the
I total or annular
nd we shall have a
e centra] line will
theMrifls; in the
diesMMs, Mid will

Icuvu the earth by thu other ]k)Iu ut the end. Tun or
twulvu partial u(!li|MuM will follow, and this particular ite-
rics will cuHHu. Tliu wbolu iiuinbur in the series will avur-
age iHitwuun 00 und 7U, occupying u fuw uenturies over a
thoiiHiuid years.

$( 6. 0HABA0TBB8 OF B0LIP8B8.

Wc have seen that tho |ioMibility of a tutal eclipso of the sun
iiriaeH from the occaHional very Hiight excesa of tho apparent anaular
diameter of the moon over that of the sun. This excess is so slight
that such an eclipse can never last more than a few minutes. It
may be of interest to point out the circumstances which favor a
long duration of totality. These are :

(1) That the moon should be as near as possible to the earth, or,
technically speaking, in perigee, because Its angular diameter as
Hccn from the earth will then be greatest.

(2) That the sun should be near its greatest distance from the
earth, or in apogee, because then its angular diameter will be the
least. It is now in this position about tne end of June ; hence the
most favorable time for a total eclipse of very long duration is in
the summer months. Since the moon must bo in perioee and alao
between the earth and aun, it follows that the longitude of the
perigee must be nearly that of the sun. Hie longitude of the sun
at the end of June Iwing 100*, thia is the most favorable longi-
tude of the moon's perig«e.

(8) The moon must m very near the node in order that the cen-
tre of the shadow may fall near the equator. The reason of this con-
dition is, that the duration of a total eclipse may be oonaidenibly
increased by the rotation of the earth on ita azia. We have seen
that the shadow sweeps over the earth from west toward east with a
velocity of about 8400 kilometres per hour. Since the earth rotates in
the same direction, the velocity relative to the observer on the earth's
surface will be diminished by a quantity depending on thia velocity
of rotation, and therefore greater, the greater t& velocity. Tb«
vebMsity of rotation u greatest at the earth's equator, when it
amounts to 1600 kibtowtres per hour, or nearly half the velocity of
the moon's shadow. Hence tne duration of a total ecline may, with-
in the tropics, be nearly doubled bvthe earth's rot^ion. when all
the favorable cireumstances comUne in the way we have just de-
scribed, the duration of a total eclipse within the tropica will be
about seven minutes and a half. In our latitude thrmudmum du-
rati<m will be somewhat less, or not far from six minutea, but it is
only on vety ran ooeaaiona, hardly once in many centuries, that all
these faveirable conditioas can be expected to coticur.

Of late yean, solar eclipMS have derived an inoreaied in-
terest from the faet that during the few minutes which

ASTRONOMY.

thuy luht tliuy nffonl iiiii(jiio opportuiiitiun f«*r iiivuHti^itiii);
tho matter wliivh Uch in tlio iiiiiiic<]iuto noighlHirhood uf
tho Mini. IJiidor ordiiiury cinniiiiHtniicofl, this inattor Jh
rondottid untiroly iiiviHihlo by the ufTiil^'iicu of tliu Holnr
ruyA which ilhiiniiiattiouratiiRmpIioro ; hutwlieii a tMHlyeo
distant m the moon '\% intorpoMMl Ixjtwoun tlie olMiorvor and
tlie Ban, the ray^ of tliu latter are cut off from a region a
hundred miles or more in extent. TIiuh an amount of
darkness in tho air is secured wliich \» lm{)oHHilile under
any other circumstanceH wlien the sun is fur alN>vo tho
horizon. Still this durkness is by no iiieaiiH complete, bccausu
the sunlight is reflecte<l from tlio region on which the sun
is shining. An idea of tho amount of darkness may lio
gained by considering that the face of a watch can be road
during an eclipse if the oluierver is careful to shade his
eyes from the direct sunlight during tho few minutes be-
fore the sun is entirely covered ; that stars of the first
magnitude can be seen if one knows where to look for
them ; and that all the prominent features of tho land-
scape remain plainly visible. Au account of the investi-
gations made during solar eclipses belongs to the physical
constitution of tlie sun, and will therefore be given in a
sabseqaent chapter.

Oooultation of Stan by the Moon. — A phenomenon
which, geometrically considered, is analogous to an eclipse
of the sun is the oooultation of a star by the moon.
Since all the bodies of the solar system are nearer than the
fflted stars, it is evident that they must from time to time
pass biBtween us and the stars. The planets are, however,
so small that such a passage is of very rare occurrence,
and -when it does happen the star is generally so faint
that it is rendered invisible by the superior light of the
planet before the latter touches it. There are not more
than one or two instances recorded in astronomy of a well-
authenticated observation of an actnal ocoaltation of a star
by the opaque body of a planet, although there are several
cases in which a planet has been known to pass over a star.

^ituJ.

■Wfi!

)» for iiivcMti^ititi^
J Tioij<hlM>rho«Hl uf
COM, this iiiattor m
l^uiicu of tlio »M>lar
l)utwhun u iMxlyBo
n the olworvor aiul
ff from a region a
iiiH an amount of
impoHHihlu under
h iar alM>vo the
rt c<»nipleto, becaunu
I on wliiuh the sun
(larkneiw may )hs
i watcli van be road
reful to sliado \m

few minutes bo-
Btars of the first

where to look for
turps of the land-
unt of the investi-
ngs to the physical
jfore be given in a

I. — A phenomenon
logons to an eclipse
itar by the moon,
are nearer than the
i from time to time
lanots are, however,
ry rare occurrence,

1 generally so faint
perior light of the
rhera are not more
istronomy of a well-
occnltation of a star
igh there are several
1 to pass over a star.

(KnmLTArioN oif ntahn.

Rut the moon is so largo and hur angular motion so rapid,
that she |>aHHOS over Kome star visible to the naked uye
uvery few days. Such phononiona are toniiod oi^eultations
of star» hy the nwim. It mast not, however, be supposed
that they can l)e observed by the naked eye. In general,
tliu moon is so bright that only stars of the first magnitude
can Ih) seen in actual contact with her limb, and even then
the ("ontact must be with the nnilluminated limb. But
with the aid of a telescope, and the pretlictions given in
the Ephomcris, two or threu of thefju occultations can be
ol)served during nearly every lunation.

1 1^

i,'»'

i 'I'.

CHAPTER VIII.

THE EAKTH.

Our object in the preeent chapter is to trace the ^ecte

of terr^trial gravitation and to study the changes to

v,rn is subject in various places. Since every part

any odJ«^ j ^ ^^ ^ow belonging to the

« 1-

„AS8 Airo MBsrre ot tb» "abth.

We begin by ««»» definitioiie »id Bome prmciple. i«-
orier to make it ™»'V™* * ,*£fjSoa. A«M

II.

to trace the effects
idy the changes to
. Since every part
irt as well as every
that the earth and
Testrial form a sort
of which are firmly
action. This attrac-
mpoBsible to project
Tth into the celestial
owbelon^ng to the
ain upon it forever.

p TBS BABTH.
1 some principles re-

etc. ,

ioA aBthe qwmtUy qf

this quantity of mat-
ht of the body— thiB
orce of attraction be-
By the inertia of the
we muBt apply tott^
aite velocity. Mathe-
^two method* shwdd
iment it i» f ««»<* ^»"*

MA88 OP THE EARTH.

189

the attraction of all bodies is proportional to their inertia.
In other words, all bodies, whatever their chemical consti-
tntion, fall exactly the sjune numl»er of feet in one second
under tlio influence of gravity, supposing them in a vacu-
um and at the same place on tlie earth's surface. Although
the mass of a body is most conveniently determined oy its
weight, yet mass and weight must not be confounded.

The vieight of a body is the apparent force with which
it is attracted toward the centre of the earth. As we
shall see hereafter, this force is not the same in all parts of
the earth, nor at different heights above the earth's sur-
face. It is therefore a variable quantity, depending upon
the position of the body, while the mass of the body is re-
garded as something inherent in it, which remains constant
wherever the body may be taken, even if it is carried
through the celestial spaces, where its weight wonld be
reduced to almost nothing.

The unit of mass which we may adopt is arbitrary ; in
fact, in different cases different units will be more con-
venient. Generally the most convenient unit is the weight
of a body at some fixed place on the earth's surface — ^the
city of Washington, for example. Suppose we take such
a portion of the earth as will weigh one Ulogram in Wash-
ington, we may then consider the mass of that particular
lot of earth or rock as a kilogram, no matter to what part
of the universe we take it. Suppose also that we conld
bring all tlie matter composing die earth to the city of
'W^ashington, one kilogram at a time, for the purpose of
weighing it, returning each kilogram to its place in the
earth immediately after weighing, so that there should he
no disturbance of the earth itself. The sum total of the
weights thus found would be the mass of the earth, and
would be a perfectly definite quantity, admitting of being
n kilograms or pounds. We esn readily cal*
MM of a v<dnme of water equal to that of the
ue we know the magnitiule of the earth in
Am mass of one litee id mlm. Dividii^ &u

190

ASTBONOMY.

into the maso of the earth, Bnppofiing onrselves able to de-
termine this mass, and we shdl have the specific gravity,
or what is more properly called the density of the earth.

What we have supposed for the earth we may imagine
for any heavenly body — namely, that it is brought to the
city of Washington in small pieces, and there weighed one
piece at a time. Thns the total mass of the earth or any
heavenly body is a perfectly defined and determined
quantity.

It may be remarked in this connection that our units of
weight, the pound, the kilogram, etc., are practically units
of mass rather tlian of weight. If we should weigh out
a pound of tea in the latitude of Washington, and then
tidce it to the equator, it would really be less heavy at the
equator than in Washington ; but if we take a pound
weight with us, that also would be lighter at tlie equator,
so that the two would still balance each other, and the tea
would be still considered as weighing one pound. Since
things are actually weighed in this way by weights which
weigh one unit at some definite place, say Washington,
and which are carried all over the world without being
changed, it follows that a body which has any given
weight in one place will, as measured in this way, have
the same apparent weight in any other place, although its
real weight will vary. But if a spring bidance or any
other instrument for determining actual weights were
adopted, then we should find that the wdght of the tame
body varied as we took it from one part of the enrth to
another. Since, however^ we do no^ use this sort of an
instrument in weighing, but pieces of metal which are
carried about without <^nge, it follows that what we call
units of weight are property units of hums.

DMurity of the Barth. — ^We see that i^ bodies aronnd
us tend to fall toward the centre of the «aiih. Aeoonfing
to the law of gravitation, this tendaaey is not 8im[4y a
single force directed toward the oentre of tiie earth, bnt
is the resultant of mi infinity of wsftenSse f oroes arising frmn

^''SMIiiF'

MASS OF THE EARTH.

191

areelves able to de-
le specilic gravity,
mty of tlio earth,
h we may imagine
t is brought to tlie
1 there weighed one
>f the earth or any
d and determined

on that onr nnits of
are practically units
e should weigh out
ishington, and then
be less heavy at the
iwe take a pound
hter at the equator,
ih other, and the tea

one pound. Since
R,y by weights which
JO, say Washington,
irorld without being
hich has any given
d in lihis way, have
r place, although its
ring bdance or any
ictusl weights were
> weight of the same
I part of the earth to
t use this sort of an

of metal which are
>W8 that what we call

lat^l bodies around
ti« earth. Aoectt^Bg
isaey is not simply a
tre of the eartii, but
lie f oroes Mrinng frrai

the attractions of all the separate parts which compose the
earth. The question may arise, how do we know that each
particle of the earth attracts a stone which falls, and that
the whole attraction does not reside in the centre ? The
proofs of this are numerous, and consist rather in the
exactitude with which the theory represents a great mass
of disconnected phenomena than in any one principle ad-
mitting of demonstration. Perhaps, however, the most
conclusive proof is found in the observed fact that masses
of matter at the surface of the earth do really attract each
other as required by the law of Newton. It is found, for
example, that isolated mountains attract a plumb-line in
their neighborhood. The celebrated experiment of Cav-
endish was devised for the purpose of measuring the at-
traction of globes of lead. The object of measuring this
attraction, however, was not to prove that gravitation re-
sided in the smallest masses of matter, because there was
no doubt of that, but to determine the mean density of the
earth, from which its total mass may be derived bj simply
multiplying the density by the volume.

It is noteworthy that though astronomy affords us the
means of determining with great precision the rdaUve
masses of the earth, the moon, and all the pknets, it does
not enable us to determine the absolute mass of any hea-
venly body in units of the weights we use on the earth.
We know, for instance, from astronomioal rasearch, that
the son has about 828,000 times the mass of the earth,
and the moon only ^ of tiiis mass^ bat to know the abso-
lute mass of either of them we must know how many
kili^rams of matter the eardi contains. To d^ermine
this, we mi^ know the mean douity of the earth, and this
is something about which direct observation can give us no
inf<Mtnation, btieanae we cannot penetrate mora than an
ioaigiiiiaait distaBoe nito the earth's interior. The only
way to detecmfaie the density of the earth is to ifind how
mnflb matter # mart oonteia in order to attract bodies on
itesnrfaeawttd^alerae eqnalto their observed weight^

lOS

ASTRONOMY.

that is, Mrith such intensity that at the equator a Inxly sliall
fall nearly ten metres in one second. To find this we
must know the relation between the mass of a body and
its attractive force. This relation can be found only by
measuring the attraction of a body of known mass. An
attempt to do this was made by Maskelynr, Astronomer
Royal of England, toward the close of the last century,
the attracting object he selected lieing Mount Sohehallien
in Scotland. The speciiic gravity of the rocks com])osing
this mountain was well enough knoMm to give at least an
approximate result. The density of the earth thus found
was 4*71. That is, the earth has 4.71 times the mass of
an equal volume of water. This result is, however, un-
certain, owing to the necessary uncertainty respecting the
density of the mountain and the rocks below it.

The Cavendish experiment for determining the attrao-
tion of a pair of maasive balls affords a much more perfect
method of determining this important element. Thd
most careful experittients by this method were made by
Bailt of England about the year 1846. The essential
parts of the apparatus whidi he used are as follows :

A long narrow table T'bearatwo massive spheres of lead
W Wy one at each end. This table admits of being
turned around <m a pivot in a borixontal direction.
Above it is suspended a balance — tliat is, a very light deal
rod e with a weigh!' at each end suspended horisontally
by a fine silver wira or fibre of silk FE. The weights to
be attracted are attached to each end of the deal rod. The
right-hand (me is visible, while the other is hidden be-
hind the left-hand weight W. In this position it will be
seen that the attraction of the weights W tends to turn
the balance in a direction opposite that of the haodl <rf a
watoh. The fact is, the bahuiee begins to tarn in tUs di-
rection, and being carried by its own niomentmn beyond
the point of cqnilibrinm, comes to vest by a twist ^ the
thread. It is then carried part of the way back to its
original position, and thus makes several' ▼ilM«lions>iliiali

Ifi

DBNsrrr of tbb barth.

I equator a l»ody sliall
d. To find this we
) mass of a body and
jan be found only by
)f known masa. An
iKKLYNK, Astronomer
) of the last century,
ig Mount Sohehallien
I the rooks comiMwing
wn to give at least an

the earth thus found
:.71 times the mass of
■esnlt is, however, un-
rtainty respecting the
ks below it.
etermining the attimo*
\ a much more perfect
rtant element. Thd
neihod were made by

1846. The essential
d are as follows :
nassi ve spheres of lead
able admits of being

horisontal diraotioii.
at is, a very light deal
nupended horiiontally
FE. The weights to

of the deal rod. The
e other is hidden be-
this position it will be
l^ts W tends to turn

that of the hao^ of a
igins to tarn in this di-
rn niomentnin beyond

test by a twist of the
)f the way bsok to its
)vent' ilb^oBS mliioli

require several minutes. At length it comes to rest in a
position somewhat different from its original one. This
position and the times of vibration are all carefully noted.
Then the tahle T is turned nearly end for end, so that one
weight TT shall be between the observer and the right-
luuid ball, while the other weight is beyond the left-hand
ball, and the observation is repeated. A series of observa-
tions made iu this way include attractions in alternate di«

na. 61 .

reotions, giving a result from which accidental errors will
be very nearly eliminated.

A tibird method of detenniiiiag the density of the earth
is fo i iidM d on obserraljons 4Mbe <^H"^ ^^ ^^ intensity
of gmntf as we descend Wkf*f the snrfaoe into deep
mines. Hie prinmples on wfa^^is method rests will be
«q[>lil|lifl presoitly. The most^||^rBfal tpfdiostion of it
liide hy Thnhmm Aist in tj||| j^srton Colliery, Ing-

194 ABTR0N0M7.

land. The results of this and the other methods are as

follows :

Oavbitoish and Hution, from the attraction of balls, 5-32

R«'C«' „ a « 6. 66

nl'sKkYNB, from the attraction of Schehallien 4-71

AiET, from gravity in the Harton Colliery «-66

Of these different results, that of Baily is probably the
best and the most probable mean density of the earth is
St H times that%f water. This is more than double
the mean specific gravity of the materials which compose
the surfaced the earth ; it follows therefore, that the in-
ner portions of the earth are much more dense than its
outer portions.

82. LAWS OF TMRBB8TBIAL OBAVITATIOir.

The earth being very nearly spherical, certain theorems
respecting the attraction of spheree^may be »ppUed to it.
ThPf undamental theorems may be regwded asj^ose
which give the attraction of asphencal shell of matter.
The demonstration of these^Aeorems inquires the tise of
the Integral Calculus, and will be omitted here, wily the
i^dhioTand the results being rtated I^t usjien im-
agine a hollow shell of matter, of which the «»ten»^ «^
eSemal surfaces are both spheres, attnustmg any o^«
masses of matter, a small particle we may suppose. Ttaj
^e will be attracted by every partide of the A^
SSaforce inversely as Ae.qu«e of itedj^«m It

The total attraction of the shd^ wiU ^e^he ««d^^
this infinity of separate •*«J~«7«/°'^ .^T^
this reAultimt by the I»t«KnJi^«»*"*\"^^ /TS^Jffl

cetOrated in itt centre. .... .j^rf^^iji ihsMh

ATTRAVTION OF 8PHRRE8.

195

lior methoda are aa

iction of balls, 5.32
i( <« 5-58

t( « 5-66

hehaUien 4-71

iiery 6*66

AiLY is probably the
isity of the earth is
is more than double
rials which compose
beref ore, that the in-
more dense than its

, aBAVITATIOli'.

ioal, certain theorems
may be applied to it.
e regarded as those
ioal shell of matter,
ui requires the use of
mitted here, <mly the
»d. Let UB thai im-
rhich the internal and
, attracting any other
e may suppose. This
r particle of the shell
ot its distance from it
ill be the nwdtMit of
forces. Detenmning
lnB,iiiafonnd4liat:

p the JM wre cm-

ponte attraeiiong in every direction vnU neutralize each
(tther, no matter whereahout* in the interior t/ie particle
may be, and t/ie resultant attraction qft/ie s/iell will there-
fore be zero.

To apply tliis to the attraction of a solid sphere, let us
first suppose a body either outside the sphere or on its sur-
face. If we conceive the sphere as made up of a great
number of spherical shells, the attracted point will be ex-
ternal to all of them. Since each shell attracts aa if its
whole mass were in the centre, it
follows that the whole sphere at-
tracts a body upon the outside of
its surface as if its entire mass
were concentrated at its centre.

Let us now suppose the attract-
ed particle inside the sphere, as
at Py Fig. 66, and imagine a
spherical surface P Q conoeutric
with the sphere and passing
through the attracted particle.
All that portion of the sphere lying outside this spherical
surface will be a spherical shell having the particle inside
of it, and will therefore exert no attraction whatever on
the particle. That portion inside the surface will con-
stitute a sphere with the partide oi| its surface, and will
therefore attract as if all this portion were concentrated
in the centre. To find what this attraction will be, let us
first snppoee the whole sphere of equal dennty. Let us
pat •>

Oj the radius of the entire sphere,
r, the diptanoe P Cot the particle from the centre.
The total volume of matter inside the sphere jP Q will

then be, by geemetiy, j jr r*. Dividing by ihe square of

Vto. M.

the (^stattoe r; we
sented hj

that ti)e attraetion will be re^e-

i i iili < s u t w i> iu aWMWBa

*ttm

J96 AamoNOMr.

that is, inside the sphere the attruction will be f Jf^'^y "

•6

■>ra.

Onteide the surface the whole volume of the sphere 3 »r «'
will attract the particle, and the attraction will be

— TT — ;•

3 r"

If we put r = a in this formula, we shall have the same
r«mlt is before for the surface attraction.

uJ iL nexr.«pp«« that the density of the sphere va-
riilmrllJnrits surface, b«t in Buch aw^y as o
wTnanal at equia distances fnim the centre. We may
SL^^^iv^Jit as formed of an infinity of concentric
^eSldU«Lh homogeneous in density, but not of

2>, the mean density of the .hell outside the pa^^^^^
/)', the mean density of the porUon F Q mside of /-.
We shall then have:

Volume of the Bhell,,^^ « («* - O-

Volume of the inner sphere, ^ « t'.

Massof theshell = vol.x/) = |'ri>(a'-0-

Mass of the inner sphere = vol. x 2>' = g 'f -^ ♦'•
M^ofwholesphere^tomofm^-eaofAeUandinner

«phe«=|'r(2)a'-|-(i>'-i>)4

ATTH ACTION OF SPUKRKa.

197

•n will be directly a»

centre. If the par-

aiid the attraction ia

e of the sphere g»r a
action will be

> Bhall have the aame
iCtion.

Bity of the sphere va-
Bt in Buoh a way as to
the centre. We may
1 infinity of concentric
in density, but not of
Theorems I. and II.
It will not be the same
>here for a particle in-
. 66, let US put
outside the particle P.
■tion P Q in«de of P.

1.x 2>' = |'r />'»'.
manes of ahell and inner

Attraction of the whole sphere upon a point at its snr-

Attraction of the inner sphere (the same as that of the

_ Mass 4 -y
whole shell) upon a pomt at /' = -p— = g ^ x/^ »*•

If, as in the case of the earth, the density continually in-
creases toward the centre, the value of />' will increase
also as r diminishes, so that gravity will diminish less
rapidly than in the case of a homogeneous sphere, and
may, in fact, actually increase. To show this, let us sub-
tract the attraction at P fiom that at the surface. The
difference will give :

Diminution At P = ^ir {Da+{iy - D)-^ - D' r).

Now, let us suppose r a very little less than a, and put
r=:a —d,

d will then be the depth of the particle below the surface.
Cubing this value of r, n^leoting the higher powers of
d, and dividing by a*, we find,

Substituting in the above equation, the diminution of grav-
ity at P becomes,

.., (SD'-ilTid.

We see that if 8i> < 32>', that is, if the density at tiie
surface is leas than f of the mean density of the whole in-
ner mass, this qvantity will beoome negative, showing that
the f oroe of gravity will be less at the surf atia than at a
small depth in the interior. But it must ultimately
diminish^ because it is necessarily aero at the centre,
tt was on this principle that Professor Airy determined
the density of the earth by oomparing the vibrations

108

ASTRONOMY.

of a pendnlnm at the bottom of the Harton ColUery, and
at the Burface of the ear h in the neighborhood. At the
bottom of the mine the pendnlnm gained about 2*. 6 per
day, showing the force of gravity to be greater than at the
Burfaoe.

8 8. nouBi Airo MAOirrruOT of th« sabth.

If the earth were fluid and did not rotate on its axia, it
would aBBume the form of a perfect sphere. The opinion
is entertained that the earth was once in a molten state,
and that this is the origin of its present nearly spherical
form. If we give such a sphere a rotation upon its axis,
the centrifugal force at the equator acts in a direction op-
posed to gravity, and thus tends to enkrge the circle of
STequator. It is found by mathematical analysw that
the form of auch a revolving fluid sphere, supposing it to
be perfectly homogeneous, will be an oblate ellipsoid— that
is, all the meridians will be equal and similar elbpses, hav-
ing their major axes in the equator of the sphere and their
ndnor axes coincident with the axis of rotation. Our wi^,
however, is not wholly fluid, aad Ihe wMty ol ita oonti-
nents prevents ite asraming the Um it ▼onWtake if tibe
ocean covered its entire surface. When we speA of tiui fig-
ure of the earth, we mean, not theoi^e of the ^ Hid
liquid portions respectively, but the figure whieh it wwW
assume if its entire surface were an ocean. Let wim^ffP
eanakdug down to the ocean level in every aire«ioa
through the eontineota, and the water of JheoeaM to^be
adnrfSed into them. Then the onrted surlloe toutihtog
the water in all these oanab, and ooliloideiit wi&^the ■»-
face of the ocean, is that of the ideal earth conaldewd*^
Mrtronomers. By the figure of the e«*h » meant ^
figure of this liquid surface,without refereneetothem-
equalitiesof thesoUdsurfaoe. „, «
We cannot say that this ideal earth is a perfeet eiUpM»ia,
beoanaewe know that the interior ia not homogiBeoBi,

■ . .t ' tMimm^ ' f tim mm

MRAHUBMMENT OF THE BAHTH.

199

larton Colliery, and
ghborhood. At the
lined about 2* -5 per
B greater than at the

OF THS SABTH.

i rotate on its axis, it
phere. The opinion
30 in a molten state,
sent nearly spherical
utation upon its axil,
tcts in a direction op«
enlarge the circle of
mati(»l analysis that
phere, supposing it to
oblate ellipeoid— that
I similar ellipses, hav-
f the sphere and their
rotation. Our earth,
e solidity of its eonti-
a it would take if the
en we speak of the %-
Ddhte of the solid and
fipire whidiii would
eean. Lei v»imi#Bbe
el in evety diradtkm
\iBttA theooeaa to he
nred svrfioe ton^iiig
^ddent with the snr-
»! earth eoiindered by
e flttdi is mesnt ih»
at ref««nee to tlie in-

b is a perfect elUpM»ld,
: is not homcfeaMMM,

but all the geodetic measures heretofore made are so nearly
represented by the hypothesis of an ellipsoid that the lat-
ter is considered as a very close approximation to the true
liguro. The deviations hitherto noticed are of so irregu-
lar a character that they have not yet been reduced to any
certain law. The largest which have been observed seem
to be due to the attraction of mountains, or to inequalities
of density beneath the surface.

Method of Ttiangulation. — Since it is practically im-
possible to measure around or through the earth, the mag-
nitude as well as the form of our pknet has to be found
by combining measurements on its surface with astronom-
ical observations. Even a measurement on the earth's
Hurface made in the usual way of surveyors would be im-
practicable, owing to the intervention of mountains, rivers,
forests, and other natural obstacles. The method of tri-
angubtion is therefore miiversally adopted for measure-
meuls extending over hu^ areas. A triangnlation is ex-
ecuted in the folbwing way : Two points, a and (, a few

nuiea q^wt, an ntooled m the e«traniti« of • bwe-UiM.
They most be so ehosm that thebr distanee apwt ean be
aoMMliity meimred by rodi; ^ intorvoaing ground
shooiiiittoMfora be as level and fk«e f nAn obstruction as
poiJJili Om or mora etevated points, J'j; ete., must
be ^bttld Itoot one or hiifc ends of iSa^ bese-Iiiw. ^~

mmrnttm

800

ASTROyOMT.

means of a theodolite and by obwrvatlon of tl»o polo-Btar,
the dlrectionB of these points relative to the meridian are
accurately observed from fih end of the base, as ii» also
the direction a A of the baie-lino itself. Suppose i^^ to
be a point visible from each end of the Imse, then in the
triangle abFvio have the length a h determined by actual
measurement, and the angles at a and J determined by ob-^
servations. With those data the lengths of the sides aF
and hFKm determined by a simple trigonometrical com-
putation.

The observer then transports his instruments to F^ and
determines in succession the direction of the elevated
points or hills DEO HJ, etc. He next goes in succes-
sion to each of these hilhi, and determines the direction of
all the others which are visible from it. Thus a network
of triangles is formed, of which all the angles are observed
with the theodolite, while the sides are successively calcu-
hited trigonometrically from the first base. For instance,
we have just shown how the side a J* k calculated ; this
fonns a b«n for the triangle EF^, the two remaining
aides of whioh wt ooouMtoO. Hm aid* Xf fonns the
biw of the triaai^ OBF, fho dite of wMoh aro cakm-
liifeed, efee. In tiife qpente now aa^ aie obMired
thm ai« theoratieaOy aeeMMiy to edenlrto tlw trianglea.
Tbb amplw of ai«» Mrrca to teroia <Im doiMlion of any

«K|on in «lie MMHwa, iokl to t«rt OmDt amtMej \ij the
9mvuaetAiAt^tmiS»M. AoeuMlalfaig «mc« tie fvr-

time to tiDM •• oppertttBitj oAnk

Ohaino oi triangles have thus been meanired in Buaiia
from the Danube to the Arctic Ocean, in England and
Fimnoe from the Hebrides to Algien, in this oountiy down
nearly onr entuw Athmtio coaat and along the great lakes,
and through short distanoea in numy other boontriea.
An east and west Ihie is now being run by the Coast Sur-
vey from the Atlantic to the Pacifie Ocean. Indeed it
may be expected that a network of triaaglM will bo gmd-

MAONITUDB OF THK KARTU.

301

»n of tliu polu-star,
o the meridian aro
tho base, as iii aim)
If. Buppoms F to
u iNune, then in the
)tennined by actual
h detennined by oh-
lis of the sides a F
rigonometrieal coiii-

trnments to F., and
)Q of the elevated
text goes in succes-
ines the direction of
Thus a network
angles are observed
e successively oalcu-
iMse. For instance,
' la calculated ; this
the two remaining
id* XJF fonu the
of wUdh wo oalen-
ia|^ are dwerved
0iilito tha triangles.
Om deieetkMi of anjr
kflk MeunejVthe
liHag CROI* ue fmr-
AdikimMAiUeiiram

meMured inBuadla
Mtt, in England and
in thia oonntry down
long the great lake*,
iny other bonnkiiea.
in by the Ooert Snr-
B Ooean. Indeed it
rianglea will be gnd.

MUOH

ually extenchid «>vor tho snrface of every civillxod country,
ifi ordur to conBtfliot perfect maps of it.

Siippoflo that we taka two stations situatod north
and south of each other, deterinino tho latitude of each,
and measure the distance between them. It is evident that
l>y dividing the distance in kilometres by tho difference of
latitude in degrees, we shall have the length of one degree
of latitude. Then if tho earth were a sphere, we should
at once have its circumference by multiplying the length
of one degree by 860. It is thus found, in a rough way,
that the lengtli of a degree is a little more than 111 kilo-
metres, or between 69 and 7U English statute miles. Its
circumference is therefore about 40,()00 kilometres, and
its diameter between 12,000 and 13,000.*

Owing to the elliptioity of the earth, the length of one
degree varies with the latitude and the direction in whioh
it is measured. Tlie next step in the order of accuracy i>
to find tha nia|;nitnde and the form of the earth from
measures of hng aroi iA laiitnde (and aometimea of longi-
tude) made ini Afferent regions, eqiedally near the equa-
tor and in M^ latitodes. Bnt we shall still find that dif -
ferent oombinaiions of measnrss i^re slightly different re-
sults, hd0k for the ni4piitnde and the eUiptidty, owing
to the iiMilaritias in the Section of attraction whioh we
have alftaly disoribed. ^m pcoblem is therefore to find
what el%iioid will wMtj ^ inaaMms with fha least sum
total of mw. Kaw and more aatmrata sohtlons will be
reached fiom time to time as geodatie measorss are extend-
ed over a wider area. The following are among the most
recent results hitherto reached: Listuto of Gdttiagen
in 187S found tbo earth's pokr semidiameter,6866 •270 kilo-

* Wim the metric qrstm was origiiuaiy designed by the Franoh. It
waswiMedtiMtthe kUooMtra rtMuU be Tii«9 of the dbtanoe from
the pgis of dearth to the equator. This would make a dogree of the
iMNn«»,t»inikiloaMtNo. Bat.owfaiftotte
loC WMMBiiaff a awridka of the earth, the oetf»>
I with tbs BMtn aetodljr adopted is not exact.

202 ABTBONOMF.

metres; eartli's equatorial Bemidiameter, 6377-877 kilo-
metres ; earth's compression, j^ of the equatorial di-
ameter; earth's eccentricity of meridian, 0.08319. An-
other r4nlt is that of Captain Clarke of England, who
found : Polar semidiameter, 6356-456 * kilometres ; equa-
torial semidiameter, 6378.191 kUometres.

It was once supposed that the measures were shghtly bet-
ter represented by supposing the earth to be an elhpsoid
with three unequal axes, the equator itself being an elhpse
of which the longest diameter was 600 metres, or about
one third of a mile, longer than the shortest. Thisrescdt
was probably due to irregularities of gravity m those parts
of the continents over which the geodetic measures have
extended and is now abandoned.

ae<,gt»phio and Geooentrio L»tltudei. -An obviouB re-
sult of the eUipticity of the earth is that the plumb-lme

does not point toward the earth's oentee. Jf^'f^
represent a meridional section of the earfh, ^^^^2
axis of rotation, JEQ the plane of ^J^^* «f^ ^
position of the observer. The Une MS, trogent tcr tte

beentdBenasft.tflOOTi.

■ i)imuu ' Li i j ii iL i .iii i .u iiw ti»mwjj liii imw ' w i u

mMN

MhMck

FOmB OF OBAVITT.

ter, 6377-377 kilo-
)f the equatorial di-
ian, 0.08319. An-
LE of England, who
* kilometres ; equa-
res.

roB were slightly bet-
ii to be an ellipsoid
tself being an ellipse
>00 metres, or aboat
liortest. This result
jravity in those parts
detic measares have

idM. — An obvions re-
that the plumb-line

earth at 0^ will then represent the horizon of the observer,
while the line Z jV', perpendicular to B B, and therefore
normal to the earth at Q, will be vertical as determined
by the plumb-line. The angle O JV'Qy or ZO Q\ which
the observer's zenith makes with the equator, will then be
his astronomical or geographical latitude. This is the lat-
itude which in practice we nearly always have to use, be-
cause we are obliged to determine latitude by astronomical
observation, and not by measurement from the equator.
We cannot determine the direction of the true centre of
the earth by direct observation of any kind, but only that
of the plumb-line, or of the perpendicular to a fluid sur-
face. ZOQ' ia tiierefore the astronomical latitude. If,
however, we conceive the line GOz drawn from the cen-
tre of the earth through 0, z will be the observer's geo-
cmtrio tmkhj while the angle O CQ will be his geoom-
trie latitude. It will be observed that it is the geocentric
and not the geographic latitude which gives the true posi-
tion of the observer reUtive to the earth's centre. The
difference between the two latitudes is the atigle CO If'
or ZO0; this is called the an^<2<^M««0r^»oa{. Itiszero
at the poles and at the eqnatw, because here the normals
pass tlm>ngh the omtre of the dlipse, and it attains its
maximum of 11' 80' at ktitode 46**. It will be seen that
the geocentric Ittdtnde is always less than the geographio.
In north latitudes the geooentrio Mi^th is south <xf the ap-
parent ioiitii and in southon kulltndes n<«tlk oi it, being
nearer the equator in each case.

centre. Let Fig. 6$

.earth, JV^iS bong the

le equittHT, and O the

MSy tMigent tir the

Mk, tiM polar mdlHB M«

g 4. casujxQM or OBAV iro wins tbm "lkti-

If flwanfbwena p«rf«ctq^wra, and didnol rotate OB its azta,tl»e
iateatl^ of gnvil^ would be tile iaiiieovw its oitinmvfso^ llwra
baiNibivarialJkMiftom two OMues, Moiely, (1} The dtt]^ fom
of enr dlflbe, and (n the entrifiMal ftoras flmuMted bv its rotatina
OB Hh «ds. eUgkOj fuMng. Ow latterli aot a ebHige in tike
real fpiM of gtvmj. « of u» earth's sMnetiiHi, but onl^ aa
appaMHt forae <rf aaMMr IdaA aettait in oppedkloii to gmvity.

— iii iii ijM H i m ji i i , l ui i imiiiiiaMi

304

ASTRONOMY.

The intensity of gravity i« mewured by the dirtance "Wch »
heavy bodyin a vacuum Will fall in a unit of time, «ay one second.
eS 10 metres or 82 feet may be regarded as a ^ugh approj™.-
Son to its value. There are, however, so many practical difflcol-
iS in the way of measuring with precision the distwice a body
fS, ta one second, that theWe of gravitv is, in Vf»^^\^^-
Xed indirectly by finding the lengtl of tlie »f?»^J^. I?"3^
uL shown in mechanica that if a pendulum of length ^ vttarrtes
in a tSrV a heavy body will in this time T fall through the
^TL,n beingSe ratfo of the circumference of a drcle to it.
Keter. '(.r=8.f4169 . . . ,r'=».86eM4.) Therefore, to find fte
force of gravity we have only to determtoe the length of the
gecond's Mndulum, and multiply it by this factor.

The drtermination of the mean attractive force of the wrfh is
Important in order that we may compute its -ctlon on Oiemoon
Srother heavenly bodie.,whife the variation oj »"» «""«J»°
afford us data for judging of the variations of denrity in the wth s
Sterio?^ Sentifio Seditions have therefore taken pains to
d^Vndne thelength of *Se «)cond's pendulum «*»«»»•««» P^*»

Snirglobe. ^ do tWs, it is °»t "r^.lV'^L nS^SJJ
actually measure the length of the pendulum at all *!»« P*^ »«?
visit. They have only to carry some one pendulmnof • ▼e^ ■»«»
oonstruction to each want of observation, and observe how many

SSSTS mri.es inTday. 7^^ '^""HJ^/lSSi' ?!&
ia proportional to the aooare of the nmnber of '^^'^^^^'°^
maiSter the voyage, they count the vibrations •* jwine "tonoard
Sinf-li»Sn fSSitoiiw. Thua, by simply «uariiigthe»nm^r
5f vibratiomi and comparing the squares, ti»ey hj^f ^«<J»
vridch gravity at varioaTpSnta of «he earth's surface bewrs to
JSSy™l2ndon. » ia'tiien only necessary to ^t««in^
SSeolute intenrfty of gravity at London toinfer It at aU the
StSr points for which the rrtio is known. From • «««» ™»S
S SJSrvatiomi of tills kind, it is fimnd timt tiie feigth of ^
second's pendulum in Uititude ^ may be nearly repiweiited by tiie
equation, , , ^

£ = ()•• W<>W(1 + 0-006»9 mnV).

Prom this, the force of gravity is found by mnltipiyiiig bj
ir* = 9-86M, giving the result :

y' = 9--7807(l +0-0M808ln**).

Tliese formuhe show that the awperent force of gravity iooeaeM
bv a Sle SiTthan ^ of its wteto aiiMmnt from the jWMjorto
ge X m cTrSllly caicuWe bow »««» •? ^?^«^
at the eouator is due to the oeutrifiigal f«ce of the eeim a (OwMa.
By^^rtSL of mechanic tiie Mutrifugri force is given by the
eqmtion,

.wuiiftiiimn i

TBBRS8TRIAL GRAVITY.

205

the distance which %
time, aay one second.
IS a rough approxima-
any practical difHcul-

the distance a body

is, in practice, deter-
le second's pendulum,
n of lensth L vilnrates
ae T fall through the
irenoe of a circle to its

Therefore, to find the
ae the length of the
actor.

e force of the earth is
to action on the moon
ions of tUs attraction
>f denidty in the earth's
lefore taken pains to
Imn at numerous pointa
isary that they snould
a at all the places they
mdnlmn of a very solid
and obsenre how many
tiat the force of gnvity

of TihratioBi. Before
tions at some standard
dy squaring the number
i, they have the ratio
■rth's snrfaee bears to
Mary to determine the

to infer it at aU the

From a gnat number

that the feigth of the

larly repraaeated by the

iBinV).

md by mnltiplyiBg bf

lain**).

'orce of gravity inenaiea
«nt frov tiie equator to
moett of the dio^iatioa
ie of the ewrth'a fOtaAk^
igalfcHroeisJI^raibythe

T beinir the time of one revolution, and r the radius of the cirole of
STtton. Supposing the earth a Bphe«, J'Wch will cause no
KoSnt errifin our present calculation the distance »' » P^J"*
SiKiith's surface ii latitude ^ from the axis of rotation of the

A being the earth's radius,
therefore

The centrifugal force in latitude f is

4«*acoBf

But this force does not act in the direction non>»» ^*^,«^|''?
surfiS: but perpendiciUar to the axis of tiie earth, which direction
mlk^he anSe ♦ with the normal. We may therefore resolve the

SSb iitS Xd-Tponento, "f./'^V''^""* *««^'»iSi're
toWard tiie equator,^e other./ coa ♦, downward toward He centre.
STe "rat component makes the earth a P~««te e»«P^ "iKS
shown, while the second acta in «PP«««Jo° *»,F»'S;.«t
^Sug^ force, therefore, dfaniniahes gravity by tKe amount,

/cosf =

iir'acoa*^

T the sidereal day, is 86,164 seconds of mean time, while o, for
Se eJJSTi. M77.877 metres. Substituting in this expresdon,
the oentrifngri forc«» becomes-

/co»f = 0-088»lcoa« f =0-.08«»l (1 -sin*^),

or .t the equator a little more than Hw A* 'o**" ° uf «ffi; J2,*
S^niionlorthe apparent foree o*„««~:»*y SI fa^
which we have alreiSfyfound, may be put in flie form,

/ =»-.T807 + 0».0BO87ain»f.

This is the true force of gravity diminished by the «»«trifu«l
SS>rthereftore, to find that true fbree we muatadd the centri.
f 1^ foree to it, giving the reault :

a = 9*-8146 + 0--01696ehiV
= 9-.8146 (1 -I- 00017<8sbi*f),

for tiie i«al attraction of tiie sphiiroidal earth upon a body on ita
aorfiaBe in latitude f .

It Witt be iBta^*l«to oompwe thfa »^tt.r?L*%?^?^
a hftvtog the I

ofa«Bb«Nidhft^--
by labgn^fiott tiial if «,

letU

idty aa the ea»:h. It is fbond

small, be the eoeeatridity v/l a

aad 9* ita attfaction,apoB a body

SLutSSMMiahiatit •mpB^ "rf »• «• attfactioii,«poB a body
STSS^rfSf^'SSK'.^ fwiU be given by the

,:;,„0 + f-dnV).

906

ABTRONOMT.

V^0* = OOOO667; m that

In the caie of the earth, « = 00817
the eipresrion for gravity would be,

9 = 9. (1 + 0000667 sin*^).

We see that the factor of aln* ♦, which expresses the ratio in
which cravity at the poles exceeds that at the eouator, has less than
half the value (001780), which we have found from observation.
This difference arises from the fact that the earth is n^ hooiogenu-
ous, but increases in density from the surface toward the centre.
To see how this result follows, let us first inquire how the earth
would attract bodies where its surface now is if its whole mass
were concentrated in its centre. The distance of the equator
from the centre is to that of the poles from the centre as 1 to
VT^^. Therefore, in the case supposed, attraction at the equator
would be to attiM^on at the poles t»\—f to 1. The ratio of in-
crease of attraction at the poles is therefore in this extreme case
about ten tfanes what it is for the hoDKwenoous elUpsoid. We oon^
dude, therefore, that the more newly Oie earth approaches ttjfa
extreme case— that is, the more it increases u denrity toward the
centre— the greater will be the dffierenoe of attraction at the poles
and the equator.

8 6. isxynas or thh sabtipb axis, ob pre-

GBBSIOir OF THX aQXTINOXBS.

Sidanal and Bquinoctiia TeMr.— In describing the ap-
parent motion of the sun, two ways were shown of find-
uig the time of its apparent revolntion around the sphere
—in other words, of fixing the length of a year. One of
these methods oonnsts in finding the interval betweeM snc-
oestiTe passages through the equinoxes, or, which is the
game thing, across the plane of the equator, and the other
by finding when it returns to the same positiw among
the Stan. Two thousand years ngft, Hippabohos found,
by comparing his own obaervationa with those made two
centuries before by Timoohabis, ttit these two methods
of fixing the length of the year ^ not gbe the iame
rendt It had preTioody beeo ^iso^dflrad ilw* the teqgth
of a year was about 86^^^ "ad inattemptiilgtoooR«nt
this period by oomplinng hk obnrvsd tinifla of the snii*i
poBBhig tiw equinox with those of Tonoiuaii, Hippab-
oHus found that it required a diminution of seven or tif^t

■muMMMaXMM

iNMMMeaWM

LBNOTB OF TBS TEAK

207

= 0000667; ao that

expresses the ratio in
equator, has leas than
ina from observation,
irth is not hodiogenu-
Be toward the centre,
inquire how the earth
r is if its whole mass
tance of the equator
a the centre as 1 to
traction at the equator

1. The ratio of in-

1 in this extreme case
}us elUpsoid. We con-
Mth utproachea this
in denuty toward the
attraction at the poles

AXIS, OB FBB.
irOXBS.

describing tlie ap-
rare shown of find-
around ihe sphere
of a year. One of
iterva] between snc-
38, or, which is the
lator, and the other
me po8iti(Hi among
HiPPABOHVs found,
th those made two
thieae two nMlhodB
not gire ibe iame
Brad ilipt the tei^
ttempliii^toooniDQt
1 tinwi n/t tile nmV

ion of seven or ei|^t

minutes. He therefore concluded that the true length of
the equinoctial year wa» 366 days, 6 houre, and about 63
minutes. When, however, he considered the return, not
to the equinox, but to the same position relative to the
bright star Spica Virginis, he found that it took some
minutes more than 366i days to complete the revolution.
Thus there are two years to be distinguished, the ^opioal
or eqmnoctial year and the sid^eal year. The first is
measured by the time of the earth's return to the eqmnox ;
the second by its return to the same position relative to the
Stan. Although the sidereal year is the correct astronom-
ical period of one revolution of the earth around the sun,
y«t the equinoctial year is the one to be used in civil life,
^boKom it is upon that year that the change of seasons
vdepends. Modem determinations show the respective
lengths of the two years to be :

Siderpa' year, 866*6* 9» 9* = 366*. 26636.
Equinoctial year, 866* h^ 48- 46' = 866-.24220.

It is evident from this difference between the two years
that the position of the equinox among the stars must be
changing, and must move toward the west, because the
equinoctial year is the shorter. TWs motion is called the
precemon ^ the eptinomt, and amounts to about M'
per year. The equinox bemg simply the point in which
the equator and the eeliptie intersect, it is evident that it
can change only throu£^ a change in one «r both of these
oirolfis. HwPAWJHTO found that the change ^was in the
equator, and not in the ediptie, beeanse the declinations of
the stars changed, while thrar latitudes did not.* Since

• To dewribe Am ^eoijr of (he ancient astroaaam* wltt perfect
eom^toM. w« ought to aajthfit they ooMldnwl AepteMSbothof the
muimmAmSMto^^ tavailaUe and ths notion of praoesirih» to
tediMtaadBwnviitatlonot th« wholeoslasltaa i|iheN amtad ««
MbotttiMitotfeMaattds. IWs would iitednce achvifi i» ite
^tfttaB«f tteaWMntallvBto As squator, bol aol uMUt te d»

'vmmiim

!i06

A8TR0N0MT,

the equator is defined as a circle everywhere 90° distant
from the pole, and since it is moving among the stars, it
follows that the pole most also be moving among the stars.
But the pole is nothing more than the point in which the
earth's axis of rotation intersects the celestial sphere : it
must be remembered too that the position of this pole in
the celestial sphere depends solely upon the direction of
the earth's axis, and is not changed by the motion of the
earth around the sun, because the sphere is considered to
be of infinite radius. Hence precession shows that the
ydirection of the earth's axis is continually changing.
Careful observations from the. time of Hippabchvb until
now show that the change in question consists in a slow
revolution of the pole of the earth around the pole of the
ediptio as projected on the celestial sphere. The rate of
motion is such that the revolution will be completed in
between 25,000 and 26,000 yean. At the end of this
period the equinox and solstices will have made a com-
plete revolution in the heavens.

Th« natora of thk motioa will be seen nrare oleailj by referring
to F^. 49, p. 100. We have there repneented the earth in four
poaitfons during ite aiwaal revolution. We have repreeented the axis
M inclining to the ri|^t in each of these podtiona, and have de-
aoribed it aa remaining parallel to itaelf durnw an entire revohitioiB.
The i^enonena of preMadon ahow that thia Ii not abaolutely true,
but tnat, in reality, the direction of the axia ia alov^ dttogiiw.
Tliia change is aoch that, after the Iqiae of aone 6400 yeais, %Sm
north pole of the earth, aa re p reaented in the tftuty will aot in-
cline to the right, but toward the obeerver, the Mwrnnt of the in-
elination remaliiing nearty the same. Tbe riault will evidently be
aahiftingoftheaeaaoni. At D we dwU have the winter stris&eau
beeanae the north pole will be iadined toward the obaerver and
tlMrafore from the aun, while at Am ahall have the vetnai equbwx
Instead of the i^rter Mdatiee, and ao on.

In 0400 yeara more the north pole will be incUned toward the
left, and the kaaaooa wiU be reversed. Another intarval of the
aame length, and the north pole will be iaellaed tnm the obsorvsr,
the aeaaona being ahlfted throagh another qnafthuit. fiMlly. ai
die eady abottt 15,800 years, the ask wffl hava rasamid Ita oripMd
direction.

Precearion thus aiisea from a liotlMi of the eaxth akms, aad
not of the heavenly bodies. A Hh Sl g ii tiWtaiwctio«oHheeattt*s
axia cbaagea, yet tiiepaeitkm of this axis relative to the crast <tf the^

rwhere 90** diBtant
unong the stars, it
ig among the stars,
point in which the
selestial sphere : it
on of this pole in
n the direction of
the motion of the
re is considered to
on shows that the
tinually changing.
HipPABCHVs until
consists in a slow
ind the pole of the
bere. The rate of
1 be completed in
it the end of this
have made aoom-

re olflsriy by leferring
ted tlM earth in four
re lepneMtfld the uie
Mitioiu, end have do-
ff an entire lerolntioiB.
le not abeolotely true,
I is elowly daai gin g.
■ome MDO man, iSm
be flgun, will aot in-
the amount of the in*
•ndt will wrideatly be
ve the winter eirisHML
raid the obsenrer and
ire the re»»l equinox

e inclined towaidthe
lother interval tA the
led tnm the obaerrer,

(?• leMBMa ni onpaai

the easth CkM, aad
llnelioB of fhe Mirth's^
Aire to the oniet <rf the^

ii i ii wi mi

PBEGEBaJON.

309

earth remaine inrariable. Some hare rappoeed that pveceirion
would reeult in a change in the porition of the north pole on the
Burfece of the earth, so that the northern resiona would be oorerad
by the ocean h a remilt of the different direction in which the
ocean would be carried by the centrifugal force of the earth ■ rota-
tion. This, howerer, i« a mietake. It hae been shown by a mathe-
matical investigation that the positioa of the poles, and therefore
of the equator, on the surface of the earth, cannot change except^
from some rariation in the arrangement of the earth's interior.
Scientific investigation has yet shown nothing to indicate any prob-
ability of such a change. .... •

The motion of precnsion is not uniform, but is subject to several
inequalities which are called Nutation. These can best be under-
stood in connection with the forces which produce preoession.

Oknae of Fiao— inn, eto.— Mr Isaac Nbwtom showed that pre-
cession was due to an inequality in the attraction of the «m and
moon produced by the spheroidal figure of the earth. If the earth
weie a perfect homogeneous sphere, the direction of its axis would

Vm. 48.

never ehahse in ooMeqaence of the attiaetioa of another body.
BttttheexMSsef natter around the equatorial regions of the earth
isattnwtod by the eun and aMmn in swh a way as to cause a tum-
infff^mewhhsh tends todiaage the dhreetloD of the axis of fote-
£m. Tte show tha mode ofaSon of this foiee, lea us flonsUer the

earth as a sphere eneirelad tar a large ri««f «* ■••^^«?»S'
aionad its equator, sa in Fig. W. SappoM a «^ •^n<*i>«^^
sitnsted ift Oe dlnetiDB cl^ so that &• Hnes la f "•»• ^^J?"**" i*
t 3 ifiw are attneted an Am,Bh Ot^^, wMeh wi M be neariy
paraQdT The aMmetlTa fonM wiU mdoally diminish from .d to
jTmov to t^g>M*v^^**»<» <>'**>* ^'■*^'^'*^ the attractlag
body. Mk us pot : "

r.ttM 4ttstaMMof the (Mrtre C from the attraetfag bodgr.

«! tim ndi^ 4 9 ss S <7 of the equatorial ring, mumBHad 1^ the
co2ue ottfae angle 4 (74^ so that the diatanoe oT^ ftoia the attvaet-
ing eeam is r-*a, and Oat of Jl ia r-f pk

a*. Oe mam «f the attiBotlQg body }

tio

ABTRONOMT.

The MoelerKtive sttnotion exerted st the three point* A, 0, B will
then be

The radiiu p being very iinaU compared with r, we may develop the
denominators of the first and third fractions in powers of -
by the binomial theorem, and neglect all powers after the first,
fhe attractions will then be approximately ■

mp , m

The forces ?^-^ will be very small compared with -j on account
of the smallness of p.
The principal force J will oauM all p«rts of the body to fall

equally toward the attracting centre, «>djrill therefore cause no
r^on in the bodv mmI bo dUaga in tbedinotioa of the •^^JfS.
Supposing the bocfy to wolve anHmd t^,««*" *• "» °^^\7'A
maycon<Sive tl£ii2ttncthm to be oounterbiOMioed by the soHsalled

centrifugal forae.* ^^

Subtracting tUanBifoi«priiicipdfcm»,tli«o la left a force -^

acting on ^ ta the diNetkm Am^uAm wi"^ '««» •«**"» o"* ^^
the opposite dl*«:tloii» A ^\»^i^i^*^»^J^j!;!^^'* ^"^
to mAVthe aarth rotate amad •» •«1»P#»«S!W^ ^^^^^
a direction aa to make the line C il « cofitdde with (Tc, and ttiat,
if no causemodifled the action of these forcea, the earth would os-
cillate back and forth on that axis.

• We may here mention a veiy common mtoaopwhenskm reijecttiig
what is son^timeB called ceptrfrugal force, "J^ "£P«*ft £* J^
fotoe tending to make a body fly awar from Oie oentra. «*• "^
SiSiSd^thebodywllllIyJwni 5»^««lS: :22i,2*!^*5S^
fone eieeeds the centiWa, and •?*?»* •*^*?«J2?*'^-«2S8d
a mistake, such a foroe aa this having no ezlatenoe. t™ *^!C

^JS%^ ia not pnyeriy a ^'''^^'«9^j!S*,Si:^^J^'Sl

S^i^thewhWtagQyaiinrtltocenti^^

thltdlaw €A motion, is eoual and opporite to that IqiM. wmi a aHMie

aary to make tETstone coostantty deviate from the rt ralpht tty^te

■tone offefB to this deviation to oonaejiueBoe id >..i yrtl>^ _PP '.aiS
caae of tiM phmets, tin centrifugal force is «*r tii« iwMaaoe oltewfl
^tiw toXStSe planet to tSeson'e -ttnctfoB. M *• ""WjJSSJ
Sesk.«1tttte sun shouM cease to attract tiio pianM, *« <«S*P*S
^<;)Strifi»l fowea woohl botii ««• tortantlyjjMd^tiie i^iew
Sanrt^oSdTin acconlanoe with the tot kw- d motton. fly f orwanl
b Uie stni^t line to which it was moving at the moment.

p-CTWIi«CTOgjlW»W»W W itl W 8 *IIIWI^^

l>',''jr<tV'*<!'

ii iiiliBiiiiii

ituta: t.

til

IMrfiita^0,J9wUI

% we may derelop the

ons in powers of

owen after the first.

id with -i on account

of the body to fall

ill therefore cause no
MsttM of the axis N8.
eoBtre in an orbit, we
aaoed I17 the so-called

ero is left a force

%mp

fotee Mting on B in
tlMM two forces tend
rfngthioiirii (7 in such
dewith (/«, and that,
is, the euih would os-

opnfaendon respecting
dis supposed to be a
the oeatre. It Is soma-
• when the centrifagal
opposite ease. This is
Jatenoa. The so-called
one at aD. but only the
etalfarae,wfaidi,bylha
•tfoiBe. WhenaelOM
siiiuily the fbrae naofla-
m tM straUit Hae la
ke naisluioewhidlthe
itataiertia. Bo. taithe
ly thA nsfataMe offend
OB. If the sUnK should
^aaat, th« eentrlpetal
voietf, and the atone or
of notioii. lly forwani
hei

But a modifving cause b found in the rotation of the earth on its
own axis, which prevents any change in the angle m C e , but
causes s very slow revolution of the axis N 8 around the perpen-
dicuUr line O B. which motion is that of precession.*

Nutation. — It will liel^n that, under the influence of Ihe grav-
itation of the sun and moon, precession cannot be uniform. At the
time of the equinoxes the equator A Bot the earth passes through
the sun, and the latter lies in the line B Am, wo that the small

Ktcessional force tending to displace the equator must then vaniiii.
is force increases on Doth sides of the equinox, and attains a
maximum at the solstices when the angle m Ce is Mi". Hence the
precession produced by the sun takes place by semi-annual steps.
One of these steps, however, is a little lunger than the other,
because the earth is nearer the sun in December than in June.

Again, we have seen that the inclination of the moon's orbit to
the equator ranges from 18^* to 98^° in a period of 18' 6 years.
Since the preoessioual force depoids on this inclination, the
amount of precession due to the action of the moon haa a miiod
equal to one revolution of the moon's node, or 18*6 years. These
inequalities in the motion of precession are termed ntftojiM.

Onaiisw in the Bight Aaosnaiona and DMUnatlona of
tho Stan. — Since the declination of a heavenly body is ita an-
gular distMice from the celestial equator, it is evident tluit any
change in the position of the equator must change the decUnatiuas
of the fixed stars. Moreover, dnce right ascmsiona are oounted
from the position of the vernal equinox, the change in the position
of this equinox produced by precession and nntaniDn must change
the right ascensions of the stars. The motion of the equator may
be represented by supposing it to turn slowlv around an axis lyimr
in its plane, and pointing to 9^ and 18^ of right aacension. AU
that section of the equator lying within 6^ of the vernal equinox
(see Fig. 4S, page 108) is moving toward the south ^downward in
the figure), while the oppodte swtion, from 6^ to 18^ rioht aacen-
sion, is moving north. The amount of this motion is 80" annually.
It is evident uwt this motion will cause both eouinoxea to shift
toward the right, and the geometrical student will be able to see
that the amount of the shift will be :

*The reason of thisseemingparadox ia that the rotative foroee acting
on A and 17 are as it were m t tr U mUi bgr the diurnal rotatioBanund
N8. SiqKioea, forounniple. that A receives a downward and Jl an up-
ward hnpnlae. so that thqr bq;in to move in these directions. At the
end of twtf ve hoore A ms moved around to B, so that its downward
motioii now tends to iaereaee the aa|^ m (7 e, and the upward motioo of
B has the same effect If wesiqipoeeaaeriesofimpnlMa,adimlBntloa
of the hidiuOion win be prod uc ed daring the first 18 houra. hot after
that tiie effect of eadi fanpolBe wtn be ooontariMJaneed br that of It
hours beion. so that no further diminutioo will take phwe ; but
everv itagalae wiD produce a sodden permaaentdiaage In -the direction
of theaMsJriS, ttesadJf movfa^ toward and 5 fhm« the obaarver.

This same law of rotathm ia exemiriified hi the ajf r oecop e and the
chOd'a top, eadi of whidi are kept ereot by the mmkn, thMgh grav-
ity tsmklo make thsm ftlL

ABTRONOUr

On th« equator, 20" cot w ;

On the ecliptic, 20* coMC M ; . . ^^..^ , «„

u being the obliquity of the ecliptic (88" 274'). In c<.n«equence,
the riSt ascension, of sUrs near the equator are consUntly inoreaa-
inabf about 46" or arc, or 8«.07 of tlilrt- annually. Away from
thi equator the increase will vary in amount, because, owing to the
motion of the pole of the earth, the point in which the equator to
interN»ted by the great circle pasdng through *»« PoJ "jj [J*
star will vary as well as the equinox, it being remembered that the
ri^t ascenrfon of the star to the dtotance ofthto point of interseo-

"•CSeJ? rijhJrical trigonometry will find It «. Improving
exeretoe to work out the formS. for the annual change in tfie right
Mansion and declination of the stars, arising from *>>« "otJon »'
ST equator, and consequently of the equinox. He wiU find the
remit to be ss follows : Put
n, the annual angular motion of the equator («0 W),
«, it«obliqut7(l8'»r.8), ,♦»...♦,.

a », the riffhc ascension and declination of the sU ,
Then we whaU 9nd : , ^ j

Annual change in R. A. = n cot « + n sin a tan *.
Annual change in Deo. = n cos a.

7|'). In cunRequ«nce,
•re consUntly inorcM-
uiniuUy. Awsy from
becauM, owing to the
n which the equator is
i>ugh the pole and the

P remembered that the
thia point of inteneo-

11 find it an improving
ual change in the right
ing from the motion of
loz. He will find the

or (20* 06),

f the ata ;
n a tand.

CHAPTER IX.

CELESTIAL MEASUREMENTS OF MASS AND
DISTANCE.

8 1. THB OBiaBTIAL SOAM OF UMAMTSBMMMKT.

Thr unite of length and maw eniploytd by agtronomer*
are necewarily different from thoae uwd in daily Me.
For instance, the diatancea and magnitudes of tho heavenly
bodies are never reckoned in miles or other terrestrial
measures for astronomical purposes ; wlien so expressed
it is only for the purpose of making the subject clearer to
the general reader. The unite of weight or mass are also,
of necessitv, astronomical and not terrestrial. The maaa
of a body may be expressed in terms of that of the sun
or of the earth, but never in kilograms or tons, unless m
popular language. There are two reasons for this wxune.
One is that in most cases celestial distances have fiwt to
be determined in tenns of some celestial unit— the earth s
distance from the aun, for instance— and it is more con-
venient to retain thia unit than to adopt a new one. The
other is that the values of celestial diatances in terms of
ordinary terrestrial tmito are for the most part extremely
uncertain, while the corresponding values in agronomical
unite are known with great Monracy.

An extreme instance of this is afforded by the dmien-
siona of the solar system. By a long and continued seriea
of astronomical observatloBa, investigated by means of
Kbplmi's Utwa and the theory of gravitation, it is poMMe
to determine the forma of ^ plMie»«|i «Wt% tl^r
poaitions, and th^ dimensiona in terriit^ the earth »

JBMl

214

ABTRONOMT.

mean diiitance from the sun m the unit of meaHiiro, with
great preciBion. It will be remembered that Kki- kk'm
third law enablufl us todetennino the mean diHtAiieu uf a
pbinet from tlio Bun when we know ita period of revolu-
tion. Now, all the major planets, aa far out as Saturn,
have been obaerved through bo many revolutionB that their
periodic times can be determined with great exactness— in
fact within a fraction of a millionth part of their whole
amount. The moi-e recently discovered planets, Urantu
and N^ptwMy will, in the course of time, have their
periods determined with equal precision. Then, if we
square the periods expressed in years and deeimnls of a
year, and extract the cube root of this square, we have the
mean distance of the planet with the same order of pre-
cision. This distance is to be corrected slightly in conse-
quence of the attractions of the pUnets on each other, but
these corrections also are known with great exactncBs.
Again, the eccentricities of the orbits are exactly deter-
mined by careful observations of the positions of the plan-
ets during successive revolutions. Thus we are enabled to
make a map of the planetary orbits which shall be so ex-
act that the error would entirely elude the most careful
scmttny, though the map itself should be many yard* in
octent.

On the scale of this same map we could Uy down the
magnitudes of the planets with as much prednon m our
instrumento can measure thdr anguhr semi-diameters.
Thus we know that the mean diumeter of the sun, m seat
itWD. the earth, is 82\ henoe we deduce from lormul»
^ven in conneetioB with pandbx (Chapter I., § 9)» thai
the diameter of the son is -0098088 of tbe diatanoe «f the
sun from the earth. We ean thwefore, on our WKpfeaeA.
map of the iralar system, ky down the snnr in ita true rise,
aoooidiBg to the sdale of Uie map, horn data given i&ftf&j
by obaervntion. In the aame way we cin do this f<^ e«^
of the planets, the earth and moon excepted. Tb^m^
noimniediate and direet way of finding hot^ large: tie

vxmm

MHiPKMiiS^M

mmm

lit of measure, with
ored that Kki- kk'm
meaii (liBtaiicu uf u
*» period of ruvolu-
far oat as StUum^
'evolutioiu that their
I great exactnew— in
IMrt of their whole
«d planets, Uranut
of time, have their
igion. Then, if we
s and deciinnU of a
square, we have the
) same order of pro-
ed slightly in conse-
ts on each other, but
ith great exactness.
B are exactly deter*
[MMitions of tiie plan-
bos we are enabled to
irhich shall be so ex-
ido the most careful
tld be many yard* in

could lay down the
ncU predsion m our
alar semi-diameters.
Br of the ran, a* teet^
ledttce from lormuliB
Chapter I., 8 9), thai
}f tiie cUitanoe of tiia
sre, on our tmppemA
e miL in iti true iriie,
m data given ^i«elhr
seindothisloreiw

exoepted. Tksm^
)ding how >rg« tk>B

CBLK8TIAL MEA8URE8.

tlB

uarth or moon would look from a ])laiioii;, lionoe the ox-
(^tiptiuii.

But without further spociHl rosoarchJutu thin subjoot,
wu shall know nothing about the »ade of our map. It is
dear that in order to fix the distances or the magnitudes
of the planets according to any terrestrial standard, wo
must know this scale. Of course if wo can learn either
the distance or magnitude of any one of the planets laid
down on the map, in miles or in semi-diameters of the
earth, we shall be able at once to find the scale. But thir
process is so difficult tluit the general custom of astruoo •
men is not to attempt to use an exact scale, but to employ
tiie mean distance of the sun from the earth as the unit in
celestial measurements. Thus, in astronomical language,
we say that the distance of Mercury from the sun io
0.887, that of Vmm 0-723, that of Mar$ LfiiS, that
otSaiiwm 9 '680, and so on. But this gives ns no in-
formation respecting the distances and magnitudes in terms
of terrestrial measures. The unknown qnantitiea of oor
map are the magnitude of the earth on the soale of the
map, and its distenco from the sun in terrestrial units of
length. Oould we only take up a point of observation
from the sun or a planet, and determine exactly the anga>
lar magnitude of the earth as seen from ti>at point, we
should be able to lay down tlie earth of our map in ito cor-
rect sice. Then since we already know the siae of the
effth in terrestrial units, we should be able to find the
soale ol our map, and thenoe the dimensi<ma of the whole
system in terms of those units.

It will be seen that what the aatraiMmier raaUy wants is
not so mueh die dimenatons of the solar system in miks as
to express the liae of the earth in oekatiil roewnres.
Theae, however, Moonnt to the same tUog, beeante hav.
ing !BMS the oHmt can be readily dednoed tnm. the known
maa^tnde of the eM^ in twrpatrial mearaves.

& migidtnde of tlMeafth ia not the <mly onlmown
qnumtHj <m onr map. jj^rom Kanwa'a laws we ean de-

msm

216

ABTRONOMT.

termine nothing respecting the distance of the moon from
the earth, because unless a change is made in the units of
time and space, they apply only to bodies moving around
the sun. liVe must therefore determine the distance of
the moon as well as that of the sun to be able to complete
our map on a known scale of measurement.

S a. MEASUBBS OF THE SOIJkB PAKAT.T.AT.

The problem of distances in the solar system is reduced
by the preceding considerations to measuring the distances
of the sun and moon in terms of the earth's radiiu. The
most direct method of doing this is by determining their
respective parallaxes, which we have shown to be the same
as the earth's angular semi-diameter as seen from them.
In tlie case of the sun, the required parallax can be de-
termined as readily by measuring the parallaxes of any
of the planets as by measuring that of the son, because
any one measured distance on the map will give us the
scale of our map. Now, the planets Ventu and Mars oc-
casionally come much nearer the earth than the sun ever
does, and their parallaxes also admit of more exact meas-
urement. The parallax of the sun is therefore determined
not by observations on the sun itself, but on these two
planets. Three methods of Ending the sun's pandhuc in
this way have been applied, lliey are :

(1.) Observations of Fmim in transit aorofls the sun.

(2.) ObsOTvationB of tiie declination of Mara from
widely separated stations on the earth's nirfaoe.
' (8.) Obt^vations of the right aMension of Jforv, near
the tinMB of its rising and setUng, at a ringle btation.

Solar VKral]axlhiiiiTraiiaita«rV«iva.— The genval
principal of the method of determiniiig the pMallax of a
planet by mmultaneons obeervationa at diatant atatfons
will be seen by referring to Fig. 18, p. 40. If «irQ «!»•
aervem, utnatiBd at S and /S*, make « nntritaanMM «b*
aervation of the direotioii of th» body P, it ia Mffc iw t

■M jj, i ^ai'J.satiaJlfflWWWi> 35gJffi Wm?W ' -^^

!e of the moon from
nade in the units of
dies moving around
aine the distance of
be able to complete
noent.

iB, FABALIiAZ.

ar system is reduced
asuring the distances
earth's radins. The
yy determining their
>hown to be the same
as seen from them,
parallax can be de-
e parallaxes of any
)f the son, because
lap will give us the
VemM and Jdars oc-
h than the sun ever
of more exact meas-
theref ore determined
If, but on these two
the sun's parallax in
ro:

u»it across the sun.
ition of Mart from
I's surface.

en»ion of Jforf, near
a aingle bCa^on.
''•Bua.— The gemnd
^sg the parallax <iC a
■ at dittwt Bti^iiM
(, p. 4e. If Iwo «*-
8 a f^dtanpMi •b>
ody P, it k

TRANSn'S OF VENUS.

217

that the solution of a plane triangle will give the distance
of P from each station. In practice, however, it would
be impracticable to make simultaneous observations at
distant stations, and as the planet is continually in motion,
the problem is a much more complex one than that of
simply solving a triangle. The actual solution is effected
by a process which is algebraic rather than geometrical,
but we may briefly describe the geometrical nature of the
problem.

Considering the problem as a geometrical one, it is evi-
dent that, owing to the parallax of Venus being nearly four
times as great as tliat of the sun, its path across the sun's
disk will be different when viewed from different points of
the earth's surface. The further south we go, the further
north the planet will seem to be on the sun's disk. The
change will be determined by the diferenee betwera the
parallax of Veniu and that of the sun, and this makes the
geometrical explanation less simple than in the case of a
determination into which Only one parallax enters. It
will be sufficient if the reader sees that when we know the
relation between the two parallaxes — ^when, for instance,
we know that the parallax of Venus is 3*78 times that of
the sun — ^the observed displacement of Venus on the sun's
didE will give us both parallaxes. The " relative paral-
lax," as it is called^ jnOl be 9*78 timet tiie sun's parallax,
and it is on this aione f}iil t!ie disptaeement depends;

Thb algebraic procew, wUch is tiiat actually inployed in the
■olution of astrmioaiieal proldeaw of tbis claM, Is as follows :

Baoh obaenrer is supposed «o know bk kmgitiide and lati-
txa»f and to have aaad* <nm .<w asore obswratiaui of the angular
distuee of tiie oentre of the ]da9|et from tlie oentie of the ton.
To work up tiM obsenwtbnii' the investigatOT muat have an
tmktmt ri$ of Vmm and of Oe ran— tinat it, a Jable ghrilig
W) iif(tA ascension and darilaartim of eaob body hem boor to boor
as caicubrted turn A» best aitwww laical data. The epbenMris can
never be ooMldwid dMobitaly oevMct, bat Its enw nuqr be sa-
mnnei as ewMtaat for an entita dav or nMwe. ^ means of it, the
rj^asfeenniion and deeHnatjwt of the j^wiet and of the aan, as seen
frtii tte oMtee ol the eariii, mif be eoriumted at ain ttme.

' le^Meslha. aMm ea ts <lttoohs er v a wen s to Qreen-

218

ABTRONOMT.

wich mean time, or the mean time of any other meridian. Let
those mean times for the obeerver 8i be called 7'i, 7«, T%, etc.
Suppose that at these mean times he has observed the distances of
the centre of Vmvt from that of the txxu to be 2>i, Dt, A, etc.
The corresponding geocentric distances are klien computed from
the ephemeris for these same times, 7*1, Tt, Ti, etc. If the ephem-
eris and the observations ivere perfectly correct, and if there were
no parallax, these calculated diirtances would come out the same as
the observed ones. But this is never the case. It is therefore
necessarr to calculate what effect a change in the right ascension,
declination, and parallax of the sun and kSmmm will have upon the
calculated distance. In this operation these changes are considered
as infinitely small, and the process used is that of differentiation.
Let us put :

a, i, )r, the right ascension, deoUnation, and parallax of FmtiA

a*, d', ir', the same quantities for the sun.

A a, A 4, ^o^, ^ S, the oorrections necessary to the values of the
quantities : a, d, a', and 6 in the ephemeris.

di, dt, dt, etc., the calculated geocentric distances of V<mu$ from
the sun*s centre.

Then, the corrected calculated distances, which we shall call
l/if Ift, D'l, etc., will be expressed in equations of the form :

<li + a. A a ■!■ «', A a' -f 5i A 4 + i', A d* + «i » -(■ «'i •r' = D*. ;
<fi + a<Aa + a'«A<<'+iiA4+&'t ^4'+ ei«r -f «'t ^r' = D t.

' In these equations d\, it, etc., and the coefficients, at, «i, a*, etc,
to e*!, are all known qusnnties, being the direct reralts of odcula-
tion, while A a, Aa, Ad, and Ad are unknown oorrections to the

ahemeris, and w and v' are the parallaxes of Vmm and the son,
» unknown, ffi, D**, etc., are therefore also to be Ktgaided as
unknown.

But when all corrections are allowed for, these eometed calcu-
lated distances Jft, 2X|, etc., ought to be the same as the observed
distances 1/t, If*, etc., which are known ouantitiM, being tiie direct
result of observations. So if we put Jh lor D'l, etc., and transpose
A to the other dde of the eqnatlaa, and porfonn the sane prooeas
on the other equations, we shall have :

«iAa + a'|Aa'-|>tiAd4-VtAd'-f«i)r+«'i«'saJ>i — <ii

These equationa admit of htimt modi slm pM ed. If we mppim

•ad r«Hw ohAaged l^ the atiM sMNut

the right ascensions of the __ _

-this is, if we suppose A«' s A4l tt b evidSit tiSi* tiMl^ fttitMMMs
will main sttbslaiitidlyiiBalterwi la gidtt that tUa iMy Iw 4*a«
in the equations, we vast lMiv«

«» «—•'!,

beoauie the real ehaiigawfll be, in tiw ew* anppessd,
«, A^a 4. «*! A <r as («, 4. a',) A a s 0.

■ ^. • , ' nxi.smmia

my other meridUm. Let
e called Tt, T., T„ etc.
observed the difltances of
iiu to be 2)>, Bt, Dt, etc.
are klien computed from
',, T,, etc. If the ephem-
correct, and if there were
)uld come out the tame as
he caie. It ia therefore
ee in the right ascenrion,
T«nu« will have «?»" *^
eae changes are considered
s that of differenUi|tion.

and parallax of Venui.

BMsiy to the Talues of the

ic distances of Venw from

nces, which we shall cafl
quadons of the form :

i' +e,it + e'tw' = iyy,
ii' + Ci ir +• c'l jr* = D ».

) coefficients, at, «i, «•» etCM
he direct results of calcula-
nknown oorreetions to the
utes of Ymiu and the ran,
sfoi« also to be regarded as

for, these corrected calcu-
be the same as the observed
I Quantititis, being the direct
. for D-,, etc., and tnaspose
1 porfwm the same prooess

«, ir + «'!«' = -Di ■- <*»

e,r + «'•«'=» A — *i •**•

liabnpliied. U^t»Ppim
ii^iiBffed l^ the MHpM iMMMBt

I flidflr tbrt fbia oHqr t>* «»•

RiqWOMd,
a',) A a a> 0.

TRAN8IT8 OF VENU8. 819

In the same way, we must have very nearly,

h'l = — J, ; c'l = — c.

Then if we substitute these values of the accented coefficients, the
first equation will be :

ai (A a — A a') + *i ( A «* — A iJO + «' ("f — TO = ^' — **'•
If we put tat brevity,

«a=Aa— Ao'; y=Ad— Arf',
the equations will become :

oi « + *i y + «! (t — wO = ^' — t'l

The parallaxes of the sun and Veniu, it' and ir, are inversely as the
distances of the respective bodies from the eartii. During the tran-
sit of December, 1874, these distances were :

Distance of son, 0-0847,
" " FmtM, 0-2644.

So^ if we put ir« Ust the parallax at distance 1, we shidi have:

Actual parallax of the son, it' =

Actual parallax of Vemu, it =

0-9847

= l-0165>r..
= 8-7892 If.;

Whence

0-8044

ir-ir'=sa.7e«7ir..

Sabstitating this value in our equationa, they will beoone :

at • -I- fti y -I- S-7007 «i «• s i>, — d,
at* + h%f -f S>7667 e* «• a^J), — <^ etc

AU the coneqwading eaostkns bdng foroMd in tUs way, flmn
the observatimis at the various statioB% their solotkm will ^ve the
vahiea <rf Hie three imlmown qnawtitiea, m, y, aadirt. Ilie^valtie of
w, win hi tiM pMalluc odnvspoiMltog to the astnmmnkal vbH^
that ia, tin anUar awnl'illiintiir eT the eatth taNi at the mean
cUs^mee llni «M Mu.

HlWk tmuf olia a n a llun HiriBKla, we hav« nore •quatioBa than
thw mm MjpMwmsMMitMi* t» tt datiTmliiad, V i^ Oy eqnttiooa
wiM Ma«b(pM*M^«MKM^^><«#^^ and eoold

reJiMt mj af flw aamliia mm lirHhant aia#N« til* mndt. Bat
daoi mA aqmiOoa ft»aiMai4^ alleetad Hrlth eqon of «beerv»-
Oam, «b» MwWeM p uj-t i a to «* !• toobtafca «M»«*miM»I«
vatow of -Uo — luww w l -. qjiiWi(|tai,.fcQo> the oombfaatloii ^ «& the
equatlooi. tiMMa tNAila^ mm '-mm mbkkk iwder tha mm-' of A«
sqaaiw of ttw- Bt a ta i i i ltig oiMn of e ll se MMrtfcp i-^ (or, nriiMr, of

ASTRONOMT.

we substitute ia the wiuation

1 « In ffcnerftl the cquntlon will
any a"«m»d;'»»T*"!h«iwm wmaJn a small difference between
not be satisfied, »»«* Jf" T'J^fjSu,. Let us caU A. the dUIer-
the two 'n«"»]T'\K''** n^ w^W the second equation, A, from
enee obtained ^^ ^^^ ^mS v^sZ the «mot thesq«a«.of
the third, and so on, and let us pu* o
these quantities, so that

S= A«, + A»,+ A% + elc.

Then, for e«.h svjem of vaj- of ^^-^Jj' o^^^d '^^
««ume, there will be • ^'^^af wWch makes S the lew*- ,^
probable system of '«^»«» T^" Siti" "W'*'*^ *" ^^^ *** ""^
•^Themotiiod by which 5*" "^Vortaon astronomical compu-
^ bMt $qvam, and is developed in worns on »

be^t^SJ from '^"l^^^ ^^^ Sb :tV^^ on. in the

-crthrot^r^^^

determines the declination ^JJ^£*%i^ declfnationswill be

moment of transit over hie ™»™°: *':'^"- w«<« the

■uumvu* _i..i~ amnnnt of nan

s'c;^i:^;«'tin«athr^jtjj^^^

oeiMimlW about a couple of montM. /uiy "JSfawidjle ooea •»
S?be chSen for tbS. I«'P«^,J"LXK? BhSd th« pb««t
3Se when the Pl«;l*« "TlTtlMfS^^ **• .^««S
be exactly at its Pfri^^, •*JSfJS7 iXSwhSion it would
from the Sarth would Jf- «2LS^ii£'to tiS «25S«^
he 0.68. TWs great dlllerwiee U owing »;^™T gk-driMt Wg. *8«

p.ll5,whichglTesapl«iofnortofttJwow ^^^ ^

fee fivorable oVfo^^^^l^^^SfSiS^^^
waathatofl8W,w1iichg»w«»"»of"*JJ!^rrr^ TM«

^ba was 8-.577. and «» "2*2222gi*iSl*-«d to allow

great as tills. ^ ., in t ..^ifit-^-**^-** *— ^**

of 8q>tffBb«r WM^LTSi SnJafiwJ^ *>» "*^^

)li8cnr«l quantities and
r instance, suppose that

-cneral U>e equation will
small difference between
Let us caU ^t the diiler-
lecond equation, At iiom
the sum of the squares of

I- etc. !

id If., which we choose to
ralue of S, and the most
ich makes B the lewt.
ached is called the fMthod
i on aatronomical compo-

Kan.— This paralUz may
owa,^ Inthatiu^^ly
, of bhMrrers, one in the
lemisphew, ewsh of whom
rtfromdaytodayatthe
rhese declinattons will pe
iacdi«efencebetweeii«»

Iff. 18, p. «. Th« *••!!?"

[to the *»j^jj^;y«;

PARALLAX OF MAM8.

Furallax of Man in Bight ABoenaion.— Another method
of measuring the parallax of Man is founded on principles entirely
different from those we have hitherto considered. In the latter,
observations have to be made bv two observers in opposite hemi-
spheres of the earth. But an observer at any noint on the earth's
surface is carried around on a circle of latitude every day by the
diurnal motion of the earth. In conse<}uence of this motion, there
must be a corresponding apparent motion of each of the planets in
an opposite direction. In other words, the paralhix of the olanet
must be different at different times of the day. This Aumal
change in the direction of the planet admits of being measured in
thefoUowing way : The effect of paralkuc is always to make a
heavenly body appear nearer the horimm than it would appear as seen
from the centre of the earth. This will be obvious if we reflect
that an observer moving rapidly from the centre of the earth to its
circumference, and keej^ng his eye fixed upon a planet, would seie
the planet appear to move in an opposite direction — ^that is. down-
wwa relieve to the point of the earth's surface which he umed at.
Hence a planet rising in the east will rise later in consequence of
paraUaz, and will set earlier. Of course the rising and setting
cannot be obawved with sufficient accuracy for the purpose of

parallax, but, rince a fixed star has no parallax^
the planet relative to the stars in its neighborhood will change
during the intervallMtween the rising and setting of the planet
The observer therefore determines the positon of Mart relative
to the Stan surrounding him shortly after he rises and aj^in
shortly before he sets. The observations are repeated night
after night as often as poarible. Between each pair of east and
west observations the pbmet will of course change its podtion
among the staiB in consequence of the orirital motions of the
earth and planet, bat these motions can be calcukted and allowed
for, and the changes still outstanding will then be due to paralhu.

The most fliTOiwle regions for an observer to determine the p«r-
idlax ia tbJs way we those near the earth's equator, because he is
thoie oarried around on the lamst circle. If he is nearer the poles
than the equator, the cirde willbe so smalt that the parallax wul be
hardly worth determininff, while at the poles there will be no paiu
allaene elnnge at all of ttie kind hni described.

AppHoations of this mMhod oaTe not been very numerous,
althom^ H waa ouggested b9 ThUumaD neariy two centuries ago.
The lalMt and BHMt aoeeeasflu tiki of it was made by Mir. Datid Oiu.
of B ffgHiMJ daring the oi^oaiti(m <rf Mtrt in 1877 above described.
The p^t ot obaMrvatiofi dioaen by him waa the idand of Aaeen-
skNi, wMt of Afrioa and near the eqiMtor. Hla meaqires indlei^
a euMMonibla fodiietioa in the wewflyreedved valoes of the vt
panUix, and an inerease in the dlatanoe of the sun, makinj,
htter ooBM somewhat nearer to the old vahie.

MioBmntgr of Ham PitwmiiiaWoni of BeHar PawllMc

TIm pttalbx of JUNi at oppoaitioii k nrely moro ihaa

'«im

322

ABTBONOMT.

aO', and the relative parallax of Venm and the ron at the
tune of the tmnait is lew than 24'. These qnantitiea are
w> nnaU as to ahnoat elude very preoiw meaaurement ; it
iB haidly poarible by any one set of measnree of jw^
to determine the latter without an uncertainty of ^^ of its
whole amount. In the distance of the nm this corre-
sponds to an uncertainty of nearly half a miUion of miloa.
ABtronomeiB have therefore sought for other methods of
determining the sun's distance. Although some of ttese
may be a Uttle more certain than measures of pwrillax, th«re
is none by which the distance of the sun can be detenuined
with any approximation to the accuracy wWch character-
izes other celestial measures.

Other Methods of DetMnnininc Sotar *««"«-~;^
Ycry interesting and probably the most accurate method
of measuring tiie sun's distance is by using Kght as a nwfr
genaer between tiie sun and the earth. We shall hereafter
see in the chapter on aberration, that the time reqmred for
light to pass from tiie sun to tiie earth is known witii con-
rfdenble exactness, being very nearly 4»8 seconds. If
then we can detennine experimentally how many miles or
kilometrea light moves in a second, we shall at once have
tiie distance of the sun by multiplying that quantity by
498 But the velocity of light is about 800,000 falometres
ner s*eond. This distance would reach about eight times
iroundtheeartii. It is nmjly possible tiiat two pomts on
tiie eartii's surface more than a hundred kilometrea apui
are visible from each other, and distinct vision at distenoes
of more tiian twenty kilometres is rare. B^******'
mine experimentdly tiie time required for Ui^t to pus
between two terrestrial stations reqiiir«stiMmea«rei»«tjf
an interval of time, which even under ti» most lavoreble

cases can be only a fraction of a tiMWaandtii of *««^-
MetiiodB of doing it, however, have been deri*>d and ex-
ecuted by the l«ibh physidste, IW. Boiic^'««2«*
Oa«o, La quite «p«itiy by Bm^ I hmmmm^^
U. B. Naval Academy, ^^nnapoiiB. EK»m tbei^^Mnipw

I ' ivMi&jmui'mimmm-

aOLAR PARALLAX.

tM and tlie (nm at the
These qoantities are
lifle measiiremeiit ; it
meaavres of parallax
certainty of ^ of its
the aim thb oorre-
ilf a million of miloa.
or other methoda of
though aome of theae
inreaof parallax, there
gun can be detemiined
racy which oharaoter-

Bdlar ParallaK.— A
tnoat accurate method
y naing light aa a mea-
1. We ahall hereafter
it the time required for
rth is known with oon-
arly 498 aeoonda. If
lily how many miles or
, we ahall at once have
^ring that quantity by
>ont 800,000 IdlomelnM
■eaeh about dght times
able that two ])ointa on
ndred Idlometrea apart
itinet Tiaitm at dJatanoes
rare. Hence to deter-
tdred for lig^t to pass
dnM the meanmmeat of
Oder the most lavonble
bonaandth of a aeeoad.
re been deyiaed and ex-
FuKAO. Eoe«A«uri and
rign Mjoikmm a* |be

f^KNB tha^iia^pMtaiiMi

■tti

of the bitter, which are probably the moit aoonrate, the
velocity of light would seem to be about 299,900 kilome-
tres per second. Multiplying this by 498, we obtain 149,-
850,000 kilometrea for Uie distance of the sun. The time
required for light to paw from the sun to the earth is still
uncertain by nearly a second, but this value of the sun's
distance is probably the best yet obtained. The corre-
sponding value of the sun's panllax is 8**81.

Yet other methods of determining the sun's distance
are given by the theory of gravitation. The best known
of these depends upon the detennination uf the paiallaotio
inequality of the moon. It is found by mathematical in-
vestigation that the motion of the moon is subjected to
several inequalities, having the sun's horiaontal parallax
as a iaetiMr. In oonseqnenfw of the laigeat «( these in-
eqnaUtiea, the motm ia about two minutea beliiiid ita mean
phMe near the lint qnartor, and aa far in advance at the
last quarter. If ^ position of the moon eoidd be deter-
mined hgr obaervstioa with-the same eiaetaesa that the po-
siti(« of a alar or planet eaa, tUa would probably afford
the BMBt aoenrate method of diAerjdniiif the adar par-
allax. Bnt aa obaervatkm <tf the moon haa to be made,
not upon ita centre, but upon ita Bmb w etreumfuMice.
Only the limb neareat the sun ia viaible, the other one
bei^g; uniUuminated, and thua the illuminated limb on
whieh the obaervation iato be made is difEerent at the first
and third quarter. Theae oonditiona induee an uncertain-
ty in <1k. eomparisim of obaerrationa made at the two
qnaitara whieh cannot be entiraly overomne, and therefne
leave a doubt n^eeting the oemetnaai of the reanh.

Itekf gjategr ef PatarinlnatlnnB of the WtHmt garallaK.
— Ae diafeaaoe of tiie aon muat at all timet have been one
of tiie BMMt iBteresting aekntifieprdblona prnented to the
human mfaid. The £at known attempt to effeot a adn-
tioB^f-^ problem waa made by AmarAiiicnnn, who flour-
iihfilii ^ thbd eentwy before Obbir. It waa founded
oftiivfiiMiple that the time of the moon*a fiiat quarter

<vai

224

ASTRONOMT.

will vary with the ratio between the distance of the moon
and Bun, which may be shown as follows. In Fig. ii
let JS* represent the earth, M the moon, and S the sun.
Since the sun always illuminates one half of the lunar
globe, it is evident that when one half of the moon's disk
appears illuminated, the triangle iT if ^S must be right-
angled at M. The angle M E S cxa. be detennined by
measurement, being equal to the angular distance between
the sun and the moon. Having- two of the angles, the
third can be determined, because the sum of the three
must make two right angles. Thence we shall have the
ratio between EM, the distance of the moon, and ES,
the distauoe of ihe sun, by a trigonometrical computation.

Fie. TO.

Then knowing the distance of the moon, which can be
detennined with comparative ease, we have the distance of
the sun by multiplying by this ratio. Awbtarohcs con-
eluded, from his suppMed measures, that the angle M ES
was three degrees less than a right angle. We should

then IwveJ^ = sin 3" = ^ very nearly. It would

follow from this that ihe sun was 19 times the distance
of the moon. We now know that this jwsult is entirely
wrong, and that it is impossible to determine the time
when the moon is exactly half illuminated with any ap-
proach to the accuracy necessary in the solution of the
problem. In fact, the greatest angular distuioe of the

i^W i aft»fe<.W» i MStHWSBIfe.W | !aM8^

Iwtance of the moon
'ollowB. In Fig. ifr"
oon, and S tho sun.
e half of the lunar
if of the moon's disk
M S muBt he riglit-
1 he detennined hy
liar distance bet\<reen
J of the angles, the
16 stun of the three
dce we shall have the
the moon, and £S,
aetrical computation.

moon, which can lie
B have the distance of
). AmsTAROHVs con-
that the angle JlfiS'.^
t angle. We should

r neaiiy. It wonld

19 tunes the distance
this result isentarely
} determine the time
tminated with anjr ap-
X the solution of the
pAai distaaee of t)ie

SOLAR PARALLAX.

226

earth and moon, as seen from the snn — that is, the angle
E8M — is only abont one quarter the angular diameter of
the moon as seen from the earth.

The second attempt to determine the distance of the
snn is mentioned by Ptolemy, though Hippabchds may be
the real inventor of it. It is founded on a somewhat com-
plex geometrical construction of a total eclipse of the
moon. It is only necessary to state the result, which
was, that the sun was situated at the distance of 1210 radii
of the earth. This result, like the former, was due only
to errors of observation. So far as all the methods known
at the time could show, the real distance of the sun ap-
peared to be infinite, nevertheless Ptolemy's result was
received without question for fourteen centuries.

When the telescope was invented, and more aocnrate
observations became possible, it was found that the sun's
distance must be greater and its parallax smaller than
Ptolkmy had supposed, but it was still impossible to give
any measure of the parallax. AH that could be said was
that it was less than the smallest quantity that could be de-
cided <ni by measurement. The first approximaticm to the
true value was made by Hokbox of England, and after-
ward by HuYOHKNs of Holland. It was not founded on
any attempt to measure the parallax directly, but on an
estimate of the probable magnitude of the earth on the
scale of the solar system. The magnitude of the planets
on this scale being known by measurament of their appar-
ent angular diameten as seen frmn the earth, the solar
paralkx may be found when we know the ratio between
the diameter of the earth and that of any planet whose
angular diameter has been measured. Now, it was sup-
posed by the two astronomers we have mentioned that
the earth was probaUy of the same order of magnitude
with the other planets.

HojBBox had a theory, which we now know to be erro-
neous iAak tiie diameters of tiie pbn^ were proportional
to tita^ distMioes from the Hun—in other words, that all

"""Mm

tl6

ABTBONOMT.

tlie planetR would appear of the same diameter when seen
from the stin. This diameter he estimated at 28', from
which it followed that the solar parallax was 14". Ucyobkns
aisamed that the actual magnitude of the earth was mid-
way between those of the two planets Ventu and Jian on
each side of it ; he thus obtained a result remarkably near
the truth. It is true that in reality the earth is a little
kuger than either Ventu or MarSf bat the imperfect tel-
escopes of that time showed the planets Uu^r than they
really were, so that the mean diameter of the enhufged
planets, as seen in the telescope of HmroHrars, was such as
to correspond very nearly to the diameter of the earth.

The first really successful measure of the parallax
of a planet was made upon Man during the opposition of
1672, by the first of the two methods already described.
An expedition was sent to the colony of Oayenne to ob-
serve die dedinatioii of the planet from nig^t to night,
while corresponding observations were made at the Paris
Observatory. From a discussion of thesi observations,
OAsson obtained a solar parallax of 9' '5, wuicih is within
a second of the truth. The next steps forward were made
by the transits of Vmtns in 1761 and 1769. The leading
dviUied nations caused observadons on these transits to be
made at various pmnts on die globe. The method used
was very simple, ocmsiBting in the determinati<m of the
timM at which Vmut entered upon the son's disk and left
it again. The absolute times of ingress iad egress, as wen
from different points of die gioto, might differ bjr 90
minutes or more on acoonnt of panUax. Tlw reMha,
however, were found to be diso»d«nt. It was not imdl
more than half a century had elapsed: diat the obsemliiE^
were all carefully calculated by ^okb of Germinyy who
concluded that the paraUax of the sun was 8'' 8ft7, aad the
distance 95 millions of miles.

In 1854 it began to be onspeeted duit Eirea't vaihie of
die paraUax was m«^ too small, and gMak labor imnnF
devoted to a solndon of die jwoUem. Hi

MA88B8 OF TBB SUN AND EARTH.

8S7

I diameter when seen
bimated at 28*. from
xwasU'. HcYOHraa
E the earth was mid-
t Veniu ttad Mara m
MTult remarkably near
the earth is a little
mt the imperfect tel-
leta lu-ger than they
leter of the enlarged

[UTOBBNB, was BUOh 88

meter of the earth,
imire of the parallax
Ufing the opposition of
[)ds already deeoribed.
ly of Cayenne to ob-
from ni^t to nij^t,
ere made at the Paris
of theei obserratioos,
! 9'-5,wiuoh is within
eps forward were made
ndl76». The leading
B on these transitB to be
w. The method used
B determination of the
1 the sui's disk and toft
nwsimd egress 88 seen
«, mi^t differ hj 90
pmOax. The nsiiHa,
rd^ni. It was not until
led! thai the observtliiins
HOKB of Germany, who
8nnwaB8'.867,aBdthe

d that "Bxam^M "nSm of

Md giwt yborymmf

em. Hi "

parallaotio inequality of the moon, first fonnd the parallax
oi the Sim to be 8' -07, a quantity which he afterward re-
duced to 8". 016. This result seemed to be confirmed by
other observations, especially those of Mara during the
opposition of 1862. It W8S therefore concluded that the
sun's parallax was probably between 8' '90 and 9^-00.
Subsequent researches have, however, been d i min i s hin g
tliis value. In 1867, from a discussion on all the data
which were considered of value, it was concluded by one
of the writers that the most probable parallax was 8' '848.
The measures of the velocity of light made by Miohblson
iu 1878 reduce this value to 8' '81, and it is now doubtful
whether the true value is any larger than this.

The obeervati<»s o^the transit of Vmut in 1874 have
not been completely discussed at the time of writing these
pages. When this is done some further light may be
thrown upon the question. It is, however, to the deter-
mination of the velocity of light that we are to look for
the best result. AH we can say at present is that the so-
lar pandhuc is probably between 8' •79 and 8" -88, or, if
outside these limits, tluit it can be very little outside.

Ol* THS SUIT AVD

8 8. XKJLTZVa

In sstfmatiiw oetoitUl naMS at w«U ss dIslsBOM, it k I
to ttss t^at we may can cs k s ri s l uaiti ^ that is, to tsks the bism <rf
aaedfBStialboilfasaaait, iastMdof saynoUiplsof tbspoaad
kaofCBB. Ite MMOB of tMs is that the Ados wmmm the

«f the phHMlafy ifstMai. or,whleh is the mim thbg, the
t aaeh be^te tanas oftiiat of Mne oae body as the valt,

eaabe(btenniae& ind^pMideatly of th«m«Mof any one MT thcv.
'AteanveH a BMHs in Idtognne or othor tanestrial vmts, it is Beesa*
■aiTtoiad liM aMMof the eerth in endi anils, as already ex^aiaad.
TUi,hew«*«t, isnot a eoMW f ylersetwmositeai pnip cys, wkmnmiij
Um rriJattw msMW of the sevwal iilsneti ere remnitea. Ineetiaiat*
iiBtf tt» SMHMs of QMinffividiHa ptaaels, tiiat of Ihe eim Is geaefslN
tdlsnaaannit The planetary nuMee v^ titen all be very mbsU

or fk« avCh mA Sui^We Shan int
^ >«arthbeQsweitis«0MMcf;8d hf
iM|wnJBas «f the an. Eagn^Hmh

we earn

jjgSf^ggi^mm^Bmm muMmifmm mmfsimimmi

AaTUONOMY.

»!.« mu. of the mn relatlre to the euth, which is the iMiie thing
'i^£S,^rAilZlSZm\c^\ m- o'tb* •^^h, th.t of the .«n
hllnff unity. Thl« m«y be dearly wen by reflectin« th»t when we
knol the Sdliw of the ewth'i orbit we can detennjne how fw the
ilSh movJr wSe from a .tndght line in one wcond in connequence

force of the ran at the dItUnce of the earth. Comparing it with
the attractive force of the earth, and making »"ow«>ce for the
dlieSn^of dUtancea from centres of the two bodie., we deter-
mine the ratio between their inaMos. .i„„u .n<i •!•.

The calculation in oueetion la made in the mo.t •imple and ele-
mentarr manner as follows. Let us put :

ir, tS ratio of the circumference ol a circle to its diameter (ir =

"■"151 mL radius of the earth, or the radius of a sphere baring
thd same volume as the earth.

a. the mean distance of the earth from the sun.

« the force of Krarity on the earth's rarface at a point where the
„&i i.T.ttait*S; the distMice which a body will fall in one

"* o*, the sun's attractive force at the distance a.
y. the number of seconds in a sidereal year.
.¥, the mass of the sun.
m, ttie uinsa of the earth.

ktt^ZY^yl^'^T^-^^^J be considered a. equ^ to
JSjatffiW^ of 't&'eart^, or »» the -taUnj^W^
Ihe earth falls towarTthe sun in one second Bj the formula for
centrifufal fowe given in Chapter VIII., p. »04, we have,

■nd by the law of gravitation,

vriienM

and

M 4«*o
„ 4ir»a'

We have, in the same way, for the earth,

whenee

MASS OF THK BUN.

lich U th« Mine thing
e»rth, that of the sun
sflecting thkt when we
dntf nnlne how fur the
! second in conaequenee
seMuret the attrMtive
h. Comparing it with
ling Allowance for the
two bodies, we deter-

9 moat timple and ele-

:le to its diameter (ir =

liuB of a sphere haring

e sun.

kce at a point where the
body will fall in one

cea.
•r.

be considered aa equal to
or to the distance which
nd. By the formula for
S04, we have,

Thenifore, ft>r the ratio of the

4.r'

of the earth and sun, we liave :

4»«

« ~ (? I" r'
By the formula for parallax In Ohapter I., | 8, we hare:

r = (*8lni'.*. — .=

Therefore

4»'
ft

r
1

sln« P

(»).

The (luantities T, rand fl may be regarded as all known with great
eiaotness. We see that the mass of the earth, that of the aun being
unity, is proportional to the cube of the solar parallax.

Prom d»U already giren, we hate:

T^ 8M days, « hours, »" »*; In seconds, r= 81 688 14»,
Mean radius of the earth in metres,* . . r = 870 008,
Force of grarity in metres, . . . .g— ■•8X0»,

while log w' = 1 • 59686. SubetUutIng these numbers in the formulw,
it may be put in the form,

!lz=[7-88W41sin"P,t

where the quantity in brackete is the logarithm of the factor.

It will be codrenient to make two ohanges in the Miallax P. This
angU ia so exceedingly small that we may r«prd it as Mual to He
2^7 To express it In wtcaai* wa must midttply it br the number
clMoonds in the unit radiua-that is, by «0«»«5". iWa will make
P (in seconds) = 806865' sin P. Again, the standard to which par-
alkxea are re/errwl is alwaya the earth's equatorial radiua, which to
oraatar than r by about x\n of ito whole amount. So, if we pat /^
for the «f«a(«rM hortoontal paiaUu, expreaaed in aeoMda, we shaU
bave^

p' « (1 4- ill) 806866' ahiP= 18. 81488J ahiP,

whence, for sin P in terms of P*,
■inP'

• tliemeanradlntof the earth to not the ««« of tito Po>f u£
equatorial iwlU. but oae tUrd the ram of the polar n^nAV^
ttw enwtoiial om, beeause we can draw three such radii, each mak-
inc«r|ghtaBdt with tin other twa ^ ^ ....u.

^ A wmbwenclo^d ta byMfcat i to^fcwwitty need to rfgriiy tlie

980

ABTRONOMT.

If we Bubatitute this T»lue in the expreBaion for the quotient of
the masses, it may be put into either of the forms :

M _ [6-85498]

»\4

P- =[2-78498] (^j

The first formula gives the ratio of the masses when the solar pM-
allax is known ; the second, the parallax when the ratio of the mMSM
is known. The following Ubfe shows, for different values of the
solar paimllax, the corresponding ratio of the masses, and distence of
the sun in terrestrial measures :

M
m

DlMAMOS or TBM BVK.

Solar

In equatorial

ladUor the

earth.

In miUioDS or
mOee.

In miiUoM of
kikmietna.

8' -76
8' -76
8* -77
8" -78
8'-79
8*. 80
8' -81
8' -86
8'-88
8' -84
8' -86

887992
886885
885684
884588
888896
886968
881186
880007
868867
867778
866664

88578
23546
28519
28486
88466
68469
28418
68886
88860
80888
68807

98-421
98-814
98-206
98-108
96-996
96-890
96-788
96-680
66-675
96-470
96-866

160-848
160178
150001
148-880
l«>-660
148-400
148-860
148-161
148-966
148-814
148-646

We have said thattfae aoiar pamlla: b wohdrtTeontafaied betwewi
theifanits 8".79 and 8'.88. It is oertrinly baidW wm than on* or
twohandndttMoCaseooiidwithoatthem. So,if wewlah to«Mf«M
the oonstantsv^ting tothe sonin roond rnimben, wemayaaytlMt--

»■ iiMW is 880,000 times flwi of the earth.

It. i««i«» In miles is 96 milHoofc «r pfb^p* » H^ hM.

Jti distance in kfloawtrss is pwWily betwem 149 and 160 mil-

liens. ji

IlMiat^ ^ tlw ton.— A temaikable res^ of the pnoedlug
inveatioaikmisthat the denrf^ of the taa, witaHve to tt^ <rf ttie
e^STSnbe detnmined indep^ently of the ma* or distence of
the san by measuriag its appwent aoguUr diaawter, and the fowe
of gimvity at the earth's surface. I«t us pot
.^, the deiu% of Um son.

nH^^S;

n for the quotient of

ms;

M when the solar pur-
he ratio of the mMses
lifferent values of the
asses, and distance of

>r TBM BVH.

lODSOf

In milUoM of

kikNmtm.

lSO-848

114

1S0178

906

180001

102

148-880

B96

l«>-800

148-480

786

148-880

880

148- in

S7S

148-988

410

148-814

888

148-648

Mt contained between
ardlT more than on« or
>, if we wish to onreaa
ben, wemajaayftal^

MaHttielats.

reen 148 and 160 mil-

MoH of the preoedliq;
leitatiTe to tiSat «rf tin
iM nuM or distance of
Uattflter, and the fone

t ■

JramtfMMVtti. Hmmi,
U

MASS OF THE -8K2V.

S81

Linear radius of the sun = a sin*.
Tolume of the sun

4^ , . ,
= — o' sin* •
8

(froui the formula for the volume of a sphere).

4ir

Mass of the sun, Jf = - 3 «' ■» b»«>' »•

4ir
Mass of the earth, m=-^r a.

Substituting these values of M and m in the equation (a), and
dividing out &e common factors, it will become

D . 4irV

J sin •= yiy*

from which we find, for the ratio of the density of the earth to that
ofthesun, ^ .

This eouation solves the probten. But the wlution may be trana-
f«™idt2?™«irion We\now from the Uw of falUng bodies that
?Wvv bX^rin the time «, fall through the distance 4 «r/.
H^TheffitoTiVi. double tile distance which a bod, wouli faU
• ^a«1j^ if flie force <rf aniTity could act upon it oontinu-

^wffl be the number of radU of the earth through which the
b!d/ will fall in a sidereal year. If we put F for this number, the
proeeding equation will become,

We therefoce have thia rak fbr finding the denaity of the earth
'^ jSj?:tJi^'^' «• «ra a Aesey fe.^ .P^

■ "y. *°^ rTFlr^zJ^.^*!^ 4Sm»»«f aMmitina «a« «»<»'• stir-

riom the namerieal data alrei^y given, we find :
DoMity of earth, that of ran being unity.

i
5'

>8-8Me.

232

A8TR0N0MT.

Density of the aun, that of tho eurth being unity,
? = 025606.

Them relations do not give us the actual density of either body.
We have said that Uie mean density of the earth is about 6t, that of
water being unity. The sun is therefore about 40 or 60 per cent
denser than water.

Mtt—oa of the Flanete.— If we knew how far a body would
fall in one second at the surface of any other planet than the earth,
we could determine its mass in much the same way as we have de-
termined that of the earth. Now if the planet has a satellite re-
volving around it, we can make this detennination — not indeed
directly on the surface of the planet, but at the distance of the sat-
ellite, which will et^ually give us the required datum. Indeed by
observing the periodic time of a satellite, and the angle subtended by
the major axis of its orbit airound the planet, we have a more direct
datum for determining the mass of the planet than we actually have
for determining that of the earth. (Of course we here refer to the
masses of the planets relative to that of the sun as unity.) In fact
could an astronomer only station himself on the planet Vemu and
make a series of observations of the angular distance of the moon
from the earth, he could determine the mass of tho earth, and
thence the solai parallax, with far greater precis'o" than we arc like-
ly to know it for centuries to come. liet ui u^< a-XQOaider the
equation for M found on page 288 :

Jf=f

4ir»a'

Here a and 7* may mean the mean distance and periodic time of

Or*

any planet, the quotient -^ being a constant by Ebtucb's third

law. In the same equation we may suppose a the mean distanoe of
a satellite from its primarv, and T its time of revohition, and JTwill
then represent the maas of the planet. We shall have timefme for
the mass of the planet,

4ir«««

a' bdng the mean distance of the satellite from 'the planet, and t'
its tinw of revolution. Therefore, for the masa of the phHMt lel
ative to that of the sun we have :

m of T*

Let na Mnmoae a to be the mean diataaoe <rf the phnefe fran the
son, in.wUeh eeae Tmuat lepreaent its time of nmdatioii. Tbnm,
if we put • fw the angle subtended hythemdhM of tiie oiMt of the

MA88B8 OF TUR PLANKTB.

383

nity,

nsity of either body.
1 IB about Sf, that of
ut 40 or 60 per cent

w far a body would
lanet than the earth,
way as we have de-
let has a satellite re-
linaAion — not indeed
e distance of the sat-
l datum. Indeed by
lie angle subtended by
re have a more direct
;han we actually have

I we here refer to the
a as unity.) In fact
he planet Venxu and
listance of the moon
Bs of the earth, and
is'n" than we arc like-

II m" ) consider the

tnd periodic time of

\ by KBn.BB's third

) the mean distance of
reTolntion, and JTwill
laU have therefore for

imthe planet, and T'
taw of the ptauwt rel

\ the pianet from ths

of NVtHOtlOll. ^MBf

ihM Of th9 oiliik of ttiB

satellite, as seen from the sun, we shall have, assuming the orbit
to be seen edgewise,

8in< = —
a

If the orbit is seen in a direction perpendicular to its plane, we
should have to put tang < for sin « in this formula, but the angle
B is 80 small that the sine and tangent are almost the same. If we
put T for the ratio of the time of revolution of the phuiet to that of
the satellite, it will be equivalent to supposing

The equation for the mass of the planet will then become

5:=r*8ln«.,

which is the simplest form of the usual formula for deducing the
mass of a phinet from the motion of its satellite. It in true that we
cannot observe • directly, since we cannot place ourselves on the
sun, but if we observe the angle a from the earth we cm always
reduce it to the sun, because we know the nroportion between the
distances of the pUnet from the earth ud frmn the sun.

All the Uu^ planets outside the earth have satellites ; we can
therefore determine their masses in this simple way. The earth
having also a satellite, its mass could be determined in the smm
way but for the ofarcumstance ahteady mentioned that we capnot
determine the distance of the moon ip planetary units, as we (wi
the distance of the satellites of the othor planeU from their pri-
maries.

file phwets Mtnwry and Vanut have no satellites. It is therefore
necessary to determine their masses by thdr influence in altering
the elliptic motions of the other planets rmmd the son. The altera'
tions thus prodnoed are for the most part so small that thefar deter-
mination is a practical problem of some difBiml^. Thusthe action
of JftrwMrw on tiie neighboring planet Vmu» rarefy changes the po-
dtion of the hitter \if more than one or two seconds <4 are, mileae
we eompare observatimu more than a cmtnry apart But regular
and accurate obaervatlmis of Ymim were rarely made until after tlM
beginning of this oentary. The mass of Vmtu is best detemhMM
by^idliience of tke plaaet fa dmaging the porition of the pine
of the euib*s orbit. Altogellwr, the determination of the bmssm
of Jbmcrw and Vmtm preseata one of the most complicated |^rob>
loDB with wUch the mathematieal artrommier has to deal.

CHAPTER X.

THE REFRACTION AND ABERRATION OF LIGHT.
i 1. ATMOSPHXBIO BBFBAOTIOH.

When we refer to the place of a planet or star, we
usually mean ita tnte place-*.*., its direction from
an obierver ritnated at the centre of the earth, consid-
erad as a geometrical point. We have ahown m the aeo-
tion on parallax how obeervationa which Me nef«anly
taken at the anrfaoe of the earth are reduced to what they

wonld have been if the observer were Mtuated at toe
earth's centra. In this, however, we have auppoeed the
Btarto appear to be projected on the celertial «phef "^
the prolS^Ition of the line joining Ae observer MidAe
star TlM ray from the star is considered as if It Buffered
no deflection in passing through ihe stellar spaces^
through the earth's atmosphere. But from the prmc^
of p^ics, welmow that such a luminousray pa«ng from
^^^tr«P«» («. the rtdlar qp«»i are), and ihroiyj^
.tmo.Jh^™.5afferarohjjd^^

is known to do in pamng fewm a »««™o .vST^
riH)dium. As we see the star in the direction which ha

Hriit beam has when it enteia the ej^-0»t ». •■ *« F»-
i^ the star on the celestial sphere by l^^^^J^
&t beam backwaid into space-there murt be ""TO"-
ent dispUwement of the star from refraction, and it is

this which we are to eoosidw.

We may reoaU a few definitions from 0iy««». ^
i»y which Ujaves the itM and implngei on the outer m-

[ON OF LIGHT.

AOnOH.

planet or star, we
s direction from
the earth, consid-
I shown in the sec-
ich are neoewarily
inoed to what thej
ire sitnated at the
have sappoBod the

celestial sphere in
e ohaenrer and the
red M if it infEend

steDar spaoea and
from the prinoipliM
)iuT»7pMRing tnm
re), and ihro«|i^ aa
IB ever/ my of li^i
rare into a deoMf
diraetion whksh ita
-that is, aa we pio-
by pn^mging lliia
pemnatbeanappar-
efraetion, and it ia

bom phyrioa. The
a on tii0 oater m^

RBFRAOTION.

285

face of the earth*B atmosphere is called the inoident ray ;
tdXeir its deflection by the atmosphere it is called the re-
fracted ray. The difference between these directions is
called the aatronamical r^raation. If a normal is drawn
(perpendicnlar) to the surface of the refracting medium at
the point where the incident ray meets it, the acute angle
between the incident ray and the normal is called the
angle of incidence, and tiie acute angle between the nor-
mal and the refracted ray is called the angle of refraction.
The refraction itself is the difference of these angles.
The normal and both incident and refracted rays are in
the same vertica] plane. In
Fig. 69 i^^ ia the ny incident
upon the snrfaoe BA of the re-
fracting medinm B' B A Sf,.
A C n the refracted ray, MJf
the normal, SA Jf and CAN
the angles of inddoioe and i«-
fraction respectively. Prodvoe
C A backward in the direotion
AST : SAJSn»the refraetion.
An observer at (7 will aee tiie
star .$ as if it were tAST. AS
is the apparent direction of tiie ray from the star 8^ and
S ia the qgparmU plant ot Um atar aa affaeted by refrac-
tion.

This suppoaes the qiaoe above ^ ^ in tlie figure to be
entirely empty apaoea, and the earth's atmoaphere, equally
denaethroq^ont,tofiUtheapaoebelowJ?J9'. Intact, how-
evw, the eaoith'a atmoaphere b moat denae at the snrfaoe of
the earth, and gradually diminiahea in dwiaity to ita exterior
bonndary. Therefore, if we wish to repreamt the facta aa
they are, we mnat auppoae the atmoaphere to be divided
into a great number of parallel layera of air, and by as-
suming an infinite number of these we may also assume that
throoi^oiit eaeh of tiiem tiie air k equally dense. Hence
Hie pieoeding figum wiU only rcpre a e nt the refraetion at

jtStmHmmtmmmmm

886

A8TB0N0MT.

a sinirle one of these layere. It follows from this that t lo
path of a ray of light through the atmosphere is not a
straight line like A C, but a curve. We may suppose
this curve to be represented in Fig. 70, where the num-
ber of layers has been taken very small to avoid conf usmg

the drawing. , , . , . .

Let C7 be the centre and A a pomt of the surface of the
earth ; let -S" be a star, and 5 « a ray from the star
which is refracted at the various layers into which we buj,
pose the atmosphere to be divided, and which finally

na. 79.— nvBAonoiT or t^mB or An.

enters the eye of an observer at A in the JPP^"* ^^
tion A JSr. He will then see the star m the direction ^
instead of that of S 8, and SASTy the refraction, will
throw the star nearer to the zenith -Z. .

The angle i^AZis Uie apparent zenith distance of A ,
the true^nith distance of -S is Z^ ^, and this imyr be
assumed to coincide with 8e, as for all heavenly bodies
except the moon it practically does. The hne^. pro-
longed will meet the line ^ Z in a point above A, sup-
pose at &'.

HEFRACTION.

237

rs from this that tlio
itmosphero is not a
We may suppose
0, where the num-
1 to avoid confusing

of the surface of the
ray from the star
B into which we bui>
, and which finally

or tOL.
i the apparent direc-
tar in the direction S
', the refraction, will

'* '.

zenith distance of ^;

A. Sy and this may be
r all heavenly bodies

B. The line Se pro-
point above A, s^p-

Law of Beflraotion. — A considvration of tlio pliyHicitl condi-
tiona involved has Ivd to tlio following form for tliu rcfrucition in
zenith distance (A i),

(A{) = ^tan(f'-aAO),

in which T i* the apparent zenith distance of the star, and ^ is a
constant to be determined by observation. A is found to be about
67', so that we may write (A = "''" t*** ^' approximately.

Thi<« expression gives what is called the mean refraction — that is,
the »<f raction corresponding to a mean state of the barometer and
thermometer. It is clear that changes in the temperature and pres-
sure will affect the d' •»<*« of 'he air, and hence its refractive power.
The tables of the mt * - <kCtion made by Besbri., based on a more
accurate formula than >.iie one above, are now usually used, and these
are accompanied by auxiliary tables giving the small corrections for
the state of thii meteorolo^cal instruments.

Let us consider some of the consequences of refraction, and for
our purpose we may take the formula (A{)s=57' tan C, m it
very nearly represents the facts. At T = (A () = 0, or at the
apparent zenith thnre is no refraction. This we should have antici*
pated as the incident ray in itself normal to the refracting surface.

Tlie following extract from a refraction table gives the amount of
refraction at various zenith distances :

(AC)

(Af)

0°

C 0*

70»

8' 89'

10"

V 10'

80°

5' ao'

ao°

0' 88*

86°

W 0"

45°

V 08'

88°

18' C

no*

r w

88°

84' 8S'

»•

1' 40'

•0°

84' 80'

Quantity and SflBbota of Beflraotion. — At 45° the refrac-
tion is about 1', and at 90° it is 34' 30"— that is, bodies at
the zenith distances of 45° and 90° appear elevated above
their true places by 1' and 841' respectively. If the sun
has just risen — that is, if its lower limb is just in apparent
contact with the horizon, it is, in fact, entirely below ihe
true horizon, for the refraction (SS*) has elevated its cen-
tre by more than its whole apparent diameter (32').

The moon is faU whran it is exactly opposite the son,
and tlMwfore were thei« no atmosphere, moon-rise of a
ftdl mbmt and simiet wonld be simnltaoeons. In &ct,

atiMllilHii ilil i* !**"'^"! ! '' i i 'W-iMiiiiina w iu

yaummmf^

A8TR0N0MY.

both bodiei being elevated by refraction, we see the fnll
moon risen before tlie sun has set. On April aotli, 1887,
the full moon rose eclipsed before the snn had set.

We see from the table that the refraction varies com-
paratively little between 0° and 60° of zenith distance, but
that beyond 80° or 85** its variation is quite rapid.

The refraction on the two limbs of the sun or moon will
then be different, and of course greater on the lower limb.
This will apparently be Ufted up toward the upper limb
more than the upper limb is Ufted away from it, and
hence the sun and moon appear oval in shape when near
the horizon. For example, if the zenith distance of the
sun's lower limb is 85°, that of the upper will be about
84° 28', and the refractions from the tables for these two
zenith distances differ by V ; therefore, the sun will ap-
pear oval in shape, with axes of 82' and 81' approxi-
mately.

Detarmination of Befraotion.— If we know the law aeeordiBg
to which refmotioii varies — ^that is, if we have an accurate formula
which will give ( A C) in terms of {; we can determine the absolute
reft«ction for unr one point, and from the law deduce it for any
other points. Thus knowing the horizontal refraction, or the t«-
fraction in the horiaon, we can determine the refraction at other
known senith distances.

We know the time of (theoretical or true) sunrise and sunset 1^
the fimnute of 1 7, p. 44, and we may observe the time of apparent
riring and settuig of the sun (or a star). The difference of these
times gives a means of determining the effect of refraction.

Or, m the observations for latitude by the method of { 8, p. 47, we
can measure the apparent polar distanoes of a drcnmpolw star at
its upper and lower culmination. Its polar distances above and
below pole should be equal ; if there were no refraction they would
be so, but they really differ by a quantity which it is easy to see b
the difference of the refractions at lower and upper culminations.
By chooring suitable ciicumpolar stars at various polar distances,
tlus difference may be determined for all pobur distwoes, and tiiere>
fore at all senith distances.

g S. ATWBBATIOW AXD THX WyBtXXS OF LKIHS.

Berides rafradion, there is another oanae whidi preTents
our seeing the oekatial bodies exaet^ in the tnw direoHoa
in which they lie &om i»— namely, Ae progreMve mo-

ion, we see the full
►n April aoth, 1837,
sun had Bot.
fraction varies com-
' zenith distance, but
quite rapid,
the sun or moon will
ir on the lower limb,
^ard the upper limb
I away from it, and
in shape when near
nith distance of the
upper will be about
tables for these two
ore, the sun will ap-
12' and 31' approxi-

e know the law Mcording
lave tn accunte fonnuta
a determine the abwlute
« law deduce it for any
lUl fefraction, or the n-
e the refraction at other

le) annrise andninaetl^
ivre the time of apparmt
The difference of theee
Eect of refraction,
le method of 1 8, p. 47, we
M of a drcnmpolar atar at
ofaur distances above and
» no refraction they would
rwhichHiseaqrtoMeis
r and upper culminations,
i Twrloua polar distances,
polar ^stances, and th«e-

montoK ov uobs.

sr cause wl

i^ in the tme diraotka

ly, the progroMive ma-

ABmsATioir.

339

tion of light. We now know that we see objects only
by thu light which emanates from them and reaches our
eyes, and we also know that this light reijuirus time to
pass over the space which separates us from the object.
After the ray of light once leaves the object, the latter
may move away, or even be blotted out of existence, but
the ray of light will continue on its course. Consequent-
ly when we look at a star, we do not see the star that now
is, but the star that was several years ago. If it should be
annihilated, we should still see it during the yean which
would be required for the last ray of light emitted by it to
reach us. The velocity of light is so great that in all ob-
servations of terrestrial objects, our vision may be regarded
as instantaneous. But in celestial observations the time
required for the light to reach us is quite appreciable and
measurable.

The discovery of the propagation of light is among the
most remarkable of those made by modem science. The
fact that light requires time- to travel was first learned by
the observations of the satelUtes of Jupiter. Owing to
the great magnitude of this planet, it casts a much longer
and larger shadow than our earth does, and its inner sat-
ellite is therefore edipeed at every revolution. These
eclipses can be observed from the earth, the satellite van-
ish^ from view as it enters the shadow, and suddenly
reappearing when it leaves it again. The aoenracy with
which the times of this disappearance and reappearance
could be observed, and the consequent value of «ach ob-
serrationB for the detormination of longitudes, led the
artronomms of the seventeenth oentnry to make a careful
study of the motions of these bodies. It was, however,
neoessaiy to make tables by which the times of ^le eclipan
could be piredi<tfed. It was found by Bomont that these
timcn depended on the dirtanoe of Jt/ypHmr from the earUi.
If he made his tables agree with obaemitiiMM when the
enth wae nearest tft^pUert it was found ^t as the earth
receded &mn«Aifwlsr in ^ aDnnaloonne around the snoi

TT"?

' "nmmm,

ASTRONOMY.

tlio oclipficM wcro constantly seen later, until, wlion ut itH
gruuteHtdiKtance, tliu tiniuH apjiearud tu liu 22 niinutiw latu.
lioiiifKK saw that it was in the highesc degree improbable
that the actual motions of the satellites should be affected
wttli any such inequality ; he therefore propounded the
bold theory tliat it took time for light to come from Ju-
piter to the earth. The extreme differences in the times
of the eclipse being 22 minutes, he assigned this as the time
required for light to cross the orbit of the earth, and so
concluded that it came from the sun to the earth in 1 1
minutes. We now know that this estimate was too great,
and that the true time for this passage is about 8 minutes
and 18 seconds.

DiMMTcrj of Ab«rr»tioii. — At first this theory of 'Ron-
iiBR was not fully accepted by his contemporaries. But
in the year 1729 the celebrated Bbadlbt, afterward As-
tronomer Boyal of England, discovered a phenomenon of
an entirely different chunoter, which confirmed tlie theory.
He was then engaged in making observations on the star
y Dro/DOM* in order to determine its parallax. The effect
of parallax would have been to make the declination
greatest in June and least in December, while in Mardi
and September the star would occupy an intermediate or
mean position. But the result was entirely different.
The declinations of Jnne and December were the same,
showing no effect of parallax ; but instead of remaining
oonstant the rest of the year, tJie declination was some 40
seconds greater in September than in March, when the
effect 6i paralha would be the same. This showed that
the direction of the star appeared different, not aooording
to the position of tlie earth, but aooording to the direction
of its motion around the ran, the star being apparently
displaced in this direction.

It has been said that the explanation of this singular
anomaly was fint snggested to Bbaduet while sailing on
the Thames. He notioed that when his boat moved nq^d-
ly at right angles to the tme direction of the wind, die

ABMlUtATION.

r, until, when vX its
o tic 22 ininutott late,
t degree improbable
» Bhould be affected
fore propounded the
t to come from Jtt-
{erences in the times
igned this as the time
of the earth, and so
n to the earth in 11
itiraate waa too great,
« is about 8 miirates

t this theory of Rok-
Bontemporariea. But
ADLET, afterward Aa-
sred a phenomenon of
confirmed the theory,
servations on the atar
, parallax. The effect
nake the declination
mber, while in Hardi
py an intermediate or
as entirely different,
smberwere the same,

instead of remaining
iclination was some 40

in March, when the
le. This showed that
ifferent, not aMording
ioiding to the direction

■tar being apparently

tation of this singular
iDLCT while sailing on
p hit boat moved r«|p$d-
stion of the wind, the

apparent direction of the wind changed toward the point
whither the boat was going. When the boat sailed in an
opposite direction, the apparent direction of the wind sud<
denly changed in a corresponding way. Here was a phe-
nomenon very analogous to that which he had observed in
the stani, the direction from which the wind appeared to
come corresponding to the direction in which the light
reached the eye. This direction changed with the mo-
tion of the observer according to the same law in the two
cases, fie now saw that the apparent disphuwment of the
star was due to the motion of the rays of light combined
with that of the earth in its orbit, the apparent direction
of the star depending, not upon the absolute direction
from which the n,y comes, but upon the relation of this
direction to the motion of the observer.

To show how this is, let J. j9 be the optical axis of a
telesoope, and S a star from which emanatea a ray mov-
ing in the true direction S A R,
Perhaps the reader will have a clearer
oonoeption of the subject if he imi^
iuea ji J? to be a rod which an ob*
server at B w^ to point at the star
a. It ii evi4«|it Hun he wiU pomt j
thia rod in wtidk • 1P|^ that the ray
of light sitallifi ^ ^B H WM U Jy along iti
length. SappQ# iHiw that the ob-
server Ia moviiif Iron JSu>wud£'
with auch a vdkMitj that he movw I
from B Ut B* during the time to. _.

quired for any of light to move from '». tb.

AXttS. Bappoie alio that the ray of light ^:iiieaehea
.i at the wme time that the end of his rod deea. Then
it is elear that wUk the rod ia movfaig from the position
^ .ff to the poaition utV^, the my of %ht win move from
A to JS'^ittid win tiMiefaranmaoonmtely along the kngth
of therod. ggg iiwrwim, if th one tMid of the way
tram ir to ^,than tlLe]i|^t,at theinatantof tho rodtak.

KMMI

ABTRONOMT.

ing the porition h a, will be one third of the w»y from A
to B\ and will therefore be aoourately on the rod. Con-
loquently, to the observer, the rod will appear to be point-
ed at the star. In reality, however, the pointing will not
be in the true direction of the star, bnt will deviate from
it by an angle of which the tangent is the ratio of the
velocity with which the observer is carried along to the
velocity of light. This presopposes tliat the motion of the
observer is at right angles to that of a ray of light. If
this is not his direction, we mast resolve his velocity into
two components, one at right angles to the ray and one
parallel to it. The latter will not affect the apparent di-
rection of the star, which will therefore depend entirely
upon the former.

Sflbota of Abemtion. — The apparent displacement of
the heavenly bodies thns produced is called the aberration
qf light. Its effect is to cause each of the fixed stars to
ascribe an apparent annual oscillation in a very small w-
bit. The nature of tlie diq>laeement may bo conceived
of in the following way : Suppose the earth at any moment,
in the coarse of its annual revolution, to be moving to-
ward a point of the celestial sphere, which we may call P.
Then a star lying in the direction P or in the oj^posite di-
rection win tuffer no displacement whatever. A star ly-
ing in any other direction will be disphUsed in the direc-
tion of the point P by an an|^e propoiti<»ial to the sine of
its angnlar distance from P. At 9Cr fro^ P the dis-
pUcement will he a maximum, and its angular amonnt
will be snoh that its tangent will be equal to the ratio of
the velocity of the earth to that of light. If ul he the
"aberratiim" of (he star, and P8itB angular distanoe
from the point P, we AaXt have,

tan ^ = -, sin P^,

Vand « being the respective veloeitieB of H^t and <tf the
earth.

of the w»y from A
y on the rod. Con-
Ilappeartobepoint-
the pointing will not
at will deviate from

is the ratio of the
carried along to the
liat the motion of the

a ray of light. If
>lve hia velocity into

to the ray and one
lect the apparent di-
sfore depend entirely

jrent displacement of
1 called the aberratim

of the fixed atan to
m in a very amall or-
int may be conceived
a earth at any moment,
ition, to be moving to-
whioh we may call P.
P or in the oppoaite di-
whatever. A atar ly-
diipUoed in the direc-
iportional to the aine of

M* iroiA P the dia-
id its angular amount
B eqnalto the ratio of
irf light. If ^ be the
'5it8 angular diatanoe

PS.

dtiea of Uj^t and of the

vniooitT Of umiT.

«4d

Kow, if the atar liea near the polo of the ecliptic, its di-
rection will always be nearly at right angles to the direc-
tion in which tlie earth is moving. A little consideration
will show that it will seem to describe a circle in conse-
quence of aberration. If, however, it lies in the plane of
the earth's orbit, then the various poinds toward which
the earth moves in the course of the year all lying in the
ecliptic, and the star being in this same plane, the appar-
ent motion will be an oscillation back and forth in this
plane, and in all other positions the apparent motion will
be in an ellipse mori and more flattei ed as we approach
the ecliptic.

Velocity of Light. — The amorii^. of aberration can be
determined in two ways. If wh know the t^me which
light requires to come from tho snn to trc earth, a simple
calculation will enable us to determinn ' t. i ratio between
this velocity and that of the earth ii tis orbit. For in-
stance, suppose the time to 498 seconds; on light
will cross the orbit of the eti th i>* 996 seoondtt. The cir-
cumference of the earth being found by multiplying it:;
diameter by 8 • 1416, we thus find that, on the suppoeitiuu
we have made, light would move around the drcumior-
ence of the earth's orbit in 62 mmutes and 8 seconds.
But the earth makes this aaire circuit in 866^ days, and
the ratio of these two quantities is 10090. The nazimum
diaplaoement of the star by aberration will therefore be the
angle of which the tangent is Trffvi >nd this angle we
find by trigonmnetrical calcn]ati<m to be ao** 44.

This calenlation presupposes that we know how long
light requires t^ come frmn the sun. This is not known
with great aorivy; owing to the unavoidable enrora with
which the obaerva^ona of Jupiter** satellites are affected.
It is therefore more usual to reverse the process and de-
termine th" diaplaoement of tiie stars by direct obaerva-
tioo, and then, by a calculation the nf9va» of that we
h«V6 lust made, to determijoe tlie time required by lof^t
to reMh us from the snn. Many patnatakiog detiermina-

itWTnrvftwtrf'rf'*^

244 ASTttOKOitr,

r^J deviate from 20-.« by n.o« tlmn two or three
'"■tt;^fS."^o^iS°i bydetem-ining th.«>n^of
.b^^L or by ob^rving the -"iT?' *' "w ^^

irZil^^^f the Bun, we may obtain the vel<Kity of
uirbvStagitbym But, on the other hand, a we
'ideteTne^wmLy miles light mov« ma seo^^
r tS infer the distance of the «m ^y ™5^^22S<^
Z the same factor. During «^«.lf ^^^'^^ t^*^^
of the aun was found to be certainly between 90 and 100
^S^rSmUes. It was therefore c<««cayoondud^
Cthe velocity of light was somet^leBB th«^^»0O0

mL ner second, and probably between 180,000 and
^"XSvtiocityhL since boen dete^ned moj.

exactly by the direct measurements at the surface of the

earth abready mentioned.

ie since the time of
e may say that the
1," as it is called, is
tiechancesarethatit
e than two or three

ning the constant of
ies of the satellites of
ired for light to pass
»nnot thus determine
how far the sun is.
^ and the distance of
, can infer the other,
he time required for
seconds, a time which
second. Then know-
obtain the velocity of
tt the other hand, i| wo
moves in a second, we
J sun by multiplying it
at century Uie distance
iy between 90 and 100
re correctty oonolnded
thing less than ^)0,000
between 180,000 and
boen determined more
Lts at the surf ace of the

CHAPTER XI.

CHRONOLOGY.

% 1. ASTBONOMIOAI. MSASXTBEBQ OF TDOS.

The most intimate relation of astronomy to the daily
life of mankind has always arisen from its affording the
only reliable and accurate measure of long intervals of time.
The fundamental units of time in all ages have been the
day, the mouth, and the year, the first being mensured by
the revolution of the earth on its axis, the seccmd, prim-
itively, by that of the moon around the earth, and the third
by that <^ the earth round the sun. Ilad the natural month
consisted of an exact entire number of days, and the year
of an exact entire number of months, there would have
been.no history of the calendar to write. There being no
such exact relations, innumerable devices have been tried
ior amoothlng off tlie difficulties thus arising, the mere
description of which would fill a volume. We shall en-
deavor to give tlie reader an idea of the general characto'
of these devices, including those from which our own cal-
eadu ori^nated, witiiout wearying him by the introduc-
tion of tedUnu details.

Of the three units of time just mentioned, the moet nat-
ural and starring is the shortest— namely, the day. park-
ing aa it does the regular ahemations of wakefohn^ and
rest for both man and animab, no artronomioal obeerva-
tions were Mceasary to its recognition. It is so neariy
unifcMrm in Imgthtiiatthe most refined astroiuMnical ohmf-
vatioas of modem times have nover certainly indicated

246 A8TB0N0MT.

any change. This uniformity, and ita entire freedom from
all ambiguity of meaning, have always made the day a
common fundamental unit of astronomers. Except for
the inconvenience of keeping count of the great number
of days between remote epochs, no greater umt would
ever have been necessary, and we might all date our let-
ters by the number of days after Chmst, or after a sup-
posed epoch of creation. ,

The difficulty of remembering great numbers is sucli
that a longer unit is absolutely necessary, even in keeping
the reckoning of time for a single generation. Such a
unit is the year. The regukr changes of seasons in all ex-
tra-tropical latitudes renders tliis unit second only to the
day in the prominence with which it must have struck the
minds of primitive man. These changes are, how^ever, so
slow and ill-marked in their progress, that it would have
been scarcely possible to make an accurate detenmnation
of the length of the year from the observation of the sea-
sons Here astronomical observations came to the aid ot
our progenitors, and, before the beginning of extant his-
toryfit was known that the alternation of seasons was due
to the varying declination of th« sun, as the latter seemed
to perform its annual course among the stars m tiie
« obUque circle" or ecUptic. The common people, who did
not understand the theory of the sun's motion, knew that
certain seasons were marked by the position of certain
bright stars rehitively to the sun-that is, by those stare
ristog or setting in the morning or evemng twiOight.
Thus arose two methods of measuring the length of the
year— the one by the time when the son crossed the eqm-
noxes or Botedoes, the other when it seemed to pass a cer-
tain point among the stars. As we have already exphun-
ed, these yea» were slightly diflfeient, owmg to the p»-
ceidon of the equinoxes, theHrst or equmoct«l year being
alittle less and the second or sidereal year a litfle g«»ater

than 865J d*y* ^ i* ^

Themunberof days in a year is too great to admttol

OHRONOLOQT.

247

entire freedom from
yg made the day a
omers. Except for
►f the great number
greater unit would
ght all date our let-
[M8T, or after a Bup-

3at numbers is such
Eiry, even in keeping
generation. Such a
\ of seasons in all ex-
t second only to the
must have struck the
iges are, however, so
, that it would have
[•urate determination
bservation of the sea-
ls came to the aid of
inning of extant bis-
on of seasons was due
I, as the latter seemed
»ng the stars in the
nmon people, who did
I's motion, knew that
le poeition of certain
that is, by those stwu
or evening twilight,
[ng the length of the
) ran crossed the equi-
seemed to paw a cer-
) have already explain-
nt, owing to the pie-
> equinoetittl year bmng
Mdyetfalitae gcmter

too great to •dmHof

their being easily remembered without any break ; an in-
termediate period is therefore necessary. Such a period
is measured by the revolution of the moon around the
earth, or, more exactly, by the recurrence of new moon,
which takes place, on the average, at the end of nearly
2di days. The nearest round number to this is 30 days,
and 12 periods of 30 days each only lack 5^ days of being
a year. It has therefore been common to consider a year
as made up of 12 months, the lack of exact correspondence
being filled by various alterations of the length of the
month or of the year, or by adding surplus days to each
year.

The true lengths of the day, the month, and the year
having no common divisor, a difficulty arises in attempting
to maJke months or days into years, or days into months,
owing to the fractions which will always be left over. At
the same time, some rule bearing on the subject is necessary
in order that people may be able to remember the year,
month, md day. Such roles are found by choosing some
oyde or period whidi is very nearly an exact number of
two units, of months and of days for example, and by di-
viding this cycle up as evenly as possible. The principle
on which this is d<me can be seen at once by an example,
for which we shall choose the lunar month. The true
length of this month is a9-580&884 days. We see that
two of these months is only a little over 69 days ; so, if
we take a cy<de of 69 days, and divide it into two months,
the one of 80 and tiie other of 29 days, we shall have a
first approximation to a true average month. But onr
cyde will be too short by O' • 061, the excess of two months
over 69 days, and this error will be added at the end of
every cycle, and thus go on increasing as long as Ihe cycle
is used without ohaage. At the end of 16^cyoles, or of
32 lunar m<niths, tlie aocnmulated error will amount to
one day. At the end of this time, if not sooner, we
alMNdd have to add a day to one of the months.

Wiling that we shall uhimatelj be wrong if we hav<> a

i i' U i Janil li MH

248

ASTRONOMY.

two-month cyde, we seek for a more exact one. Each
month of 30 days is nearly 0*.47toolong, and eadi monfli
of 29 days is rather more than 0* • 68 too short. Bo m the
lonir run the months of 30 days ought to be more numw-
om than those of 29 days in the ratio that 63 bears to
47, or, more exactly, in the ratio that -6306884 bears to
. 4694116. A close approximation will be had by having
the long months one eighth more numerous than the diort
ones, the nnmbers in question being nearly in the ratio of
9 : 8. So, if we take a cycle of 17 months, 9 long and 8
short ones, we find that 9x30 + 8x29 = 602 days for
the assumed length of our cycle, whereas the true length
of 17 months is very near 602*.0200. The error will
therefore be -02 of a day for every cyde, and wiH not
amount toaday till the end of 60 cydes, or nearly 70

^Titill nearer approadi will be found by taking a qjde
of 49 months, 26 to be long and 23 Aoit ones. These
49 months ^iU be composed of a«^;; «> + 28 x 29 =
1447 days, whereas 49 true lunar months will eompnse
1446.998882 days. Eadi cycle will therefow be too long
by only -001168 of a day, and the error would n«t«jmo^t
to a day tai the end of 84 cydes, or more th«j 8000 y«ffl^
Although these cycles are so near the truth, ihgr oorfd
not be Ld with convenience be«u«e Aey ^^^^
at different thnes of the year. The problem is therefore
to find a cyde whidi shall comprise an entire n^^^er of
years. We shall see hereafter what solutions of this
problem were actually found.

§ 2.

lOBKATIOV or GAXOHDABt.

The months noW or heretofore in ™« •'^^.P^^'jJ"
of the globe may for the mort part be divided mto two

''^The lunar month pure and simple, or the mean
interval between sttcoeottve new moons.

9 exact OBe. Each

>ng, and eadi month

00 short. 80 in the
to be more numer-
tio that 58 bears to

1 .5305884 bean to
ill be had by having
lerouB than the short
learly in the ratio of
uontiis, 9 long and 8
< 29 = 502 days for
)reasthe true length
!00. The error will

cycle, and will not
cycles, or nearly 70

ad by taking a cycle
18 short ones. These
26x80 + 28x39 =
nonthswill comprise
therefore be too long
ror would not amonnt
aore than 8000 years,
the truth, ih^ could
ise they would begin
> problem is therefore
) an wtire number of
tiat sdntionB of this

ase amwig A» P«o0«
t be divided into two

simple, or the mean
ons.

THB OALBNDAR

(2.) An approximation to the twelfth part of a year,
without req>ect to the motion of the moon.

The Lunar Month. — The mean interval between con-
secutive new moons being nearly 29^ days, it was common
in the use of the pure lunar month to have months of 29 and
30 days alternately. This supposed period, however, as just
shown, will fall short by a day in about 2| years. This de-
fect was remedied by introducing cycles containing rather
more months of 80 than of 29 days, the small excess of
long months being spread uniformly through the cycle.
Thus the Greeks had a cycle of 235 months (to be soon
described more fully), of which 125 were full or long
months, and 110 were short or deficient ones. We see
that the length of this cycle was 6940 days (125 x 30 +
110 X 29), whereas the length of 235 true lunar months
is 235 X 29 • 53088 = 6939 • 688 days. The cycle was there-
fore too long by leas than one third of a day, and the error
of count would amount to only one day in more than 70
years. The Mohammedajos, again, took a cycle of 360
months, which they divided into 169 short and 191 long
ones. The length of this cyde was 10631 days, while the
true length of 360 lunar months is 10631 • 012 days. The
count would therefore not be a day in error until the end of
about 80 cycles, or nearly 23 centuries. This month there-
fore follows the moon closely enough for all practical pur-
poses.

MmaXbB othmr than Lunar.— The complications of the
system just described, and the consequent difficulty of
making the calendw month represent the course of the
moon, are so gr^ At that tiie pure lunar month was gen-
erally abandoned, except among people whose religion re-
quired importuit ceremonies at the time of- new moon.
In cases of such abandmiment, the year has be«i usually
divided into 12 montiis of sli^^tly different lengths. The
ancient Egyptians, however, had 19 months of 80 days
each, to whidi they added 5 snpplfanentary days at the
dose <rf each year.

l!i„'li>lillllMili'lil I «»;!»!«»»««»>•»"»»■»"•»""

WMMti

350

A8TR0N0MT.

Kinds of Tear.— As we find two different syBtems of
months to have been used, bo we may divide the calendar
years into three classes— namely :

(1.) The lunar year, of 12 Innar months.

(2.) The solar year.

(8.) The combined Inni-solar year.

The Lunar Tear.— We have already called attention to
the f Mt that the time of recurrence of the year is not weU
marked except by astronomical Phenomena which the
casual observer would hardly remark. But the tame of
new moon, or of beginning of the month, is always weU
marked. Consequently, it was very natural for people to
begin by considering the year as made up of twelve luna-
tions, the error of eleven days being unnotic«ible ma

singte year, unless careful astronomical o^^^^^J^^J^fJ
m.Se. Even when thiserrorwas fully recogmzed,itimght

be considered better to use the regular year of 12 lunar
months than to use one of an irregular or varymg number
of months, f-hayearis^erehg^us^^^^^^^^
hammedans to this day. Ihe excess oi xx uj-
amount to a whole year in 83 yews, 82 «>1«»! y«*" ^^
nearly equal to 33 lunar years. In this period therefore
^^B2>nwill havecoirsed through ^times of ^e
^. The lunar year has therefore been caUed the

" retlllf C:lln forming this year, the aUem^to
measure the year by revolutions of the moon » «^f«V
Sdoned, id its Lg^ "^Lt T^^tlS^

length has been known to ^^\^^^ ^^J^y^
tim^of the earliest astronomera, and f^^^J^,
in our calendar of having tliree yeamof 866 d^ «^«»
lowed by one of m days, has ^ ««^P^5^?^",
from the remotest hiirt«ric times T^J^,^^^
is nowcalled by us the JWKon r«r, after JiTUO. Oi»A«,

from whom we obtained it.

THE CALENDAR.

361

Lifferent syBtems of
divide the calendar

tntha.

y called attention to
I the year is not well
momena which the
:. But the time of
lonth, is always well
natural for people to
le up of twelve luna-
ig unnoticeable in a
•al observationa were
f recognized, it might
liar year of 12 Innar
UP or varying number
pons one of theMo-
seu of 11 days will
83 solar years being
this period therefore
igh all times of the
ore been called the

9 year, ihe attempt to
the moon in entirely
» depend entirely on
ar year thus indicated
d modem times. Its

r 866i d»y» from ^
id the qrrtem adopted

Bof SeSdiqrBrtcli^^p'-
en employed in CJhina
This ye« al 36H day"
r, after J^uuvs jmab,

The lAiii4kdar Tear. — If the lunar months must, in
some way, be made up into solar years of the proper av-
erage length, then these years must be of unequal length,
some having twelve months and others thirteen. Thus, a
period or cycle of eight years might be made up of 99
lunar months, 6 of the years having 12 months each, and
3 of them 18 months each. Such a period would comprise
2928i days, so that the average length of the year would
be 865 days 10^ hours. This is too great by about 4 hours
42 minutes. This very plan was proposed in ancient
Oreeoe, but it was superseded by the discovery of the
MeUmio Oyde, which figures in our church calendar to
this day. A luni-solar year of this general diaracter was
also used by the Jews.

The MMonio Qyole. — The preliminary considerations we
have set forth will now enable us to understand the origin
of our own calendar. We begin with the Metonic Cycle
of the ancient Greeks, which still regulates some religious
festivals, although it has disappeared from our civil reck-
oning of time. The necessity of employing lunar months
caused the Greeks great difficulty in regulating their cal-
endar so as to accord '«rith their rules for religious feasts,
until a solution of the problem was found by Mkton, about
488 B.O. The great discovery of Mbton was that a period
or cyde of 6940 days could be divided up into 235 lunar
months, and also into 19 sohu* yean. Of these months,
125 were to be of 80 days each, and 110 of 29 days each,
which wonld, in all, make up the required 6940 days. To
see how nearly this rule represents the actual luotions of
the ann a^d moon, we remiark that :

M6 lunations require 6989

l»JuliMiyetn " 6989

19 tmesolar years require 6989

Huan. MlB.

la 81

14 27

We aee that thon^ the cyde of 6940 dajs is a few hours
toQ^kng, yet, if we take 985 true lomr mimths, we find

252 ASTRONOMY.

aew duv. Mch, md . Utile more than W true •oto yem.
T^bZ.no,»w«t.Uk,tl««a85m.nth.jnddmd=

««fl«»l on mbUc montunente in letter, of gold. Ibo rule
^ Mng *e golden nnmbe, i. to divid^he nj«nb.r o
the ycT b, 19, «.d .dd 1 to the -"J^; ,!^ ^

to 1899 it ,n.jbe fonnd by ""Ply "■*t^2 forS
ftoye«. It i. employed in onrehnrehcdendK for and

inc the time of Ewter Bnnd«y. ,

*l.riod of <«1T,«..-We have •«»;,*",*• jtn^
8940 dam i« a few honr. too long either for 886 Innar
WtoOTforWwtaryeara. CAU.r,.» therefM. ««.^t
7^^ it by taW.* on. day o« of ^^i^ ^S
TO that the fonr cyde. Aonld h«« S"6» dayj wm™
"ere to be divided into 940 month. Kid int. W y»».
^Lveamwonldthaihe Jnli». ye«», wM. the ^^

he would iMtTe been yet newrter **»« *™*^,, ^^_^_„k.
able calendwiirhicb bare '*^«»«d JL"^^ Jf2i^

THK MOHAMMEDAN CALENDAR.

368

uilOJvliuiyeanof
19 true sokr years.
5 months and divide
mid have 12 months
The long years,
those corresponding
19, while the first,
years. In general,
smately, bnt it was
or a short one every
jTcle there should be

the number of the
I to owe itsappella-
s over Mkton's dis-
ed the division and
r calendar to be in-
■B of gold. The mle
livide the number of
oainder. From 1881
abtractmg 1880 from
irch calendar for find-
en that the ejrde of
either for 286 lunar
TPUs therefore sought
of every fourth jgrde,
re 27769 days, which
IS and into 76 years,
ears, while the raenr-
X hours in error at the
en a day from every
1 month of ^t <r)rcle,
truth.

mong tbe most remark-
in use to the pnnnt
The yew ii oovnogd

of 12 lunar months, and therefore, as already mentioned,
does not correspond to the course of the seasons. As with
other systems, the problem is to find such a cycle that an
entire number of these lunar yean shall correspond to an
integral number of days. Multiplying the length of the
IxsMX month by 12, we find the true length of the lunar
yeu' to be 864-86706 days. The fraction of a day being
not far from one third, a three-year cycle, comprising two
years of 864 cud one of 866 days, would be a first approx-
imation to' three ^unar years, but would still be one tenth
of a day too short. I:: tc such cycles or thirty years,
this deficiency would amount to an entire day, and by add-
ing the day at the end of each tenth three-year cycle,
a very near approach to the true motion of the moon
will Im obtained. This thirty-year cycle will consist of
10681 days, while the true length of 860 lunar months is
10681 • 01 16 days. The error will not amount to a day until
the end of 87 cycles, or 2610 yean, so that this system is
accurate enough for all practiMl purposes. The common
Mohammedan year of 354 days is composed of months
containing alternately 80 and 29 days, the first having
80 and the hst 29. In the years of 866 days the alter-
nation is the same, except that one day is added to the last
month of the yesr.

The <dd custom was to take for the first day of the
m<mth that following the evening on which the new moon
oould first be seen in the west. It is said that before the
exact arrangement of the Mohammedan calendar had been
oomjdeted, the nde was that the visibility of the ereaeent
moon should be certified by the testimony of two wit-
nesses. The time of new moMH given in our modem
al m a n acs is that when the moon passes neariy between us
and the mn, and is therefore entirely invisiUe. The moon
is generally <me or two days old before it can be seen in the
eveofaig, and, in conseqnoioe, the lunaf moitili of the Mo-
hammedaM and of othemoomuMooes about two daya after
«ilui.iOtiia] aLDUue time of new ibo<ml

'MMMHIMHMiiliMtaiMMMHH

A8TB0N0MT.

The civil calendar now in use throuKhoot Christendom
had its origin among the Romans, and its foundation was
laid by Jcuus Cjbbar. Before his time, Rome can hardly be
said to have had a chronological system, the length of the
year not being prescribed by any invariable rule, and be-
ini^ therefore changed from time to time to suit the caprice
or to compass the ends of the rulers. Instances of this
tampering disposition are familiar to the historical student.
It is said, for instance, that the Gauls having to pay a
certain monthly tribute to the Romans, one of the govern-
ors ordered the year to be divided into 14 months, in
order that the paydays might recur more rapidly. To
remedy this, CjBbab odled in the aid of Sosiobnes, an as-
tronomer of the Alexandrian school, and by them it was
arranged that the year should consist of 865 days, with the
addition of one day to every fourth year. The old Roman
months were afterward adjusted to the Julian year in
such a way as to give rise to the somewhat irreguUr
arrangement of months which we now have.

Old and Hew Styles. — The mean length of the Julian
year is 866| days, about 11^ minutes greater than that of
the true equinoctial year, which measures the rwurrenoe
of the seasons. This difference is of little practical im-
portance, as it only amotmts to a week in a thousand years,
and a change of this amount in that period is productive
of no inconvenience. But, desirous to have the year as
correct as possible, two duu^raB were introduced into the
calendar by Pope Gbbqoby XIII. with this object. They
were aa follows :

1. The day following October 4, 1689, waa callf^ the
15th instead of the 5th, thoa advancing the count 10 days.

a. The doeing year of each oentory, 1600, 1700, etc.,
instead of being always a leap year, aa. in the Julian
calendar, is such (miy when the number of the cnntuiy is
divisible by 4. Thus while 1600 remained a kap year, as
before, 1700, 1800, and 1900 wen to be common yean.

This change in the calendar was speedily adopted hy0^

THE CALKNDAR.

255

[toot Christendom
tB foundation wm
;onie can hardly be

the length of the
ftble rule, and be-
to suit the caprice

Instances of this
historical student.

having to pay a
[>ne of the govem-
tto 14 months, in
aore rapidly. To

SoBiOENES, an as-
id by them it was
866 days, with the
. The old Boman
he Julian year in
omewhat irregukr
have.

Qgth of the Julian
reater than that of
iree the rAnirrenoe
little practical im-
n a thousand years,
leriod is productive
\ have the year as
introduced into the
I this object. They

L682,WMcaUKl the
I the count 10 days.
y, 1600, 1700, etc.,
, as. in the Julian
)er of the century is
Bined a leap year, as
be common yean,
ledily adopted by t^

Catholic countries, and more slowly by Protestant ones,
England l.olding out until 1762. In Rwsia it has never
been adopted at all, Uie JuUau calendar being stiU con-
tinned without change. The Russian reckoning is there-
fore 12 days behind ours, the ten days dropped m 1682
being increased by the days dropped from the years 17iM)
and 1800 in the new reckoning. This modified calendar
is called the Or^n(mtm Calendar, or JVew Style, while tiie
old system is cai.od the Julian Calendar, or Old Style.

It is to be remarked that the practice of commencing
the year on January 1st was not universal until compara-
tively recent times. During the first sixteen centuries of
the JuUan calendar there was such an absence of definite
rules on this subject, and snch a variety of practice on the
part of different powers, that the simple enumeration of
the times chosen by various governments and pontiffs for
the commencement of the year would make a tedious
chapter. The most common times of commencing were,
perhaps, March 1st and March 22d, the latter being the
time of the vernal equinox. But January 1st gradually
made its way, and became universal after its adoption by
England in 1762.

Bolar Oyole and Dominioal Letter.— In our church cal-
endars January 1st is marked by the letter A, January 2d
by B, and so on to G, when the seven lettere begm over
again, and are repeated through the year in the same
order. Each letter there indicates the same day of the
week throughout each separate year, A indicating the day
on which January 1st falls, B the day foUowing, and so
on. An exception occurs in leap years, when February
S9th and March Ist are marked by the same letter, so that
a diange occurs at the beginning of Mardi. The letter
corresponding to Sunday on this scheme is iBalled the Jkh
mmiotd or Sunday lottef^ and, when we once know what
letter it is, all the Sundftjs of the year are indicated by
that letter, and hence all the other days of the week by
^bmr letters. In leap years there wUl be two Dominioal

i^^itm

fB6

ASTRONOMY.

lettere, that for the Iwt ten months of the year being the
one next preceding the letter for January and Febniary.
In the Julian calendar tlie Dominical letter must alway»
recur at the end of 28 yean (beaidea three "^"ff «««;»*
unequal interval, in the mean time). This period is called
the wi«r cycle, and determines the days of the week on
which the days of the month fall during each year.

Since any day of the year occur* one day earUer m the
week than it did the year before, or two days earlier when
a 29th of February has intervened, the Dominical letters
mmr in the order G, F, E, D, C, B, A, G, etc. A
simihff fact may be expressed by saying that any day ol
the year occur* one day kter in the week for every year
that has eUipsed, and, in addition, one day later for eveir
29th of February that has intervened. This fact wiU make
it easy to calcuhte the day of the week on which any his-
torici event happened from the day corresponding in any
past or future year. Let us take the f ollowmg example :
On what day of the week was Washwoton bom, the
date being 1782, February 22d, knowing that February
22d, 1879, feU on Satmrday. The interval is 147 yean :
dividing by 4 we have a quotient of 86 and a remainder
of 8. showing that, had every fourth year m the interval
been a leap year, there were either 86 or 87 leap yean.
As a February 29th followed only a week after the date,
the nmnber must be 87 ;• but as 1800 was dropped from
the Hat of leap yean, the number was leaUy only 86.
Then 147 + 86 = 188 days advanced m the week, in-
riding by 7, becau«» the same day of the w«* rwun
afterleven days, we find a remainder of 1. So Febru«y
22d. 1879, is one day further advanced than was iebmary
22d, 1782 ; so the former being Saturday, WASHWoroir
was bom <m Friday. . .,_

• PBihapslhemort cmiv«leBtw«raf a*!*^/*^*?"-!!;

S. W 8C0UIB iwtween tto two dats^ only • we* altar aia *(•».

DIVISION OF THE DAT

367

the year being the
itry and February,
letter uitiBt always
hree recurrences at
'his period is called
ys of the week on
ig each year.
I day earlier in the
o days earlier when
e Dominical letters

B, A, G, etc. A
ig that any day of
eek for every year

day later for every
This fact will make
k on which any his-
orreeponding in any
following example :
kSHiHOTON bom, the
nring that Febmary
itervalis 147 years:
86 and a remainder
year in the interval
86 or 87 leap yean,
xreek after the date,
was dropped from
was really only 86.
i in the week. Di-

of the week reenn

of 1. So Februaiy
id than was Febmary
torday, Washimgtov

•riitoMMnotitfilMi^
MBlnterrMiM. MitnMit>
tav« Fehfoary M. 1878,
ty ft wMk afiar ttw iMk.

I 8. Diviuoir or ram day.

The division of the dny into hours was, in ancient and
medinval times, effected in away very dififerent from that
which we practice. Artificial time-keepers not being in
general use, the two fundamental moments were sunrise
and sunset, which marked the day as distinct from the
night. The first subdivision of this interval was marked
by the instant of noon, when the snn was on the meridian.
The day was thus subdivided into two parts. The night
was similarly divided by the times of rising and culmina-
tion of the various constellations. Evripidks (480-407
B.O.) makes the chorus in Rhetus ask :

" CHOBiit.— Whose ii the guard T Who takes my turn T Tk» fir^

miOwi^ tkroutfi heium. Awake ! Why do you detey T Awake from
your beds to watch t See ye not the brUlhmcy of the moon T Mom,
mom indeed is iqtproaching, and hiOur Uon$^ Oefonntniting ilan. "
—The Tragedies of Enripidea. LlteraUy Translated by T. A. Buckley.
London : H. O. Bcdu. 1854. Vol. i, p. 888.

The interval between sunrise and sunset was divided
into twelve equal parts called hours, and as this interval
varied with the season, tlie length of the hour varied also.
The night, whether long or short, was divided into hours
of the same character, only, when the night hours vere
long, those of the day were short, and vice vena. These
variable hours were called temporary houre. At the time
of the equinines, both the day and the night hours were
of the same lengtii with those we use— namely, the twenty-
fourth part of the day ; these were therefore called egui-
noetial houre.

The use of these temporary honn was intimately an-
ioaiated with the time of be^^ing of the day. Instead
of commencing the dvil day at midn^t, as we do, it was
fflMtwhary to oommenoe it at sunset. The Jewish &tbbath,
for inrtUice, oommeneed as soon as the smi set on Friday,
and ended when it set on Saturday. This made a more
distiBotive <!yviai<m of the avtronomieal day than that

258

A8TR0N0MT.

whicli we employ, and led. natnrally to considenng the
day and the nigkt as two distinct periods, each to be di>
vided into 12 hours.

So long as temporary hours were used, the beginning of
the day and the beginning of the night, or, as we should
call it, six o'clock in the morning and six o'clock in the
evening, were marked by the rising and setting of the sun ;
but 'When equinoctial hours were introduced, neither sun-
rise nor sunset could be taken to count from, because both
varied too much in the course of the year. It therefore
became customary to count from noon, or the time at
which the sun passed the meridian. The old custom of
dividing the day and the night each into 12 parts was con-
tinued, the first 12 being reckoned from midnight to
noon, and the second from noon to midnight. The day
was made to commence at midnight rather than at noon
for obvious reasons of convenience, although noon was of
course the point at which the tune had to be determined.

Bquatlon of Time. — To any one who studied the annual
motion of the sun, it must have been quite evident that
the intervals between its successive passages over the
meridian, or between one noon and the next, could not
be the same throughout the year, because the apparent
motion of the sun in right ascension is not constant. It
will be remcirbered that the apparent revolution of the
starry sphere, or, which is the same thing, the diurnal
revolution of the earth upon its axis,naay be r^;arded
as absolutely constant for all practical purpows. This rev-
olution is measured around in rig^t asoendon as explained
in the opening chapter of this work. If the sob inereased
its right ascension by the sameamounieveiy day, H would
pass the meridian 8' 66' later every day, as measi|rad by
sidereal time, and hence the intervals between saooeirive
passages would be equal. But the mod<m of the nm in
right ascension is unequal firom two earnes : (1) the un-
equal motion of the earth in its annual rMUJttttion arouad
it, arising from the eocentridty of the oriiit, and (d) Om

APPARENT AND MEAN TIME.

259

to considenng the
odS) each to be di-

jd, the beginning of
it, or, as we should
I six o'clock in the
1 setting of the sun;
dnoed, neither sun-

from, because both

year. It therefore
on, or the time at

The old custom of
to 12 parts was oon-

from midnight to
midnight. The day
rather than at noon
ilthough noon was of
id to be determined.
10 studied the annual
n quite evident that
e passages over the

the next, could not
[)eoau8e the apparent

is not ooDfitant. It
snt revolution of the
M thing, the diurnal
xi8,may be regarded
[pHipomft. Thisrev-
uoendon a» explained
If thesuninoeiied
aievery day, H would

day, as measured by
k between suooeisive

motion of the ion in
o causes: (1) ttoun-
aal resiihition arouad
the orbit, and (2) tlw

obliquity of the ecliptic. How the first cause nroduces an
inequality is obvious, and its approximate amount is readily
computed. We have seen that the angular relodty of a
planet around the sun is inversely as the sqnare of its ra-
dius vector. Taking the distance of the earth from the sun
as unity, and putting e for the eccentricity of its orbit, its
greatest distance about the end of June is 1 + « = 1 • 0168,
and its least distance about the end of December is
1 — • 0168. The squares of these quantities are 1 • 034 and
1_.034 very nearly ; therefore the motion is about one
thirtieth greater than the mean in December and one
thirtieth less in June. The mean motion is 3*° 56* ; the
actual motion therefore varies from 3"" 48' to 4" 4'.

The effect of the obliquity of the ecliptic is still greater.
When the sun is near the equinox, its motion along the
ecliptic makes an angle of 23^" with the parallels of dec^
lination. Since its motion in right ascension is reckoned
along the parallel of declination, we see that it is equal to
the motion in longitude multiplied by the cosine of 23^°.
This cosine is less than unity by about ^OT ; therefore
at the times of the equinox the mean motion is diminished
by this fraction, or by 20 seconds. Therefore the days
are then. 20 seconds shorter than they would be were there
no obliquity. At the solstices the opposite effect is pro-
duced. Here the different meridians of right ascoasion
are nearer togetiier than they are at the equator in the
proportion of the ooaina of 2S|° to unity ; ^erefore, when
the sun moves through one degree along the ecliptic, it
changes its rig^t ascension by 1*08° ; here, therefore, the
day* are about 19 seconds longer than they would be if the
obliquity of the ecliptic was zero.

Wo thna have to recognize two slightly different kinds
of days : aciaf days and mtmk days. A solw day is the
interval of time betweon two successive transits of the sun
over the same meridian, while a mean day is the mean of
all the solar days in a yea?. If we had two docks, the
one going with perfect uniformity, but regulated so as to

260

A8TR0N0MT.

keep M near the sun as poBBible, and the other changiTig
its rate so as to always follow the sun, the latter would gain
or lose on the former by amounts sometimes rising to 22
seconds in a day. The accumulation of these variations
through a period of several months would lead to such
deviations that the sun-clock would be 14 minutes slower
than the other during the first half of February, and 16
minutes faster during the first week in November. The
time-keepers formerly used were so imperfect that these
inequalities in the solar day were nearly lost in the neces-
sary irregularities of the rate of the clock. All clocks
were therefore set by the sun as often as was found neces-
sary or convenient. But during the last century it was
found by astronomers that the use of units of time vary-
ing in this way led to much inconvenience ; they there-
fore substituted mean time for solar or appcvrent ^ame.

Mean time is so measured that the hours and days shall
always be of the same length, and shall, on the average, be
as much behind the sun as ahead of it. We may imagine
a fictitious or mean sun moving along the equator at the
rate of 8" 56* in right ascension every day. Mean time
will then be measured by the passage of this fictitious sun
across the meridian. Apparent time was used in ordinary
life after it was given up by astronomers, because it was
very easy to set a dock ftova. time to time as the sun
passed a noon-mark. But when the dodi was so far im-
proved that it kept much better time than the sun did, it
was found troublesome to keep putting it backward and
forward, so as to agree with the sun. Thus mean time
was gradually introduced for all the purposes of ordinary
life except in vety remote country distriots, where the
farmers may find it more troublesome to allow for an equa-
tion of time than to set their docks by. the sun every few
days.

The conun<m household almanac should give the equa-
tion of time, or the mean time at which the sun passes the
meridian, on eadi day of the year. Then, if any one wialiM

tUPBbVlNO TUB OALBNDAB,

^61

I the other changii g

the latter would gain

ometimes riaing to 22

of these variations

would lead to such

)e 14 minutes slower

of February, and 16

in November. The

imperfect that these

arly lost in the neoes-

he clock. All docks

sn as was found neces-

le last century it was

f units of time vary-

venience ; they there-

lar or appewent time.

le hours and days shall

hall, on the average, be

' it. We may imagine

Dg the equator at the

<rery day. Mean time

ge of this fictitiouB sun

le was used in ordinary

lomers, because it was

ne to time as the sun

le dock was so far im-

ae than the Mm did, it

ittingit backward and

(un. Thus mean time

B purposes of ordinary

ry districts, where the

ne to allow for an equa-

I by. the sun every few

I should give the equa-
rhich the ran passes the
Then, if any one wiakM

to set his clock, he knows the moment of the sun passing
the meridian, or being at some noon-mark, and sets his
time-piece accordingly. For all purposes where accurate
time is required, recourse must be had to astronomical ob-
servation. It is now customary to send time-signals every
day at noon, or some other hour agreed upon, from obser-
vatories along the principal lines of telegraph. Thus at
the present time the moment of Washington noon is sig-
nalled to New York, and over the principal lines of rail-
way to the South and West. Each person within reach of
a telegraph-office can then determine his local time by cor-
recting these signals for the difference of longitude.

8 4. RmffARTTB ON DCPBOVma THE OAXMSDAIL

It is an interesting question whether our calendar, this
product of the growth of ages, which we have so rapidly
described, would admit of decide<l improvement if we
were free to make a new one with cae improved nuiterials
of modem science. This question i» not to be hastily an-
swered in the affirmative. Two small improvembPte are
undoubtedly practicable : (1) a more regular divisicn of
the 866 days among the months, giving February 80 diiys,
and so having months of 80 and 81 days only ; (2) putting
the additional day of leap year at the end of the year in-
stead of at the end of February. The smallest change
Afom oui ^iresentoystem wonld be made by taking the two
additional days ic» February, the ooe from the erd of
July, and theotL <v ,*rom the end of December, leaving
thelait wlb 30^&,'i in rommoa yean and 31 in leap
yeats. When wp c-o; i Jder more radical changes thnn this,
we find advaiihges set off by disadvantages. For in-
stance, it WA^td on some ^yonuts be very ocHimikient to
divide th6 /t-^ into 18 monUtf. of 4 weelm each, the last
month liavinf one or two extra (kys. The months wonld
then begin cm the aanie day of she week throi^ oaeh
year, ai^ woidd admit of a luuoh moie oonvwoient aabdi-

ASTHONOMT.

\ 1

vision into halves and qnarters than tliey do now. But the
year would not admit of snch a subdivision without divid-
ing the months also, and it is powible that this inconven-
ience would balaDce the conveniences of the plan.

An actual attempt in modern times to form an entirely
new calendar is of sufficient historic interest to be men-
tioned in this connection. We refer to the so-called Bepub-
lioan Oalendar of revolutionary France. The year some-
times had 365 and sometimes 366 days, but instead of
having the leap years at defined intervals, one was inserted
whenever it might be necessary to make the autumnal
equinox fall on tlie first day of the year. The division of
the year was effected after the plan of the ancient Egyp-
tians, there being 12 months of 30 days each, followed by
5 or 6 supplementary days to complete the year, which
were kept as feast-days.* The sixth day of course occur-
red only in the leap years, or J^emciads as they were call-
ed. It was called the Day of the Bevolution, and was set
apart for a quadrennial oath to remain free or die.

No attempt was made to fit the new calendar to the old
one, or to render the change natural or o-onvenient. The
year began with the autumnal equinox, or September 22d
of the Gregorian calendar ; entirely new names were
given to the months ; the week was abolished, and in lieu
of it the month was divided into three decades, the last or
tenth day of each decade being a holiday set apart for the
adoration of some sentiment. Even the division of the dar
into 24 honrs whs done away with, and a division into
ten hours was substituted.

The Republican Cfdendar was formed in ' 7')8, the year
1 commencing on September 22d, 119:^, and it was
abolished on January 1st, 1806, after 13 years of con-
fusion.

* Hi^ reeeived the niduumw of »an»-euk4IUlt$, from the oppoMOti
(rf the new etato of thlaga.

ey do now. But the
ivision without divid-
e that this inconven-
} of the pUm.
8 to fonn an entirely
interest to be men-

the 80-called Bepnb-
ice. The year some-
days, but instead of
rvals, one was inserted

make the autumnal
ear. The division of
of the ancient Egyp-
ays each, followed by
)lete the year, which

1 day of couTM occur-
iads as they were call-
evolution, and was set
iu free or die.

ew calendar to the old
1 or convenient. The
tox, or September 22d
ely new names were
i abolished, and in lieu
■ee decades, the last or
>liday set apart for the
1 the division of the dar
1, and a division into

rmed in ' r')8, the year
Id, l'<92, and it was
kfter 13 years of con-

kUUm, ftam die opponento

THE ABTRONOMJOAL EPHSMBSIS.

263

$i 6. THE ABTBONOMiaAL SPHXICEBIB, OB NAU-
TIGAIi ALMAirAO.

The Aatronomvcal EpJiemeris, or, as it id more com-
monly called, the UTaviical Almanac, is a work in whicli
celestid jAenomena and the positions of the heavenly
bodies are computed in advance. The need of snch a work
mnst have been felt by navigat.rs a^id astronomers from
the time that astronomical predictions became eofficicutly
accurate to enable them to determine their position on the
surface of the earth. At first works of this class were pre-
pared and published by individual astronomers who had
the taste and leisure for this kind of labor. Manfredi,
of Bonn, published Ephemeride9 in two volumes, which
gave the principal aspects of the heavens, the positions of
the stars, planets, etc., from 1715 nntil 1725. This work
included maps of the civilized world, showing the paths of
the principal eclipses during this interval.

^e usefulnem of such a' work, especially to the naviga-
tor, depends upon its regular appearance on a uniform plan
and upon the fiilness and accuracy of its data ; it was there-
fore necessary that its issue should be taken up as a gov-
ernment work. Of works of this class still issued the
«arlie8t was the ConnaiMmuse dea Ternps of France, the
first volume of which was published by Picabd in 1679,
and which has been continued witilout interruption until
the present time. The publication of the British Na^Moci
.AlmamiiC was commenced in the year 1767 on the repre-
sentations of the Astronomer Soyal showing that such a
work would enable the navigator to determine his longi-
tude witiiin one degree by observations of the mo<m. An
astronomical or nautical almuiao is now published annually
by each of the governments of Germany, Spain, Portugal,
Fnuuw, Ghreat Biitein, and the dnited States. They have
gradnatty inereMed in size and eitent with the advancing
waotaW tiie artrmunner until those of Great Britain and
this oQfontry have become ootovo vohiinee of between 500

264

ABTRONOltT.

and 600 pages. These two are published three yean or
more beforehand, in order that navigators going on long
voyages may supply themselves in advance. The Ameri-
can Ephsmeris and Nautical Almanac has been regular-
ly published since 1855, the first volume being for that
year. It is designed for the use of navigators the world
over, and the greater part of it is especially arranged for
the use of astronomers in the United States.

The immediate object of publications of this class is to
enable the wayfarer and traveller upon land and the voy-
ager upon the ocean to determine their positions by obser-
vations of the heavenly br "^ies. Astronomical instruments
and methods of calculation have been brought to such a
degree of perfection that an astronomer, armed with a nau-
tical almaiiac, n chronometer regulated to Greenwich or
Washington time, a catalogue of stars, and the necessary
instruments of observation, cai> determine his position at
any point on the earth's surface within a hundred yards
by a single night's observations. If his chronometer is
not so r^ulated, he can stUl determine his latitude, but not
his longitude. He could, however, obtain a rough idea
of the latter by observations upon the planets, and oome
within a very few miles of it by a single observation on
the moon.

The Ephemeris furnishes the fundamental data from
which all our household almanacs are calculated.

The principal quantities given in the Amniiam Rphemeri* for
eaflb year we as follows ;

The poeitiont of the sua and the principal large i^aaete for Qmn'
wich noon of every oay in each year.

'tha right aaceaiiiitt and aeoiiniition of the nioon*s eentn far
evwy hmtr in UN year.

The dietaam of ^he moon from certain bright itan aad p l i w li
for everv thira hour of the year.

The niriiteaaeaaions and aeciinationsof upward of two hundrad

^ the bdigliler fixed etan, corrected for pteoeieion, nttt ert c w , aad

abemtfoiL for eveiy ten dnrs.
TlMMUtioMOf fbe principal plWMts at every visible trai^t over

Oonplete iliwiiitii oTaU tha aoUpies of tbe mm iad wooii, with

)li8hed three yean or
igators going on long
dvance. The Ameri-
mae has been regnlar-
rolume being for that
f navigators the world
especiidly arranged for
d States.

lions of this class is to
pon land and the voy-
leir positions by obser-
tronomical instmments
een brought to such a
ner, armed with a nan-
ated to Greenwich or
ars, and the necessary
termine his position at
ithin a hundred yards
If his chronometer is
line his latitude, but not
r, obtain a rough idea
ijie planets, and oome
single observation on

'nndamental data from
ire calonkted.

t AmniioHi Fphemerto for

psllMgairiMMto for anrap

of the mooB's eotn for

B bright atut sad plMMli

at upwud of two ItOBdrad
» pteoearion, nntallaii, and

tA erery vUibU traiytt ovsr

of fli0 nw iDfl mooiii iHth

TITS BPHBMBRja.

265

maps showing tho passage of the moon's shadow or penumbra over
those regions of the earth where the eclipses will be visible, and
tables whereby the phases of the eclipses can be accurately com-
puted for any place.

Tables for predicting the occultations of stars by the moon.

Eclipses of Jupiter'' I satellites and miscellaneous phenomena.

To give the reader a still further idea of the Bphemerit^ we pre*
sent a small portion of one of its pages for the year 1888 :

Fbbroart, 1888^at Qrbbnwich Mban Nooif.

week.

Tn Sim

'•

BqnaUoa

orUmeto

beub-

traeted

time.

Of
M

lereiUUma

AppMent

rlghlMeeB-

■lon.

Diff.
fori
boar.

ipperentde-
Uiwitlou.

Die
fori
how.

rMitaa-
niSonof

ICUMUI.

Wed.
Tbnr.
Frid.

4
8

1.
18-04
K-84
19-a

■.

w-m

10-141

lo-ior

•

817

45
87

■

a-4

6-4

a-9

•

44-a

a- ■.

U 61-84
18 W-U
14 6-01

0-818
0-984
OIW

a
a
a

v. •.

a n-m
a u-a

64 14-M

Mm.

19
16

91-a
aa
a-a

10 on

1O-O40
10-087

18
16
16

9
M

a-9
a-8

8-1

-f44-a

Tea

a-a

14 10-81
14 16-41
14 19-a

0-918

oia

0-lW

91
91

a 11 -a
9 7a
8 4-a

Thw.

n
n
n

a
a

a-fli
a-ra

8-a4

t-Nl
9-8W

16
14
14

li
u

a-4
a-i

17-7

-HT-a
«-a

14 um
14 a-01
14 a-a

0-117

o-a4
0-oa

81
91
91

10 l-«
ts 67-a
17 M-14

Md.

Hal
Siw.

11
ai

40
44

1S:S

lo-a

9-877
9-8a
9-816

61-8
11-9

a-9

a-47
a-a

.14 a-61
14 r-a
14 a-a

o-ao

0-011

o-oa

n
n

91 a-a

a 47-a
a ua

Kba.
Tms.
Wed.

18
14
IS

tl
91

a
a
a

S:8

64-M

9-784
9-ia
9-TB

9-1

a-8

14-9

4w.a
61-n
61 a

14 aa
14 aa
14 a-a

0-184

a
a
a

a aa

M
17
M

4717
88^
81 -a

9-8a
9-8M

9-8a

It
11

IS
64

a-8

ai
a-8

-H»l4
Ti-a

14 1MB

14 19-a

14 T-N

0184

o>ia
o>9a

SS:S

a a-ii

Of the same general nature with the Sphemeris an catalogues of
the fix >d stars. The ol^Jaet <rf such a oanlogue is to give the rj|riM
aaeaiuioB and deelinstioa^ a nomber of atars far soate epock,^a
b^gnuBing of the year 1875 for isitaiice, with Ha data by wMA tl»
nodtion of a star can be fauid at aay other opoch. awh oalih
logoaa ar& however, imperfeet owing to the c ww uta nt naall nhaaiia
in the poatlonsfrf tito aara and the enon aw^ iuaerl^eMoM ofwa
older ooaervations. In conaequMwe of theae taapernoaiMs, a oomM-
eraUe part of the work of the astronomer eagaMd %k accurate d»>
tanfautioiu of geoaraphioal poaltioas oomfaitlk 8m^ tfew i
aoeunt« poaittsBS oFtta atara which he aaka -mi oi.

PART II.

THE SOLAR SYSTEM IN DETAIL

CHAPTER I.
STRUCTURE OF THE SOLAR SYSTEM.

Thb solar system, as it is known to ns through the dia-
ooveries of Copebnious, Kepleb, Newton and their sue-
oeasors, consists of the sun as a central body, around which
revolve the major and minor planets, with their satellites,
a few periodic comets, and an unknown number of meteor
swarms. These are permanent members of the system.
At times other comets appear, and move usually in par-
abolas through the system, around the sun, and away from
it into space again, thus visiting the system without be-
ing permanent members of it.

The bodies of the system may be classified as follows :

1. The odntnil body —the Sun.

2. The four inner planets— Jferottry, VentUy the fourth,
Mw.

8. A group of pmall planets, sometimes dSkA AKteroidi^
revolving outside of the orMt of Mara.

4. A group of fcwr, outer planets — J-upitett Saturn,
Urtmm^ KadJ^tpinme.

6. The MitenitflS, or secondary bodies, revolving about
Urn piMMli, mMat primaries.

ft, A number of comets and meteor swarms revolving
in ^pfy eooenlric orbits about the Sun.

jjgg ABTRONOMT.

by Sir Wil ..taL Hi^hboukl in 1802, are worihy of repe-
*'*'^et. are celestial bodies of a certain very conaider-
''"Th^'move in not very eccentric ellij-ea abont the

'"^The pUnea of their orbita do not deviate many degreea
from the plane of the earth', orbit. ^^

Their motion abont the ann ia direct. 1^

mm, Umb^ how far thb in»y 1» "»*« to y«t »»

*^ „,« to v«7 »»»«« elMp» " "- P-"^
-^i^:j:i«b motion .*nll,rf ihep-i-t «<.*r

'"SlfS:: of **«»*- i. *» '"-^ -"^
alt;

md 4 are BometimeB
I, to distinguiBh them
,r jdaneUt oi Gronf 9.
)nB claaaefl, laid down
J, are worthy of repe-

certain very conaider-

tric ellip«» about the

deviate maiiy degreea

rect.

ideiable extent, which,
)le proportion to their

iderable dirtanoea from

y known as mmU w
which move about the

of oonaiderable eooen-
may be inclined to the

They may or may not

be Mmtoed ia y«k un-

eliipaea or in paraboHo

n^of thegreatatt v«riety

a i» dao totaBy «id||ir-

ny jpwit exMoW*****

Th« nillttt afpwrai n^ ihe shn, as leen

from ^ ^Moai i^lMiet8» is ahdWA^i the next figure.

JPfard and JffMMMyiM an two of tiM asteroids.

A oiirioiswlilfcm between the disfeHMes of the planets,
known is Bani^lMr,denmsmentkNi. IftoAennm-

bers,

O,8,0,1%«A,48,»«»1M,884,

^M-.

870

ASTROlfOMT.

eaoh of which (the tiocond exorptod) ib twioo the prooed-
ing, wo add 4, we obtain the Berics,

4, 7, 10, 16, 28, 52, 100, 106, 888.

Those last numbers represent approji i itely {\w dia-

Fie. 76.— ijrrAauTT UMiKxtnam or

vnurr

vn MM

rmm Mr>

tonoes of tiie pluietB from tiie am (exoept for JffplmMf
which was not disoovered whm the ao-oalled bw was an-
nonnoed).
Thia ia ahown in the following table :

-■«%^\-V--,*^j<::^-^^,^.:^i^-;ff.^!l.'£-^<^ifrgr^'

is twice

, 106, 888.

pproA .1 >tely tlm dia-

an (except for Ntfti^uMf
to 80-called law waa «a-

teble:

IMAGE EVALUATION
TEST TARGET (MT-3)

1.0 ^tma

Itt 122 a 2.2
lu —

Itt 12.0

CIHM/ICMH

Series.

CIHM/ICMH
Collection de
microfiches.

Camdiwi liwdtuM lor HiMorieal Mlcroftproductloiit / InMNut caMcHwi <(• nrtcroreproductlOM Muoriqim

0HABACTERT8TI08 OF THE PLANETS.

871

PLAinm.

Mereary
Venas. .
Earth. . .
Man . . .
rCerai]. .
Jupiter .
Saturn..
Uranus. .
Neptune

Antul

Distance.

Bode't Law.

8-9

100

15-3

160

87-7

380

08-0

9S-4

100.0

191-8

106-0

800-4

8880

It will be observed that Neplnme does not fall witiiin
this ingenioos scheme. Cere» is one of the minor planets.

The relative brightness of the sun and the various
planets has been measured by Zoixnbr, and the results
are given below. The column -per oent shows the per-
centage of error indicated in the separate reanlts :

Suit Axn

Bitlo:lto

PucantorBmr.

Moon

618,000

6,99i000i«»

5,479,000,000

180J80,OdO,000

8,488,000,000.000

lo^no.ooo/100,000

1>6

Man

6-8

Jupiter

6-7

Batam (ball alone)

Urmwi i

60
6*0

Neptnne......

5>5

The d^OnooM in ihe dm^ty, aiae, mam and distance
of the aoiiillilltiieti^ and ih the amoani fA, aokr li^t
and heafe viliii titej ■•n owi v,' are immonae. IPie diatmoe
of Neplm0^li:nil^^isam libtit of JfaroMy, and it re-
ceivw <n3i^t4i% m aoaoh I^i^ and heat fimm the aim.
The detiril]^ tH the earth !■ abofvt aSx timea tiwt of ?Mlor,
whOe Saimi?i moan ^bmmtbj ia la* than tfaft of urattr.

Hm maoa <lf the ann ia iu graater than that olaii|f

alng^ |l«Mt in tiie ayslflitt, or indeod than the oonOiiBted

pumidt&^ikBm. !bi gip«nkl)itia it rNnarfcaMe fact

, thiA the nam of any giT«n phmrt eaBoeeda tiie anm of the

■mtmu of aH the phaeta of laai mm tibaa itielf. Thfiila

-.-/■'^.-.-.T.-.j.Ttifrri^r'^

272 A8TB0N0MT.

Bhown in the followingtable where the ma«^ of th^^
ets are taken as fractions of the sun's maw, which we here
express as 1,000,000,000:

SM l;»8 8,000 44^

Bi.aoo «5;i8o. w4,aoB

Pi^Mm.

1,000,000,000 Mmm*.

MO <

634 <
»,8Ty <
5,087 <

80,187 <

884

8,858
8.080

too

81.800
886,580
864;806

The nuw of Mercuty ta te« tlwn the maw)
of Man: >

The samof OMwesof Mercury and Mare)
is leaa than the man of Yenoa : )

Mercury + Mars + Venus < Earth:
Merwuy + Mars + Venus + Bwth < Um- )

nus: '

Mereury + Mars + Venaa + Barth + Ura-)

BUS < Neptune : >

Meieurr + Mars + Venus + Earth + Ura- J tOl.787 <

una + Neptune < Batnm : )

Meieuiy + Mara + V«ins + »«*+J?l»-| 887,887 <
iSi + Neptune + Saturn <J«plter: J

ComMaed mass of all the plaaeta ialess) |^«n <; ififM^fiMfiM
tlMA that of the San: i

The total mass of the smaK phneti, like ^^^J^^^

of ^ aboT* nu-et of Hie lokr |y^ by """^^ T*
or two units. The -un's m«8 i- *b» oi»r 700 time, thrt
of r&e o&er bodie., «id him« tto f^ of iti ««.^
poritioa in the soUir •y»tf\ *• f**^ ^^^

oatiide the body of the Mm, and will be taild^^ J'*'***
/«mtor and .8Wim» are in opiporfto difjejo^^

the aim have been expWnrf to »aSL^J^J2
i. there said it .ppewB tin* the b«t tl«ete»#«i» «« ««

PLANET ART ABPBGTB.

373

B masses of the plan-
aass, which we here

PiiAifvn.

4.806

1.000,000,000

MaMM.

900 <

8»

outer planets will be when it is in opposition— that is, when
its geocentric longitude or its right ascension differs 180°
or 12^ from tbat of the sun. At such a time the planet
will rise at sunset and culminate at midnight. During the
three months following opposition, the planet will rise from
three to six minutes earlier every day, so that, knowing
when a planet is in opposition, it is easy to find it at any
other time. For example, a month dfter opposition the

684 <

»m

%m <

<.0«0

mt <

Imw

80,187 <
101,787 <

vfim <

51,000

tMMiOO

tlMjM»

ts, like their number,
than one ttwuMidth
iaanma^mm idtal
kem by wa^^km one
iw o^ 700 tfmes that
tthe faekof Uieentnkl
c|laiiied. In lMt,i)w
IV Mwfeem it ^^1^9^ liktie
mbeiniidealitwbifi
diraetloMfroaiit
M of 43w ^taaoli libmit
iplwIT. Fremwbift
I tteeto«M) ^MM ef tte

fkn^mB^htimoUi 4iim boars bi|^ abont miiiMl,and
wIlL enlninitoidMil nfaie or tea o'elodk. ^Of oowie the
hwwr pi Witti aoiit eoaw ^ito q>pQsition, and benee are
bMl Mm abiMt Ibe t&Mt of tbeir gieeutest elqiigetioiw.
^ «bofe Ignv ^PM ft roai^ fSm of pact ^ tbe

lyit i uft m^imoHmpf^ to ft^^eetator immr^ieHjy

t or MOW' Jie fii«*ol Ibe ed!]^

874

ABTBOirOMT.

It is drawn approximately to scale, the mean distance of
thee«rth(=l) being half an inch. The mean diatMice of
Sa^tm would be 4-77 inches, of Uranwt OoD inches, of
Nep^tme 1503 inches. On-the same scale the distance of
the nearest fixed star wonld be 103,133 inches, or over one
and one half miles. .

The arrangement of the planets and satellites is then—

« AatamUa The Oatw OcMqk

TheliuwrOfoop. Aiteronn. / Jupiter and 4 moon*.

Mercaiy. ) aoo minor pUaeU. \ htam Mi SaMona

VewM. \ ud probably < Unuiu ■■« 4 pwaa.

Earia ma Mom. i maar mon. f Waniaaa aad liMaoa.

BlanaiitWMMM. J ^^ ^ »ap«ma aw » -ip"

To awid lepetitiona, the elements Of ihe major plwets
and o«lier data are ooUeotod into the two foUowtog ««Wtt»,
towhidi iwfaence may be made by the atudwit. _The
unite in terms of which the varioua ^nantitwa «• fiten
arelhow familiar to m, ■• mileB, daya, etc, y«fc Jon» of
the dklMwea, etc, aw ao immenwily greater tbio any

lounm to our dafly experience that we muat I*'' »««"*
to ffl-trationa to obtdn «y id«t rf ^ at JL F«rex-

annle.the dJataaoeol the aoniaMd tobeW* «««»»
3^^ It i. of i«pert«ce tM eoB* idea d«mM^
of tliitdistaiifle,ie it it the unit, in tenM of wMA Jot

on^ flie cHrtMH*. in the '^'^S^ S^.S^'Html
w^ i«v«a aa a b«ib for nwatuaeia tkeetcfiur vttNtw.

tST^ we ..y that th^«lt-« 2.^

.90%M» tbnea tbe hmhi dlrtttice «f ^' «?« .^> y ^^

^Z^a», to M if aen» eoMifMo» fltii beditaiMM «>»
SS^thic Of *• rtlitiiit i«i*^
STnTconoeption. »fc ftar too g«at f «r w to We
counted. We have never taken in at one vtow, ejren
, niinion Bimihr di«»ete objects. To "onntftwrn 1^
900 leqnirw, with veiy rapid counting, «0«eeoiidf. BJ*
pose^ kept up for ♦ day without i"*««^« v** ^
Uwe ihouM have eennted 288,000, wM«^ ^/f^,^

of W.6eO,000. Henoe over 10 f'«^,^"^°3f^

«^ hy ni^t and dg i«-ddbe ^

^^ ,ll»eiM«i*r,«dkingbBlwet»ie^««*w^

EXTENT OF TUB SOLAR SYSTEM.

376

;hemean distance of
l^he mean distance of
nm 9-i9 inches, of
scale the distance of
(3 inches, or over one

id satellites is then —

The Oatw OfMp.

! Jupiter and 4 mooiM.
ftalam m4 SaMont.
Naptiuw Md 1 ■won.
of the major planets
two following taldes,
f the ila^ait. The
qiiantitk» fro #ven
ya, etc, ytfc •orae of
Aj groater thtn any
ra mnat haTV^nHNnrse
them at all. lor ex-
id to be 09^ mUlion
a idM ahooMVt luid
i termaof wUili&ot
ni are wpmmAf but
la tfaaateUar obiVBe.
I of tiM alMi il «ver
f theano, it b pw mm
eanbeobfeiilMi^one
illkb«»»M«M%we
great f or ns to nave
in at one view, wma
yTo eomit iKNO^ 1 ^
ting, flOaeeoBuli^ Bo^
I iiitenaiMtoa; M tin
)0, wMcli io dMiitvb

the task all idea of it would have vanished. We may take
other and perhaps more striking examples. We know,
for instance, that the time of the fastest express-trains be-
tween New York and Chicago, which average 40 miles per
hour, is about a day. Suppose such a train to start for
the sun and to continue running at this rapid rate. It
would take 868 years for the joumej. Three hundred
and sixty-three years ago there was not a European settle-
ment in America.

A caimon-ball moving continuously across the interven-
ing space at its highest speed would require about nine
yearn to reaeh the sun. The report of the cannon, if it
could be conveyed to the sun with the velocity of sound in
air, would arrive there five years after the projectile.
Such a distance is entirely inconceivable, and yet it is
only a small fraction of those with which astivnomy has to
deal, even in our own system. The distance of ITeji^mne
is 80 times as great

If we examine the dimensions of the various orbs, we meet
almost equally inconceivable numbers. The diameter
of the son is 800,000 miles ; its radius is but 480,000, and
yet this is nearly twice the mean distance of tiie moon
from the earth. Try to oonodve, in looking at the moon
in a clear sky, tlu^ i£ the centre of the sun oould be
placed at the eeiitra of the earlJi, the moon would be far
within the raa'a aorface. Or^^jain, omioeive of the f<mie
of gmvity at the mrlioe of the vaiioua bodies of the ays-
tras. At tibtf aui it i| neaily S8 times tbatjknown tons.
A pendidant beating seeondi here would, if tiwi8p<nfted
to the sim, viinwte witii a motion more ra]Hd than HuA of
a watoh'bdanee. The muacleB of the strongest man would
nibk tttfpiai tdm ereet m tibe aurfaoe o| &» ami : evto
lying damn he would erash himfelf to dei^ uncter his
oiHl Wfight of two ton*. We n«y by these illnstvatiens
gttiiHM10i(jph Idea of the meaning erf the numbers in
litm$^i^i^iiii0uiit^ ^ Jae^afcOity of our Hmited Jdeaa to
wm^iat9tmAik»tin^ el even I3ie sohar qntem.

S76

ABTBONOMT.

■a 58 «5 S 9 »9 9 -

^S BB 95 • S 8^ S 8

•8 Si ** 8_J_r^_?_I_

8 8 88 :s *-

9 s ss e 8

$ to 88 8 ^

<» 4) 88 8 S
S S 88 9 9

« S9 5551 8 8 88 9 S

- S6 aa s « •" 8 •

e 88 gj g ^ 88 g 9

iliiil

ni""iroiiT|

8 f^*- ^e

itt

a as? 9 *
s S9 s s

e» ae « •?

8 88 ?: *•
S SS !S 8

to S8 8 ^

9 88 8 S
S 88 9 9

^ me* o !■*
et lOflO. ►• y*

8 88 9 S
S •" 8 •

?3 88 g 9

3 8g

II III I

msTi

CHAPTER II.

THE BUN.

« 1.

To the rtudent of the preBent time, armed with the
powerful meani. of research devised by modem science,
Sie sun presents phenomena of a very varied and complex
character. To enable the nature of these phenomena to be
dearly underetood, we preface our account of the physical
constitution of the sun by a brief summary of the mam
features seen in connection with that body.

FhotaMplMre.— To the simple vision the sun presents
the aspect of a brilliant sphere. The visible sWning sur-
face ofthis sphere is called the photosphere, to distinguish
it from the body of the sun as a whole. The apparent^
flat surface presented by a view of the photosphere is caUed

the sun's dUk. , , ,. . ,

Bpoto.— When the photosphere is exwmnedwith a tele-
nope small dark patches of varied and irregular outlme
I^^iJ^ilyfouiduponit. These a^caUed the «*«.

'bIiMIoii.— When the spots are observed from day to
day, they are found to move over thesun's disk in sudi a
w/y M to show that the sun rotates OB^t. aas in a period

ofWoraedays. The sun, therefore, hsa «*», iw<^, ««
^„«ter, Uke Ae earth, the axis being.the line around

which it rotates. uj j.4« a-, a*

f^MWl».-Groupe of minute speeks bri|0itor than tte

tood of ipotoOT elsewhere. They aw oilled/«»«lA

FSATURMB OF ThJ BUN.

279

hXT.

armed with the
modern science,
iraried and complex
le phenomena to be
ount of the physical
nmary of tlie main
>ody.

n the mm presents
visible shining mr-
|;A«r0,todistingaish
e. The apparently
photosphere is called

xamined with a tele-
ad irregular outline
are called thoMZor

served from day to
sun's disk in such a
nits axis in a period
,has«Bi«,iw2Wf and
iug the line around

a brin^i^nr Uian the
leen in the neif^bor-
re aOkd/dMilai.

CHuromoaphMre, or Uamu — The soUr photosphere is
covered by a Uyer of glowing vapors and gases of very ir-
regnhur depth. At the bottom lie the vapon of many
metals, iron, etc., volatilized by the fervent heat which
reigns there, while the upper portions are composed prin-
cipally of hydrogen gas. This vaporous atmosphere is
conmionly called the ohromoapheref sometimes the tierra.
It is entirely invisible to direct vision, whether with the
telescope or naked eye, except for a few seconds about
the beginning or end of a total eclipse, but it may be seen
on any clear day through the spectroscope.

Fromlnenoss, Protube r ano— , or Bed Tiaacaam. — ^The
gases of the chromosphere are freffuently thrown up in
irregular masses to vast heights above the photosphere, it
may be 500,000, 100,000, or even 900,000 kilometres,
like the chromosphere, these masses have to be studied
with the spectroscope, and can never be directly seen ex-
cept when Uie sunlight is cut off by the intervention of the
moon during a total eclipse. They are then seen as rose-
colored flames, or pUes of bright red clouds of irregular
and fantastic i^pes. They are now usually oalied " prom-
inences" by W^ English, and "protuberances" by
French writers.

Cknmia. — ^During total eclipses the sun is seen to be en-
veloped by a mass of soft wldte light, much fainter than
the diromosphere, and extencting out on all sides far be-
yond the hi^est pfrominences. It is IwighteilliRNind the
edge of the son, kdA UdMoft toward its outer hoondaiy,
by iuensiblegradatleiis. This halo of lig^t is ealled the
wrmO) and is a v«7 sfarikiBg object dnringatotal eeUpee.

MpeekaadStraotwMoftlMllMtoqplMr*^— The disk
of the son id einnlar in shape, no matter ytfoA aide of tiie
sub's §^obe is turned toward us, whence it follows duijt^
SUB itself is a sphere. The aspect of the disk, when

380

ABTBONOMr.

viewed with the naked eye, or with a toletoope of
low power, is that of a uniform bright., shining Hurfaoe,
hence called the photoaphere. With a telescope of
higlior power the photospliere is seen to be diveraified
witli groups of spots, and under good conditions the
whole mass has a mottled or curdled apiwaranoe. This
mottling is caused by the presence of cloud-like forms,
whose outlines though fidnt are yet distinguishable.
The background is dso covered with small white dots
or forms still snudler than tlie clouds. These are the
" rice-grains," so called. The clouds themselves are
composed of small, intensely bright bodies, irrq^larly
distributed, of tolerably definite shapes, which seem to be
suspended in or superposed on a darker medium or back-
ground. The spaces between the bright dots vary in
diameter from 2' to V (about 1400 to 9800 kilome-
tres). The rice-grains themselves have been seen to
be composed of smaller granules, sometimes not more
than 0''8 (186 miles) in diameter, clustered together.
Thus there have been seen at least three orders of
aggregation in the brighter parts of the photosphere :
the laiger cloud-like forms ; tiie rice grains ; and, soDoall-
est of aJI, the granules. These forms have been studied
with the telflsoope by Sboohi, Hvoons, and Lakolit,
and their relations tolerably well made out.

In ths Amuuin of ths Bureau of LoMtitiidss lor 187B fo. 089).
M. J AMiSBH givM an soMunt of hk rsosaft OMKivsiy of the NttBttlatod
amngoMBt of tlM solar photospbcN. Ths pi^sr is aosotipMMsd
by a jdwtograph of ths appeanasas dcserlM, wUoli Is «ilaif«d
thraefold. Pnotogn^th* uas than four IboImS la msiMfcif cannot
ntkfaotorily show meh tfslafle. As the mwAitlsBsef > the sOhr
Mirfaoe an, in goMral, not graatiy Isrger thaa 1" or W, th* photo-
graphic imdisSon, which is soowtiBBCs M" o# mtan, im^ caBsphtety
obwuM their eharsetcriatf ei. This dtflooHv M. Jamshw has over-
oome bj enlarging the image and shortaanig ihe thae of czpos-
ure. In this way the irmfflstion is dfariMMted, beeaan m tls dt-
ametcis in cr ea s e, the linear dimensions of the details ars towaassd,
and " the imperfections of the sensitive plats havs iM nlative iss-

h a toleioope of
k, shining Burf»ce,
[ a telescope of

to be diversifled
)d conditions the
piMjaranoe. This

cloud-like forms,
it distinguishable.

small white dots
i. These are the
ds themselves are
hodies, irregularly
, which seem to be

medium or back-
right dots vary in
) to 2800 kilome-
kave been seen to
metimes not more
clustered together.
St three orders of

the photoaphere :
gruns ; and, amall-
s have been studied
»»8, and Lamolbt,
tout.

Idas lor 1898 ^ ««»)•

IMS la tfasuliit cauiot
HHMlatisMQftbs solMr
ta»il"ofr,tl»l*o4o.
oi awa, SMJ oompleUjly

fiwihstime of npof
h&beea«aastl!a«-
liadstaUssia hiew sss J .
Its bava Ms rdattva Un-

Htrif'a

Affain, M. jAWSsaif has noted tlwt in short expomira the photo*
gnpnic •pectnim it slmoat monochiomatio.

In this wsy it differs greatly from the visible spectrum, und to
the advantage of the former for this special purpose. The diameter
of the solar photograms have since 1874 been successively increased
to 12, IS, 90. and 80 centimetres. The exposure is made equal all
over the surface. In summer this exposure for the largest photo-

282

ABTRONOMT.

urt' genenlly circles or ellipiea, but these curres «re sometimes
gresUv altered. This ^nuialstion is ftpparently spread equally all
o^er the disk. The brilliancy of the points is very variable, and
they appear to be rituated at different depths below the photo>
sphere : the most luminous particles, those to which the solar light
is chiefly due, occupy only a small fraction of the solar surface.

He most remarkable feature, however, is " the reticulated ar-
rangement of the parts of the photosphere." " The photo^rams
show that the constitution of the photosphere is not uniform
throughout, but that it is divided in a series of regions more or
less distant from each other, and having each a special constitution.
Thew regtoDB have, in general, rounded contours, but these are
often slflMMit rectilinear, thus forming polygons. The dimensions
of these flgnres are veiy variable ; soma an even 1' in diameter
(over MLMO miles).'* "Between thew flgorea tiia grains are
sharply defined, but in their interior tliqr b« almost eAiced and
run tof^rther as if by some force." These phenonMna can be best
underrtood by a reference to tiM figure of 1l jAnsanf (p. Ml).

Light ■Dd HMife ftom tbm VliotoiplMra. — ^The fholo-
sphere is not equally bright all over the apparent disk.
This is at onoe evident to tite eye in observing the snn with
a telescope. The centre of the disk is most brilliant, and
the edges or limht are shaded off so as to f (Mreibly suggest
the ids* of m absorptive atmosphere, which, in £iot, is the
canse of this appearaaoe.

Bncb absorption ooonn not tmly for die rays by which
we seethe son, the so-called wmmA ra^f bat tor those
which have the most powerfnl effect in deoomporing the
salts of silver, the so-MUed i^emioal royt, by whidi the
ordinary j^K^ograph is taken. •

The amonnt of heat reoeived imm WbawA portions of
the son's disk is also variaUe, Mowding to tita part of
the a^Nurent disk examined. This ia what «« shoiikl ex-
pect. Thatis,!ftheiiiteo[^ofiaiy4»eof tlMsendi«ttons
(as felt at the eartili) varies from centre to oironmferunoej
that of every other shonld also vary, since they an all
modifications of the same primitive moti<m of the son's
constitnent particles. Bot the cottstitation of tiie son's
atmosphere is soch that the law of variation fw the lluree
dassea Js different. The intensi^ of the radiation in the
son itself and. inside ai the absolve atmosphaiie is i»<qb»

..:m^^. ...>...■.-. -.^^- ,. ............. -^.^.^v,^ «.^.^. ..■„...-.,■■■. --.,...,^«.,- ........ ^^....^^^1^

unres are ■ometimes
tlj spread equally all
ii very Tariable, and
M below the photo-
whicb the solar light
the Bolar surface,
"the reticulated ar-
"The photograms
here is not uniform
s of reigns more or
a special oonstftuiion.
intoarajbut these are
MM. The dimensions
I erea 1' in diameter
gnns the pains are
rs almost dnced and
kenomflna can be beat

jAMtBN (p. Wl)>

BOLAR BADIATIOir.

283

iMr*.— The .
the apparent disk,
lerving the snn with
most brilliMit, and
to f <Hrcibly raggest
rhioh, in &ot, is lihe

r the fmjB by which
ray«, bat fur those
in decomposing the
roftf by which the

difiereufc portions of
^ding to tile part of
what we ilioald ex-
M of ^flseaiiitioDB
re to circnmferuneei
r, since they an all
mo^oa of tiie sun's
titationof the Kin's
nation for tiie tfoee
the radiation ill tlie
« atmos||^h«Ri ii 1^^

ably nearly constant. The ray which leaves the centre of
the sun's disk in passing t-o the earth, passes through the
smallest possible thickness of the solar atmosphere, while
the rays from points of the sun's body whidi appear to
us near the limbs pass, on the contrary, through the maxi-
mum thickness of atmosphere, and are thus longest sub-
jected to its absorptive action.

This is plainly a rational explanation, since the part of
the sun which is seen by ns as the limb varies with the
position of the earth in its orbit and with the position of
the sun's surface in its rotation, and has itself no physical
peculiarity. The various absorptions of different classes
of rays correspond to this supposition, the more refrangi-
ble rays suffering most absorption, as they must do, being
composed of waves of shorter wave lengtii.

The following table gives the observed ratios of the amount of
heat, light, and cheidcal action at the centre of the sua and at
raiioas diataaoea from the centre toward the Umb. The flrst
column of the table ^ves .the a^iarent distaneea from the centre
of the disk, the san*s radios being 1*00. The second oohum gives
the peroentage of heat-raya recced by an obsiTrer on the earth
from pdnts at these various diatances. That ia, for every 100 heat-
raya reaching the earth from the san*a owtro, M teach ua from a
point lialf way from the centra to the limb, and so on.

AttSlMous data an given for the IMit-nqrs and the ehamical
raya. Ae data in regud to heat are mw to Prof enor LMMatMi :
those in regard to li|^t and chemical action to Prof essor Pzoxaawo
and Dr. Voobl tmpeMnlj,

PwfAWCT mem

Cmw*

EastSsgra.

ligktB^ri.

OhnUcatB^Mw

e-eo

100

• • * •

• • • '

OS
80

• • • •

100
Wt

• « • •

• ■ • •

87-

100
88
80
86
46
95
»
18
18

9.aB

9.n...

0>t6

0.tB

0.M

0.tt.

1-00

• iKir tmo equal a^arant sorfaeea, A aear the saa's osatra sad B
mm Hm UndH w* Mqr mf tkat the nt* <>«» tiio tiwaoiiaaas wtai

ASTRONOMY.

I-

raoeired at the earth hare approximately the following relatire
effects:

A has twice as much effect on a thermometer as B (heat);

A has three times as much illuminating effect as B (light);

A has seven times as much effect in decomposing the photo-
gratriiic salts of silver as B (actinic effect).

It is to be carefully borne in mind that the above numbers refer
to vwdations of the sun's rays received fma different equal surfaces
A and B, in their ^*et vpon etrtam atiUrary Uri ' Mtr itU tUmdarda qf
mmuurt. If, for example, the decompoduon of other salts jthan
those employed for ordinaiy jphotogrannic worlc be taken as stand-
ards, then the numbers will be alteraa, and so on. We am simply
measuring the power of solar rays selected from different parts of
the sun's apparent disk, and hence exposed to different condiitions
of absorption in his atmosphere, to do work of a certain selected
kind, as to raise the temperature of a thermometer, to affect the
human retina, or to deconipose certain salts of silv«r.

In this the absorption of the earth's atnioephere is rendered con-
atut for each kind of experiment This ataiosphere has, however,
a vary strong abswptive effect We know that we can look at the
aettiag or rising sun, which sends its lij^t rays through grmt
deplka of the ewth'a atOMMqpliere, but not upon the sun at noon*
day. Tke temperature is lower at sunrise or at sunset than at noon,
and tlM absorption of chemical rwsis so marked that a ^lotograph '
of the solar spectrum which can be taken in tiiree seconds at noon
re quir es six hundred seconds about ■unset— that is, two hundred
tinea as long (Dbafbb).

Amoimt of Haat amitfead bf the Bun.— Owing to the
absorption of the aohur atmoqilierB, it followa that we re-
eeive only * portion— peihapa « yeiy small pwtion — of
the rays emitted by the snn's |iiotoq>here.
^ If the snn had no absorptiTe atahosphen, it would seem
to IIS hotter, brighter, and more bine in color.

Exact notions as to hoir grtit ibis absorption is are hard
to gain, but it may be said fm0y thai the beat authori-
ties tgree that althoni^ it irffillii possible that the son's
«t«Mv)kere abaoibs hatf tt*4iPed nj^
not absorb four fifths of tbMil.

It k a cnrions, and as yet if«i bdiave vnaxiMiMd lMt»
tiiat the absorption td iSb» silfiM^iitmosphairedoes nut iplofc
the daritness of the FnMnhelaar fines, ^nicy seam «0B^
UmsIe at the eentie and e%B ef the san.* fkmi

Prol. TovMihaa

ofa

nut rlHi»lniiiffiilfilHhlllliiwMft|

HEAT OF THB SUIT.

le following relatire

vtt»B (heat);
ct 18 A (light);
omposing the photo-
above numben refer
iflerent equal mrf aoea
t w ii Mff fcrf itandanU ^
■ of other aalta jkhaa
ark be taken a* ttand-
10 on. We are simply
rom different parts of
o different oondiitiona
c of a certidn aelected
IOmeter, to affect the
f diver.

ibere is rendered con-
oaphere haa, however^
lat we can look at the
it rays throngh great
p<m the sun at noon'
tt sunset than at noon,
ked that a photograph
three seconds at noon
4hat is, two hundrad

im.-— Owing to the
foUowi that we ra-
anaU portion — of
lera.

)here, it wonld seem
in color.

ibsorption is are hard
lat the best aothori-
Mible that the son's
^ it probably does

m nnexplabMd lMt»

pbeife does nut i^set

They seem efpl^

of this absorption is a practical question to ns on the earth.
So long 88 the central body of the snn continnes to emit
the same quantity of rays, it is plain that the thickness of
the solar atmosphere determines the number of such rays
reaching the euth. If in former times this atmosphere
was much thicker, then less heat would have reached the
earth. Professor Lanolkt suggests that the glacial epoch
may be explained in this way. If the central body of the
sun has likewise had different emissive powers at different
times, this again would produce a variation in the tempera-
ture of the earth.

Anmmt of Heat Badiated.— There is at present no way
of determining accurately either the absolute amount of
heat emitted ^m the central body or the amount of this
heat stop]>ed by the solar atmosphere itself. All that can
be done is to measure (and that only roughly) the amount
of heat really received by the earth, without attempting to
define aecvrately the drcnmstiaoes which this radiation
has undergone before reaching the earth.

The difficulties in the way of determining how ni iioh
heat readies the earth in an| definite time, as a year, are
twofold. Hist, wemnsl J»ilAe to distinguish betwew
the heat as received by • tiiermometrio apparatos from
the smi itself and that from external objeete, as onr own
atmosphere, adjaoent bnUdings, ete.; and, second, we
must be sible to aDow fw the absorption of the eardi's

Fotnujff has Mperimenled spoa this qaestisiiviwiWng
i^owaaee for the tfane that tiie nm is below (Imi Iioriaoo
of wbf ^ha$, and lor tluf taet tkstt the solar my»4» Mfr^ia
geiMil ttiiieB pmfml&eii3mAj b«ft obUqvely i^ any
gifW ipai!t of dearth's sailMe. His^oomflnsloni msgr
IM alM as laBows : if our 0(1^ atmiMfiiere were re-
laolMdi liM BOkf figrt wwdd hvn emigy enongfa. to nielt
m igfir of lee 9 eenlimotfai thidc over j^ whole eaitii
ill^^«li^«rotali0itt:«»iin»^ti^^ ' :

atittleltl anooBl oTImI radiate* % the aim, flao

■^•T' AJ^" !-' ■ '■'''

^iimmitfitmitt^iatmm

ASTBONOMT.

earth receivea but an inBignificant share. The son is
capable of heating the entire Bnrface of a aphere whose ra-
dins ia the earth's mean distance to the same degree that
the earth is now heated. The surface of such a sphere is
»,170,000,000 times greater than the angular dimensions
of the earth as seen from the sun, and hence the ewih ref
ceiyee less than one two billionth part of the solar, radia-
tion. The rest of the solar rays are, to far as we know,
lost in space.

It is found, from direct neMiires, that a ■on-qwt riTM 1«P ^«^
MM for area; tiMUl the unepotted photoaphere, and »* *■ "jnj^^-
h^mJomYum much thTeUmAe of tlie earth can be affected by

ProfeeMV Laxolbt, of Htteburgh, hM made meuuieinento of the
dlwcteihet of eon-epote on tcrreetrW temperature. 'n»-<**^_^
SonTcoadeted to mSJurtogtherelyflTeywrnteofumbra^ya^
h^udnhotaaDherieradiatkm. TherelaliTeumbnd, penmdmL
IS phSJSSTSL were deduced from the g«w obeemgoue of
!Se r «31*om a conrideratlon of thcMi data, and ccaftoiBg 0»
SSSkm^to^to changwof temetrial temperature doe to this
SSTSbSjSiSjSr dSuce. the .«ult that " ««»-«P«*- J« «-
MMM aSroct effect on terreetrW temperatare by decrcMiM the
^teSieMeof the earth at their marimum." l^toS-K
SrSSSSTW^-wU, aa " it U repieiented by a change to tEe

thadilt. on the whole, oootar to narinnm ■••■^. y*^"?*.
Sy ?i2rJ^M»«MMMjroea it tends to mafce the wrth ^^^
SS^ASteauouBt What other cau«s.«»y co«riit with the

I Hfiy, VampaMfeoM.— -Froo the amoiint of heat iotaa]^
ndJKtedby tiM a^ altetopta haw be«iimideted«ton«to»
tbi Mtaal teupeMtare of tiie K^lar ratftee. Tlie Mil-
uMlMMMlifldbyTariuu anUioritiei dilleriride|y, « tkft
Imn «Ueh gomn tlw abaoviit&ea iwiOiiii Oit *Mbr m-
Tiiop* an aknart unknown. Soma mmIi hmM ablM^
m^hm to beampoaed in any mill imrmtiffUmttaA^
MtfaMtea htm muni iHNMy MooMttiig to «iM li^ftea
Imp.

iimmitk

8P0T8 ON THE aUJT.

S87

share. The son is
of a sphere whose ra-
the same degree that
se of such a sphere is
e angular dimemdons
id hence the earth re?
irt of the solar, n^a-
I, CO far as we Itnow,

a nin-apot giru l«p |ieat,
here, and it is an ioterett-
e esrth can be affected by

nade meamiementa of the
mperatore. The o beervv
■KHUits of umbral, pemmi-
latire umbral, peBmabral,
m the Kew obMrratloiM of
data, aad oonflniBg the
tempentofe doe to this
.. tiiat " soB-Rpots do ex-
entare by decreadiw the
Mzimitm." Tliia cbaiiae
leuted byaehaiHp in Um
en yean not gmOtr than
I not intended to show that
dmrnn MUMpot y«M, iMt
» make the f«rtb eooler br
MS nay oo^eiist wMi the

amount of heat «otiN^7
been made todfOtemfo*
\u nabm. The mH-
MaUleriride^,MtlM
1 iwithto tlit*Mlar <■»•

Bofe«bN|«i» tiwiii^ilta
»«i«bo«t^lOO»OOOP 0.

philosophy, tLe temperature must far exceed any ter-
restrial temperatnre. There can be no donbt that if the
temperature of the earth's surface were suddenly raised to
that of the sun, no single chemical element would remiun
in its present condition. The most refractory materids
would be at once volatilized.

We may concentrate the heat received upon several sousre feet
(the snrnce of ahiue Iraming-Iens or mirror, for instance),
ezsaine its effects at me focus, and, makinip allowance for the con-
densation by the lens, see what is the minimum possible tempera-
ture of the son. The temperature at the focus of the lens cannot
be hiriier than that of <:lie source of heat in the sun ; we can only
concentMie the heat neeived «■ the snCMe of 4m Imb to one
point and examine iU effects. If a leas three feet In dlMMter be
hsed. the most refractory materials, as flf»«lay, jdatimnb the dia-
mond, aia at once melted or valatiUasd. The effect <tf Hw lens is
phdnlythei " " '" *

the ra "
the

mond, aia at once melted or valatiUasd. The effect <tf Hw lens is
phdnly the same as if the earth wan brai^t doesr to tta sun, fai
the ratio of the diameter of thafoDatimage to that of the tins. In
the case «t tho lens of thres Isat, aflowiiw for the absorjpMM, etc.,
this dManeeis yet MMler than fhatot tha moon tnmltte east,

so that tt appean
sun, if eamposedof
beTUflriaed.
If wa oaleolate at what rate the

MWMt ar plaaat so dose as ttli to the
' " to tlioee kk the eim, must

lofthesoaiioaldbe

lowered Annually by the radlatkm fraas itaattftM^ we M And it
to be U* Centigiade yearly If itt sMdle teat la imM
ud be^mn fuA «• peraaan tf%WM^ •^ *" ^ '

water,

tiiat^liMTariaiisooiis&tiie^ ItiSdtheie-

fore oool down la a few thoasaad yean by an appasdaMa MBOOiit.

i 8.

A very cnnory ex«mina:don of the ran's disk with a
Bindl IdflMepe witt gMMidly show one or mora da^ i|Mii
uMm tltepliOtMiilien. Then are of vMiMMirini» fran
ntante m^ dote 1' or 9* in diameter (IMO Irilomelm
otf iM^ 40 llilie ipoli wveral mimitM of ara ki eiMa*,

Selftr apoli fBiiewBy luwe a dM* eenteJ i imfl i i i r »r
um km ^ Mrroqadedby a border or pmmim ol ffi^
thU, tetemedtrte fai dMde tetween tifo iiM lilMtoMi
and^die lN%fitl phoioiplMvo. ^ ii
H>e UliiBMp*, ^ ilMii ■- mm ♦»» <>»:#»^

MiiH*MiitilH«MiMd«lri^^

I8S

ABTRONOMT.

and is BometimeB crossed by bridges or ligaments of sliining
matter. The penumbra is composed of filaments of
brighter and darker light, which are arranged in striae.
The appearances of the separate filaments are as if they
were directed downward toward the interior of the spot
in an oblique direction. The general aspect of a spot un-
der considerable magnifying power is shown in Fig. 78.

The first printed account of solar spots was given by
FABBrmrs in 1611, and Oauleo in the same year (May,
1611) also described th«n. They were also attentively

fro. W.-'xmwmk. tarn rxmaamk m mm-wrvi.

rtncUied by Hm Jesnit SoaimBB, wli» Ji^^fQMd tbem to b<
■auOI pli^ projected agiiiHt tibe tOaf^SO^ Thb u
WM diiprofved by GAUtun, whoM oiwlyittofti dMfW
tfaann to belong to tiie ann itself, ^tad lo imif^ iiiiipi«4)
MRNitlieMlardiakfromewfctoimt. A tpo||«t iHrifel«
it1lM»«Hit faib of the mm on iittyifM.4l^]teKtm
MKOH Hie (fide lor IS or 1^ diqri^Aa"ili ii l d it J: tili>liii

jp«riod» itiMfiptesd aft^^^lhb «Mtai»la^
lid aiior it Iwd iii lite vmm^m niM m A .

.ii^

■•■'■ "-"'l i ' 1 1 'ih -■•■'* ■'■'i-rT- i rfi'fi" ■'iu'a

rr.

68 or ligaments of sluning
mpoBod of filaments uf

are arranged in striee.
) filaments are as if they

the interior of the spot
neral aspect of a spot nn-
er is shown in Fig. 78.
Bolar spots was given by
in the same year (M4y,
ley were also attentively

8UjrB SPOTS AND ROTATION.

289

, whoittpfQMd^hemtQlM
«he sobi'diik.. TiBkMm

f , jAiid lo wem^ larffcrtnljr
vim. AllSridKM^^MiMM

The spots are not permanent in their nature, but are
formed somewhere on the snn, and disappear after lasting
a few days, weeks, or months. But so long as they last
they move regularly from east to west on the sun's appar-
ent disk, making one complete rotation in about 25 days.
This period of 25 days is therefore approximately the rota-
tion period of the sun itself.

Spotted Bagion.— It is fonod tbat the qwts are ohiafly eoa-
flned to two soBct, one in each hemliphere, •ztending from about
10° to 8S* or 40* of helfogia]^ latitoclfl. In the iMlar regions,
Bpotsansearoelj ever wen, and on the sobr equator tliey are much

fW. Tl>.^

i>tth

of tke

lyffca.-ipr-

ntoathaii iv^'la^Mtai iy a(in# iht-i
pMi. hot Mm 0* or ' rt iiWi ll ii. #ilar i

• tte pfltH wteo t\e sii^ It i

b dM^ iha aaasC fari«def IMidafiyfiii

, -u .>.. 'tail MaiaeACMtft'ilkHMiaiaMi'i

iaiiMiinifiiiiinmr

i ■■ iiiilAiiitittailSiiiili

too

ASTROirOMJ.

■olar equator. A BeriiM of obMiratiom made by Mr. Cabbihotoii
of SnglKDd (by the eye) give the following values of the rotation
tlnyM T, tot spots in different heliographic latitudes L :

r<=MOM M-89e

Tab period of rotation

10*

15°
S5-800

97MS

45*

alio to Tary ionewhat in <Uflertat

TAB period of rotation Mema aiao lo vary sonewnac m iguinnini.

Sh eaMwt JSn any OM dalaitoMtatkM ti»* to the an, la
^mMM to Mm MOth or tha aMOo.

""IbovralMbiUtyiathattheMU^ iiotMM«oUd,l"Mi^VMefM
period of roUtion, but dtflBfOit portioiia of lu surface and of ita in-

a'atain of th* Spoil.— Hie mm-qxits are redly depNi-
lieitaW&epliotMpliflW, ww*» int fdfaiAMl <M ligr iof-

elUptioit & ahype. Am the rotatton «iHnp|iH H fidlilMr i^
fBvdMv mk i» th* diiky it beoomM moi» aad mote neulj
dfwa«r te (*ife, -ii .Iter fertsr%«ili» el 11-^^
Am •ppaMEMMs take pteoe in revwie oMv.

teHdr dirtt ooor mm, wno u iiaW l W

ude by Mr. OARBiifOTON
IS valuca of the rotation
B Iktitudes L :

IB"
2n-500

97WS

awMiiewlwt in <UflartBt
itioa tbM to tlM «n,lt

KaoUd, hMNtUf M *m
U lurface «id of MU m-
> titont 1»<i»MiMlwi t-

ipote are redly Hiaftm-

R isitff tw it fnnMr Ji|M

int oioir.

rwo b^inni of elN

■Mviiitii

HM ASTROKOMT.

tnl Md MUd nucleu.to the J"" ». "°J^ J°°J",^tlY by ^rwt.
The .pp«ently bl«k centre^ <*eBgjta»w^«^^^

ftitpMr Tery bright, h >»• ^'^ P!^T~ ii& nucW beneath «ich an
or'Kofe-or ^^^"'"'■^^J^ iJSld won become gM«>«»J»y

ninplT of «>»«>' »»?*'^*?f*',J^ STM^iiStuted haw •endbly
the'Brtorto period, wouM to a «, ^^J^J'SS other !«•«>«.
aiHrfaUbed to a few hundred 7*^.*^^JS^ Mve at to the fMt
4j!ri»»n*iMda of HBiaoHBL most be modmea, »▼« ■■ w •m-
{S» gS^^ SSySSttoi to the photoephere.

mice of cloudy and clew ye-r. on tte ^h. :^^^^

D««(«eeihe toble), eo«itfai»ed by hfai for <ff J ^
TO?hSiU»d been pwTk«dy e-i^

.;iM»^

t B fw*i " ''^ i 'wp m > ■

PBJtIODIOJTr OF BUNBPOTB.

the ipota aw depw«rfoiw
10 eitatenc6 of a cool con-
known to bo impoMlblc.
ire BO mostly by contrast.
: bMkground, they would
the photometnc meamire*
nucleua beneath rach an

won become BMeo«»,^y
>f the photoai*ere. The
f nearly conatant daring
miatitated hare aendbly

theae and other nam
idUed, mve aa to the fact
otoaphere.

hut it was independeutl}' snggeated aiid completely proved
hy SoiiwABB.

fiB um Ain^ 'iMittl^^

■ iid|^t iwnt fo be ^i^
rostanoe; Kfce flie ooear-
n the ^h, 7«i ^ i«^
J Holnih SomrAm of
I br him for lortjr jf«M»,
nbwTail6A>««Mli8a%-

TABLB or SOHWABB'a RBSULT&

YaAK

Dajmof
ObMrratlon.

Dm of no

N«w anwiw.

vSUllMin

ttMllMMUe
MmK

1886

977
978
989
844
917
980
970
947
978
944
900
168
908
900
968
M8
807
819
881
889
814
976
978
988
808
808
817

SIS

894

848
889
8M

817
880
886
907
849
818
801

ISO

190

148

111

146

196

98.
78
196
98

118

161

995

188

180

148

178

978

888

988

169

189

108

114

107

907

880

986

188

101

195

186

988

911

160

194

190

101

•

8'78

1897

11-88

1888

11-86

1899

14-74

1880

19-18

1881

19-89

1888

1884

1885

1886

887
19-84

1887

1888

18-97
19-74

1888

11-06

1840..

0-91

1841

7-86

1849

1848

706
7-10

1844

6-61

1848

6>18

1848

8-61

1847

9>86

1841..

11-16

vm :.......::.

10-64

IMO

10*44

1881

'.:8

lOOt

1888

T-06

1884

6-61
6«41

6-86

iM. ..4. .

6-68

7.41

18M

10'67

1880

10-06

1881

8-17

18M

6-00

1888

6-64

1884

6-06

1888

8*14

1888

18fr..,..

7*88
7-06

1888

8-10

■iiMiaiiaiiaiii

204

AUTRONOMY.

The periudicity of tho spots is ovidont from tliu tahlu.
It will appear in a more striking way from tho following
■nmmary :

FVoa 18W to 1881, sun

without ipotfl

on onljr . . . .

1 day.

In 1888,

180 d»7B.

From 1886 to 1840, "

8 "

In 1848,

147 "

Piom 1847 to 1851 **

8 "

In 1868,

•1

«•

. 198 "

From 1858 to 1881» '*

no A».y.

In 1887,

«l

. 198 dayi.

Every 11 years there is a minimum number of spots,
and about 6 years after each niinimum there is a maxi-
If instead of merely counting the number of spots,

mum.

measurements are made on solar photograms, as they
are called, of the extent of spotted otmi, the period comes
out with greater distinctness. This periodicity of the
area of the solar spots appears to be connected with mag-
netio phenomena on the earth's surface, and with the num-
ber of auroras visible. It has been supposed to be con-
nected also with variations of temperature, of rainfall,
and with other meteorological phenomena such as the mon-
soons of the Indian Ocean, etc. The cause of this period-
icity is as yet unknowE. Oakukotoh, Db la Bus,
LoBWT, and SrswAkr have given reasons which go to show
that there is a connection between the spotted area and the
configurations of the planets, particularly of Jupiier^
VenitSf and Mercury. Zollnkb says that the cause lies
within the sun itseU, and assimiktes it to the periodic
action of a geyser, which seems to be ^ priori probable.
Since, however, the periodic variations of the spots oor-
respond tq the magnetic variation, as exhibited in the last
column of the table of Sohwabk'h results, it appears that
there may be some connection of an unknown nature
between Uie sun and the earth at least. But at praient
wtt oan only state our limited knowledge and wait for
further information.

■awe!

idont from tho tal>lu.
y fruiii tho following

onl/..

1 day.

. 189 dsjri.

8 "

. 147 ••

2 "

. 198 "

no day.

. 108 daya.

im nnml)cr of epote,
luiii there is a inaxi-
^ the number of spots,
photogrsms, as they
rea, tho period comes
IS periodicity of tho
connected with mag-
loe, and with the nnm-
snpposed to be oon-
iperatnre, of rainfall,
imena such as the mon-
le cause of this period-
iNOToir, De la Bue,
iBons which go to show
tie spotted area and the
ticnlarly of JupUery
ys that the cause lies
tea it to the periodic
be a priori probable,
ions of the spots oor-
KB exhibited in the last
results, it appears that
' an unknown nature
least. But at preaent
dwledge and wait for

mmm

S96

ABTRONOMT.

From the first serios of earlier obflervations, the period
comes ont from observed vfwnvma, 11>20 yean, with a
variatioii of two years ; from observed maxima the period
is 11 '20 years, with variation of three years — ^that is, this
series shovrs the period to vary between 18 '3 and 9>1
years. If we sappose these errors to arise only from errors
of observation, and not to be real changes of the period
itself, the mean period is 11-20 ± 0-64.

The results from the second series are also given at
the foot of the table. From a combination of the two, it
follows that the m>ean period is 11 -111 ± 0*307 years,
with an oscillation of ± 3 -030 years.

These resnlts are formulated by Dr. Wolv as follows :
The frequency of solar spots has continued to change
periodically since their discovery in 1610 ; the mean length
of the period is 11^ years, and the separate periods may
difEer from this mean period by as mudi as 2*03 years.

A general reladon between the frequency of the spots and the
Tuiaaon of the magnetie needle is mown by the nombers which
have been giveu in the table of Scbwabb's resolts. This relation
has been most closely studied by Wour. He denotes by t the
number of sronps of spots seen on any day on the sun, eonntiag
each iaolateld spot as a group ; br/ is denoted the number of spots
in each gmupC^is then ptoDornonal to the spotted area) ; Iv i a
ooeOdent depending upon the size of the telescope used for (wser-
vatiop, and by r the oidly twdrtJM memlir so called ; th«u he snp^
poses

r = * (/+ t^i'ff^

From the daily relative numbers are formed the meaa oMithly;
and tlw mean annual relative numbers r. Then, accordiae to
Wour, If • is the mean annual variation of the magnetic ueeiue at
any plape, two omrtaats for that place, a and /a, can be found, so
flu* the follonrtqg f ormida is true for all years :

e = a + /i'r.

Thus for Munich the formula becomes.

9 = r-»7 + V-OBl r;

and lor Prague,

TOTAL BOLIPasa OF THB SUN.

S97

lervations, the period
11 '20 yean, with
d maxima the period
le yean — ^that is, this
tween ld>3 and 91
uise only from errors
unges of the period

64.

ies are also given at
ination of the two, it

111 ±0.307 years,

r. WoLT as follows :
continued to change
)10 ; the mean length
leparate periods may
inch as 2 '03 years.

loy of th« ipots and the
D by the nnmberB which
'a reaolta. This relation
\ He denotes hy 9 the
day on the mn, counting
died the anmber of spots
the spotted area) ; bv i a
teleaoope used for omwr-
r so odied ; then he njf-

tnned the mean monthly
r. Then, acoordiu; to
*f the magnetic aaeue at
r and A can be fomd, so
rears:

id so on.

TlAB.

MuMioa.

PBAAUa.

ObMmd.

Compated.

OtMerrad.

Compatad.

1870

1871

1878

18-27

11 70

10-86

9-18

18*77

11. 56

11-18

9-84

-0-50
+ 0-14
-017
-0-48

1141

11-60

10-70

905

18-10

10-88

10-46

8-87

-0-68
+ 0-71
+ 084
+ 0-18

The above comparison bears out the conclusion that the
magnetic variations are subjected to the same pertorba-
tions as the development of the solar spots, and it may
be said that the chimges in the frequency of solar spots
and the like changes of magnetic variations show that
these two phmomena are dependent the one on the other,
or rather upon the same oosmioal cause. What this cause
is remains as yet unknown.

8 4. TBDi BUIPB COSBOKOtPHMBJI AHD OOBOIIfA.

TbfliioiiMsift of Total JtflipaM. — ^The beginning of a
total solar eclipse is an insignifieant phenomenon. It is
marked simply by the small blaok notch made in the lu-
minous disk of t^ sun by the advancing edge at Hmb of
the moon. This always occurs on tiie western half of the
sun j aa the moon moves from west to east in its ort^ An
hour or more must elapse b^<ne the nioon haa advanoed
snffimantly far in its orbit to cover the ran's disk. Zhuing
this time the disk of the nm ia gradually hidden imtil it
beounea a thin creaocnt To like genoni spertator theie
is little to aodee during the fint two thirds of this period
fnm the beginning of the edUpse, unlesajt be perh^ia the
altered fHavsm of the imagee formed by small holpi or
i^erlnres. Under orcUQaiy ohremMtanoei, the image d!
thvnu, m^de by the aolar caya whiehpaas thim^ a flMll
hoW-^lii*ei)Bd»£(i««aiiip]fa.--«(» deodar ia ih^ Uwlle
dn|» of ^ liii iiaait When tiio ana ia OMaoent, Hie

MMMM

398

AaTBONOMT.

image of the eon formed by sach rays is also crescent,
and, under favorable circumstanceB, as in a thick forest
where the interstices of the leaves allow snch images to be
formed, the effect is quite striking. The reason for this
phenomenon is obvious.

The actual amount of the sun's light may be diminished
to two thirds or three fourths of its ordinary amount with-
out its being strikingly perceptible to the eye. What is
first noticed is the chuige wUch takes place in the color
of the surrounding landscape, which begins to wear a rud-
dy aspect. This grows more and more pronounced, and
gives to the adjacent country that weird ^ect which lends
so much to the impressiveness of a total eclipse. The rea-
son for the change of color is simple. We have already
said that the sun's atmosphere absorbs a large proportion
of the bluer rays, and as this absorption is dependent on
the thickness of the solar atmosphere through wiueh the
rays must pass, it is plain that just before the sun is total-
ly covered the rays by which we see it will be redder than
ordinary sunlight, as they are those which come from
points near the sun's limb, where they have to pass throng
the greatest thickness of the sun's atmosphere.

The color of the light becomes more and more lurid up
to the moment when the sun has nearly disappeared. "U.
the spectator is upon the top of a high mountain, he can
tiien begin to see the moon's shadow rushing toward him
at the rate of a mile in about two seconds. Just as the
riiadow reaches him there is a sadden increase tA darinuMi
-^e brighter stars begin to ddne in the daik lurid dcy,
the thin eresoent of the sun breaks up into anmll pdnts w
dots of light, whidi suddenly disiqvptar, and the moon it-
self, an intensely black ball, appewa tohai^iadat«d in tiie
heavens.

An iuBtant afterward, the corona is seen sinToimdbw tike
Made disk of tiie raoim widi a soft eMgsnee cp^wkft-
flttt from wy odwr Bglit laio^^Btttas. IBkm ik»m^m^%
UfBb it is liKteMiSy bfi|^ and toUw iMfctd«7»

— . iMifciiiaiiniiiiii

msssBssmsm

TOTAL EOLIPSBB OF THE SUN.

rays is also crescent,
as in a thick forest

ow snch images to be
The reason for this

^ht maj be diminished
ordinary amount with-
to the eye. What is
es place in the color
begins to weara md-
lore jnonounced, and
eird effect which lends
x>tal eclipse. Therea-
We have already
>bs a laige proportion
ption is dependent on
re through which the
}ef ore the sun is total-
) it will be redder than
Nse which come from
)y have to pass through
itaiosphere.
ore and more lurid up
learly disappeared, tt
iSf^ mountain, he can
w rushing toward him
seconds. Just as tiie
on inerease of dailniflM
in the daik lurid aky,
up into nun points er
p0ar, and the moon i\r
I tohuigisola*«d in tibe

is seen twrcnui^^ die

dMgniee quite dUkr*

na. S«ir iw oMtf^s

in nted «9»

in structure ; 5' or 10' from the limb this inner corona
has a boundary more or less defined, and from this extend
streamers and wings of fainter and more nebulous lif^t.
These are of various shapes, sizes, and brilliancy. No
two solar eclipses yet obseoved have been alike vx this re>
spect

These wings seem to vary from time to time, though at
nearly every eclipse the same phenomena are described by
observera situated at different points along the line of
totality. That is, these appearances, though dumgeable,
do not change in the time the moon's shadow requires to
pass from Vancouver's Island to Teias, for ezamplei whidi
is some fifty minutes.

Superposed upon these wings may be seen (sometimes
with the naked eye) the red fitunes or protuberances whioh
were fint discovert during a solar eclipse. These need
not be more closely described here, as they can now be
studied at any time by aid of the speotrosoc^)*.

The total phase lastk for afew minutfls (nevor more than
six or seven), and during this time, as the eye beoomea more
and more accustomed to the faint lights the outer oorona is
sem to Btretoh furi&er and fnrtliMr away fnna th* «aii'«
limb. At the «eHpBe of 1878, July 2Mi, it was «em by
Prdeaor Lavouet, and by one of the writen, to eortend
noie than 6** (lAxNit 9,000,000 miles) from 4iba son's Mb.
Just b^fera ^ end of the total pinae flwre is a raddm
inawaia <rf the brightwas qf tbealy, due to the i aay aii d
ilhudBation «f ilM «M43i*t atuwaph we near tiie 'ofaMrvw,
and in a momMit men ^ sim^a nja are again viASe,
mmOa^mh^ii^mmm. IbmntiieeBdef telaMfytfll
liielMkeMrtaaltfieylMMNDMna ef the fiat Utt «< tfie
esBpae aw wp e ato d in iuy — e esdir. ^

" ' ue «!►

800

ABTBONOMT.

ter are sometimes seen to be almost totally black. The
appearances are extremely irregular, but they are often as
if the inner corona were made up of brushes of light on a
darker baokground. The direction of these brushes is
often radial to the sun, especially about the poles, but
where the outer corona joins on to the inner these brushes
are sometimes bent over so as to join, as it were, the
boundaries of the outer light.

The great difSculties in the way of studying the corona
have been due to the short time at the diqrasal of the ob-
server, and to the great differences whi(^ even the best
drau^tsmen will make in their rapid sketches of so com-
plicated a phenomenon. The figure of the inner corona
(m l^e next page is a copy of one of the best drawings made
of the eclipse of 1869, and is inserted chiefly to show the
nature of the only drawings possible in the limited lime.
The numbers refer to the red prominences around the Emb .
The radial structure of the corona and its different ezten-
tton and nature at different points are also indicated in the
drawing.

The fifpin <m page 802, Is Mopy of a envoa drawing inade in 1878.
verldeiiee whieh w« cm gain of the detdls of tlM««

nubeet

oookes, however, f mni a eetiae of photognqriu taken daring the whole
of totality. A photoglyph with a ihort expoeure f^ves the detaik
of aie inner ooiona wdl, bat it not dbeted Iqr the fidnter ootlving
parte. One of loiuni ezpoenre shows details inrilisr away ham
ttesoB'sUnb, wh& thoee near it are lost hi a riam of light, hifaw
«ver-«zpowd, and so on. In this w4y a aenes of phofc M inplis
fAnm OS the neaas iA hidldfaig op, as it Were, llie whoHi eMona
fiwB Us hrii^iteak parts near tiMaan'slisril> onttothefsiBlsskpa*-
tiaas wUdi will hnpnss thaaMshpes on a photagiaplde ph4a.

Tln6 oorona and rod promiBiraoeB aro aolar appoidagea.
It was lonneriy donfatfol whetbar :>th« omnia w« an
atmosphere belonging te the auner to the 9M0B. <At^
eoU^ of 1860 it wan piwved hj mmmn miBm tilil tiw
mA fttm&moom beli»|(ed to the im wid Mlti^lhtiipoB,

tiM mam gnMB^ ooiw«d thaiift bg^^ i^^
^Mr wuMiiiriiiiC-ittadiBd to tiwirm Tpht i

iiiiiittillili

totally black. The
but they are often as
bnuhee of light on a

of these bnuhea is
abont the poles, but
le inner these bnuhes
join, as ii were, the

I studying the corona
be dii^KMal of the ob-

whioh even the best
d sketches of so com-
) of the inner oorona
lie best drawings made
id chiefly to show the

in the limited time.
)nces aronnd the Bmb .
nd its. different exten-
n also indioated in the

roa drawing mafle la 1878.

the detdk of 'tlM«oiona
ihs taken dofinif tlie wliole
izpoMin ghrw the aetalk
ed hy the Mater ootMog
etaite farther away mm
t in a olan of U|^ hriag

a eem of iihotamphe
b wen, the n^^lMom
lb ont to the frinlest pov-

I tm aqlir appidagcs.
r 'the owona mm an
toihftinooii. i At the
mmmwffnwnti ^IbAl ihe

THE SUJTS PBOMnfENOBB.

808

mm. There were others of varions and perhaps varying
shapes, and the haaes of these were oonneoted hy a low
band of serrated rose-colored light. One of theM protn-
berances was shown to be entirely above the sun, aa if
floating within its atmosphere. Around the whole disk
of the sun a ring of similar nature to the prominenoee
exists, whieh is brighter than the corona, and seems to
form a base for the protnbenmoea theniBelves ; this is
the sierra. Some of the red flames were of enormous
height ; 000 of at least 80,000 miles.

(l«68j l«|r)^nM totil in Ind{% loaiiii tilMeiNn^

▲ 4inoff«7 of iLiiMniHi'^irffl

and ty ft eVi<>i wnjf^m |wif ii|«inMi
iihB^lnlthir -irta' ifrj* Vait- tfw. iutfi'ii&fn

WM iBOeCt v^Mii. 1^ lii'';^<SOiBiP'-WWiieii*

1^ hri^ linni ^ IgribwgW 1^

*1iimrVllt0imMmimkimmtnmHfi*'i^^ BMT Finis.

■Ml

804

A8TR0N0MT.

The brightnoM of the spectrnm was so marked that
Janbsen detenninod to keep his spectroscope fixed upon it
even after the reappearance of snnlight, to see how long it
could be followed. It was found that its spectrum could
still be seen after the return of complete sunlight ; and not
only on that day, but on subsequent days, similar phenom-
ena could be obiserved.

One great difficulty was conquered in an instant. The
red flames which formerly were only to be seen for a few
moments during the comparatively rare occurrences of
total eclipses, and whose observation demanded long and
expensive journeys to distant parts of the world, could
now be regularly observed with all the facilities offeied by
a fixed observatory.

This great step in advance was independently made by
lb. Lotnnrn,* and his discovery was derived from pure
theory, unaided b/ the eclipse itself. By this method
the prominences have been carefully mapped day by
day an around the tnn, and it has been proved that
anrand this body there is a vast atmosphere of hydn^;en
gas — the (Arwrniotphere or titrra. From out of this the
praninenoes are projected imnetimes to hei^^ts of 100,000
kiknpietru w more.

It win bq neoeMuy to recall Um main faeto of obaarvatkm which an
ftuidaiMatal in tiM 1U8 of Um qwdnaoope. WhanaWlUantpalatb
examiiMd with the spectroeoope. It ia q;n«ad oat by tin priam hito a
band-^he apac tmiii . Dringtwopcianu, thaqtectnuBlwoaiiHalaa«Br,
bat the li^t of the aarfaoe, beiac ipnad over a neater ana, ia en-
feebled. Thne,foar, ormove pnana ipmad pat tte speetrem propor-
tionally mora. If the lyeotwim ia of ah la c a n d ea c entaoiidorliqaw, it
iaalwaya omtinuoaa, and it can be eofealiled to any dagne ; ao that
any part of it can be made aa feeble aa deaired.

TTO BMthod fapndaelyaimBarfanrinfltelatotheBaeofth et elaaaipe
In viewing ataia in the daytinM. The tefcuffipe loaMm the brBHawqr
of the aky, while the dlA of the atar la kSpt ctf the aaawdnlenity,
aa it la a pdnt in itadf . ItthuabaeoneavUbla. If It'^ajdiiwbiffgaa,
ita apaetram trill oonaiat of a dell&ito nomberof Uaea, aav nine-^, B.
O.foreiainiile. Kow aajgywe the apeetrom of ttii gaa tojn aMpaipnae d
OB the eonliuMNia apectrnm of the son; bgriMiBf onlyoae pmaa,^

* Mr. J. NoBiua Looam, F.R.8., of
the Bdenoe and Art Department ^ the Sooth K«

TUB SUIT a UKAT.

300

was 80 marked that
stroBcope fixed upon it
ght, to see Itow long it
lat its spectrnm could
>lete sunlight ; and not
days, similar phenom-

d in an instant. The
y to be seen for a few
r rare occurrences of
1 demanded long and
« of the world, conld
the f adlitieB offered by

ndependently made by
as derived from pure
)elf . By this method
'nlly mapped day by
has bem proved that
noaphere of hydrogen
From out of thk the
»to heights of 100,000

sU of obMnration which an
«. WhaaabfOUantpoiatia
•d oat ti7 flie primi faito a
iMspeotmmbeoaiiMS longBT,
o««r a neater ana, is ea-
■d oat the qieelrani propor-
oaadesoent solid or liquid, it
lied to anjdsgiee; so that
lied. ^'^
;ile to the we of flw tdMoope
anwpe iDwui the traBaacy
kSptof the saaMttateailtr.
libk IfU%a|dswfa«gM,
berotUaes, anr fluee— A, B.
of Ote BM taVi aopeipoied
roataff ooifOM priHt,tke

ithK<

Bolar qwctrum is abort and briUiant. and t -erypart of it may be more
brilliant than tlw line spectrum of the gh ly incieaaing tne disper-
sion (the number of prisms), the sohu- spt;^ am is proportionately en-
feebled. If tlM ratio of the light of the bodiee theoMelTes, tlie sun and
the gas, is not too groat, the continuous spectrum may be so enfeebled
that tlM IfaHs spectrum will lie Tislble wnen superposed upon it, and
the spectrum of the gas may then Im seen even in tne presence of true
sunlight. Such was the process Imagined and successfully carried out
by itr. LooKTBB, and such is in essence the metlwd of viewing the
prominences to-day adopted.

The Ooroiialllpaotnun.— In 1880 (August 7th) a total aolur
ecliiwe was Tisible in the United States. It was probiably otMerved
by more astronomers tlian any preceding eclipoe. Two American
astronomers, Professor Totme, of Dartmouth Oollcne, and Professor
HAREHasa, of the Naval Observatory, especially observed the spec-
trum of die corona. This spectrum was found to consist of one
fabt greoiish line croHsing a faint oontinoooa spectrum. The

6 lace of this line in the mi^ of the solar spectrum published by
[iROBHoiPr waa occupied by a line which he had attributed to the
tnm spectrum, and which had been numbered 1474 in his list, so
that it is now spoken of aa 1474 K. This line is probably due to
some jgas which must be present in large and possibly variable
quantities in the corona, and which is not Known to us on the earth,
in this form at least. It is probably a sas even lifter than hydro*
gen, aa the existence of this line has been traced 10' or SO' fhaa
the snn*s limb nearly all aroand the disk.

In the eclipse of JulySMh, 1878, which was total in Colorado
and Texas, the omi^aoaa spectrom of the corona waa found to be
cross e d by the dark lines of the solar roectrum, showing that the
coronal light was composed in part of reflected sunlight.

% 6. SOUBOm OT TBM SUITS HSAT.

Thaoriaa of tba 8nn*a Oooftitatioii. — No considerable
fraction of the heat radiated from the sun returns to it
from the celestial spaces, since if it did the earth would
intercept some of ue returning rays, and the temperature
of night would be more like^that of noonday. But we
know the ran i» daily radiating into space 2,170,000,000
timea as muc3i heat aa is daily received by the earth, and
it follows that unleM the supply of heafu infinite (which
ire cannot believe), this enormous daily radiati<m murt in
time exhanat the ra^y. Wh«i the supply is exhausted,
or even 8erk>u8ly trenched upon, the result to the inhab-
itants of the earth will be fatal A slow diminnUon of

806

ABTRONOMV.

the daily snpplj of heat would prodnce a slow change of
climates from hotter toward colder. The Berions results
of a fall of 60° in the mean annual temperature of the
earth will be evident when we remember that such a fall
would change the climate of France to that of Spitzber-
gen. The temperature of tlie sun cannot he kept up by
the mere combustion of its materials. If the sun were
solid carbon, and if a constant and adequate supply of
oxygen were also present, it has been shown tliat, at the
present rate of radiation, the heat arising from the com-
bustion of the mass would not last more than 6000 yean.

An explanation of the solar heat and light has been
suggested, which depends upon the fact that great amounts
of heat and light are produced by the collision of two
rapidly moving heavy bodies, or even by the passage of
a heavy body like h meteorite through the earth's atmos-
phere. In faet, it we had a certain mass availalle with
which to producb heat in the sun, and if this mass were of
the best possible materials to produce heat by burning,
it can be shown that, by bnming it at the surface of tbs
sun, we should produce vastly less heat than if we simply
allowed it to fall into the sun. In the last case, if it fell
from the earth's dirtuice, it would give 6000 times more
heat than by its buniing.

I'ii^ Uati velocity with which a body from space oonld
fall dpon the sun's surfaoe is in the ndghborhood of 280
miles in a second of time, and the velodly may be as great
as 860 miles. From these facts, tiie meteoric theory of
solar heat originated. It is in effect that the heat of ^
•nn is kept up by the impact of meteors up<m its surfaoe.

Ko doubt immense numben of meteorites fall into the
sun daily and hourly, and to each one of them a certain
considerable portion of heat is due. It is found that, to
account for the present amount of radiati<m, meteorites
equal in mass to tiie whole earth would hare to fall into
the mm every cMitury. It is extxemely haprobthle that a
mass one tenth as lai^ as this is added to ^e sun in this

SUPPLY OF 80LAU HEA1\

nee a slow change of
The Berions resultfi
temperature of the
lembertliat snch a fall
to that of Spitzber-
cannot be kept np by
als. If the sun were
ado(]nate supply of
ten shown that, at the
arising from the com-
Tiore than 5000 yeans.
It and light has been
act that great amounts
|r the collision of two
ven by the passage of
gh the earth's atmos-
n mass availal!e with
nd if this mass were of
noe heat by burning,
t at the surface of the
leat than if we simply
the Uwt case, if it fell
give 6000 times more

body from space could
) neighborhood of 880
elocil^ may be as great
he meteorio theory of
t that the heat of the
eora upmi its snrfaoe.
leteoritea itSi into the
ne of them a oertain
It is found that, to
f radiation, meteoritea
trald hare to fall into
lely improbable that a
led to the sun in thia

way per century, if for no other reason because flx' tt^ .t
itself and every planet would receive far more tliai* m
present share of meteorites, and would itself become (|i»i *<
hot from this cause alone.

There is still another way of accounting for the sun-s
constant supply of energy, and this has the advantage of
appealing to no cause outside of the sun itself in tlie ex-
planation. It is by supposing the heat, light, etc. , to be
generated by a constant and gradual contraction of tlie
dimensions of the solar sphere. As the globe cools by
radiation into space, it must contract. In so contracting its
ultimate constituent parts are dravm nearer together by
their mutual attraction, whereby a form of energy is de-
veloped which can be transformed into heat, light, elec-
tricity, or other physical forces.

This theory is in complete agreement with the known
laws of force. It also admits of precise comparison with
facts, since the laws of heat enable us, from the known
amount of heat radiated, to infer the exact amount of con-
traction in inches which the linear dimensions of the sun
must undergo in order that this supply of heat may be
kept unchanged, as it is practically found to be. With
the present sixe of the sun, it is found that it is only
necessary to suppose that its diameter is diminishing at the
rate of about 390 feet per year, or 4 miles per century,
in order that the supply of heat radiated shall be constant.
It is plain that snch a change as this nuty be taking place,
since we possess no instrmnento suffldently delicate to
have deteoted a ohimge of even ten times this amount
since the invention of the telescope.

It may seem a pandoxical oonclnsion that the cooling
of a body may cause it to become hotter. This indeed is
true only when we sappoae the interior t<Fbe gaseous, and
not solid or liquid. It is, however, proved by theory that
this law holds for gaseous masses.

If a iplierical mais of gas be eondenfwd to om half ths prindtiTe
' r,ttieoentimlattne(ioiiapi»say partofitsuMHswUlbfliB*

mmi

.'J08

ASTRONOMY.

croMed fourfold, while tho turfMO ■iibjoctod to this attraction will
lie reduced to one fourth. Hence the preMure per unit of surfm i>
will be ftugmeuted aiiteen time*, while the deniltv will be incrcMed
but elttht time*. If the elutic and the gnivitkting forces w«ri> in
equilibHtim in the original condition of the omm, tho tempemturu
muet be «loublod in ordtr that thov aiay itiU be in equilibrium when
tho diameter ia reduced to one half.

If, howerer, the primitire Ixidy ia originally aolid or liquid, or iif,
in the oounw of time, it liecomes so, then thia law c«aaea to hold, and
radiation of heat produces u lotroring of the temperature of tho
body, which progressively continues until It ia flually reduced to tho
temperature of sunoundfng space.

We cannot say whether the snn hiu yet begnn to liqnofy
in his interior parts, and hvnco it is impoisible to predict
at present the dnratiou of his constant radiation. Theory
shows us that after about 6,000,00U years, the sun radiating
lieat as at present, and still remaining gaseous, will be re-
duced to one half of its present volume. It seems prob-
able that somewhere about this time tlie solidification
will have begun, and it is roughly estimated, from this
line of ai^^ment, that the present conditions of heat radi-
ation cannot last greatly over 10,000,000 yean.

The future of the sun (and hence of the earth) cannot,
as we see, be traced with great ex-\otitude. The past can
be more closely followed if we assume (which is tolerably
safe) that the sun up to the prnent has been a gaseous, uid
not a solid or liquid mass. Four hundred yean ago,
then, the^un was about 100 miles greater in diameter
than noy^ and if we suppose this process of contrac-
tion to have regularly gone on at the same rate (an
uncertain supposition), we can fix a date when tho son
filled any given space, out even to the orbit of Nep-
ttMM— that is, to the time when the solar system consisted
of but one body, and that a giieous or nebulous one.
It wfll subsequently be seen that the ideas here reached
dpotikriori have a striking anal<^ to the li priori ideas
of Kant and La Plaor.

It is not to be taken for grantMl, however, that the
amount of heat to be derived from th« oontraotion of the

-^nMM

ictod to this attraction will
»reMure per unit of siirfiK c
hedenritV will bo incruiMed
gravitating forces were in
the mnat, the temperuturu
■till be in equilibrium when

(inally Mlid or liquid, or f,
thi> law ceases to hold, and
of the temperature of the
1 it is finally reduced to the

hm yet begnn to liquefy
is impoflsiblo to prodict
itant radiation. Theory
yean, the sua radiating
ling gaseous, will be re-
rolnme. It seems prob-
tiine the solidification
hly estimated, from this
t conditions of heat radi*
D00,000 years,
loe of the earth) cannot,
xvstitude. The past can
Mume (which is tolerably
it has been agaaeous, and
mr hundred yean ago,
lies greater in diameter
this procesB of oontrao*
a at the same rate (an
ix a date when the sun
in to the orbit oX Ifejr-
he soUur system conusted
laeous or nebulous one.
i the ideas here readied
gy to the <i priori ideas

ited, however, that the
in th« oontraetion of the

AOH OF TllK BUN.

800

Hiin'H diinonftionR is infinite, no matter how liirgo tho prim-
itivtt tJiiiiiiiiMuim iiiiiy hiivu Im^uii. A Innly fuiliii|f from
,iiiy (liHtunru tu the huh can 4»iily liuvu » (;urtnln fiiiito vulm*-
i -y deptuiding un this diHtuncu niid the iriiUM uf tho sun
ilHolf, which, even if tho fall bo from nn infinite distance,
nmnot exceed, for tlio sun, 850 miles (icr second. In
tho same way the amount of hcnt generated by tho con-
traction of tho sun's volume from uny size to any other is
finite, and not infinite.

It has been shown that if the sun has always l>eei)
radiating lieat at its present rate, and if it had originally
fille<l all space, it has required 18,000,000 yean to contract
to its present volume. In other words, assuming tlie pres*
ont rate of radiation, and taking the most favorable case,
the ago of the sun does not exceed 18,000,000 yean. The '^
earth, is of course, less aged. The supposition lying at the
base of this estimate is that the radiation of t)io sun has
)>oen constant thronghout the whole period. This is quite
unlikely, and any changes in this datum affeot g^atly the
final number of ycara which we have assigned. While
this number may be greatly in error, yet the mothod of
obtaitiing it Mems, in the present state of science, to be
satisfactory, and the main c^gdnsion remains that the past
of the sun is finite, and that ■jiLsrobability its future is
a limited one. The exact nui^^^H|||hitariee that it is to
last are of no moment even we^^R^Mta at hand to ob-
tain them : the essential point is, that, so far as we can
see, the sun, and incidentally tho solar system, has a finite
past and a limited fntnre, and that, lile other natural ob-
jects, it passes through its regular stagM of birth, vigor,
decay, and death, in one order of progress.

^1 } J ^ , t yit ^ i -^

teammm

,,.xr\Ujc

(^.^AO^i-P/vMrvc

r^'^^
(^^

^fcC^

tJtoE

Wwv^XifC^'^ \../Qjif<\. c^yf*^^

CHAPTER III.

THE INFERIOR PLANETS.

g 1. MOTIONS AND A8FSCT8.

Thk inferior planets are those whose orbits lie between
tlie shn and the orbit of the earth. Commencing with the
more distant ones, they comprise VemUy Mereuryj and, in
the opinion of some astronomers, a planet called Vulean^
or a group of plaaets, inside the orbit of Mercury. The
planets Mercury and Venus have so much in common that
a krge part of what we have to say of one can be applied
to the other wiUi but little modification.

The real and apparent motions of these planets have
already been briefly deeoribe|^ Part I. , GhapterJY. It

will be remembered t
third law, their
less than that of
the latter betw
The interval between

irdance with Eeplkb's n
ition around the Gun are
iquently they overtake
tfeiior conjunctions.
iDonJTUietions is about four

vtaidSttB in the case ol Jf^noMry, and between nineteen and
twwity months in that of Vm^9. At tl» end of this
period eadh repeKts the Moie series of motions rebtive to
the sun. What th«M notkms vm can be readily seen by
studying fig. 84. In. &e first pkoe, mippose the eurth,
at any point, E^ of its <wbit, and if we draw a line, S L
or EM, from E, tangent to the orbit of dther ci these
j^ets, it is evident that the angle which ^ut line mdJKMi
with that drawn to the sun is the groateat dbngatioB <tf
the pUiMt from the wpn. The orbits being eeoenteie, tiib

A8PB0T8 OF MBROURT AND VENUS.

311

III.
LANBT8.

ASFBOTS.

hose orbits lie between
Commencing with the
^ewus, Meveury^ and, in
I planet called Yulcany
»rbit of Mercwry. The
10 much in common that
jr of one can be applied
ation.

of these planets have
'art I., Chapter IV. It
>rdance witii Kbplbc's
ion aronnd the sun are
equently they overtake
ior conjunctions,
junctions is about four
d between nfaieteen and
r. At the end of this
3jB of motions reliMiTe to
9 can be readily seen by
lace, mippose the evrth,
if we draw a line, M L
orbit of dther <4 tiM«9
le which 1^ line mdbes
E) greatest doi^pitfaNi of
^its bdng eeoeiitiio, t^

elongation varies with the position of the earth. In the
case of Mercury it ranges from 16° to 29", while in the
case of VenuSf tlie orbit of which is nearly circular, it

varies very little from
45°. These planets,
therefore, seem to have
an oscillating motion,
first swinging toward the
Mst of the sun, and then
toward the west of it, as
already explained in Part
I., Chapter lY. Since,
owing to the annual revo-
lution of the eartL^ the
■on has a etHiataiit east-
wwd BOKytictti aimflfig the
staiB^ tlMse pluMii must
have, on ^ whole, s edfreiqpandhig thom^ inlsniiittent
motion fai the same direetion. Therrfere Hw aneient
astronomers supposed their period of fevolation to be one
year, the suae as thi^ of tlw sun.

If, afpubiy we draw a line JSSCfnm the e«r& liirougfa
the sun, it is evident that the first point /, in which this
line cuts the orbit of th^ planet, or the point of inferior
conjunction, will (leaving eccentricity out of the question)
be tiie least distance of the planet from the earth, n^tflethe
second point (7, ot the point of
superior conjunction, on the op-
posite side of the sun, will be
the greatest distance. Owing to
the differaioe of these cfotaaoes,
the appuent nagmtnde of these
I^Miets, as seen from the earth,
is subject to great varfi^om.

Fig. dfi shows these vwriatiom in the ease of Mereurji^
A r^raMttting its iqppMmitini^j^tiidd when at its graatetl
^BlMee, M lAtm al its mean dktenw^ «id C wlMn at fts

312

A8TB0N0MT.

least diBtance. In the case of Venus (Fig. 86) the varia-
tions are inndi greater than in that of Mereury, the great-
est distance, 1-72, lieing more tlian six times the least
distance, which is only • 28. The variations of apparent
magnitude are therefore great in the same proportion.

In thns representing the apparent angular magnitude
of these planets, we suppose their whole disks to he visible,
as they would be if they shone by their own light. But
since they can be seen only by the reflected light of the
sun, only those portions of the disk can be seen which axe
at the same time visible from the sun and from the earth.
A very little consideration will show that the pn^pmrtion
of the disk which can be seen constantily diminiBheB as the
planet approaches the earth, fnd kxdn laiger.

'.— An*AsnT mmmitOum ov Dm <w vBAn.

When the planet is at its greatest dwtanoe, or in superior
oonjnnction {jC\ Fig. 84), its whole iUumiiutked l»Haiii|>here
can be seen from the earth. As It moves wtwoii and ap-
ftsmSam dM«wtii, diftiUiimiiuitedhcnEaspbfflnisgraduaUy
litfMMlfrMttw. Ai tile point of greatest «lon^on, Jf
or JC^ cme failf Ibi Iwnisphere is^bie, and iL> f^saet
Ihmi ^ ImMi «£ tf» pMon at fint os second ^mirtsr. As
ft ^gf9mimki» Mm «m]'nncti<Mi, tlie wppumli visibled&dc
assumes the form of a ovpsoent, whieh beeomes thiayBer
and Uiinner as tke ^MMt appiOieim tipe suL

f%. 87 shows the appnraBt c^k of JGpoNry at yaiiww
j^Koes during its iqmodie vevoliition. The plplsl iiM ta^
pMT br^ihtest wh«n ty» disk has the fvsttMt m^bm^

wmm

ASPECTS OF MBROUUT AND VENUS.

813

ms (Fig. 86) the varia-

of Mertmry, tlie great-

lan six times the luaHt

variaticng of apparent

le same proportion.

int angular magnitnde

lole diflkg to be visible,

their own ligbt. Bat

reflected light of the

can be seen which are

nn and from the earth.

ow that the pn^portion

tantly diminisheB as the

Kdnhuger.

ov vnK ov fCMtife.

distance, or in snperior
illuminated hemisphere
t moves areund and ap-
heauspheie is gradually
greatest dongation, M
▼istblA, and tibe phuMt
PC seoMid qnaitsr. As
the sppMvnt visible dUc
whioh beeomes iSbSwatst
lestliesaiL

I of Jf«Mwy at yaifaMH
n. The plpiife will ap-
« the

This occurs about half way between greatest elongation
and inferior conjunction.

In consequence of the changes in the brilliancy of these
planets produced by the variations of distance, aud those
produced by the variations in the proportion ot illuminated
disk visible ^m the earth, partiaHyTSmnpensating each
other, their actual brilliancy is not subject to such great
variations as might have been expected. As a general rule,
J<«fOTffy shines with a light exceeding that of a star of
the first magnitude. But owing to its proximity to the
sun, it can never be seen by the naked eye except in the
west a short time after sunset, and in the east a little be-
fore sunrise. It is then of necessity near the horicon, snd

tiwreiore does not seem so bri^tas if it were at a graafeer
aUitade. In our Jatitndeiwe mig^t almost say that it is
never visible exoapt in the morning or evening twiUdit
In hif^ latitndsa, or in ngions whnw the air is Ms
tnMpaiBBt, it ia soaroefy ever visible without & teksoope.
It is nii tiwt OonunoDa died without ever obtaining a
viaw ef lilt flMMi JTsrvury.

On the olhar hand, the planet Fsihm ii; next to the sun
and moon, the moat biiliant object in the heavans. It is
so mnqii brlf^iter than any fixed star fluit there oan seldom
he aaj dJibaUy in iden^jping it. The unpraetiaed ob-
server ib||^ vndar sene drenfiBtanoas find a diflleulty in

jtmsMA

il^

814

ABTBONOMT.

distinfniiBhing between Venug and Jupiter ^ bnt the differ-
ent motions of the two planets will enable him to distil^
gnish them if they are watched from night to night dur-
ing several weeks. . .

g a. ABFBOT AHD ROTATION OV MXBOUBT.

The varions phases of Mercury t as dependent npon it3
yarions positions relative to the snn, have already been
diown. If the planet were an opaque sphere, without in*
equalities and without an atmosiriiere, the apparent disk
would always be bounded by a oinsle on one side and an
ellipse on the other, as r^resented in the flgnre.
Whether any variation from this simple and perfect form
basjivier bemi detected is an open qn^MtkMi^ the balanee of
evidenoe being very sfanmgly in the negiliTa Sfaioe no
spots are vidble upon it, it would follow ihat unksi vari-
atioui of form due to InequaUtieB on its surfiuse, sneh as
mountains, can be deteeled, it is impossible to (btermine
wh^fiT tile planet rotatee on its axis. The only evidence
in lavwr of nch vetatioii iathat of SoHsSras, the eaMbsftted
astretuHner of IflienUul, wlw made the telflM(^ study
of tito moon and planets his pindpal woric. About the
beginning of the present century he noticed that at certain
tiineB the south horn of Hie cresoent of Jf«»vMry seemed
to be blunted. Attributiiig tins appetnuMb io \kk duidow
of a lofty mountain, he eooiduded tluiitiiib l^^aiiM, JfifiVMry
revolved on its axis in a little more tlttn %^i ImMos. But
this planet has sinee been studied with inr^ownMis weaA
more powerful than those of SoaaSmnt, fMSt
Hoa of Us rsMilts has been obtidiM. We ni||i
eottolude that the pwiod of volition of Mt0trM on ill
axis fa entirely nntorown.

an atnuMpbere of JfMVNvy, tiw fjNKtoflt ii

sfMctram «f iUk

'-•"•^'^j^'

VaS^^^^nsi^i^Maitekv '

ifbiyindtthnkil^

"•- ^ Y""'-^--'T \ W tg Ui

Jupiter, but the diifer-
rill enable him todistiikk
pom night to night dnr-

[ON OV MBBOUBT.

f, as dependent npon ita

gun, have already been

Mqne sphere, without in-

(here, the apparent disk

irele on one i^de and an

resented in the figure.

ample and perfect form

I qniitioi^ the btlanoe of

the negitiTe. ffinoe no

1 follow that unlesi Tari-

I on its sorfaee, soeh as

impossible to dMermine

axis. The only evidence

f SoHB&m, the oeWntted

tad* the tdesoopie skndy

Indpalwork. About ihe

f henotioed that at certain

■cent of Jf«ro«ry seemed

I appewMMb ^ ^ AtOom

id ihtitivb -^H^ Mttomty

Bor^thm »! iMMurs. Bat

jdwfth inrxrnnMBls noiBh

tfiMi. We^nMipiMfom
Aition of JfMNtoyoB its

f jrM«wy,l3wt$fitefliis
gildtthaliliyfii^^

ASPROTS OF MBROUnY

810

coincide with those of the snn. Of course we should
•expect this because the planet shines by reflected solar
li^t But he also finds tiiat certain lines are seen in the
spectrum of Merewry which we know to be due to the ab-
sorption of the earth's atmosphere, and which appear
more dense than they should from the simple passage
throu^ our atmosphere. This would seem to show that
Merewry has an envelope of gaseous matter somewhat like
our own. On the other hand, Dr. Zollmeb, of Leipsic,
by measuring the amount of light reflected by the planet
at various times, concludes that Merewry, like our moon,
is devoid of any atmosphere sufficient to reflect the lig^t
of the sun. We may therefore regard it as doubtful
whether any evidence of an atmosphere of Mereury can
be obtained, and it is certain that we know nothing defi-
nite respecting its pl\yuoal oonstitation.

AVD BUFPOaBD BCTATIOK OW

vnruB.

As Fmmm sometimes comes neater the earth than any
other primary planet, astKmomera have examined its snr-
faoa uriHk graal interest ever since ^ inventi(m ci the
tdeseope. But no oonehiaive evidence respecting the ro-
tation of tiie phaet and no proof of any ehaages or any
inequalities en its suRboe hav« ever been obtafaied. The
dMrvatioiit am either Tery diseordMi t , or so diiBeatt
and vDNttible diet w<e mi^ readtty nq^pose the ob-
serv«n to btve Inmb misled as to whattlwy saw. In 1767
OissdA tiroimiM bft saw « bright spot on Vmm te^ng
aevsMl mwfisirifii' •vndiiyiy nd eon^adsd, fram Us msp^
yomAJtkmmnaku<Smik»iit^^ onitsadtii •

UttbmtitethaiPkttlMmn. The snlqeatwM next tdM
by BLUWiii^ u ItaMw astroMnMr, irbo. mppmi
he flitw * SMite <iif 4mIe f«|^OM OB <i^
eiwildbMd to bt iMS or oeeaas, tad his if0t m ftr it t6
giv^ diMt niaisA^ WatdiiBg tham fkom Bi|^ to night,

816

ABTBONOMY.

he.oondnded that the time of rotation of Ventu was more
than 24 days. Again, Sohbotes thought that, when Ve^
nus was a crescent, one of its sharp points was blunted
at certain intervals, as in the case of Mercury. He formed
the same theory of the cause of this appearance— namely,
that it was due to the shadow of a high mountain. He con-
cluded that the time of rotation found by Gassiki was near-
ly correct. Finally, in 184S, Db Yioo, of Kome, thought
he could see the same dark regions or oceans on the planet
whidi had been seen by Blanohini. He concluded that the
true time of rotation was 23'' 21" 22*. This result has gone
into many of our text-books as conclusive, but it is contra-
dicted by the investigation of many excellent observers
with much better instmments. Hkbsohbl was never able to
see any permanent markings on Venus. If he ever caught
a glimpse of spots, they were so transient that he could
gather no evidence respecting the rotation of the planet.
He therefore concluded that if they really existed, they
were due entirely to clouds floating in an atmosphere, and
that no time of rotation could be deduced by observing
them. ItuB view of Hebsohbi., so far as concerns the
aspect of the planet, is confirmed by a study with the most
powerful telescopes in recent times. With the great
Washington telescope, no permanent dark spots and no
regular hhmting of either hom has ever been observed.

It may seem curious that skiUed observers oould have
been deceived u to what they saw ; but we must remem-
ber that there are many celestial phenomma which are ex-
trem^jr diffienlt to miike ovt By looking at a drawing
of a planet or nebula, and seeing how pli^ every thing
seams in the {rieture, wemay be oi^ly deceived as to the
aotnal aspect with a telesoope. Under tftedremnstaneqi, if
the observer has any preeonoeived thfeory, it is veiy eaqr
fcnr him to think he aeei eveiy tbing in aeoortoMe urith
thattiieory. Kow, thaie are at all times gnsttdiileraneei
in ihe brimaaAy of thediiierMit pMrtsol^ disk of F«m«ic
It is brightest near the rooild e(|ge wMch 'm tUMd

<m^fsssmiBmmtmam!miiiia

ion of Vmiu was more
bought that, when F«-.
\rp points was blunted

Mercury. He formed
8 appearance— namely,
igh mountain. He con-
id by Gassini was near-
ly loo, of Rome, thouj^t
I or oceans on the planet

He concluded that the
2*. This result has gone
elusive, but it isoontra-
uiy excellent observers
BsoHVL was never able to
nus. If he ever caught
transient that he could
rotation of the planet,
they really existed, they
ig in an atmosphere, and
) deduced by observing
, BO far as oonoems the
[)y a study with the most
imes. With the great
nent dark spots sad no
IS ever been observed,
id observers oonid have
w ; but we must remem-
jhenonien* which are ex-
By looking at a drawing
g how ph^ every thing
niirely deoaived as to the
ndertheciroiiiiMtaiMKs, if
id thisoiy, it is Tsiry eaqr
Mag in aeeontaMe wiHi
iB times giiMit difleranoet
tttsoitlitf diiko# Vmm.

vigB wUdb is tttiBid

MiBilii

MiaBi i M i

ABPB0T8 OF VENUS.

817*

toward the sun. Over a small space the brightness is such
that some recent observers have formed a theory that the
sun's light is reflected as frmn a mirror. On the other
hand, near the boundary between light and darkness, the
surface is much darker. Moreover, owing to the undu-
lations of our atmosphere, the aspect of any planet so small
and bright as Vemu is constantly changing. The only
way to reach any certain conclusion respecting its ap-
pearance is to take an average, as it were, of the appear-
ances as modified by the undulations. In taking this aver-
age, it is very easy to inugine variations of light and dark-
ness which have norealexisttnce ; it is not, therefore, sur-
prising that one astronomer should follow in the footsteps
of another in seeing imaginary markings.

▲tmoaphere of Venus. — Xt^e evidence of an atmosphere
of Vmut is perhaps more conclusive than in the case of
any other planet. When Vmru is observed voy near
its inferior conjunction, and when it therefore presents the
view of a very thin .crescent, it is found that this orescent
extends over more than 180°. This would be evidently
impossible unless the sun illuminated more than one haU
the pbaafe One of the most fortunate observers of this
phenomenon was Professor G. S. Lr..^AN, of Yale GoUege,
who observed Vmut in December, 1866. The inferior
oonjunotiom of the planet occurred near the ascending
no^, so that its angdar distaaoe from the sun was lass
than it had been at any former time during the present een-
tury. Professor Lrwa saw the disk, not as a thin ores-
omt, but as an entire and extremely fine oirde ci li|^t.
Wis therb-ore condude that V(miu hss an atmosfiliere
whioh ezeroisfls so powerful a refraotifm upon the H^t of
the son that the latter illuminates several degrees more
than one half the |^obe. A phmomeiion whidk must be
attribated to the same cause hss sevend times been ob-
sapv«ddu&ig tkanaits of VeMU. Ihiiti^ the traarit of
IkiftmAm d&, 1874, most of tibe obaerven who enjoyed
a fine Hcm^ atmoi^ere saw that when Fmmw was par-

MMM

818

A8TB0N0MT.

tially projeofeed on the mm, the outline of that purt of iti
disk oatside tho sun ooold be dittingoiahed by a delicate
line of light. A similar appearance -WMnotieadbjDaTiD
RriTBffHousK, of Philadelphia, on June 8d, 1769. From
these several observations, it would seem that the refractive
power of the atmosphere of Vmu9 is greater than that of
the earth. Attempts have been made to determine its ex-
act amount) but they are too uncertain to be worthy of
quotation.

ft 4. T&Airarra ot kbboubt akd ynrns.

When Mermvry or F^niM passes between the earth and
sun, so as to appear projected on the sun's disk, the phe-
nomenon is called a tramii. If these planets moved around
the sun in the plane of the ecliptic, it is evident that
there would be a transit at every inferior conjunction. But
since their orbits are in reality inclined to the ecliptic,
transits can occur only when the inferior conjunction takes
place near the node. In order that there may be a transit,
the latitude of the planet, as seen from the earth, must
be less than the angular semi-diameter of the sun — ^that is,
less than 16'.*

The lon^tnde of the descending node of Merewry at the
present tune is 337", and therefore that of the ascending
node 47°. The earth has these longitudes on May 7th and
November 9th. Since a transit can occur only within a
few degrees of a node, Mwcwry can transit only within a
few days of these epoehs.

The longitude of the descending node d Fmmm is now

• Tlie nstbciiMUori stiidsnt. loMmiiutttMtttM laoliBatkmof thsoi^
or Jr«r«Nfy hr y sad thrt of y«M»Vt^\ wfll faA H sa iulM Ss MH
prabtaa tooslenlste On HmiisoCdMaaoeflnaittMMdsWilUiiwkidii la-
ieiior oonjonotkn most tsks^aos teoiderttsta tnasttnurc

K I

'vm'^m'mmir ■

TRANSITS OF MERCVRT.

ine of that part of iti
igniihed by a delicate
imMiMtteed bj Datid
Tune 8d, 1769. From
eem that the refractive
is greater than that of
deto determine its ex-
irtain to be worthy of

IT AMD vMinni.

between the earth and
le sun's disk, the phe-
B planets moved aronnd
»tio, it is evident that
erior conjunction. But
islined to the ecliptic,
erior conjunction takes
there may be a transit,

from the earth, must
ter of the sun — ^that is,

node of Mercury at the
that of the ascending
gitudes on May 7th and
n occur only within a
n tramit only within a

; node of Vemu is now

•t tbe iaoUaatkNi of the acUt
r.wmfladHanJBiwailii
MBtttaods^lttlBwhkhla-
er tlMt « tiwHit aaj eeenr.
■trie iMltada aM^ M flnmd

aUMsgiMlar ft
■■iBDBiMlna. uA

about S56°, and therefore that of the ascending node is
76**. The earth has these longitudes on June 6th and De*
oember 7th of each year. Transits of Venut can there«
fore occur only within two or three days of these tiroes.

Beounenoe of Transits of Meroury.— The tnuieite of Mer-
eurp and Vmui recur in eyelet which reaemble the eighteen-

irear cycle of eclipies, but in which the precision of the recurrence
■ leae eMking. From the mean motions of Meremry and the earth
already given, we Und that the mean eynodic period of Mereury ia,
in dedmala of a Julian year, Oi'- 8179M. Three aynodic period* are
therefore aome e^teen daya leas than a year. I^ then, we suppose
an inferior cmninnotioa of Meratrf to occur exactly at a node, the
third conjunction foUowing will take phww about eighteen daya
before the earth again reachea the node, and therefore about 18"
from the node, since the earth moves nearly 1* in a day. This is
far outside the limit of a transit ; we mu^ therefore, wait until
another conjunction occurs near the same place. To find when
thia will be. the successive vulgar fractions which converge toward
the value of the above period may be found by the method of oon-
tinued fractions. The first five of these fractions are :

i A »'f H ^

Here the denomiaaton are numbers of synodic periods, while the
numeratorB are the approxtanate corresponding number of years.
By actual multiplication we find :

8 Periods:.- Or MITW = 1' -

19 « = «087864=> • +

n " = 9vt9m= 7-

41 " = is-<Nrr«6= 18 +

145 •' = 46001180= 48 +

04a» ».

087864.

068110.

Error = - 17'

• = + 10*

•• — 7*

•• = + r-i
» «+ tr-n

In tUs table the erron show «he waaOitft of AagMss fmi Aw
node at whick the inferior coaJnnetioB will oeenr at t)M0M of «ai
year, rix yevra, srrea yemrs, etc. Tlisf are fiiHid bj s wUt ii^ y i ai
UiefiBstimibywhiflhtiMlatervabeaesMl or Ml i^vt of •■ MtM
nnariMro(yMntb7 880*. ItwUlbesenthat tke 18th,sa4,^ii
and 146th oonJuaMoaa oooar-nemer sad n eaw r ttw aOM, sr, s«|^
posiag thai we do not start from a mtda, asam aM MMW Ito |iii||.
of the ofMta fima which we do start It foilims that tba vpsa^
lof atraasltof Jfovuryat the sbms ao4a is poaailils al UK

end of 7 fsan, prabaUa at the end of 18 years, and alaMSt esttain
at ti»oiMl^ 40 yean. Hm lattor is the ^le wbieh it wwidd be

tabseaigr

to take as that im mhSch aU the traaslts would
. but it wwdd stlHaotbeso exaet -as the eellpss cjck of 18
ysais 11 &^.

8«0

AaTBONOMY.

Tin following table ihowi the datee of ocouimmoe of tnuuito ol
Jftrawy durins the preeent centurj. They are Mpuated into Mny
tnuultL whioh ooonr nenr the deecending node, md NoTember
ones, wnidi oocur near the aeoending node. November trandto an
the most muneroua, beoauae JKfreioy is then nearer the sun, and
the transit limita are wider.

/ »
Z 5

Vm, May 6.
1889, May 8.
1848, May 8.
1878. May «.
1881. May 9.

7
' J

7
/ 3

I $

I 3

1808. Not. 8,
1818. Not. 11,
18M. Not. S.
188S. Not.
1848, Not
1861, Not.
1888. Not.
1881, Not,

7.
10.
19.

1804. Not. 10.

/f/^

It will be seen tliat in a cycle of 48 years thei^ are two May tran-
sits and four NoTember ones, so that the latter are twioe as nu-
maroos as the former. These numbers may, IwweTer, change slightly
at some future time through the failure of a recurrence, «r the en-
trance of a new tran^ into the series. Thus, in the May series, it
is doubtful whether there will be an actual truisit 46 years after
1801— that is, in 1987— or whether JTsrmfy will only nass Tory near
the limb of this sun. On the other hand. JftrBwry passea within a few
minutes of the sun's limb on May 8d, 1868, and it will mobably
graio the Hmb 46 years bter— that is, on May 4th or 8th, 1911.

BMrnrrniM or Tnmita of voniM.— For many centuries
past and to come, tranrits of FShmm oocur in a cycle more exact than
Oiose of JfsrvNnr. It hi^pens that dght ttanes the mean . Mttion of
I^Mtt ia Tory nearly the same aa thirteen times the meaii motion

of the earth; in other words, Vrnvu
makes 18 rerolutions around the
son in nearly the same time that
the earth makes 8 rsrolutlons—
that ia, in eight yean. During
this period than wUl be 6 inferior
eoaijiinetionaof Vmut, becanae tiie
lallar hM made 6 randutioaa mon
ttan the eaith. OMMeq(aen*ly, if
we wait eigiit yean ftom an inferior
floqjuaetion of Fsmh^ we shalL at
the end o| that tlme^ hwre aaouer
inferior ecajonotioB, ihi flfth in
Mndar order, at nearly the same
mttat of the two ocMta. It wfll,
flMnfon, oeoir 1^ the I
of the year, and in aan^ the I
position MlatiTe to the node of FsMM. bVlg. SSletdi
Um mn, and the dnde drawn around It the orbit of ^ earth.

B lilBjM^aM^llli!^ i «B^y»t. ^

f occuirnmoe of tnuuiu ot
1*7 an Mparsted into May
ing node, and Novwiber
le. November truuita m
then nearer the tun, nnd

TRANBira or vknub.

331

18M, Not. «.
181S. Nor. 11.
1899. Not. 5.

1880. Not. 7.
1848. Not. 10.
1801. Not. 19.
1808. Not. 8.

1881. Not. 7.

[ 1804. Not. 10. ><-/(/

irs ttwre are two May tran-
Im lataterare twloe aa nu-
jr, howerer, change alightly
of a lecarrence, «r the en-
rhua, in the May wriea. it
Btnal tnuuit 40 year* after
ny will only paai Tery near
Ifiireiwy paiaea within a few
1805, and it will probd>ly
May 4th or Stii, Itll.
ilM.— For many eenturiea
in a cycle more exact than
i timea the mean '. Mt^n of
m timea the meau motion
arth ; in other worda, Vmm
18 rerolntiona anxiiid the
Marly the aame time that
th makea 8 reTohitlona—
in eight yeara. Doting
iod then wUl be 5 inferior
itionaof FbMM, becanaethe
B« made 6 rartdutioaa more
• emtt. Oooaeq^wntly, if
d^ veam f mm an innnor
ition of Fmim^ we dmll, at
ol that timn^ hnve aqoUMMr
eoBJmietfoB, iho Uih in
order, nt nearly the aame
f the two MfUta. It wfU,
occur ak the

fa, occur

reM>,andinnenita[tha
ta fig. 8Slefc0ian«aant
H the orbit of «be ear^

* i;S ' M:<*:.^»S ' ?m^*l!.:mi

8unpoae alio that at the moment of the inferior conjnnction of
Kmim, we draw a itndght line 8 1 through Vmvt to the earth at 1.
We ahall then haTC to wait about If yeati for another inferior con-
junction, daring which time the earth will haTc made one ictoIu-
tion and | of another, and Vmtu 9| reTolution*. The straiBht line
drawn through the point of inferior conjtuiction will then M 8 9.
llie third conjunction will in the mme way take place in the poai-
tion S 8, which ia 1| rcTolutiona further adTanoed ; the fourtn in
the poaition 8 4, and the ilfth in the poaition 8 8. If the corre-
spondence of the motions wen exact, the sixth conjnnction, at the
end of 8 yeara (0 x 14 = 8), would again take phwe in the original
poaition 8 1, and all subaequent onea would follow in the same
order. All inferior conjunctions would then take phuw at one of
these Atc points, and no transit would CTcr be possible unless one
of thtae pcnnts should chance to be Tcry near the line of nodes.

In fact, howcTcr, the correapondence is not perfectly exact, bat,
at the end of 8 years, the sixth conjunction will take place not
exactly along. the line fi'l, bnt a little beforathe two bodiea reach
this luie. The actual angle between the line ^1 and that of the
sixth conjunction will be about 9° 99', the point ahifting back to-
ward the direction 04. Of course, each followins conjunction will
take ;|^aoe at the same distance back from that of mght yean befora,
leaTing out amall chugea due to the eccenuicitiea of the OtMta and
the Tariatimia of their elements. It follows then that if we rappMe
the fire lines of conjunction to bare a retrograde motion m a
direction the op«oaite.of that of the arrow, amoonting to 9" M' in
right yeara, all the inferior conjunctions will take jriace along theaa
Htc llnea. The distance apart of the linea betag 79" and the
motion about 18' per year, the interTals between tiie paaaagea of
the aaTcral conjonetion lines oTer the line of nodes will be aboat
940 yenra. Really, the exact time is 948 years.

Boppose, now, that a conjunction should take phM» exactly at a
node, then the fiftii following conjunction would take ]^o
9* M' befon reachfcng the node. The Umitn within whidk » tnHtit
can oeoor an, however, only 1° 40' on each side of the Mdarnmi-
seqiwnthr, tharw would be no further transit at that node mttl the
next following conjonetion point naehed It, wbkii woaMh^ppMat
the end of MSyeata. If, howerer, the ooitiwietini shooldtakejpbce
between 0" SO^and 1* 40' tifUr reaehli« ^ nod% then wonUT be a
tnuiait, and the Ulth foOowing conjoaottoii wooM also ooaor williin
the Umit on the othw aide of the node, so thiat we ahoald ham two
tranaita eight yean apart We may, thereon, Iwre ailher one
traadt or two aeooid^ to the distance from the node at iHdflii the
flnt tnurit ocean, m thna haTc at a|iy om node eiOiern iliiie
tranalt, or ajplr of trantita dsht yem uMtr^B • <7d« ol »M y«n.
At the addme of thia cycle the node will be half wi^ batwera two
of tin coajonetkm pcinta— the points 1 and 8, for inatance ; bat it is
eTUkmt that In tUa caae the qraoaite node wUl eeindde with the
con jonotien pdnt 9, since there is an odd nomber of aoeh pointa.
It f<dto«a, tifonfon, that dtoat the middle of tite Interral between
two cooaoentiTe sets <rf tnAaits at one node we shnU hum a tnttrit
orn pafr of tntuita at thf8 (Opposite node.

332

ABTRONOMT.

Eilit

Tho earth pmsm through th« line of the deeeending node of the
orbit of K«i«M ewrlx in June of eeoh yew, ud through the MModiuff
node enrly in December. It followe, therefore, that the leriee will
be • tmneit or a pair of tnuuiti in June ; then an intenral of about IM
veart, to be followed by a transit or a pair of transit* in December,
and so on. Owing to the eccentricity of the orbita, the interrals
will not be exactly equal, the motiona of the several ooniunction

Kints not being uniform, nor their diatanoe exactly 79 . The
tee and interrala of the traneite for three cyoiea nearest to the
present time are as follows :

1S18, June %. 1701, Jun« S. 9004, Jane 8.

1898, June 1.
1681. Deo. 7.
1888. Deo. 4.

1708. Jane 8.
1874, Deo. 9.
1888, D«c. 6.

9019, Jane 6.
9117, Dee. 11.
9198, Dm. 8.

Intwvala.
8 years.

lOOi "

8 ••

191* "

1*he 9487ear cycle i« so exact that the actual deviations from it
nre due almoet entirely to the secuUr variation of the orbits of
Ymut and the Earth, Moreover, the conjunction of December 8th,
1874, took place 1° 96' past the ascending node, so that the con-
iunotion of 1883 tekes pUce about 1* 4' before reaching the node.
Owing to tho near approach of the period to exactness, several pairs
of transits near this node have taken place in the past, at equal in-
tervals of 948 years, and will be repeated for three or four cycle* in
the fntnre.

Nearly the same remark applies to those which take place at the
descending node, where pairs of transits eight vean apart will
occur for about three cyoles in the future. Owb|L however, to
seenlar vaiiaiiuns of the orbit, the oonjunction pdnt lorthe second
June transit of each pair and the first December transit will, after
perhapa a tboosand years, Uk» pboe so far from the nod* that tho
pbiMl will not quite touch the sun, and then during a period tA
many oentuiiaa there will only be one teanait at each node in
•very 948 yean, instead of two, aa at present

«8.

Some astronomerff are of opinion that there is a small
planet or a group of planets revolving around the son
inside the orbit of Merewry. To this supposed phmet the
name Vuioan has been givoi ; but astronomers generally
disoradit the existenoe of sneh a planet of ooarfderaUe
si«e, because the ovidenoe in its Urm is not Ngirded as
condniiTe. .

nn»-mm»mim«mKmi "i^mmnHim'tmuiiiamsj i mwi^SB

deMending nodo of ths
id through UM Moendiiiji
ton, th*t the mtIm wlU
u Ml intenml of About IM
of tmuiii in December,
the orbits, the interrala

the MTenl ooniunction
Moe exMstlj 79% The
Be cydee newreat to the

Jane 8.
Jane 6.
Dee. 11.
Dm. 8.

IntwvaU.
8 jenre.

lOSi "

8 "

kctunl devlntioni from it
wintion of the orbits of
■notion of DecemlMr 8th,
( node, M tlMt the con-
efore reaching the node.
toexnctncM, Mrerkl pnira
I in the past, at equal in-
brtliree or four oyolea in

B which take place at the
• eight Tean apart will
ire. Omag. however, to
bUou point for the Moond
eember traaait will, after
t froaa the node that the
then during a period <rf
\muAi at each node in
anL

JKUOm VLMMWrn.

ihftt there is « snudl
Iving aronnd the mm
it snpposed phaiet the
utrdnomen generally
planet of ooBrfderaUe
wis not ngirded as

THB SUPPOSED VULCAN.

The evidence in favor of the existence of such planets may tie
divided into three classes, as follows, which will be considered in
their order :

(I) A motion of the perihelion of the orbit of Mtreury, supposed
to M due to the attraction of such a planet or group of planets.

(3) Transits of dark bodies across the disk oT the sun which have
been supposed to be seen by various otieervers during the past cen-
tury.

(8) The observation of certain unidentified objects by Professor
Watson and Mr. Lbwis Bwirr during the total eclipse of the sun,
July »iKh, 1878.

(1) In 1808, Lb Ycrkur made a careful collection of all the obser-
vations on the transits of Mtnury which had been recorded since the
invention of the telescope. The result of that Investigation was
that the observed times of transit could not lie reconcilra with the
calculated motion of the planet, as due to the gravitation of the
other bodies of the solar system. He found, however, that if, in
addition to the changes of the orbit due to the attraction of the
other planets, he supposed a motion of the perihelion amounting to
86" in a century, the observations could all be satisfied, wch
a motion might be produced by the attraction of an unknown
planet inside the orbit of Mereury. Since, however, a single
planet. In order to produce this effect, would have to be of oui. Td-
erable slse, and since no such object had ever been observed during
a total eclipse of the sun, he concluded that there was probably a
group of planets much, too small to be separately distinguished.
So far as the discrepancy between theo: y and obwrvatlon is con'
cemed, these results of Le Vkhribb's have been conmletely con-
firmed bv the mathematical researches of Mr. O. W. Uax, and by
observations of transits since La Ybbbibb's calcutetions were com-
pleted. Indeed, the result of these researches and observations is
that the motioivof the perihelion is even greater than that found
by Lb Ybbbibb, the suiplus motion being more than 40" in a cen-
tury. There is no known way of aotiountins for this moCioB in
aooordanoe with well-eatabliriied lawa, exsept oy supposing nMtter
of soma sort to be revolving around the sun in the suppcSed posi-
tion. At the saoie time it ia always poadble that the effect may
be praduoed \ij some oaknown causa.*

(8) Astronomical reoords oontain upward of twenty iBstaaeea
in whi«b dark bodiea have bean supposed to be seen in transit
aorasa tlie disk of the son. If we suppose these obaervatimia to be
all psrfeethr eoRWt, theexistenoe of a great number of ooasidaabla
j^aaets wlwla the oibit of Jbrewy wookl be placed beyond doubt.
Bat a oitkal aaaMs allows that Uieaa observations, eonsidarad aa a
olasa, an aot an^kM to tha sUgl^eat credeaae. In the irai plaM»

* Ab ebotrD-dyaaada theory of attmetkm has beea wltldn die past
twMtar jMM sMwastsii hgrarvanl Genaavahyalois;*. which lavaivaB
a and varlrimnaat tha osdkMKT thaory of gravitatto

tthaoidlBaiTthaoryotgiravitattoB. Ithaabaea
sbMra ttit,l9M|ioaiR« fUa dw% tnie, tta BMthm df te paittidloB
of Jfiway o0Uhb» aooooiUsd for bf tha aMmotkai of tta I

t!WJW."''4w, ' . ' Jt!ipa ! iwswwii

824

ASTSONOitr.

•OATcely any of them were made by experienced obaerren with
powernil iutnunenta. It ia very eaay for an unpractiaed obaenrer
to miatake a round solar spot for a planet in transit. It ma]f there-
fore be supposed that in many cases the observer saw notlung but
a spot on the sun. In fact, the very last instance of the kind on
record was an observation by Wbbbb at Peckeloh, on April 4th,
1870. He published an account of his observation, which he sup-
posed was that of a planet, but when the publication reached other
observers, who had Men ezamininff the sun at the same time, it
was shown conclusively that what he saw waa nothing more than
an unusually round solar spot. Amia, in mos*i of the cases referred
to, the object seen was describra as of such magnitude that it
could not ndl to have been noticed during total edipaes if it had
any real existence. It is also to be noted that if such planets ex-
isted they would frequently pass over the disk of the sun. Dur-
ing the past fifty years the sun has been observed almost eveiv
day with the grMtest assiduity by eminent observers, armed with

ewerfnl instruments, who have made the atudy of the sun*s snr»
w and spots the prlndnal work of their lives. None of these
observers has ever recordea the tranait of an unknown planet Thia
evidence, thouygh negative in form, ia, under the dreumstances, oon«
elusive asainst the existence of such a planet of such magnUode
aa to be ^sible in trandt with ordinary instruments.

(S) The observations of Professor Watbox during the total
eclipse above mentioned seem to afford the strongest evidence yet
obtained in favor of the real exirtenoe of the planet. His mode of
proceeding waa briefly this : Sweepiiw to tne west of tlM sun
dnrina the eclipse, he saw two objects m positions where, snmioa-
ing m« pointing of his telesoope accurately known, no fixed star
ensted. lliere Is, however, a piur of known stars, one of which is
about a degree distant from one of the unknown objects, and the
othor aborn the sane distance and direction frmn the aecmid. It
is considered by some that Profeaaor Watboii's sup p ose d phnets
Biay have been this pair of stara. Still, if Professor Watsos's
iriaiiets were capable of produdng the motion of the perihelion of
JftrmHy already refened to, we aitonid nguA their existenoe as
plaoed bmrond reasonable doubt But his dbservfttMoa and tbt.
theorettoai results of Ln Ybbbiu do not in any manner streafthaa
each other, because, if we suppose the obsoved per tu rb a tions in
the orbit of Jfiwwifv to be due to planets so soiall as thoae seen by
WATioir, tiie number of these pmnets must be many thovnaadi.
Now, it ia verv certain that there an not tlMusaaaa ef iNaaeti
than Mister tban Ou sixth magnitude, because thcry^MoIa ham
been seen by other teleaoopea engaaed in the mbm search. The
matSkx we suppose the individnal ^mets, the aarsnomteovs O^y
must be, and. finally, if we consider them asjodividaally invisibli^
thnrwiUprababiyMinBbeiedbytaisof thoaaanda. Theamaller
•ad mm onmenMa Ihsy are, sapnosiag thair ooabinad masi the
aam, the^Mrtar ttaavm total of li^t they wookl niaei At a
(tetab jap tha amount of UtM would baooaa ao eoMManMa
that tm^ i te trwUd appear m > otond-llka mass. Hev,tlWMia

MtMMRWimii

THE SUPPOSED VULCAN.

826

lerienced obaerren with
an unpnctised obienrer
in tranait It may thera-
tbaerrer aaw nothing but
instance of the kind on
Peckeloh, on April 4th,
•enraticn, which he tap-
publication reached other
sun at the same time, it
' waa nothing more than
moel'i of the caaea refemd
such munitude that it
ig totJeclipaea if it had
that if tuch planeta ex-
j diak of the aun. Dnr-
m obeerred almost eveiy
int obserrers, armed with
lie study of the sun's sur-
leir lives. None of these
an unknown planet Thia
ier the dreumatances, con-
planet of such magidtade
istruments.

Fatsoh during the total
the strongest eridenoe yet
the planet. His mode of
to ttw west of the sun
i porilions where, sumioa-
ately known, no fixed star
lown atars, one of which is
unknown objects, and the
don from n» aeeond. It
^ATaoH's supposed planets
U, if Professor WAxaoa'a
Hilion of the perihelion of
nguA tlMir existence aa
hia obaerraitHiiis and th^
t in any manner str«q[thMi
observed per t u rb ations in
I so small as thoae seen by
must be maoy tbousan d a.
not tiMosaada of phUMta
', beeaose the y w ula Vvn
in the snm* aearoh. Ite
te, the awra mnnteoas Oi^y
m asladiTidnaUy iuTlstble.
of thouaaBda. The w M ller
gthdr oooriiiiMdBMBtiM
( they would niMt At»
lid beeoM so eoMManMa
i4Uw aMB. Nov, flierels

a phenomenon known as the zodiacal light, which is probably caused
by matter either in a gaseous state or composed of small particles re-
volving around the sun at various distances from it. This light
can be seen riring like a pillar from the western horizon on any
very clear night in the winter or spring. Of its nature scarcely
any th^ is yet known. The spectroscoi^c observations of Pro-
fessor T^iOBT, of Tale GoUese, seem to indicate that it is seen by
reflected sunlight. Very different views, however, have obtained
respecting its constitution, and even its position, some having held
that it is a ring surrounding the earth. We can therefore merely
sun^t the possibility that the observed motion of the perihelion
ofjurvury is produced by the a(' - .l.

I attractton of this mass.

I«BM5R»3

JT^l'^liiSBIB

CHAPTER IV.
THE MOON.

In Chapter VII. of the preceding part we have de-
scribed the motions of the moon and its relation to the
eartL We shall now explain its physical constitution as
revealed by the telescope.

When it became clearly understood that the earth and
moon wei« to be regarded as bodies of one class, and that
the old notion of an impassable gulf between the character
of bodies celestial and bodies terrestrial was unfounded,
the question whether the moon was like the earth in all its
details became one of great interest. The oo., ' of most
especial interest was whether the moon cc ' i e the
earth, be peopled by intelligent inhabitants. * ingly,
when the telescope was invented by Gaulw), one of the
fint objects examined was the moon. With every im-
provement ot the instrument, the examination became
more thorough, so that the moon has been an object of
carafnl study by the phyrical astronomer.

The immediate Bucoe8M>n of Gauuo thoni^t thafc they
peieeived the snrfaoe of the moon, like that of our globe,
to be divenified with hadand water. Certain regions ap-
peared dark and, for the most part, pmooth, while others
wera bright and evidently broken up Into hilband vaDeys.
The former regions wefe supposed to be ooeHia, and w-
odved names to correspond with this idea. These naoMa
ormtlnue to the present day, although we now know that
there are no ooeans there.

With evoiy improvwnent in the meaaa of naatroiit »

TH« MOON.

897

ig part we have de-
d its relation to the
ysical constitation as

)d that the earth and
of one class, and that
between the character
[trial was unfounded,
ike the earth in all its
The t>Oi. ^ of nioet
moon cc ' a-e the
ntantB. .»n Ingly,
' Galilbo, one of the
ion. With every im-
examination became
as been an object of
omer.

iLBO thoui^t that they
like that of onr globe,
. Certain r^ons ap-
, pmooth, whUe othws
p Into hnbaad vall^fa.
to be 006MU, vaA re-
b idea. TheaeiiMiMa
l^we now know titii

meana of iaMii«h,it

has become more and more evident that the surface of the
moon is totally unlike that of our earth. There are no
oceans, seas, rivers, air, clouds, or vapor. We can hardly
suppose that animal or vegetable life exists under snc^
circumstances, the fundamental conditions of such ex-
istence on our earth being entirely wanting. We might
almost as well suppose a piece of granite or lava to be the
abode of life as the surface of the moon to be such.

Before proceeding with a description of the lunar sur-
face, as made known to us by the telescopes of the present
time, it will be well to give some estimates of the via-
bility of objects on the moon by means of our instruments.
Speaking in a rough way, we may say that the length of
one mile on the moon would, as seen from the earth, sub-
tend an angle of 1' of arc. More exactly, the angle sub-
tended would range between O'-S and 0'-9, according to
the varying distance of the moon. In order that au'ob-
ject may be plunly viable to the naked eye, it must sub-
tend an angle of nearly 1'. Consequently, a magnifying
power of 60 is required to render a round object one mile
in diameter on l£e surface of the moon plainly visible.
Starting firom this fact, we may readily form the follow-
ing table, showing the diameten <A the smdlest objects
that ean be seen with different magnifying powers, always
ft- jimtng that v&n<m with these powers is perfect :

Power 60 ; diameter of object 1 mile.
Power 160 ; diameter 9000 feet.
Power 600 ; diameter 600 feet
Power 1000 ; diameter 800 feet
Power 9000 ; diameter 160 feet

U telaieo^ power oonld be increased-indefinitely, there
woidd of oovnse be no limit to the minuteness of an ob-
ject TiriUe OB the moon's sorlaoe. But the necessary
lamtffMtiou of all teksoopm an saoh that only in wtn-
oi&iyeMaseMiMy thing be gained by inersMiilg <lie

IkMMIB

wimam

MHM

888

ABTBOITOMY.

magnif jring power beyond 1000. The inflnenoe of warm
and cold onrvnts in oar atmosphere is such as will for-
ever prevent the advantageous use of high magnifying
powers. After a certain limit we see nothing more by
increasing the power, vision becoming indistinct in pro-
ptxrtion as the power is inoressed. It may be doubted
whether the moon was ever seen through a telescope to so
good advantage as she would be seen with a magnifying
power of 600, unaccompanied by any drawback from at-
mospheric vibrations or imperfection of the telescope.
In <^er words, it is hardly Ukely that an object less than
600 feet in extent could ever be seen on the moon by any
telescope whatever, unless it were possible to mount the
instrument above the atmosphere of the earth. It is there-
fwe only the great features on the surface of the moon,
and not the minute ones, which can be made out with the
telescope.

GhatMtsr of the lEooa'a 8nfflM».-^The most striking
point of difference between the earth and moon is seen in
the total absence from the latter of any thing that looks
like an undulating surface. No formations (^lilar to our
valleys and mountidn-ehains have been detected. The
lowest surface of the moon which can be seen with the
tdeseope appears to be nearly cmootii and flat, or, to
speak more exactly, spheriesl (because the nuNm k a
sphere). This suiliwe has difhrent shades of color in
dfiSerait regiims. Some poitiouaniof alft^t, rilvery
tint, while others have a dark gray «|^peanuM6w These dif-
fersnees of tint seem to arise from (dKflsNUOMol mateiiaL

Upon this surfiMe as a fouiiiitUm ar» bvilk anmerous
formationB of vartods siise% b«t dl of am^^ stmj^ ehar-
aoter. Their geneval fonn esa be made ool by; tt« aid of
Fig. 88, and their dinensionB by ^ soale^ ittifai at
tiie bottwn of it The laigeet and meM ptonddbttflnt
leotues are known as craters. They have a ^jrpMl fona
wmw is Hwg of a rawid or onl nuged wall iWiig fropi Uto
plane in the mauMr of a driSii*. IMMmIIoii..

iii

Theinflnenoe of warm
ore is meh m will for-
se of high magnifying
B see nothing more by
ming indistinct in pro-
It may be doubted
hrongfa a telesoope to so
leen with a magnifying
any drawback from at-
ution of the telescope,
that an object less than
sen on the moon by any
) possible to moont the
ftheearth. Itisthere-
le surface of the moon,
an be made out with the

00.— The most striking
■rth and moon is seen in
of any thing tihat lodu
'ormations i^iilar to oar
re been detwsted. The
h can be seen with the
smooth and flat, or, to
beeanse the moon is a
vent shades of eolor in

15 are of atirii^t, silvwy
yippeanme^ These dlf-
m dUEeraiees of matoiaL
Bthm are built BmaMrons
dlof a tfif simpte ehar-

16 made oift by, tht aid of
by tlie SQito^ fllEkn at
it and moM pcomlnsnt
They have a typkal f«m

TUB MOOITB BUBFAGB.

waUs are frequently from three to six thoussnd metres in
heif^t, very rough and broken. In their interior we see

lis. A.— Mno* or na mom's somtmb.

moen lAraady deseribed. Itis,
iHth fwjguitfito or broken «p

1bk^fimtmxim» of the
AuWllfei'i gcMVi^ eofwad

880

ABTBONOMT.

hj small inequalities so as not to bo easily made oat. In
the oentre of the craten we frequently find a conical for-
mation rising up to a considerable height, and much larger
than the inequalitieB just described. In the craters we
have a vague resemblance to volcanic f ormati<Hi8 upon the
earth, the principal difference being that their magnitude
is very much greater than any thing known here. The
diameter of the larger ones ranges from 50 to SOO kilo-
metres, while the smallest are so minute as to be hardly
visible with the telescope.

When the moon is only a few days old, the sun's rays
strike very obliquely upon the lunar mountains, and they
cast long shadows. From the known po8iti<A of the sun,
moon, and earth, and from the measued length of these
shadows, the heights of the mountains can be calculated.
It is thus found that somoof the mountains near the south
pole rise to a height of 8000 or 9000 metres (from 9S,000
to 80,000 feet) above the general surface df the moon.
Heights of from 8000 to 7000 metres are v«ry common
over abnost the whole lunar suxfaoe.

Next to the so-called craters visible on the lunar disk,
the moet curious features are certain long bri^t streaks,
which the Germans call riUa or fmrmw. These extend
in l<mg radiations over certain of the craters, and have the
appearance of eraeks in tiio lunar surfaoe which have been
BubMquently filled by a brilliant wliite material Na-
sMtra and CAB^Bmaihave deseribed some experiments
detuned to ]m)duoe this appeana w aitiMatty. They
took hdlow ^ass globes, fiUedthem irftli water, and heat-
ed them untS the swiifle waa enusked. IThe oracka gen-
erated at the weakest piiint of tkeioriMsenMJiate fifon the
p<rfnt in a manner strOdngly dmilariin appeanaee to the
riUs on the moon. It wmdd, however, be jwenkature to
conclude that the latter were actually iproduoed in this
way.

The question of the origin of the lunar features has «
bearing on theories of teriestrial geology as well as upon

'-"^■"UWiig

easily made oat. In
lUy find a conical for-
sight, and much larger
In the craters we
iC formations npon the

that their magnitude
ig known here. The
from 60 to aOO kilo-
inuteas to be hardly

lys old, the sun's rays
r mountains, and they
m poaitioi of the sun,
asmred length of these
ins can be calculated,
mntainsnear the south
metres (^m 95,000
surface df the moon,
itres are vtry oommon

t)le on the lunar disk,
in long bri^t streaks,
vrowt. These extend
6 craters, and hare the
irf aoe iHtioh have been
white material Na-
tbedsome esperimrats
BM artlfldatty. They
iwlthwater, andheat-
kod. 5!beenidn gen-
uriMe ndiato from the
iriin appeanuM to tbe
ever, be pruilalwre to
nally prodnoed in thia

le Innar features hM *
;eologyasw«U as upon

LIGHT AND HBAT OF THB MOON.

Stl

various questions respecting tite paafc luatory of the moon
itself, it has hmn. a wwi d ered in this aspect by various
geologista.

Lunar ▲tmomdiara. — ^The question whether the moon
has an atmosphere has been much discussed. The only
condnsion which has yet been resohed is that no positive
evidence of an atmosphere has ever been obtained, and
that if one exists it is certainly several hundred times rarer
than the atmosj^ere of our eartL The most delicate
method of detecting such an appendage would be by its
refracting the light of a star seen throu|^ it. As the
moon ad vanoes in * .onthly course around the earth, she
frequently appears to pass over bright stars. These phe-
nomena are called ooou^to^MMM. Just before the limb of
the moon appears to reach the star, the latter will be seen
throu|^ the moon's atmosphere, if there is one, and will
be diq>laoed in a direction from the moon's centre. But
the most careful observations have failed to show the
sli^test evidence of any such displacement. Hence the
most delicate test for a lunar atmosphere gives no evi-
dence whatever that it exists.

The speetra of stars when about to be ooeulted have
also been examined in order to see whether any absorption
lines which m^^t be prodnoed by the lunar atmosphere
became visiUe. The evidence in this direction has also
been negative. Moreover, the spectrum of the moon itself
does not seem to dlfEer in the slightest from that of the.
sun. We eonelude tbarafol« that if there is a lunar at-
moepliere, it is too nra to exert any sensible absoiption
upon the rays of lijg^t.

IdglitMiABMlorikfelleeai— Many attempts have
been made to measure tbe ratio of the li^^t of the full
moon Hid tiial of the nm. The results have been veiy
disowdwit, but att have agreed in showing that the sun
•mite several hundred thousand times as much light as the
fnllmooiit Th« hwl and woit careful deterainatioft is

832

ASTRONOMV.

that of ZdLLRBR, who finds the sun to be 618,000 times as
bright as the fnll moon.

The moon most reflect the heat as well as the light of
the snn, and most also radiate a small amoont of its own
heat. But the quantities thus reflected and radiated are so
minute that they have defled detection except with the
most delicate instruments of research now known. By col-
lecting the moon's rays in the focus of one of his large re-
flecting telescopes, Lord Bossi was able to show that a
certain amount of heat is actually received from the
moon, and that this amount varies with the moon's phase,
as it diould do. He also sought to learn how much of
the moon's heat was reflected and how much radiated.
Thu he did by ascertaining its capacity for passing
through glass. It is well known to students of phyrics
that a very much hu^r portion of the heat radiated by
the sun or other extremely hot bodies will pass throuj^
glass than of heat radiated by a cooler body. Experiments
show that about 86 per cent of the sun's heat will pass
through ordinary optical glass. If the heat of the moon
were entirely reflected sun heat, it would possess the samo
property, and the same {NPoportion would pass through
ghMB. But the experiments of Lord Bossk have shown
that instead of 86 percent, only 19 per cent passed throufj^
the glass. As a general remit of all his resoudies, it may
be supposed that about six sevenths of the heat given out
by the moon is radiated and one seventh reflected.

Is tkere aaj ekaaae on tte muAm of tlM Mtoonf—
When the surface of the moon was first found to be cov-
ered by craters having the appeanmoe of voloanosa at the
surface of the earth, it waa veiy nalnrally thoof^ that
these supposed volcanoes mig^t be itill fai activity, and ex-
hibit themselves to our teleaoopes by thev flames. Sir
William Hkbsohsl supposed that ho law several safih vol-
canoes, and, on his authority, they were "Umg beBeved to
exist. Snbeequent obanrvations have ahown that tl^ was
a mistaken opinion, though a very natural one under the

wmm

\ to be 618,000 timw m

M well M die light of
uUl unonntof its own
ctedand radiated are bo
ection exoept with the
«h now known. By ool-
u of one of his large re-
able to ihow ^t a
illy received from the
with the moon's pluwe,
to learn how much of
id how much radiated.
• capacity for paning
to students of physics
t the heat radiated by
odieswill pass through
>lerbody. Experiments
he sun's heat will pass
f the heat of the moon
would possess the samo
ion would pass through
[jord RossK have showu
9 per cent passed throuf^
all his resoudies, it may
faa of the heat giren out
leventh reflected.
nuflMe ct tbm Voenf —
as first found to be oot-
■aaee of volcanoaa aft the
y naturally thonglit that
e Mill in activity, and ex-
es by tiieir flaoMS. Sir
i ho law aevend •aflh vol-
)yw«re long beBevedto
have shown that this was
7 natural one under the

CttANOKS ON TBS MOON.

888

clrcnmsUnoes. If we look at the moon with a telescope
when she is three or four days old, we shall see the darker
portion of her surface, which is not reached by the sun s
rays, to be faintly iUuminated by Ught reflected from the
earth. This appearance may always be seen at the right
time with the naked eye. H the telescope has an aperture
of five inches or upward, and thfB magnifying power does
not exceed ten to the inch, we shaU generally see one or
mora spots on this dark hemisphere of the moon so mudi
brighter than the rest of the surface that they may well
suggest the idea of being self-luminous. It is, however,
known that these are only spots possessing the power of
reflecting back an unusually krge portion of the earth s
light. Not the slightest sound evidence of any incandes-
cent eruption at the moon's surface has ever been found.

Several instances of supposed changes on the mowi's
surface have been described in recent times. A few yeais
ago a spot known as linnaus, near the centre of the
moon's visible disk, was found to present an appearance
entirely diilerent from its representation on the map of
Bran and Hakdlkr, made forty years b^ore. More
recently Kltot, of Cologne, supposed himself to have dis-
covered a yet more decided ohaiige in anodwr feature of
the moon's surface.

The question wfaeTher these changes are provwi is one
on which the opinions of astroiu»nen difler. The difficul-
ty of reaehing a oertain oonohision arises from the fact that

each leataie nees»»ily varies in appearance, owingto the
dUlevent ways fai which the sun's light falls upon it
SomellmeB the changes an very diflleult to account for,
even whan h is certain that they do not arise from any
dungeon the oMonitwlf. Henee while some regard the
apparent ehaagea as real, othen regard^them aa due only
to dilieienesa in the mode ol iUamination.

CHAPTER V.

THE PLANET MABS.
% I. DIBOBIFTIOir or TBM VLAMWS.

Mara is the next planet beyond the earth in the order
of distance from the sun, being about half as far again as
the earth. It has a decided rad color, by which it may
be readily distinguished from all the other planets.
Owing to the considerable eccentricity of its orbit, its
distance, both from the sun and from the earth, varien in a
larger proportion than does that of the other outer planets.

At the most favorable oppositions, its distance from the
earth is about 0'88 of the astronomical unit, or, in ronnd
numbers, 67,000,000 kilometres (86,000,000 of miles).
This is greater than the least distance of Venutf bat we
can neverthelefls obtain a better view of Man under these
circumstances than of FmiM, because whm the lattor is
nearest to us its dark hemisphere is turned toward us,
while in the case of Man and of the outer planets the
hemisphere turned toward ns at oppgsition la fully illur
minated by the sun.

The period of revolution of Jfors around the son is a
little leas than two years, or, more emetfy, 98/f days. The
sueoessive oppositions oocmr at interrala vi two yean and
(MM or two months, tlie earth having made duing tiiia
interval a little more than two nmAaiicm mmmdilMnui,
and the planet Mara a little more than one. The dates
<^ sevend past and future oppoaitioiN an shown in the
following table :

IfABS.

the earth in the order
mt half as far again as
>lor, by which it may
ill the other pUuiets.
fcricity of its orbit, its
m the earth, varien in a
the other outer planets.
IS, its distance from the
nioal unit, or, in round
(85,000,000 of miles),
woe of Vtnua, but we
w of Man under these
HUM when the hitter is
) is turned toward us,
the outer phmets the
if^positioii is folly illu-

r* around the son is a
e>«Qtfy^<)8?days. Tho
Mtals of tivo yean and
liag made dwii^ this
Dla^itHui mmmdtJMmn,
than one. The dates
ions are shown in the

OPPOSmOlTB OF MARS.

1871 March 20th.

1878 April 27th.

1876 June 20th.

1877 September 6th.

1879 November 12th.

1881 DecomW 26th.

1884 January Slst.

1886 March 6th.

Owing to the unequal motion of the planet, arising Aom
the eccentricity of its orbit, the intervals between sue*
ceosive oppositions vary from two years and one month to
two years and two and a half months.

About August 26th of each year the earth is in the sam6
direction from the sun as the perihelion of the orbit of
Mart. Hence if an opposition occurs about that time,
Mar» will be very near its perihelion, and at the least
possible distance from the earth. At the opposite season
of the year, near the end of February, the earth is on
the line drawn from the sun to the aphelion of the orbit
Mar». The least favorable oppodtionB are therefore
those which occur in February. The distance of Mam is
then about 0*66 of the astronomical unit.

Tho &vorable oppositions occur at intervals of 15 t/t
17 yean, the period being that required for the successive
increments of <me or two months between the times of the
year at which successive oppodtions occur to make up an
entire year. This will be readily seen from the preceding
taUe of the times of opposition, which shows how the op-
poritioiis nutgsd trough the entire year between 1871
and 188ft. Thtt opposition of 1877 was remarkably fa-
vorable. Hw not most favoraUe opposition wHI occur
in 189».

Mmt WBBMnrny eiidbits phases, but they are not s6
w<^ muked as in Hm owe of Vmui, because the hani-
tfkan wljeh it {ffssents to the obMrver on the earth is
i4w»ys mora tim half illuminirted. The greatest phase

886

ABTRomitr.

oooun when its direction is 90° from that of the «un, and
even then six aeventha of its diik is illuminated, like that
of the moon, three days before or after full moon. The
pliaaea of Mar$ were observed by Galilko in 1610, who,
however, oould not describe them with entire certainty.

BoUtion of Man.— The early telescopic observers
noticed that the disk of Mara did not appear uniform in
color and brightness, but had a variegated aspect In
1666 the celebrated Dr. Bobut Hookb found that the
maridngs on Mara were permanent and moved around in
inoh a way as to show that the. planet revolved on its axis.
The markings given in his drawing can be traced at th«
present day, and are made use of to determine the exaok

Eiriod of rotation of the planet. Drawings made by
mroHiNS abont the same time have been used in tlM
same way. So well is the rotation fixed by them that the
Mfcronomer can now determine the exact number of times
the pUmet has rotated on its axis since these old drawings
were made. The period has been found by Mr. Pbooto*
to be 24i> 87" 32*>7, *a result which appears certain to one
or two tenths of a second. It is therefore less than an
hour greater than the period of rotation of the earth.

■nfftioe of Mars. — The most interesting result <tf these
nuurkiiigs on Mara is the probability that its surface k di-
Tondfied by land and water, ooverad by an atmos^^ierB,
and altogether very similar to the surface of the earth.
Some portions of the surface are of a dedded red ookM*,
and thus give rise to the well>known fioy aspeei of tiie
planet Other parts are of a greeniah hue, and are there-
fore supposed to be seas. The meet striking features are
two brilliant white regions, one lying around Mohpcd* of the
planet It has been supposed that thia appeeiwce is due
to immense masses of snow and ioe snrroukling tiie poles.
If thia were so, it would indicate thai ^prooessea of evap-
oiation, doud formation, and ewideneation of vapor iiito
lain and snow go on at tJie turfaoe of Jf«rt aa at the snr<
Imo of the earOi. A certain amount of color is given to

IqjI^!

wm^^

rom that of the iun, and
is illuminated, like that
r after full raoon. The
f Galileo in 1610, who,
I with entire certainty,
rly telescopic obaervera
1 not appear uniform in
I variegated aspect. In
' HooKB found that the
mt and moved around in
lanet revolved on its axis,
ing can be traced at th«
if to determine the exact
St. Drawings made by
have been used in the
on fixedbythem that the
lie exact number of times
since these old drawings
>n found by Mr. Pbootob
ch appears certain to one
is therefore less than an
rotation of the earth,
nteresting result of these
ility that its surface k di-
ivered by an aimoKpbmPt
the surface of the eurtli.
d of a dedded red ookv,
oown fieiy nqteot of tiie
eeniah hue, and are thero-
most striking featurw are
ring around each p(de of the
lihet thii appeaivttoe is due
ice surrouk^ng the polfls.
ithiKtIlieprooeiMt oferap-
Mmdensadon of vapor into
loe of Jf«rt M at the snr.
uonut of eotoris giveata

ASP/ecr OF MARS.

tliitt theory by supposed uiiangus in the inugiiitudu uf
tltuttu icu-caps. Uut thu prublunt uf eittablisliing such
changes is one of oxtromo difficulty. The only way in
which an ado<juate idea of this difficulty can be formed Is
by the reader himself looking at Mara through a telescope.
If he will then note how hard it is to make out the
difierent slutdes of light and darkness on the planet, and

"Si^mwmm

how they must vary ill aspect under different oonditiims
of clearness in our own atmosphere, he will readily per-
ceive that much evidence is necessary to establish great
changes. All wf, o;.'.say, tiierefore, is thai the formation
of tK« ioe^saps lu v/inter and their melting in summer has
some evidence in its favor, but is not yet oompl^l|y
provMi.

■mKKim

nnr

838

ASTRONOMT.

g 2. 8ATBLUTBS OF MAB8.

Until the year 1877, Mar» was supposed to have no sat-
ellites, none having ever been seen in the most powerful
telescopes. But in August of that year, Profeeeor Hall,
of the I) aval Observatory, instituted a systematic search
with the great equatorial, which resulted in the discovery
of two such objects. We have already described the op-
porition of 1877 as an extremely favorable one ; otherwise
it would have been hardly possible to detect these bodies.
They had never before been seen, partly on account of
tiieir extreme minuteness, which rendered them invisible
taoept with powerf^jl instruments and at the most favor-
•I>le ^imes, and partly on account of the fact, already al-
IlilkMito, that the favorable oppositions occur only at inter-
vals of 15 or 17 years. There are only a few weeks A\a-
ing each of these intervals when it is practicable to distin-
gnJah them.

These satellites are by far the smallest celestial bodies
known. It is of course impossible to measure their <Ham-
elere, as they appear in the telescope only as poiots of
Ii|g^t. A very careful estimate of the amount ol fi^t
tiHUeh they reflect was made by Professw £. C> Floiun-
no, Director of the Harvard Ooll^^ Obaorwlory, mho
wJeulrted how large they ought to be to refleet tt&i ll|^t.
%9 ttos f<MUOKi that the outer satdlite was flvMtify idSi»nt
ii^ mUes and tiie inner one about wesvmiaSim te (Jltmillwr,
impfioAux them to Msfleok the Mbifiiiv^fitdMljr «i Jlin
(MM. The <Hiter one wm mbh «m #^ lelnQope al « IHi-
tanoe from the earth of 7,000,000 thnei tiiis diameter.
The proportion woukk be that <tf a baB two inohei fa di-
ameter viewed at a distanoe isqiud to that faetween tlM
oHies of Boston and Kew YoA. Snehaifeat of tdeaeoph
seeingiB well fitted to give an ideaof tlia power of modem
optiod instmmeDta.

Professor Hall found that ^ onler ntdllfa, iriiiel
he called JMmoty revdvea jronnd thai planet Itt 9^ UPP,

^'^^^^m^mm^'v^mM-rnhki'mi

fT.

I OF MABS.

s supposed to have no sat-
en iu the most powerful
bat year, Profeeeor Hall,
;uted a systematic search
resulted in the discovery
already described the op-
favorable one ; otherwise
)le to detect these bodies,
sen, partly on account of
\ rendered them invisible
its and at the most favor-
int of the fact, already al-
witions occur only at inter-
ire only a few weeks d^r--
L it is practicable to distin-

B smallest celestial bodies
ble to measure their ^Kam-
iescope only as pointa of
) of the amount ol lii^t
y Professor £. 0. tmxa.-
Oollef^ Observiiory* who
t to be to reMi &}« li#it.
iteQHe waa fi«i«bfy i^ut
nt seven v^oi fat#uniiier,

Asm n^fnOm^ m J^
wi1ii^tilMQ0pe«l*iiB-
1,000 timei tills diameter,
of a bail two inohai ftt di-
lepuX to that .between Hio
:. 8aeh«feat of teleaeopic
toiof tlis power of modern

Hm onier aatelMi^ uMi

SATELLITSa OF MARS.

339

and the inner one, called Phcloa, in 7** 38*". The latter is
only 5800 miles from the centre of Mare, and less than
4000 miles from its surface. It would therefore be almost
possible with one of our telescopes on the surface of Mar»
to see an object the size of a large animal on the satellite.
This diort distance and rapid revolution make the inner
satellite of Mars one of the most interesting bodies with
which we are acquainted. It performs a revolution in its
orbit in less than half the time that Mars revolves on its
axis. In consequence, to the inhabitants of Mars, it
would seem to rise in the west and set in the east It will
be remeral)ered that the revolution of the moon around
the earth and of the earth on its axis are both from west
to east ; but the latter revolution being the more rapid, the
apparent diurnal motion of the moon is from east to west.
Iu the case of the inner satellite of Mars, however, this
is reversed, and it therefore appears to move in tl e actual
direction of its orbital motion. The rapidity of ix.' phases
is also equally remarkable. It is less than two hours from
new moon to first quarter, and so on. Tlius the inhabit-
ants of Mars may see tlieir inner moon pass through idl
its phases iu a single night

tmmmimima tm

CHAPTER VI.

THE MINOR PLANETS.

Whkn the solar system was firet mapped out in its trne
proportions by Copbeniccs and Kkplkb, only six primary
planets were known — namely, Merowry, Vemu, the
£arth, Mars, JvpUery and Saium. These suooeeded
each other according to a nearly regnkr kw, as we have
shown in Chapter I., except that between Mars and .AipH
fer a gap was Icrft, where an additional pknet might be
inserted, and the order of distance be thns made complete.
It was therefore snpposed by the astronomers of the seven-
teenth and eighteenth centuries that a planet might b^
found in this region. A search for this object was insti-
tuted toward the end of the last century, but before it
had made much progress a planet in the place of the one
so long expected was found by Pia«m, of Palermo. The
discovery was made on the first day of the pvesent century,
1801, January Ist.

In the couree of the foHowing seven yean the astronom-
ical worid was surprised by the discovery of tiiree othei
planets, all in the same region, though not levolviag m
the same orbits. Seeing four small planeto where on<
huge one ought to be, Olbhbs was led to hi» eelebwtec
hypothesis that ^msm bodies were the fn«meiits of a la>g(
planet which had been broken to pieeea by the aetkm a
some unknown f<Nroe.

A generation of astronomen now passed imr^ ^^^
,the discovery of more Aan these four. But in ^^
1846, Hrhokk, of Dreisen, being engeged Hi

■MFfMMM

^ VI.

LANB'rS.

rrt mapped ont in its trae
Kbpleb, only six primary
, Mercury t Venus, the
Uum. Theee suooeeded
' regular law, as we have
I; between Mars and Jvpi-
Iditional planet might be
se be thus made complete,
astronomen of the seven*
» that a planet might }y*
for this object was insti-
ast oentnry, bat before it
et in the place of the one
Puzu, of Palermo. The
day of the praamt century,

^ seven yean tiie astrcmom-
) discovery d! tiiree other
k, thoii(g^ not nvolvii^ m
small planets where one
was led to his eelebnited
ire the fragmeRts of a laige
to pieces by the Mtkm oi

now passed «wn/ without
lefoar. Bntir. Doeenhpr,
)eing engaged in manptng

THB MINOR PLANETS.

841

down the stars near the ecliptic, fonnd a fifth plauot of
the group. In 1847 three more were discovered, and
discoveries have since been made at a rate which tlius far
shows no signs of diminution. The number lias now
reached 200, and the discovery of additional ones seems to
be going on as fast as ever. The frequent announcentents
of the discovery of planets which appear in the public
prints all refer to bodies of this group.

The minor planets are distinguished from the major
ones by many characteristics. Among these we may
mention their great number, which exceeds that of all the
other known bodies of the solar system ; their small size ;
their positions, all being situated between the orbits of
J^<ir«and JvpUer; the great eccentricities and inclina-
tions of their orbits.

number of Small Planets. — It would be interesting to
know how many of these planets there are in all, but it is
as yet imposdble even to guess at the number. As
alrouly stated, fully IKK) are now known, and the number
of new ones fonnd eVery year ranges from 7 or 8 to 10 or
12. If ten additional ones are fonnd every year during
the remainder of the oentnzy, 400 will then have been
discovered.

The disoovery of these bodies is a v^ difficult work,
requiring great jwactioe and skill on the part of the as-
tronomer. The difficulty is that of distinguishing them
amongst the hnndreds of thousands of telescopic stars
which are scattered in the heavens. A minor planet
presents no sensible disk, and therefore looks exactly like
a small star. It can be detected <mly by its motion among
Lhe sommnding stan, which is so slow that hours or even
days must ebpse before it can be noticed.

liH(BitadM.-^In oonsequenoe of the mmor pknets hav-
ixig no visible disks in the most powerful telescopes, it is im-
pMsible to make any precise measurement of their diam-
•Ian. These can, however, be estimated by the amount
M fisht which the planet rejlects. Supposing the propot-

849

ASTRONOMY.

tion of light reflected about the same as in the ease of the
lai^r planets, it is estimated that the diameters of the
three or four largest, which are those first discovered,
range between 300 and 600 kilometres, while the smallest
are probably from 20 to 50 kilometres in diameter. The
average diameter of all that are known is perhaps less than
150 kilometres — that is, scarcely more thaii one hundredth
that of the earth. The volumes of solid bodies vary as the
cubes of their diameters ; it might therefore take a million
of these planets to make one of the size of the earth.

TOrm of Orbita.-~The orbits of the minor plairata are much
mora eccentric than thoae of the hrger ones ; their distiince from
the sun therefore raries venr widely. The most eccentric orbit jet
known is that of AMm, which was discovered by Professor Wat-
soM in 1878. Its least distance from the sun is I'Al, a very little
further than JTort, while at afriielion it is 8 -59, or more than twice
as far. Two or three others are twice as far fnnn the son at aphe-
lion as at perihelion, while nearly all are so eccentric that if the
orlnts were drawn to a scale, the «ye would readily pero^e that the
sun was not in their centres. The largest incUiumon of all is that
of PMu, which is one of the original four, hairinff been d is cov e red
by OLBUia in 180S. The inclinimon to the eeHpoe is S4% or more
than one third of a r^t angle. Five or six others have ineUaations
exceeding M*; they therefore range eatireW outside the lodiae, and
in fact sometimes culminate to the north of our aenlth.

CMgin of tlMlUiior Flail0ta.--The question <rf the ori|^n of
these bodies was long one of great interest The features which we
have described associate themselves veiy naturally with the oel»-
brated hypothesb of OLana, that we here hava the Aiagaasirta of a
single Inge planet which in the beginning revolved in its proper
phwe between the orblu of Jftr* ana J^pitir. Qusaa Umsetf siw-
1 a test of his theory. If these bocBea were raally ftmned hj

rtoaioB of the kige one, the sepante oitilB of the frs g rneats
all pass through thejpoiiit where tiw «qpIoaioa occurred. A
comown pdnt of intersectfen was tbenfore hmg looked for ; but
although two or three of the first foor did maa vnMj asar each
oAer, the required point ooold not be f oond for all four.

It waa then sugested that the secular chaiwes in the oiMts pro-
duced by tiie aettmi <rf the other phuieti would in tiiM diatMe the
Crftiona tS all the orMts in saeh a way ttat thqr woald ao {eager
TeatqreoauaoQiateneeUoo. The seenlarvarlanoBs<rf their omts
weretiMrdioneoBsputed, tosee if thero waaacyaignof the reqidred
intersection in past sges, but bow» couM be found. Ko support
has beea gtvea to Olbbbs* hypothesis by aubsoqunt fanresti|atioBS,
and it is ao hwger considered by aatranooMn to have any founda-
tioB. 00 Iv as cui be judged, these bodies have been remrfviMr
arovud uie sua as separate paaets ever siaoe the aofav s y s t wa itaNl
was fomed.

aa^eapli
woulai

me RB in the case of the
Eit the diameters of the

those first discovered,
letres, while the smallest
letres in diameter. The
lown is perhaps less than
Qore than one hundredth
: solid bodies vary as the

therefore take a million
:e size of the earth.

he minor plaiMta are much
r ones ; their diatiuiM from
The most eccentric orbit jet
scovered by Prof ewor Wat-
he sun is 1*61, s very little
it is 8*60, or more than twice
as far from the son at aphe-
am so eccentric thatif tlie
Mild readily pera^e tliat the
rest inclimmon of all is that
four, having been d i sc o v e red
D the eettpoe is 84% or more
* six others have inetiBations
tirelv outside the ndiao, and
^ m our Muith.
he queatfou <rf the origin of
rest The fsatnna which we
rery naturally with the cele-
here have tte in«MBts of a
uin^ revolved in its propw
vfUtr. OUBM himself mm-
lodiet wen really formed 1^
HUte oibito of tile ftagmeats
a tiie exnloaioB occurred. ▲
mf ore long looked f ov ; but
or did pH« wettyMsr eadi
fooad for all four. ^^
ar cha^eaiathe oiMtapn>>
m wouu fai time eharae tho
ly tiMt thqr would no lennr
eular vailatloBs of tMr oiwts
B wa« acy ^gn ^ the requlrad
ottld be fonnd. Bo sap|mFt
Iqr s u b se m w rt investJ a a a oy,
moaanto have anyfoundap
bodies have hem *«*<>^[^
r siM» the sohw ay s t s m UsaB

CHAPTER VII.

JUPITER AND HIS SATELLITES.

§ 1. THB YiJkSws nrevasBL.

Jupiter is mnch the largest planet in the system. His
mean distance is nearly 800,000,000 kilometres (480,000,-
000 miles). His diameter is 140,000 kilometres, corre-
sponding to a mean apparent diameter, as seen from the
snn of 86' . 6. His linear diameter is about ^^ his surf aqe
is flvy and his volume xhv ***•* ®* *^® ■""• ^^ "»■» i«
J™, and his density 48 thns nearly the same as the ana**—
v£,0.»4oftheearth'B. Herot«te8onhia«xi«hi»»6ft-a0*.

He fa attended by four satellites, whidi wore diwovend
by Oaulso <m JanuMy Tib, 1610. He named then in
honoroftheM»Diois,theJfo*fo«m«tor#. These sateffites
were independently discovered on January 16th, 1610, by
HAsnor, of England, who observed them through several
subsequent yeaifc Smow Mawos al«o appeaw to have
eariy obeerved tlwm, and the honor of their disoovery m
cUtimed for him. They are now known as Batelhtes I,
II, III, and rV, I being the nearest.

The surface of JvpiUr has been carefully studied with
the tekicope, pe-ticukriy within the p«it 20 years. Al-
though further from ua than Jfow, the details of his disk
aie hiueh earier to wcogniae. The most charactenstic
featnwB are given in the drawings appended. These feat-
ures are, i8r^, the dark bands of the equatorial ryons,
and, a^wmay, the cbnd-like forms spread overneariyUie
wfa^iaoifaoe. Atthelimballtheaedetaihbeeomemdis-

imiWI Ii l i

AarHONOMY.

tinct, and finally vanish, thus indicating a highly absorptivo
atmosphere. The light from the centre of the disk is twice
aa bright as that from the poles (Akaoo). The bands can
be seen with instruments no more powerful than those
used by GALtuto, yet he makes no mention of them, al-
though they were seen by Zuocni, Fontama, and others be-
fore 1638. HinvHKNS (1659) describes the bands as
brighter than the refiA of the disk — a unique observation,
on which we must look with some distrust, as siitce 1660
they have constantly been seen darker than the rest of the
planet.

The color of the bands is frequently described as a brick-
red, but one of the authors has niade careful studies in

•— TBunnopio vnnr or nmm ukd m «a<

ool<» of tUi planet, and finds the prevaiUng tint to b0 a
wtkuoxk oolbr, exactly similar to the odior of JVorv. > Tbe
position of the bands varies in latitude, and the shapes of
the limiting curves also change from day, to day ; but in
the nuun they nmaan as permuient features of the region
to which they belong. Two such bands are usually vis-
Able, but often mmre are seen. For eitam^e, Oassidi
(1690, December 16th) saw six parallel ba&ds extending
completely anmnd the planet. HutsbaKL, in the yeair
1798, attributed iStta aspects of the bands to zones of the
planet's atmoqdiiero more tran<^il and less filled vl^ilh
doads than ^ rerauning. parnbns, so as to permit the

§IIWJiiSi»WWmW»i^^

lating a highly uheorptive
iontre of the disk is twice
Ikago). The bands caii
»re powerful tlian those
no mention of them, al-
FoNTANA, and others be-
describes the bands as
■a unique observation,
le distrust, as since 1660
rker than the rest of the

ntly described as a brick*
made careful studies in

noi Axommtti

e imvittUng; tint to be a
yhe color of JViir*. > ThA
bitnde, and the pluipes of
■om day.to day ; but in
at features of the region
1 bands are usually tis-
For example, Oassh^
parallel ba&dfi extending
HsBsbBKL, in the yea^
e bands to zones of the
lil and lew filled #ith
sns, so as to permit the

A8PE0T OF JUPITBR.

845

true surface of the phmet to bo seen tlirongh these zones,
while the prevailing clouds in the other regions give
a brighter tint to these latter. The color of the bands
seems to vary from time to time, and their bordering
lines sometimes alter with such rapidity as to show that
these borden are formed of something like clouds.

The clouds thenuelveB can easily be seen at times, and
they have every variety of shape, sometimes appearing as

BAVMU&nS'AXP

biQIisiit draW'^iHetnasses, but oftenerthey are rimilar
in f <«ic k> a scilb of white eanmlons clouds such as are
ib^qoently seen pQed up new tiie horiison on a rammer's
day. Dm twadi; ^emselvei seon fre^riiratly to be veiled
over with solnelliili( Vice ^ thin omtm donds of onr
stmoii^^ On <Mi« oeeisiofi an ammlns of white eloud
i^sMtt^ OM lill^ diurk bands lor many days, retain'
lag its fll^qpe liidraiq^ ^ whole period.

346

A8TR0N0MT.

Snch donds can be tolerably accurately obeerved, and
may be used to determine the rotation time of the pknet.
These obeervatiouB show that the clouds have often a
motion of their own, which is also evident from other con-
siderations.

The following results of observation, of spots situated in

various legions of the pUmet will illustrate this :

h. m. *>

Gamimi.... WM, roUtloBUii» = » S6 00

HUMOBU. 17TB, •• =9 SS 40

HnnoHBt. Vm, •« « 80 48

BoBKonwi. i«5. •• Bf «• ae

Bbui*M1oucb.... 1888. "b 8 85 88

A»T 1888. " •• = 8 86 81

BoBXiiyr 1888, " •' = 8 88 »

% 2. TEQi flATKiUnm OT JUFITMR.

MottonaoftlMtet^UitM.-'The four satellitei move
about JufiUer from west to east in nearly ciroubr <nMti.
W2ien one of these satellites passes between tlie nm mm!
JupUefy it easts a shadow upon Jvpiter'* disk ^ Fig. 98)
preeiaely a* the shadow of our moon is thrown upon the
earth in a solar edipee. If the satellite paam tbiMtth
JupUer't own shadow in its revolntiooi, an ipdfpae of tUa
satelUte takes plaoe. H ft pMaes betireea the eMIli and
/«^A^, it iapiojeeted upon .^itfwM« dUc* and m han »
tranrit ; if JvpUtr^B between the earth ud the saidfite,
an occultation of the latter oooois. All theae phenomena
can be seen from the earth with a oonun<m tdeaeope, and
the timeaof observation are all found predicted in the
Naiuticdl Almanae. In this way we aie sure that; the black
spots which we see movii^ across the .disk of JvjpUer ai«
really the shadows of the satel^tee ttouwlvee, and not phe-
nomena to be otherwise ezplaiaed. These shadow* being
seen blaok npon J^ipUer^t warfMoe, show tint this planet
synes by reflecting the li^t of the snn.

msmms^mmmmmm

Mjurately observed, and
tion tiiue of the planet,
e clouds have often a
evident from other con-

iion, of spots situated In

Uustrate this :

A. m. A

OB tlms = 9 fi6 00

•• = 9 5S 40

" s 9 90 48

» B t M 86

•• B 9 85 M

•' s 9 89 91

•• z= 9 89 »

OF jurmttL

e four satellitea move
nearly cironlar orbits.
IB between tin ran and
piW'«disk^Fig.98)
Mm is thrown npon the
satellite panes tiWMtth
Btiom, an 9clipie of ttja
I befeireen the eerth and
E«r*« 4Uki mi we have a
I earth and the satellite,
All these phenomene
oomuMm tdeseopOf and
found predicted in the
re are sure that; the black
tiie.disk of Jiipiier are
Itonnlves, and not phe-
. 3%ase shadows befaig
e, show tin* this planet
le sun.

SATKLLITBa OF JUPITBR.

847

lUeaoopio Appeaianoe of the teteUites.— Under ordi-
nary circumstances, the satellites of JupUer are seen to
have disks— that is, not to be mere points of light. Un-
der very favorable conditions, markings have beeen seen
on these disks, and it is very curious that the anomalous
appearances given in Fig. 98 (by Dr. Hastimos) have been
iteen at various times by other good observers, as Sboohi,
LHwKs, and RtrruKuruRD. Satellite III, which is much
the '^rgest, has decided markiny on iU faoe ; IV some-
times app?4n, as in the figui, to have iti eiroolar oatUne

Fni.98,

trrmtmntiM or nrmai's satbixrMi

cut o£E by right lines, and sajPlte I sometimes appears
gibbous. The opportnaWes for observing these q>pear-
ances are so laie that v/lifm$ h known beyond the Iwe
fact of their existence, ui/i Ho |bnsiUe explanation of the
figure shown in IV haa tecnjNn-

^EMaSil^Slli-^MWlSliMHiH :fUIs «Ms'tai«Mi'to

MMMMiaS^tesI '^SSrmm tlw''astttd Haat diMni'froai
ii*?"!S!iT iKnmi W^ -^R difll-f sdgss of ttas flaMl and
SiStoralSisi «lotatAm the oelliass of the

•'^'iiSSlidwthe Doritkm of J^yitormsfkid/tothslrft
of th. tg«^ It l«4iig ihenlnwiiiodtfcm to tbM^^

on the tSrtli at FoSdd -o* t^ «• ?^**^wI7S JL2f
rtukUm of .?i»«<r !»««« ti«ktt« to wtiw^

Hraoa. as th?«tdllto -owsawaad, bewttlses i^^^^Pf*^j°«^
grtOliSto the oAto «tf ^M**" to » g»«* thrt it soMsthw- «--»

— xw-w^wpppiPHBn

■t

348

entirelj »bove or bvlow
ktall.

ASTRONOJIir.
the planet, and therefore U nut occulted

I^et us next conaider Jupiter in the noaition J" near the bottom of
the figure, the shadow, aa before, pointing from the planet directly
away from the sun. If the shadow were a visible object, the ol>-
•erver on the earth at T could see it projected out on the right of
the f 'wet, because he is not in the line between Jupiter and the sun.
BcBce aa a satellite moves around and enters the shadow, he will sec
it disappear from sight, owing to the sunlight being cut off ; this

ti called an eMpm Ht^f m n m rn. If tbe iitalllto k oqe «r the two
outer oDon, he wiU be aUe. to see K vrnffrnf agaia after it oomea
oak of the shadow befora it ia ocevHed brtriad tte pkMt

Boob afterwafd theocoiiUatioft wttl oeow, Md it wfll afterward
reaniaw oa the left In the ean^tiwl«Mrior;iMtiilellifo, bow-
ever, tho point of ensigenee tmm tke O m itm iahMden behM the
pl ane M o n ae q nettllytheobeervwv after itoswtdlwmi^
ow, iiffl net aee it ie«Mpear until it enenMa fkoMl^d'OMrplMet

IftbeplMetiaiBtle peiitioni^,tiMarttiliftewffl be oeoSted

SATKLLlTSa OF JUPJTAJt.

340

therefore ia nut occulted

ition J" near the bottom of
ng from the planet directly
re a visible object, the ol>-
>jected out on the right of
Btween Jvpiter and the sun.
ten the anadow, he will see
mlight being cut off ; thia

I *ttliU* fa oqe of the two
ipfMr uaia aft* it cooMa
teldad flwnkaet
«owr,;aMl ft wffl aftermrd
lumionintmuimd. how-
nimR b.liid(l«i bebM tba

BM.InMaliM^ tha,pi««t
'MtaUitaifiU iM omSed

behind the planet where it roarhea tlio first dut( '-d linn. If it ia the in-
ner aatellite, it will not be been to reapptiar on the other aide of the
planet, because when it reaches the aecond dotted line it haa entered
the ahadow. After a while, however, it will reappear from the
ahadow aoine little distance to the left of the planet ; thia phe-
nomenon ia railed an eelipte reoftpearonee. In the caae of the outer
aatellitea, it may aometimoa hapnen that they are viaible for a abort
time after they emerge from benind the diak and before they enter
the ahadow.

Theae different appearances are, for convenience, repreaentod in
the figure aa correaponding to different poaitiona of JuvUtr in his
orbit, the earth having the aame poaition in all ; but since JvfUer
revolves around the sun only once in twelve years, the changes of
relative positioto really correspond to different positions of the earth
in its orbit duriof ' ' he course of the year.

The satellites cuiupletely disappear from telescopic view when
they enter the shadow of the planet. Thia seems to show that
neither planet nor satellite is self-luminous to any sreat eitent. If the
aatellite were aelf-luminoua, it would lie aeen by Its own light, and
if the planet were luminous the satellite migbt be see* by the re-
flected light of the pUnet.

The motions of these objects are connected by two curious and
important relations discovered by La Placb, and expressed as fol-
lows:

I. Th» mean motim <tf the flmA mUettiU added to twiee the mean
motim vf the tJiird i» mutl^ equal to three timee the meoH tuetim <(f
the eieoiuL

n. ^tethe mean bmaitude of the Jlrtt tatettUe m add twiee the
mean lanfUude <^ the third, ana mUraet three timee the mean longitude
o/theieeond, the differenee m tdmoMe 180°.

The first of these reUtions is shown in the following table of the
mcian daily modons of the satellites:

SatelUte I In one day moves M8°-«MW

II « " lOl'-niS

•• III , 60* mw

•• IV " " 2r«7n

Motion of Batfvlllte I W-m»

Twice tut of SatelUte III 10(r-«S4

Bam 804* 1944

Three times notion of SatelMte II 804° '1944

Observations showed tiiat this condition was fulfilled as exaetly
as possible, hot the discovery of La Plack consisted in showing tli^
if the approximate coincidence of the mean motions was once e«-
(ablidiea, they could never deviate itoas exact coincidence with
the hiw. The cas« is analogous to that of the moon, which alwMs
psaanti the same face to u« an2 which always will sinCo the nu-
nott \(Aa% once approziiusus'.y t:^^ it will bocone loaot and evo*
lemainsOi

850

ABTROirOMr.

:'>WI

The diwovi- uii the anulu«l prop««tioii of liaht by meMM of
theM Mtellite* h«i ftlready been aeKiiMd, and it rm alM been ex-
piniDed that they are of -um in the roush determination of longi-
tudea. To facilitate their obaenration, the Nautical Almanac gives
complete ephemerides of their phenomena. A apecimen of a por-
timi of such an ephemeria for 1865, March 7th, 8th, and 9th, ia
added. The time* are Washington mean times. The letter IK in-
dicates that the phenomenon ia viaible in Waahington.

1M0— Mahcb.

h. m. $

Eclipse

Diaapp

18 97 88S

Occult.

Bespp.

91 M

III.

IngTMS

7 97

III.

Shadow

Bgrew

9 88

III.

Transit

Ingnas

19 81

II.

Eellpw

Disapp.

18 1 997

III.

Tranalt

Bgnw W.

IS 6

II.

Eclipse

RMpp. W.

18 94 111

II.

Oecolt.

Diaapp W.

18 97

Shadow

Ingreaa W.

16 48

Transit

InRfcss W.

18 88

Shadow

Egroas

17 OT

11.

Occult.

Heapp

17 69

I.'

Transit
Eollpss

Um^

8
9

19 18

19 88 88-4

Occult.

Beapp W.

IS 96

Suppose an obsenrer near New York "City to have determined his
local tune accurately, lliis is about IS" faster than Waahington
time. On 1868, March 8th, he would look for the reappearance of
II at about 18^ 84" of bis local time. Suppcw he obsenred it
at 18^ 86*> 99"7 of his time : then his meridian is 19" ll'-6
east of WaaUngton. The diffleulty of obaerring these eclipses with
accuracy, ai^ the fact that the aperture of the teleaoope employed
baa an fanportant effect on the appearances seen, have ke^ this
nugthod frmn a wide utility, which it at first seemed to promise.

The apparent diameters of these aatellitea have been meas u red by
Sntmra, Bboobi, and others, and the best results are :

I, l"-0; n, <r-9; in, 1"'8; IV, l"-8.

Their masses {,J*mUer=\) are :

L 0*000017 ; 11, 000098 ; HI, 0000088: IV, OHMMKMB.

The third aatelUte is thus the largest, and it Iws about the den-
si^ of the phuiet The true diameters vary £mn 9900 to 8700
ouiea. ThcTolumeofn is about that of our moon; III approwdiss
our earth in size.

Variations in the light of these bodies have constantly been
noticed which hsTc hem rappoeed to be due to the fact that they
turned on their axes once in a revolution, and thus presented various
Ikoes to us. The recent socwate photoawtrie ws— ntss of I>»ab-
luaii show that this hypotheds wfll not aooonnt for all the chwifH
observed, some of whicb appear to be quite sudden.

'•'piW5S!PrS?'

{Ktion of light by mesnii of
M>d, tnd it hH «lio been e%'
ugh detenninttion of longi-
the Nauticftl Almanao givei
leiw. A tpecimen of a por-
HarchTth, 8th, and 9th, ia
san times. The letter TK in-
in Waahiogton.

88-8

88-7

111

89-4

City to haTe detennined hla
18" faater than Waahington
look for the reappearance of
M. 8uppow he obaenred it
hi* meridian U 18" 11-6
Dbaerring theae ecUpaea with
e of the teleacope employed
irancea teen, have ke^ this
t first seemed to promise,
llites have been meamred by
test results are :
8.

)0088: TV. 0*000048.
■t, and it liaa abont the den-
ers vary from 8900 to 8700
»f oar moon ; III approaohea

lodies have ooostantly been
Iw doe to the fact that they
n, and thua presented variooa
mnetrle m— sarsaof Sksbl-
>C aoooont fw all the c haa f
quUe sudden.

i^m^mm^^-

BATKLLITEJH OF JUPITEB.

"^ ^ P r*

851

s I I I

§ § § §

CHAPTER VIII.

SATURN AND ITS SYSTEM.

g 1. QEinBIlAL DBSGBIFTIOir.

Saturn is the most distant of the major planets known
to the ancients. It revolvfis around the sun in 29^ years,
at a mean distance of nearly 1,600,{KM},000 kilometres
(890,000,000 miles). The angular diameter of the ball of
the planet is about Id"* 8, corresponding to a true diam-
eter of about 110,000 kilometres (70,600 miles). Its diam-
eter is therefore nearly nine times and itc volume about
700 times that of the earth. It is remarkable for its small
density, which, so far as known, is less than that of any
other heavenly body, and even less than that of water.
Oonsequently, itoannot be composed of rooks, like those
which form our earth. It revolves on its axis, aoeording
to the recent observations of Professor Hall, in lO*" 14"
24% or less than half a day.

8atwm is perhaps tlie most remarkable planet in the so-
hur system, being itself the centre of a system of its own,
altogether unlike any thing else In the heavens. Its most
noteworthy feature is seen in a pair of ringi which sur-
round it at a considerable distance from the pbnet itpelf.
Outside of these rings revolve no iMl'tban eight satelB t oi,
or twioe the greatest number known to surroui^ any
otiier planet. The pknet, rings, and satellitea are alto-
geUier called the Sahtrman afdrnn. lliegeDual ^>pe■r•
ance of this system, ae aeen in a nnall UAmoof$t indiown
in Fig. es.

ASPBXjr OF SATURN.

363

VIII.

SYSTEM.
OBIFnON.

B major planets known
id the sun in 29| yean,
600,()(H),000 kilometres
r diameter of the ball of
onding to a troe diam-
0,600 miles). Itsdiaui-
B and itc volmne abont
remarkable for its small
is less than that of any
less than that of water,
led of rooks, like those
es on its axis, aooording
•fessor Hall, in 10^ 14"

arkable planet in the so-
of a system of its own,
the heavens. Its mort
or of rin^ which snr-
ifrom thejdanet itself.
W^thanei^t satellites,
nown to sommiid any
, and satellites ane alto-
). Thefensnl vpptn-
nwll tolMOopt, isshown

To the naked eye, Saturn is uf a dull yuUoMrish color,
shining with about the brilliancy of a star of Uie iirBt mag-
nitude. It varies in brightness, however, witli the way
in which its ring is seen, being brighter the wider thb ring
appears. It comes into opposition at intervals of one year
and from twelve to fourteen days. The following are the
times of some of these oppositions, by studying which one
will be enabled to recognize the planet :

Fia. 9S.

VnW or TBB BATCBIIIAH STSfBH.

1879 October 6th.

1880 ; October IStli.

1881 October 81st

1889 . . November 14th.

1P88 MovwttberilSth.

1884.. December ll'h.

During these yeare it will be best seen in the antnl^n
and winter.

iiiMiWri M

iit'

ii!P
i

854

ABTBONOMT.

When viewed with a telescope, the pliysical appearance
of the ball of Satwm is quite similar to that of Jitpiter,
having light and dark belts parallel to the direction of its
rotation. But these cloud-like belts are very difficult to
see, and so indistinct that it is not easy to determine the
time of rotation from them. This has been done by ob-
serving the revolution of bright or dark spots which appear
on the planet on very rare occasions.

8 2. THB BOrOS OF SATUBIT.

The rings are the most remarkable and diaracteristic
feature of the Batumian system. ¥1g. 96 gives two views
of the ball aud rings. The Uf^r cme shows one of their
aspects as actually presented in the tdesoope, and the
lower one shows what the ajf^wvanoe wouM be if the
planet were viewed from a direetimi at right anglca to tlie
plane of the ring (which it never cm be from the earth).

The first telesoopic observers of jSbrfurra were unable to
see the linga in their true f onn, and were greatly per-
plexed to aocotrnt for the appearance which the planet
presented. Gamlho described the plauetia *' tri-oorpo-
rate," the two ends of the ring having, in his imperfeot
telescope, the appearance of a pair of OBill planets at-
tached to the central one. " On each ride of old Satwm
were servitors who aided him on his way." This sup-
posed cUscovery was announced to his friend KKW.Mt fai
the following logogriph :

smaismrmilmopoelalevmibonenogtteviTas, which, b^^
transposed, becomes —

" Altiirimam planetam teigeminam obsevavi" (I have
ofawnrod tho most distant planet to be triform)-.

The jdienommion oonstantly remiuned a myalery to ito
lint ohaervw. In 1610 he haid seen fhe j^burat^MMiHiipft-
sied, as he snpposed, by two lateral stars; in I61i the
latter had van^hed, and the central body alone retnained.
After that Qaulho oeased to observe Saturn.

the physical appearance
lar to that of JvpUer^
$1 to the direction of its
lelts are very difficult to
>t easy to determine the
lis has been done by ob-
dark spots which appear

ns.

F SATUBir.

kable and cluuw^ristic
Fig. 96 gives two views
r <Hie shows one of their
the telescopb, and the
HMranoe would be if the
km at right ang^ to tlie
can be from the eartli).
)f Sstwm were unable to
1, and were greatly per-
inuio0 which ^e planet
he planet as " tri-oorpo-
having, in his imperfect
Niir of pnill planets at-
1 each side of old Satmm
m his way." This mp-
to his friend KjtFunin

logtteviras, which, bring

ninam obsevavi" (I hftV9
to be triform)',
wmained a myaleiy to its
nen the j^hmet^MBOOiapft-
iterai stsn; in lAU the
tnd body alone retained.
lervoiSbtom.

356

ASTBONOMY.

Tko appearances of i|ie liDg were also iacomprehensiblo
to Hkvklivs, Gabsbwdi, aud othen. It was not until
1655 (after seven yeara of observation) that the celebrated
HnroHKNS discovert^ the true explanation of the nmark-
aUe and recurring bbAvA of phenomena present by the tri>
jrate planet. ^ ,

Le aDnounped his couolusions in the following logo-

aaaaaa ooppo d eeeeegh iiiiiii 1111 mm nmmnonftn
oooo w q rr s-lttti nnnnu, " which, w|N»4inpp|||ed, VM^
M'4miiilo cingitar, t«aui, pho^ Bai||ini ^
•SeqUptieam incliii«to^' t^is|(ld|«d ^j^»|hln idtt»]
»9iirl»rae tooohii^j buS^aai^ ikiii-m^^&^. y

Th|f> deM^rip^ ii eo9i|ilal<i JMid ^Heia^M^ \ jf^

In 1665 it WIS foonid by BAi^t, of l^iid, liiafc^^l^
IltnroanB<had tiem «! ,& fi^ xing was >e|d3|r ii[«^ %,
divjUon ejEtended allthie %|y tuwi^iinalui^^
tUs ^vinon is shQ:vm in tij^j|garee.

td 1860 the MesM. Boi^ of Cimbridge, fOqudjte^dlerB
WIS a thirifl ring, of ]|, dtislcy-aad ndMpiu a<q|«w^;4pi|^
^ other two, or ttiSbiBe «((Mshed t(}'||igbiiier cl'
kkittrring. 1ft fs Ihj^rafon^cnowa as ^ui^
Itliad not ben befoi|l Ih&y 4e«^ba£o«l% to|^(
mi^-i*i color, whieh made it adiffiofilE |^U|p0l^to 8e|i
ii^ a good teieicop0. It is not sepan|i^i(|ra tlS _
1^, bat seeiitt aa if «MlBohed to it.^ ISliigfter diiiidt«s|i|E
tow^ its imur edgeV which morgai pjiMlnally into ^
Avtky ring so a* to make it diffisidt ^ dedd* pvfpiwly
wliMV it ends and the dosky lAag IwgfiDo. T&R Ii#|r «x-
toidB aboni (me half iraj iraai ^ inner ec^ 4;|i Ihe
b«%^t ring to the ball of the planet.

A a p rt t or the Bioga^ As iSnfcam revolve ni— nil the
s«^tiMpltteol the lings remains panNiltoillMlf. timt
ii, tf we o o mil waiiw^^ li ii nn wiii fc Hpm j il i i JlM
of the pl«iiei«fw3WiM8e«lKr.li«tlii|^||HMI..^ llttLfli^as
the axis of the latter, this ttds wffl 'idwiyif i[mit% the
8unm direction. In this respeet, the aaotioo is similar to

IM-

aSUMlMIMMIIM

'wrssjRjfs^^^??'*^

vere also iucouipreheiuiblo
vthore. It w«B not nnti]
oration) that the celebnted
izplanation of Ihe ramark-
lomena present by the tri-

US in the following logo-

iiiiii Ull ,mni jnmuiQimhn
oh, whioBli^iplged, m$^

»^ «ypMg># j . ■">.

ring was nt^y tfOi A.
oolid niaw- th»l|f|lbi^«||J9

HMS. -■•'■"■ ^.

imbridge, fbimd^^Mriiine
d nabnlons aiq|^eati^>^p||l|e
1 to'tlibibnier ej|ffe^4^
imaB|^«<^^.
■mbod^oi)^ to
ifllo!ilij|«ipe^to8e|i
sepantollii^in tlii bi^t

' iih laitliiter l ,.._

notges pjiianallj into ifJie

ffimdt to deeidft jfffniiMly

igboglns. Thehllir^x-

H-^e inner ed||»x^ the

tnet.

jlMn» iwolv*^. iiiiwinl iTm

mjjmmmmi0 That

wfi! 'thfrajf jfdKit^ tibo
I th^ sciotioo is similar to

RINQB OF SATUIiN.

mt'

that of the earth aroimd the snn. The ring of S(itum is
inclined about 27° to the plane of its orbit. Couhu-
quently, as tlie planet revolves around the sun, there is a
diange in the direction in which the sun shines upon it
similar to that which produces the change of seasons upon
the earth, as shown in Fig. 46, page 109.

The corresponding chfmges for Saturn are shown in
Fig. 07. Daring each revelation of Satfuim the plane

ita. 97.

or lATinui AS

BAim.

of the rim( pawea through Hw son twice. Thia ooenired
in the yean 1863 and 1878, at two opposite points of the
orUt, ::• aLown in tiie figore. At two other points, mid-
way between tlMK, the mm ahinea upon the plane d! tho^
ring «fe its graotat ia^nation, about 37*". Since the eartb
iH^KHlfrMMH) tiwa «;» tcmUi «8 far from iSb» wmm Stt^
Mm i% an tOmirm always aefle Saturn tuaaify, Jmt wrt
qittte,^ ii if he wwe mpon ^mn. Hoice at certain timoi

868

AaTBONOMT.

the rings of Satwm are seen edgeway?, while at other
times tliey are at an inclination of 27°, the aspect depend-
ing upon the position of the planet in its orbit. The io\-
lowing are the times of some of the phases :

1878, Febmary 7th.— The edge of the ring was turned
toward the sun. It could then be seen only as a thin
line of light.

1885. — The planet having moved forward 90°, the south
side of the rings may be seen at an inclination of 27°.

1891, December. — The planet having moved 90° fur-
iher, the edge of the ring is again turned toward the sun.

1899. — The north side of the ring is inclined toward the
sun, and is seen at its greatest inclination.

The rings are extremely ^ain in proportion to their ex-
tent. Their form is mudi the same as if they were cut
out of large sheets of thin paper. Consequently, when
their edges are tamed toward the earth, they appear as a
thin line of liriit, which can be seen tmly idtii powerful
tolcscopea. With such telescopes, the pUinet appean as if
it were )rfwoed through by a piece of very fine wire, the
ends of which project on each aide more than the diam-
eter of the pUmet. It has frequently been ranariced that
tUs appearance is seen on (me ride of the phnet, when no
tnee of the ring can be seen on the other.

Thme is smnetunes a period of a Urn weeks during
whieh the phme of the rinir» extmdad ontwwd, panm be-
tween the sun and the earth. That is, the sun shines on
one ride of the ring, while the othw or dark aide is turned
toward the earth. In this case, it seems to be ratablished
that (Hily the edge of the ring is viriUe. If Jiia be so,
the substance of the rings cannot be transparent to the
sun's rays, else it woald ba seen by the li|^t whidi
thh>ugh it.

»ii

_ ._j in the aiii|s.-lB 18S1 Otto flmpva era.

MBdad • BolHrorthy thaoiy of Aangas fofaw <m in fM ||m|| of
aUNim. Pnm all dM dMcriptku, fgluM, sad aeasares Mhu by
«w oM«r artfOBOMn, it qipeand tlMl two handNd yemagb tlie

^sm^:A

RINGa OP SATURN.

8ft9

geways>, while at other
27°, the aspect depend-
t in its orbit. The fol-
le phases :

e of the ring was turned
be seen only as a thin

A forward 90°, the south
m inclination of 27°.

having moved 90° fnr-
1 turned toward the sun.
ng is inclined toward the
dination.

n proportion to their ex-
aiae as if they were cut
er. Oonsequently, when
le earth, they appear as a
seen only ^tii powerfol
L, the phuiet appean as if
poo of very fins wire, the
side more than the diam-
lently been remariEed that
le of the planet, when no
theotiier.

of a few weeks daring
ended ontwtud, p aas o i be-
rhat is, the sun shines on
hex or dark side is turned
it seofns to be 4>stablished
is viaiMe. If ;his be so,
tot be tranaparent to the
by the light whieli

.—In \m Otto 9nmrm pi^
turn ffoiut OB ia Om mm of
^fBiua memum #vSi by
•t two liaiuiftNl iMM itfft tile

space between the planet and the inner ring was at least equal to
tne combined breadth of the two rings. At present this distance
is less than one half of this breadth. Hence Struvk concluded that
the inner ring was widening on the inside, so that its edge had been
approaching the planet at we rate of about l'-8 in a century. The
space between the planet and the inner edge of the bright rins is
now about 4', so that if Stbutb'b theory were true, the Inner edge
of the ring would actually reach the planet about the year 8300.
NotwithsUndiug the amount of evidence which Struyb cited in
fayor of his theory, astronomers generally are incredulous respecting
the reality of so extraordinary a change. The measures necessary
to settle the question are so difficult and the change is so slow that
some time must elapse before the theory can be established, eren if
it is true. The measures of Kaiscr render this doubtful.

Shadow of Planet and Bing.— With any good telescope it is
easy to observe both the shadow of the ring upon the ball of £btor»
and that of the ball upon the ring. The form which the shadows
present often appear* oiflerent from that which the shadow ought
to have aooordfng to the geometrical conditions. These differences
probably wise from irradiation and other optical illusions.

Oonatitutionof tlwBingaofBafeuxn.— The nature of these
objects has been a subject both of wonder and of investigation by
mathematicians and astronomers ever since they were dueovered.
They wore at first supposed to be solid bodies ; indeed, from their
appearance it was difficult to ooncrive of them as anything else.
Tne question then arose : What keep them from falling on the
planet t It was shown by LaPlacs tnat a homogeneous and solid
ring surrounding the punet could not remain in a state of equili-
brium, but must be preoii^tated upon the central ball bv the small-
est disturbbg force. HaaioinL having thoa|riit that be saw oer-
tabi irrqpilaritiai fai the figure of tiie ri^, La Flacb ooncluded that
the objwt ooald be kept in equilibrium by them, ile simply as-
sumed tills, but did not attempt to prove it.

About 1850 the fatvwtteatitm was agabi begun by Piofeaaoca Bean
and Punusa, of OambricGie. The f wmer mppoaed that tlw riQgs
could not be aolid at all, baoauia they bad sometimes shown signs of
being temmrarily broken op into a lane mamber of ooneeatrie
rings. AtttioaghtUswaapiM)aUyaa(q^aealilhiiion.beoaiMhkM
that tbe rings must be liqittd. Professor Panum took «p tin prob-
lem whan La Plaob had kit it, and showed that «v«a aaifrsgolar
solid riag would not be fai eqnillbrfaim about Sslwm. He tber^DM
adopted the view of Bomd, that the rings were tidd ; but fia i tb i g
that avan a fluid riag would be uastablewiaiMa a iMppoiVbs M|^
posed timt aaeh a mppoit aiight be fnniMad by tb* ar'
This view lias also been abaadoBed,

KisBOW
not form

small separate pavtides, each of which wirolves oa Itoown
TlMMsatelliteiianiBdivldaa^fiNrtoesBMll^baseeninaBy tsk-
team, bat so awMiwwii that when viewed ft«m Urn distasna «( liM
earth timy tipfmt as a oontiauous aaaa. 9k»fartielea «l 4hwt float-

w WW Slav novo ■ombuudou.

vm established beyond reasonable 4N«bt tbatfte iia« da
a ooBtimKNiB mam, but are real^ a oountiMs madtiMk at

360 ASTSOlfOMr.

ing in a sunbeam. This theory was first propounded by Cabbini,
of Paris, in 1715. It liad been forgotten for a century or more,
wlien it was rovlved by Professor Ci.krk Maxwell in 1856. Tliu
latter published a profound mathematical discussion of the whole
question, in which ho shows that (his hypothesis and this alone
would account for the appearances presented by the rings.
Kauir's measures of the dimensions of the Batumian system are :

BALL or SATinui.

Equatorial diameter 17''274

Ptolar '• 15'8tt8

HIMOS.

Major axis of outer ring 80"471

'* " " the great division lM-'«27

•• •« " the inner edge of ring 27-'859

Width of the ring 5-800

Dark space between ball and ring 5''299

8 8. SATBLLTFBS OF SATUBH.

Ontside the rings of Saturn revolve its eight satellites,
the order and discovery of which are shown in the following
table :

Nans.

DjjUuice

frOMl

Ptenet.

DiMOVsrer.

DsteorDiwmranr.

Mimas.

8-8

HerMshel.

178», September 17

EnoeladuB.

4>8

Hetaehel.

1788, Angnst 88.

Tetbys.

5-8

Gkaslni.

1084. Maieli.

DIone.

6-8

CtMdnl.

1084. March.

RhML

»-5

QMrioi.

1078, DsoemberSS.

Titan.

M-7

Ear"

OMalni.

1050. Mareh 85.

Hyperion.
Japetus,

88-8
64-4

1071. Oelator.

The distances from the planet are given in radii of t
latter. The satellites Mimat and Hyperim are viaibl
only in the most powerful teleoeopea. The brightest
all is TVfam, whieh can be seen in a tekioope of the smal
est ordinary riie. Japettta baa the remarkable pecnliarK

flrit propounded by Cabsini,
tten for a century or more,
IRK Maxwkll in 1856. Tho
.tical diacussion of the whole
Is hypothesis and this alone
sented by the rings,
of the Batumian system are :

DRII.

17-'274

15-'802

88"471

84*'«87

K a7-"859

8-800

5-'«98

OW BATUBH.

'evolve its eight satellites,
1 are shown in the following

nOVMVT*

OalaarDIWAfwy.

raehel.

1780,

September 17.

nehel.

1780.

Ancutt 88.

iririi.

1084, Manh.

Hint.

1084.

Manh.

■dal.

1078,

Deoember 88.

ijwhens.

1055.

MarehSS.

1848, BaptMBber 10.

■rini.

1071,

October.

Bt are given in ndii of the
and Hyperitm are visible
oeopes. The brigfateot of
in a tekooope of the amall-
the remariable pecnliarity

BATBLLITJIB OF BATUBJT.

861

of appearing nearly as bright as TiUm when seen west of
the planet, and so faint as to be visible only iu huge tel-
escopes when on the other side. This appearance is ex-
plained by supposing that, like onr moon, it always pre-
sents the same face to the planet, and that one side of it is
black and the other side white. When west of the planet,
the bright side is turned toward the earth and the satellite is
visible. On the other side of the planet, tlie dark side is
turned toward us, and it is nearly invisible. Most of the
remaining five satellites can be ordinarily seen with tele-
scopes of moderate power.

The elements of all the satellites are shown in the fol-
lowing table :

BATat4jn.

MoMwi.

DliUMA

fma
SstoriL

LoMfltade

of
Fwl-Sat.

■cecn-
tricUjr.

Inellaa-

Uoato

■allptk.

Mlnaa....
BneeladDs.
Tethjra....

DiMW.....

Rbaa.

TUaa.

HypeilMi..
JapetM. . .

881 •0&8
808-781
180-00778
181084880
78-080818
88-877088
18-814
4-888088

■

54.80

7018

178-75

814-88

514-84

857.10

40-00

851-85

• /

•0080

•185

•0888

• /

88 00
88 00
88 10
88 10
88 11

87 84

88 00
18 44

• /

108 00
108 00
107 88
187 88
100 84

187 88

188 00
148 88

if*

:| ^^.i

CHAPTER IX.

THE PLANET UKANUS.

Uranus wan discovered on Marcli 18th, 1781, by Sir
William Hersohel (then an amateur observer) with a
ten-foot reflector made by himself. He was examining a
portion of the sky near H Geminorurn, when one of the
stars in the field of view attracted his notice by its pecu-
liar appearance. On further scrutiny, it proved to have a
planetary diak, and a motion of over 2* per hour. Hbk-
soHEL at first supposed it to be a comot in a distant part
of its orbit, and under this impression parabolic orbits
were computed for it by various mathematicians. None
of these, however, satisfied subsequent observations,
and it was finally announced by Lexell and La Place
that the now body was a planet revolving in a neariy
circular orbit. We can scarcely comprehend now the
enthusiasm with which this discovery was received. No
new body (save comets) had been added to the solar system
since the discovery of the third satellite ciSaium in 1684,
and all the major planets of the heavens had been known
for thousands of yean.

HsBscnxL BUj^jested, as a name for the planet, 0«or-
gium SidtUj and even after 1800 it was known in the Eng-
lish NatUicai Atmanao as the Georgian Planet. Lalakds
suggested Bermihd as its designation, but this was judged
too personal, and finally the name Uramu was a^ptod.
Its symbol was for a time written ^ in raoognition of tiie
name proposed by Lalande.

Uranut revolves about the sun in 84 years. Itsapi
ent diameter as seen from the earth yari«i little,

( IX.

[JKANU8.

[arch 18th, 1781, by Sir
mAteur obaerver) with a
f. He was examining a
inorur/», when one of the
d his notice by its pecu-
iitiny, it proved to have a
over 2* per hoor. Hbk-
I comet in a distant part
ipression parabolic orbits
B mathematicians. None
lubsequent observations,
y Lbxell and La Plaob
let revolving in a nearly
9ly comprehend now the
»very was received. No
n added to the solar system
satellite of Saium in 1684,
heavens had been known

me for the planet, Owr-
10 it was known in the Eng-
^rgian Fhuiet. Lalaitok
ation, but this was judged
uoae Uranfue was adopted,
m ^ in recognition of tlie

on in 84 yean. Itsappw-
earth variM little, being

TBS PLANET UttANUH.

abont 8' '9. Its true diameter is abont 60,0<)0 kilometres,
and its fignro is, so far as we yet know, exactly spherical.

In physical appearance it is a small greenish disk with-
out markings. It is possible that the centre uf the disk is
Hlightly brighter than the edges. At its nearest approach
to the earth, it shines as a star of the sixtli magnitude,
and is just visible to an acute eye when the attention is
directed to its place. In small telescopes with low pow-
ers, its appearance is not markedly different from that of
stars of about its own brilliancy.

It is customary to speak of Hebhchel's discovery of
Urawus as an accident ; but this is not entirely just, as
all conditio! I M for the detection of such an object, if it '>r
isted, were i ' "^Hed. At the same time the early idenliti-
cation of it met was more easy than it would have

been eleven .j a earlier, when, as Abaoo points out, the
planet was stationary.

Sir William Hkrschkl suspected that Urcmu* was ac-
companied by six satellites.

Of the existence of two of these satellites there has
never been any doubt, as they wero steadily observed by
Hbbsohkl from 1787 until 1810, and by Sir John Hbb-
BOHKL during the years 1828 to 1882, as well as by other
later observers. None of the other four satellites de-
scribed by Hkbsohkl have ever been seen by other ob-
serven^ and he was undoubtedly mistaken in supposing
them to exist. Two additional ones were discoverod by
Lassbll in 1847, and are, with the satellites of Mart, the
faintest objects in tlie sohir system. Neither of them is
identioal with any of the missing ones of Hebschkl. As
SirWiLUAM Hbbsohbl liad suspected six satellites, the
following names for the true satellites are generally adopt-
ed to avoid confusion :

SAW*

I, Arid. Period = 2680888

U, Ufkbrid. " = 4144181

ra, IttflfiA»,H«BS0HBi.'8(II.). " = 8.706897

rV, C»«w», H«BaoiWL»i (IV.) " =18468869

864

ABTRONOMr.

U-

:|!l

• ,1

Ml.

It is an interefltinti^ question whetTier the oliscrvatio
which Uku8ciiki. uHHigiiud tu his bupposititious satullite
may not be eoiiipoHod of observations sometimes of ArU
sometimes of Unibrid. In fact, out of nine 8uppos(
observations of I, one case alone was noted by IlEBaoHi
iu which hii positions wore entirely trustwortliy, and <
tliis niglit Umhriel was in the position of his suppocM
satollite I.

It is likely that vlr»«/ varies in bright!' •; on <liffere
sides of the planet, and the same phenoMi-.ion h.u. <il
licen suspected for Titania,

The moat remarkable feature of the Mtellites of ViraMu ii th
their orbits are nearlv perpendicular to the ecliptic instead
haviDK a small iBclination to that plane, like those of all the orb!
of both planets and satellites previouKiy known. To form a corrc
idea of tne position of the ortnti, wc ra^st imagine them tipped ov
until their north pole is nearly 8° belo yr the ecliptic, instmd of 9
alwve it. The pole of the orbit which should be considered as tl
north one is that from which, if an obnervM- look down upon a i
Tolvins body, the latter would seem to turn in w direction opposl
that ofthe hands of 4 watch. When the orbit it tipped over mo
than a right angle, the motion from a point lu i\v direction of tl
north pole of the ecliptic will seem to be I ha n^vune of this ; itl
therefore sometimes considered to be rttro^adt. This tern is fi
quently applied to the motion of the utellites of UranM$, but
rather misleading, since the motion, being nearly perpendicular
the ecliptic, is not exactly expressed by the term.

The four satellites move in the same plane, so far as the most
fined observatioas have ever shown. This fact renders it hig
probable that the planet Ut(mh$ revolves on its axis in the sa
plane with the orbits of the satellites, and is therefore aa obi
sphenrid like the earUi. This conclusion is founded on the cons
eration that if the planes of the satellites were not kept together
some cause, they would gradually deviate from each other owiuj
the attractive force of the sun upon the planet. The difEerent sn
lites would deviate by different amounts, ud it would be eztran
improbable that all the orbits would at any time be found in
same plane. Since wo see them in the same plane, we conclude t
some force keeps them there, and the obUteness of the planet wo
cause such a force.

wlietlier the oliaervationB
ig tiUi)po8ititiouH satolUte I
'ationH Bometimes of Ariel,
net, out of nine aupposed
le WHB notod by IIkbsohel
ntirely tnwtwortliy, and on

I poaition of liii* Bupposed

in bright )'
jaine pheiio

; on «1 fferent

(> .ion h.it. <il8o

the MtelHtea of Uraniu it that
uUr to the ecliptic initetd of
tlanfl, like thoM of «11 the orbits
jUK"y known. To form » correct
re tiv it imagine them tipped over
jelv; / the ecliptic, instead of 90"
hicb should be considered as the
II obaerv'M- look down upon a re-
m to turn in i\ direction opposite
hen the orbit i.i tipped over more
n a point iu liv direction of the
1 to be Iha r<;vcrse of this ; it is
be rttrovrade. This tern is fre-
r the satellites of Vranm, but is
>n, being nearly perpendicular to
ed by the term.

same plane, so far as the most re-
irn. This fact renders it highly
revolves on its axis in the same
Uites, and is therefore an obhrt«
iclusion is founded on the oonsld-
tolUtea were not kept together by
deviate from each other owing to
n the planet. The different satel-
nounts, and it would be eztnnely
uld at any time be found in the
1 the same plane, we conclude that
the oblateness of the pkuet would

•I

IMAGE EVALUATION
TEST TARGET (MT-3)

J''

'SJ<'

to'

;
' 1

1.0

1.1

m IM 12.2

Sf U& 12.0

IL25 lU 11.6

Sdehces
QirporaBan

M^MM^^l^M^^^M

^^•^'^

nWKTMMNilMn

MMlHai

CIHM/ICMH

Series.

CIHM/ICMH
Collection de
microfiches.

CwiMlian InMltutt for HImofiea! HdlcrorapniduetloiM / InMhut camdlwi d* mlecarapreduetlom historiquw

' ni'.*.."'ti!^-

CHAPTER X.

THE PLANET NEPTUNE.

After the planet Uranus Lad been observed for some
thirty years, tables of its motion were prepared by
BovvABD. He had as data available for this purpose not
only the observations since 1781, but also observations
made by Le Monnieb, FLAjnTEKi), an-1 others, extending
back as far as 1695, in which the planet was observed for
a fixed star and so recorded in their books. As one of
the chief diffionlties in the way of obtaining a theory of
the planet's motion was the short period of tame during
which it had been regnkrly observed, it was to be sup-
posed that these ancient observations would materially aid
in obtaining exact accordance between the theory and ob-
servation. But it was found that, after allowing for all
perturbations produced by the known planets, the ancient
and modem observations, though undoubtedly referring to
the same object, were yet not to be reconciled with each
other, but differed systematically. Bouvabd was forced
to omit the older observations in his^ taUes, which were
publudied in 1820, and to found his theory upon the
modem observations alone. By so doing, he obtained a
good agreement between theory and the observations of
tiie few yean immediately snooeeding 1820.

Boo VABD seems to have formulated the idea that a possi-
ble canse for the discrqpanoieB noted mig^t be the exist-
ence of an unknown planet, but the meagre data at his
disposal foroed him to kave tiw subject nntonohed. In
1880 it was found tliat the tables wUoh reiwesented the

366

ABTRONOMT.

motion of the planet well in 1820-25 were 20' in error, in
1840 the error was 90% and in 1845 it was over 120'.

These progressive and systematic changes attracted the
attention of astronomers to the subject of the theoiy oi
the motion of Uramis. The actual discrepancy (120') in
1845 was not a quantity large in itself. Two stars of the
magnitude of Ura/nvs, and separated by only 120', would
be seen as one to the unaided eye. It was on account oi
'its systematic and progressive increase that suspicion was
p excited. Several astronomers attacked the problem in vari-
ous ways. The elder Stbuve, at Pulkova, prosecuted a
search for a new planet along with his double star obser-
vations ; Bessel, at Koenigsberg, set a student of his own,
FLEinNO, at a new comparison of observation with theo-
ry, in order to furnish data for a new determination ;
Akaoo, then Director of the Observatory at Paris, sug-
gested this subject in 1845 as an interesting field of re-
search to Le Yerrier, then a rising mathematician
and astronomer. Mr. J. 0. Adams, a student in Cam-
bridge University, England, had become aware of the
problems presented by the anomalies in the motion oi
Urtmus, and had attacked this question as early as 1843.
In October, 1845, Adams communicated to the Astrono-
mer Royal of England elements of a new planet so situated
as to produce the perturbations of the motion of Uraavm
which had actually been observed. Such a prediction
SxooL an entirely unknown student, as Adams then was,
did not carry entire conviction with it A series of aod
dents prevented the unknown planet being looked for bj
one of the laifiest telescopes in England, and so the mat
ter apparently dropped. It may be noted, however, tha
we now know Adams* elements of the new placet to havi
been so near the truth that if it had been reidly looked fo
by the powerful telescope which afterward ^Uscovered it
satellite, it could scarcely have fiukd of detection.

Bessbl's pupil Flbmiho died beforo his vrwk
and Bsbskl's reuearohes were temponrily bnra^^

MT.

DISOOrSRT OF NBPTUNB.

■887

0-25 were 20*^ in error, in

845 it was over 120".

itic changes attracted the

subject of the theoiy of

tual discrepancy (120") in

itself. Two stars of the

rated by only 120", would

It was on account of

icrease that suspicion was

acked the problem in vari-

at Pulkova, prosecuted a

irith his double star obser-

;, set a student of his own,

of observation with theo-

or a new determination ;

Observatory at Paris, sug-

in interesting field of re-

1 a rising mathematician

lDAMs, a student in Cam-

lad become aware of the

omalies in the motion of

question as early as 1848.

imnnicated to the Astrono-

I of a new planet so situated

of the motion of Urcmiut

)rved. Such a prediction

ident, as Adams then was,

with it A series of aod-

)lanet being looked for by

England, and so the mat-^

\y be noted, however, that

I of the new plavet to have

had been leidly looked for

sh afterward JUicoverod its

failed of detection.

[ before his vrwk was done,

B temponrily brooj^ to

an end. Stbuvb'b search was unsuccessful. Only Le
Yebbikb continued his investigations, and in the most
thorough manner. He first computed anew the pertur-
bations of Urtmut produced by the action of Jupiter and
Saturn. Then he examined the nature of the irregulari-
ties observed. These showed that if they were caused by
an unknown planet, it could not be between Saturn and
Urarnis, or else Saturn would have been more affected
than was the case.

The new planet was outside of Uranus if it existed at
all, and as a rough guide Bode'b law was invoked, which
indicated a distanee about twice that of Uranus. In the
summer of 1846, Lb Yebbiek obtained complete elements
of a new planet, which would account for the oBiprved
irregularities in the motion of Uranus, and these were
published in France. They were very similar to those of
Adams, which had been communicated to Professor Ohal-
LIB, the Director of the Observatory of Camlnidge.

A search was immediately begun by Chalub for such
an object, and as no star-maps were at hand for this region
of the sky, he began mapping the surrounding stars. In
so doing the new ]danet was actually observed, both on
August 4th and 13th, 1846, but the observati<Hu remain-
ing nnredueed, and so the planetary nature of the object
was not reoogniied.

In September of the sanie year, Le Yekbieb wrote to
Dr. Galue, ihen Assistant at the Observatory of Berlin,
addi^ him to seareh for the new planet, and directing
him to the place whwe it should be found. By the aid
of an exoelleut star chart of this region, which had just
been oorapleted by Dr. Bbbmikbb, tiie planet was' found
September 98d, 1846.

The sirict ri^ts of discovery lay with Lb Ybbbibb,
but tiie oommon consent of mankind has always credited
Adams with an equal duure in the lionor attached to this
most brilUsat acUevement. Indeed, it was only by the
most nnfortiuitte soeoeisioa of aoddents that the disoorery

388

ABTRONOMT.

did not attach to Adams' researches. One thing must j
fairness be said, and that is that the results of Lk Yei
BiKB) which were reached after a most thorough invest
gation of the whole ground, were announced with an ei
tire confidence, which, perhaps, was lacking in the oth(
case.

This brilliant discovery created more enthusiasm tha
even the discovery of ZTroniM, as it was by an exerdse <
far higher qualities that it was achieved. It appeared 1
savor of the marvellous that a mathematician could sa

to a working astronomer that by pointing his telescope
a certain small area, within it should be found a
major planet. Yet so it was.

The general nature of the disturUng force which
vealed the new planet may be seen by Fig. 98, whi|
shows the orbits of the two planets, and their res[
motions between 1781 and 1840. The inner oirbit is
of /TrofMM, the outer <me that of N«ptMine. The
passbg from the former to the latter diow the dineti^
of the attractive force of N^ptivne. It will be

mr.

xjhes. One thing mnst in
the results of LsYeb-
a most thorough investi-

9re announced with an en-
was lacking in the other

tted more enthuuann than
as it was by an exercise of
achieved. It appeared to
mathematician oonldsay

8ATBLLITB OF NEPTUNB.

369

by pointing his tekeoope to
it diGold be fonnd a new

dUtnrUng force wbieh re-
be teen by Fig. 98, which
>lanet8, and their reepective
40. The inner orbit ia that
t of 2f«ptune. The irowb
le latter show the direetiona
tiune. It wiU be wen that

the two planets were in conjunction in the year 1822.
Since that time Uromua has, by its more rapid motion,
passed more than 90° beyond N^twne, and will continue
to increase its distance from the latter until the begin-
ning of the next century.

Our knowledge regarding Neptv/ne is mostly confined
to a few numbers representing the elements of its motion.
Its mean distance is more than 4,000,000,000 kilometres
(2,775,000,000 miles) ; its periodic time is 164-78 yean ;
its apparent diameter is 2' '6 seconds, corresponding to a
true diameter of 55.000 kilometres. Gravity at its surface
is about nine tenths of the corresponding terrestrial surface
gravity. Of its rotation and physical condi^on nothing
is known. Its color is a pale greenish blue. It is attend-
ed by one satellite, the elements of whose orbit are given
herewith. It was discovered by Mr. Labsell, of Eng-
land, in 1847. It is about as faint as the two outer satel-
lites of Urcmuty and requires a telescope of twelve inches
aperture or upward- to be well seen.

ELsmiiTB or tbb SATBLun or Vmfrxma, waou WASHnieTOH

Obsbrvatiohb.

Mmo Dtil.T Motioa ei'-SMTQ

P«riodieTim« 0*'870M

Dtoton«(los. A =1-47814) l«'-875

InolinaUoa of Orbit to Ediptle 145* V

LoDgltade of Node (1860) 184' W

laenwwialOOTam 1* 84'

The gnat Inelinatioo of the orbit ihowt that it is tamed nearly
epside dowa ; the direetloii of motloii ia therefore retrogade.

CHAPTER XI.

THE PHYSICAL CONSTITUTION OF THE
PLANETS.

It is remarkable that the eight large planets of the Bokr
Bystem, conBidered with respect to their physical constitu-
tion as revealed by the telescope and Ae spectroscope,
may be divided into four pairs, the phuiets of each pair
having a great similaiity, and being quite different from
the adjoining pair. Among the most complete and sys-
tematic studies of the spectra of all the planets are those
made by Mr. Huooins, of London, and Dr. Voobl, of
Berlin. In what we have to say of the results of spect/o-
scopy, we shall depend entirely npontho reports oi these
observers.

Kwranry and Tentu. — ^Passing outward from the sun,
the first pair we encounter will be Merewry and Vmm.
The most remarkable feature of these two {danets is a neg-
ative rather than a positive one, being the entire absence
of any certain evidence of change on their surfaces. We
have ahvady shown that Vemut has a considerable atmos-
phere, while there is no evidence of any such atmosphere
around Mtircwty. They have therefore not been proved
alike in this respect, yet, on the other hand, they have not
been proved difEerent. In every other respect than this,
the umilarity appears perfect. No permanent markings
have ever been certainly seen on the disk of either. If,
as is possible, the atmosphere of both planets is filled with
clouds and vapor, no change, no openings-, and no for*

purawAL aoNsm'UTioN of thk planets. 371

I XI.

TUTION OF THE

large planets of the solar

their physical constitn-
e and the spectroscope,
bhe planets of each pair
ling quite different from
most complete and sys-
all the planets are those
don, and Dr. Yooel, of
of the results of spect/o-

apon the reports ot these

Df outward from the sun,
be Mercwry and Venua.
these two {danets is a neg-
beingthe entire absence
« on their surfaces. We
has a considerable stmos-
B of any such atmosphere
Mieforenot been proved
)ther hand, they have not
y other respect than this,
No permanent markings

1 the disk of either. If,
both planets Is filled with
no openingsj and no forr

mations among these cloud masses are visible from the
earth. Whenever either of these planets is in a certain
position relative to the earth and the sun, it seemingly
presents the same appearance, and not the slightest
change occurs in that appearance from the rotation of the
planet on its axis, which every analogy of the solar sys-
tem leads us to believe must take place.

When studied with the spectroscope, the spectra of
Mercury and Ventu do not differ strikingly from that of
the sun. This would seem to indicate that the* atmos-
pheres of these planets do not exert any decided absorption
upon the rays of light which pass through them ; or, at
least, they absorb only the samo rays which are absorbed
by the atmosphere of the sun and by that of the earth.
The one point of difference which Dr. Yooel brings out
is, that the lines of the spectrum produced by the absorp-
tion of our own atmosphere appear darker in the spectrum
of Venus. If this were so, it would indicate that the at-
mosphere of Venut is similar in constitution to that of
our earth, because it absorbs the same rays. But the
means of measuring the darkness of the lines are as yet
so imperfect that it is impossible to speak with certainty
on a point like this. Dr. Yookl thinks that the light
from Vmu9 is for the most part reflected from clouds in
the higher region of the planet's atmosphere, and thertf-
lore reaches ub without passing through a great depth of
that atmosphere.

Tb» awfh and Kin.— These planets are distinguished
from all the others in that their viable surfaces are marked
by permanent features,' which show them to be mJ&d, and
which can be seen from thi- other heavenly bodies. It is
trae that we cannot stud. i> e earth from any other body,
but we can foaa a very oov. dot idea how it woold look if
seen in this way (from the moon, for instance). Wherever
the atmoq>here was dear, the outlines of the continents
and oceans would be visible, while they would be inviiiUe
where the air was doa^y.

A8TR0N0MT.

Now, BO far as we can judge from obeervfttions made
at 10 great a distance, never much lees than forty mil-
lions of miles, the planet MaT$ presents to our tele-
scopes very much the same general i^ypearaiioe tiiat the
earth would if observed from an equally great distance.
The only exception is that the visible surface of Mtw§ is
seemingly much less obscured by clouds than that of the
earth would be. In other words, that planet has a more
sunny sky than ours. It is, of course, impossible to say
what conditions we might find could we take a much
closer view of Mara : all we can assert is, that so far as
we can judge from this distance, its surface is like that of
the earth.

This supposed similarity is strengthened by the spectro-
scopic observations. The lines of the spectrum due to
aqueous vapor in our atmosphere are found by Dr. Yookl
to be so much stronger in Mara as to indicate an absorp-
tion by such vapor in its atmosphere. Dr. HirooiHs had
previously made a more decisive observation, having
found a well-marked line to which there is no omrespond-
ing strong line in the solar spectrum. Thii would indi-
cate that the atmosphere of Mwa contains some element
not found in our own, but the observations are too diffi-
cult to allow of any well-established theory being yet
built upon them.

Jupiter and Batum. — The next pair of planets arel
Jupiter and Sdtwm. Their peculiarity is that no solid]
crust or surface is visible from without. In this
they differ from the earth and Jfar«, and resemble M«r\
ewry and Vetvua. But they differ from the latter in tl
very important point that constant changes can be seeij
going on at their surfaces. The nature of these
has been discussed so fully in treating of these planets in]
dividnally, that we need not go into it more fully at pr
ent. It is sufficient to say that the preponderance of e^
dence is in favor of the view that ^ese planets have n{
■olid crusts whatever, but consist of masses of molt

from obeervfttions made
ich less than forty mil-
presents to oar tele-
mi appearanoe tint tbe
equally great distance,
lible surface of Uw is
doads than that of the
that pUmethas a more
course, impossible to say
could we take a much
assert is, that so far as
its surface is like that of

sngthened by the speotro-
of the spectrum due to
) are found by Dr. Yoou
as to indicate an absorp-
pbere. Dr. Hooonra bad
j}ive obeerration, having
ch there is no omrespond-
^trum. This would indi-
(r« contains some dnnent
observations an toodiffl-
iblished theory being yet

lext pair of planets are
eculiarityis that no solid
1 without. In this respect
Jtfar«, and resemble Mer-
liffer from the latter in the
Btant changes can be seen
'he nature of these changes
reating of these planets in-
» into it more fully at pres-
; the preponderance of evi-
that tiiese planets have no
nsist of masses <tf molten

PHYBKAL OOirsriTUTIOy OF THtB PLANBTS. 878

matter, surrounded by envelopes of vapor constantly rising
from the interior.

The view that the greater part of the apparent voliune of
these planets is made of a seethiug maeti of vapor is further
strengthened by their very small specific gravity. This
can be accounted for by supposing that the liquid interior
is nothing more than a comparatively small central core,
and that the greater part of the bulk of each planet is
composed of vapor of small density.

That the visible surfaces of Jupiter and ScUvm are cov-
ered by some kind of an atmosphere follows not only from
the motion of the cloud forms seen there, but from the
spectroscopic observations of Huooinb in 1864. He
found visible absorption-bands near the red end of the
spectrum of each of these planets. Vooel found a com-
plete similarity between the spectra of the two planets,
the most marked feature being a dark band in Uie red.
What is worthy of remark, though not at all surprising, is
that this band is not found in the spectrum of 8atwm^$
rings. This is what we should expect, as it is hardly pos-
sible that these rings should have any atmosphere, owing
to their very small mass. An atmosphere on bodies of so
slight an attractive power would expand away by its own
elasticity and be all attracted around the planet.

Vrairaa and Neptune.— Those planets have a strikinj^y
similar aspect when seen through a telescope. They
differ from JvpUer and Salwm in that no changes or va-
riations of color or aspect can be made out upon their sur-
hoea ; and from the earth and Mara in the absence of any
permanent features. Telescopically, therefore, we might
classify them with Merowry and Ven/ut^ but the spectro-
scope reveals a constitution entirely different from that of
any other planets. The most marked features of their
spectra are very dark bands, evidently produced by the
absorption of dense atmospheres. Owing to the extreme
faintnees of the Ught whidi reaohee us from these distant
bodies, the regular lines of the sohr spectrum are entirely

874

ASTRONOMT.

- -Q

— H

invisible in their speotra, yot these dark bandu which are
peooliar to them have been seen by Uuuuinb, Bkuuhi,

VuoKL, and perhaps others.

Tliis classitication of the
eight planets into pairs is ren-
dered yot more striking i>y
the fact that it applies to
what we have been able to
discover respecting the rota-
tions of these bodies. The
S rotation of the inner pair,
Mercury and Venna, has
eluded detection, notwith-
itanding their comparative
proximity to us. The next

pair, the earth and Mar$y
have perfectly definite times
of rotation, because their
outer surfaces consist of solid
crusts, every part of which
must rotate in the same time.
The next pair, Jupiter and
Saturn, have well-established
times of rotation, but these

G times are not perfectly defi-

nite, because the surfaces of
I these pUnets are not solid,
I and different portions of their
^ I mass may rotate in slightly
■■■■■■■■■Ji different times. JwpUer and
Fie. W.— apioTBuit o» cbamub. gatium have also in common
a very rapid rate of rotation. Finally, the outer pair, Ura-
nu» and Neptnme, seem to be surrounded by atmosphere^ of
such density that no evidence of rotation can be gathered.
Thus it seems that of the eight phmets, only the central
fonr have yet Certainly indicated a rotation on their axet.

dark band* which are
by UuooiNB, Bkcchi,
, and perhaps othorB.
, classitlcation of the
ilanete into pairs is ron-
yct more etriking by
ict that it applies to
we have been able to
er respecting the rota-
of these bodies. The
tn of the inner pair,
try and Ventu, has
I detection, notwith-
ng their comparative
nity to us. The next
the earth and Mara,
perfectly definite times
otation, because their
surfaces consist of solid

J, every part of

which
rotate in the same time,
next pwr, Jupiter and
ni, have well-established
i of rotation, but these
» are not perfectly defl-
because the surfaoes of
) planets are not solid,
lifferent portions of their
I may rotate in slightly
rent times. Jupiter and
tm have also in common
ally, the outer pair. Urn-
■onnded by atmospherepol
rotation can be gathered.
it planets, only the central
la rotation on their azw.

CHAPTER XII.

METEORS.

% 1. FHBVOMBNA AND OAUBBB OT lOVnOBS.

Dunmo the present century, evidence has been collected
that countless masses of matter, far too small to be seen
with the most powerful telescopes, are moving througli
the planetary spaces. This evidence is afforded by the
phenomena of *< aerolites," << meteors," and "shooting
stars." Although these several phenomena have been ob-
served and noted from time to time sinc^ the earliest his-
toric era, it in only recently that a 'complete explanation
has been reached.

AeroUtM. — ^Reports of the falling of laif;e masses of
stone or iron to the earth have been familiar to antiqua-
rian students for many centuries. Araoo has collected
several hundred of these reports. In one instance a monk
was killed by the fall of one of these bodies. One or two
other cases of death from this cause are supposed to have
occurred. Notwithstanding the number of instances on
record, aerolites fall at such ^vide intervals as to be ob-
served by very few people, consequently doubt was fre-
quently cast upon the correctness of the narratives. The
problem where such a body could come from, or how it
could get into the atmosphere to fall down again, f ormorly
seemed so nearly incapable of solution that it required
some orednlity to admit the facts. When the evidence
became so strong as to be indiq>ntable, theories of their
origin began to be impounded. One theory quite fashion-

^.^^ »-

Aj^t'^^^'^^

376

A8TR0N0MT.

able in the early part of this century was that they were
thrown from volcanoes in the moon. This theory,
though the subject of mathematical investigation by La
Place and others, is now no longer thought of.

The proof that aerolites did really fall to the ground
first became conclusive by the fall being connected with
other more familiar phenomena. Nearly every one who
is at all observant of the heavens is familiar with holiies,
or lire-ballB — ^brilliant objects having the appearance of
rockets, which are occasionally seen moving with great ve-
locity through the upper regions of the atmosphere.
Scarcely a year passes in which such a body of extraordi-
nary brilliancy is not seen. Generally these bodies, bright
though they may be, vanish without leaving any trace, or
making themselves evident to any sense but that of sight.
But on rare occasions their appearance is followed at an
interval of several minutes by loud explosions like the dis-
charge of a battery of artillery. On still rarer occasions,
masses of matter fall to the ground. It is now- fully
understood that the fall of these aerolites is always ac-
companied by light and sound, though the light may be
invisible in the daytime.

When chemical analysis was applied to aerolites, they
were proved to be of extramundane origin, because they
contained chemical combinations not found in terrestrial
substances. It is true that they contained no new chemi-
cal elements, but only combination of the elements which
are found on the earth. These combinations are now iM>
familiar to mineralogists that they can distinguish an
aerolite from a minend of terrestrial origin by a careful
examination. One of the largest components of these |
bodies is iron. Specimens having very much the appear-
ance of great masses of iron are found in the National |
Museum at Washington.

MMeon. — Although the meteors we hare described are]
ofdaBEling briUiancy, yet they run byinsenriMe gtftda-l
tians into j^eaomeaa, whioh any ono oan see on ttiy etawl

> i iiiri .M

CAUSE OF METBORa.

377

iry was that they were
moon. This theory,
sal investigation by La
ir thought of.
lally fall to the ground
being connected with
Nearly every one who
is familiar with Joif ^,
ring the appearance of
n moving with great ve-
os of the atmosphere,
ch a body of extraordi-
irally these bodies, bright
>nt leaving any trace, or
' sense but that of sight,
irance is followed at an
d explosions like the dis-
On still rarer occasions,
ound. It is now fully
e aerolites is always ac-
hough the light may be

applied to aerolites, th^
lane origin, because they
) not f oimd in terrestrial
contained no new chemi-
on of the elements which
combinations are now so
they can distinguish an
Btrial origin by a careful
lest ooroponents of these
og very much the appear-
re found in the National

3on we hare described are
^ run by intenrible gnd**
J ODO on M6 on tay etetf

night. Tlie most brilliant meteors of all are likely to be
seen by one person only two or three times in his life.
Meteors having t!ie appearance and brightness of a distant
rocket may be seen several times a year by any one in the
habit of walking out during the evening and watching the
ricy. Smaller ones occur more frequently ; and if a care-
f nl watch be kept, it will be found that several of Ihe
faintest class of all, familiarly known as shooHnff ttara^ can
be seen on every clear night. We can draw no distinction
between the most brilliant meteor illuminating the whole
sky, and perhaps making a noise like tlmnder, and the
faintest shooting star, except one of degree. There seems
to be every gradation between these extremes, so that all
should be traced to some common cause.

Oanae of Meteor*. — There is now no doubt that aU thees
phenomena have a common origin, being due to the earth
encountering innumerable small bodies in its annual course
around the sun. The great difficulty in connecting mete-
ors with these invisible bodies arises from the brilliancy
and rapid disappearance of the meteors. The question
may be asked why do they bum with so great an evolu-
tion of light on reaching our atmosphere ? To answer this
question, we must have recourse to the mechanical theory
of heat It is now known that heat is really a vibratory
motion in the particles of solid bodies and a progressive
motion in those of gases. By making this motion more
impid, we make the body warmor. By simply blowing air
•l^niifc any combustible body with sufficient velocity, it
can be set on fire, and, if incombustible, the body wUl be
made red-hot and finally melted. Experimmts to deter-
mine the degree of temperature thus produced have been
made by Sir Wiluax Thokpson, who finds that a veloci-
ty of about 60 metres per second corresponds to a rise of
temperatnie of <me degree Oentigrade. From this the
temperature due to any velodty can be readily calculated
on tile prineiple that tiie increase of temperature is pro-
portiooel to the " enogy" of tiie particles, which agsin

378

ASTRONOMY.

is proportional to the square of the velocity. Hence a
veloci^ of 500 metres per second would correspond to a
rise of 100" above the actual temperature of the air, so
that if the latter was at the freezing-point the body would
be raised to the temperature of boiling water. A velocity
of 1500 metres per second would produce a red heat. This
velocity is, however, much higher than any that we can
produce artificially.

The earth moves ..round the sun with a velocity of
about 30,000 metres per second ; consequently if it met a
body at rest the concussion between the latter and the at-
mosphere would correspond to a temperature of more than
800,000°. This would instantly dissolve any known sub-
stance.

As the theory of this dissipation of a body by moving
with planetary velocity through the upper regions of our
air is frequently misunderstood, it is necessary to explain
two or three points in connection with it.

(1.) It must be remembered that when we speak of
these enonnouB temperatures, we are to consider them as
potential, not actual, temperatures. We do not mean
that the body is actually raised to a temperature of 800,-
000°, but only that the air acts upon it as if it were put
into a furnace heated to this temperature — ^that is, it is
rapidly destroyed by the intensity of the heat.

(2.) This potential temperature is independent of the
density of the medium, bdng the same io the rarest as in
the densest atmosphere. But the actual effect on the
body is not so great in a rare as in a dense atmosphere.
Every one knows that he can hold his hand for some time
in air at the temperature of boiling water. The nurerthe
air the higher the temperature the hand would bear without
injury. In an atmosphere as rare as ours at ihe height of
50 miles, it is probable that the hand could be held for an
indefinite period, though its temperature dionld betfuit
of ied>hot iron ; henoe the meteor is not consumed so rap-
idly as if it struck a dense atmosphere with planetaiy

irtWIIIMi.tl

CAUSE OF MSTEORS.

879

Hence a
eepond to a

the air, so
body would

A velocity
Iheat. This
that we can

velocity of
^ if it met a
■ and the at-
)f more than

known snb-

y by moving
igions of onr
y to explain

we speak of
ider them as
lo not mean
ore of 300,-
it were put
-that is, it is

ident of the
lo rarest as Ui
effect on the
atmosphere,
or some time
The rarer the
1 bear without
die hei|^t of
»e held for an
lonld betiiat
nunedsorap-
iih planetaiy

velocity. In the latter case it would probably disappear
like a flash of lightning.

(8.) The amount of heat evolved is measured not by that
which would result from the combustion of the body, but
by the vU viva (energy of motion) which the body loses in
the atmosphere. The student of physics knows that mo-
tion, when hist, is changed into a definite amount of
heat. If we calculate the amount of heat which is equiv-
alent to the energy of motion of a pebble having a veloc-
ity of 20 miles a second, we shall find it sufficient to raise
about 1300 times the pebble's weight of water from the
freezing to the boiling point. This is many times as much
heat as could result from burning even the most combusti-
ble body.

(4.) The detonation which sometimes accompanies the
passage of very brilliant meteors is not caused by an ex-
plosion of the mef«or, but by the concussion produced by
its rapid motion throogh the atmosphere. This concos-
sion is of much the same nature as that produced by a
flash of lightning. The air is suddenly condensed in ^nt
of the meteor, while a vacuum is left behind it.

The invisible bodies which produce meteors in the way
just described have been called meteoroidt. Meteoric
phenomena depend very largely upon the nature of the
meteoroids, and the direction and velocity with whidi
they are moving relatively to the eartii. With very rare
exceptions, they are so small and fusible as to be eutirely
dissipated in the upper regions of the atmosphere. Even
of those so hard and solid as to produce a brilliant li^^t
and the loudest detonation, only a small proportion reach
the earth. It has sometimes happened that the meteoroid
only graces the atmosphere, passing horiaontally'throiigh
its higher strata for a great distanoe and oontinuing its
com ; after leaving it. On rare occasions the body is so
hard and nuiisive as to reach the earth without being en<
t^rely oomnuned. The potential heat produced by ito
paannge through the atmoaph^v is then all expended in

880

A8TR0N0MT.

i '

melting and destroying its outer layers, the inner nnclens
remaining unchanged. When such a body first strikes
tlie denser portion of the atmosphere, the resistance be-
comes so great that the body is generally broken to pieces.
Hence we very often find not simply a single aerolite,
but a small shower of them.

Heights of Keteon. — ^Many observations have been
made to determine the height at which meteors are seen.
This is effected by two observers stationing themselves
several miles apart and mapping out the courses of such
meteors as they can observe. In order to be sure that the
same meteor is seen from both stations, the time of each
observation must be noted. In the case of very brilliant
meteors, the path is often determined with considerable
precision by the direction in which it is seen by accidental
observers in various regions of the country over which it

The general result from numerous observations and in-
vestigations of this kind is that the meteors and diooting
stars commonly commence to be visible at a height of
about 160 kilometres, or 100 statute miles. The separate
roeults of course vary widely, but this is a rough mean of
them. They are generally dissipated at about half this
height, and therefore above the highest atmosphere which
reflects the rays of the sun. From this it may be inferred
that the earth's atmosphere rises to a hei^t of at least
J 80 kilometres. This is a much greater he^ht than it was
formerly supposed to have.

S a. lornoBio showmbs,

As already stated, the phenomena of shooting ttan may
be seen by a careful observer on almost any clear night.
In general, not more than three or four of them will be
seen in an hour, and these will be so minute as hwdly to
attract uotioe. But they sometimes fidl in sneh numbers
as to present the appeanmee of a meteoric shower. On

y.mmU!ii:iis sssa

^4i?iMu:»AkB t*- .ui>«.

inner nnclens
y first strikes

resistance be-
oken to pieces,
single aerolite,

ns have been
teors are seen,
ing themselves
lonrses of such
Ki sore that the
e time of each
f very brilliant
th considerable
in by accidental
f over which it

vations and in-
"B and shooting
at a height of
The separate
I rongfa mean of
abonthalf this
noephere which
may be inferred
ifl^t of at least
ight than it <

loting Stan may
ny clear night.
>f them wUl be
te as hwrdlyto
ifoeh nnmben
abower. On

-wmmmmmsF

METSOniO 8H0WER8.

881

rare occasions the shower has been so striking as to fill the
beholders with terror, liie ancient and mediieval records
contain many accounts of these phenomena which have
been brought to light through the researches of antiqua-
rians. The following is quoted by Professor I^swton
from an Arabic record :

" In the year 699, on the lait day of Mohairem, ttan shot hither
and thither, and flew againat each other liJke a swariB of locnite ;
this phenomena huted until dayhruak ; people were thrown into
consternation, and made eappHfiation to toe Soet High : there was
never the like eeen except on tiie ccnning of tiie mcsienger of Ood,
on whom be be&edietion and peaee." '

It hn long been known that some ahowen of this da«
oocnr at an interval of about a third of a oeutniy. One
was obaeiyed by Humbolot, on the Andes, tm tl» night
of November 12th, 1799, hating from two o'ekxok i^
daylight. A great shower was seen in this oopntiyin
1688, and is well known to have stmck the negroes of the
SontlMm States with terror. The theory that tlw dioir*'
era cNMur at intervals of 84 years was now propfrandefi hgr
OuNEM, who predicted a return of the shower in IMf i
This prodietion was omnpletely fulfilled, but histewl ol mg^
peering in the year 1867 only, it was first notioed in 18M,
On the n^ht of November 18th of that year » reaDiribMe
shower was seen hi Enrope, while on tiie oeneipentipf
night of iiie year following it was agifki seen te tils emuir
try, and» ftilMt, was rapei^ fortwo or three yieni, gmi*
ndly dj^ng eway.

The ooenneBee of e drawer ol meteom evideaftly duypi^^
tii*^ eertii eneoanteni e swwm of meteoroNk Thm
leeidienoe «t the same thne of the ye«r, when iSb» ewtib
ieilliMauiie point of its oiUt, shows i^^ mm-
meiii the swarm at the same point in sneoesaive yeeis.
AU tlw mete(»dds of tibe swarm mnst of oonrse he moving
in the aamodiieetion, else they would soon be widely Mat-
tered. This awtion is eonneeted with the r a i imi point,
•r wdl-mednd feetnie of a meteocie siiower.

883

ASTRONOMY.

BadlMUt Folnt.--BuppoM that, during » metaoric shower, we
mark the path of each meteor on a atar map. as in the tigure. If we
continue tne pttldu backward in a atraight line, we ihall find that
they all meet near one and the tame point of the ccleatial sphere—
that is, they nore as if they all radiated from this point. The

Ite. 100.— SAMUR Mora c«r namnuo

laiHer fa, tfcewfow, calkd tta rmitmi ftbd. 1 th*%BMl0MttMi

do Bo4 an pais aocoratalj through the sane point TUitif owing

to Urn nnaraMaMi man —da ft ssaililiig nnSt the psilL

It fa found that tHe i«dfaat^p(ibit fa^^ahnys in the sHMffoittioa

the stars, wharever the obaerver may be ritoatad, and that

MSTKOm AND G0MKT8.

883

e ahower, we
Igura. If we
Mil find that
itUl sphere-
point. The

TU|J« owing

iat«d,ind tiMt

it does not partako of the diuraal motion of the earth — that is, as
the stars apparently move toward the west, the radiant point mores
with tltem.

The radiant point is dne to the fact that the meteoroids which
strike the earth during a shower are all moving in the same direc-
tion. If we sappose the earth to be at rest, and the actual motion
of the meteoroias to be compounded with an imaginary votbn
equid and oppodte to that of the earth, the motion of these in
inaiy bodies will be the same as the actual relhtive motion of
muteoroids seen from the earth. These relative motions will all
panllel ; hence when the bodies strike our atmosphere the
dewsribed by them in their passage will all be parallel b( _
linaa. Now, by the principles of spherical trigonometry, a stmi^
lin« seen by an observer at any point is projected as a great elrcj^
of the celestial sphere, of which the observer suppoees hiiaself to |^
the centre. If we draw a line from the observer parallel to tap
paths of the meteors, the direction of that line will repteaent a pobli
of the sphere through which all the paths will seem to pass ; tili
wiU, therefore, be the radiant point in a meteoric diower. '*'

A slightly different conception of the poUem may be formed
by oonceiiHing the plane passing through the observer and contain-
ing the path of the meteor. It is evident that the different PlMws
formed by the parallel meteor paths will all intonnct eadi other in
a line drawn from the observer parallel to this path. Tbla line
will then intersect the celestial sphere in the radiant point.

Orllita ofKatoOEie Btaowers.— From what has Jtut becta saM,
it vrill be.seen tiiat the position of the radiant p^t indloatea the
direetliw hi which the meteoroids move rehtUvely to the earth. If
we also knew the velocity with which ihqr m r*i3^1 ■»▼% *>
space, we cooUl taiake allowance for the motion <rf HMevtli, iM
tfoiirdatanaine the direction of their actoal motioa in ap^. It
willba lemembeted that, as just ezplaiMd. the •;(««&€ «r MAr
tivl notioB it made up of two oompoaenta— the eoa llja Mtwl
motkm (rf the body, the other the mofiiM of the e^jtaMiL Ih 'm
opporite dinetkw. We know the aepond.of thfes* eMppOMnta
abM^; andi^we kad^the v«lMityi«lativ« totMwtfli m^

diraBMMiaa8ln|nbTth«Midiantp«dnt,we .^
andflM«Mmoaeiitiaaagnitad«aBd dintitkm. Ilie <
of the other eonponent is dne (if the simplapt p r eb l wi
matlea. lima we ahaB kwre the ttstoal dIrefatiOB and v«
theneteotkewamiaqiaee. Having this direetlMi and '
th« («l|lt ef IN ftnmmMmA the son admita pf Niog cale

ITiltttnm' of MMian waA Ottatis.-— The tdtoiBi^ol'^
meteorokb does not admit of being determined from ob^
servation. One element neoeiBeiy for determining the
orbits of theM bodies is, therefore, ^ranting. In 13m e«w
of the showers of 1799, 1888, and 1866, oemmMify edlsd
the November showen, tids ebment is gttml^ the time

WVi i - wi i *ti?.MWM<*ft.?fc^:'jIyjSj,^;'ii^i^

■WiyMi-kWWii^'fiW^^MiiPWggS ai

884 AamONOMT.

of revolntion around the stm. Since the ahowen oconr at
intervals of about a third of a century, it is highly prob-
able this is the periodic time of the swann around tiiesun.
The periodic time being known, the velocity at any dis-
tance from the sun admits of calculation from the theory
of gravitation. Thus we have all the data for determining
the real orbits of the group of meteors around the sun.
The calculations necessary for this purpose were made
by Lb Yerrirk and other astronomers shortly after the
great shower of 1866. TIio following was the orbit as
given by Lb Ybrrieb :

Period of revolution 88'Myeen.

Eoeentrioity of orbit 0-MM4.

Least dletsnce frou the nm OMM.

InoUnstioii of orbit \W W.

Longitude of the node 51* 18'.

Position of the perihelion (near the node).

The publication of this orbit brought to the attention
of the world an extraordinary coincidence which had
never before been suspected. In December, 1866, a
faint telescopic comet was discovered by Tbxpbl at Mar-
seilles, and afterward by H. P. Tuttlb at the Kaval
Observatory, Washington. Its orbit was calculated by
Br. Opfolzkr, of Vienna, and his results were finally pub*
lished on January 28th, 1867, in the Atironomi$eh» Ifaak-
riehtenf they were as follows :

Period of revolution 88*18 vears.

Bocentrteity of ort>it • 90M.

Least distMioe from the sna O'VKS.

laelination of ori^ IM* 4*'.

Longitude of the node Sl'M'.

lioa^tude of the perihelioa 48* 84'.

The publication of the oometaiy orMt 014 that of the
cnrbit of the meteoric group were nuuie indepoidently with-
in a few days of each other by two aatronomam, neither
of whom had any knowledge of the w<Mrk of the other.
Oomparing them, the result is erident The marm* <f
tMUoroiig vhieh eaute the JTovemhtr $howan motw ti»
th*9am^ orbii witK TnmtL'i comet.

mmm

lowers oconr at
) highly prob-
roondUiesiin.
ity at any dis-
om the theory
>r determining
mnd the ran.
Me were made
ortly after the
the orbit as

[V.

¥.

the node).

the attention
ice which had
nber, 1865, a
SMPn. at Mar-
at the Kaval
I oalonhtted by
are finaUy pnb-
\<mitch« Jfaak-

iSlSjMn.

LOOM.

)Vns.

ler 4r.

n4 that of tiie
pendentlywith-
Korntn, neitlier
of the fliher.
The mamu (f
muen motM «»

IHK AUaUNT MKT/COUS.

385

Trmi>kl*h comet passed its perihuHon in January,
1860. Tho most striking meteoric sliower communced
in the following November, and was repeated during
several years. It seems, therefore, that the meteoroids
which produce these Hhowot« follow after Teiipki/s comet,
moving in tho same orbit with it. This shows a curious
relation between comets and meteors, of which we shall
speak more fully in t)te nuxt chapter. When this fact
was brought out, the question naturally arose whether the
same thing might not l)e tmo of other meteoric showers.

Other Showen of Meteors* — Although tho Novcmlwr
showers are the only ones so brilliant as to strike the ordi-
nary eye, it lias long been known that there are other
nights of the year in which more shooting stars than usual
are seen, and in which the large majority radiate from one
point of the heavens. This shows conclusively that they
arise from swarms of meteoroidi moving together around
the sun.

August MMeors. — The best marked of these minor
showers occurs about Augnst 9th or 10th of each year.
The radiant point is in the constellation Per»eu». By
watching die eastern heavens toward midnight on the 0th
or 10th of August of any year, it will be seen that numer-
ous meteors move from north-east toward south-west, hav-
ing often the distinctive characteristic of leaving a trail
behind, which, however, vanishes in a few moments. As-
suming their orbits to be parabolic, the elements were oal-
cukted by Sohiapabklu, of Milan, and, on comparing with
the orbits of observed comets, it was found that these
meteoroids moved in neiriy the same orbit as the second
comet of 1863. The ^exiMit period of this oomet is not
known, although the orbit is certainly elliptic. Aooord-
ing to the best oalenlation, it is 194 years, but for reasons
given in the next ibapter, it may be nnoertaift by ton
yean or moire.

Thsre is out remafkable dUhraice between the iugnst and ths
NoveMker asefeon. llw latter, ■■ we have seen, appear far two

^miim

386

ARTRONOMT.

or throe conaecutlve yMn, und then are not Men again until about
thirty yearn have elapaed. But the August metoon are leen erery
year. This showi tliat the atream of Auguat meteoroids is endleaa,
everr part of the orbit being occupied br them, while in the caae
of tne November onea they are nthered into a group.

We may conclude from this that the Novemtor meteoroidn have
not been permanent memben of our system. It is beyond all prob-
ability that a group compriaing countless million* of such bodies
should all have the same timu of revolution. Even if they had the
same time in the beginning, the different actions of the planeta on
different parts of the group would make the times different. The
result would be that, in the course of ages, those which had the
moat rapid motion would go further and further ahead of the
others until they got half a revolution ahead of them, and would
ttnally overtake those having the sloweat motion. The swiftest and
slowest one would then be in the position of two race-horses running
around a circular track for so long a time that the swiftest horse
has made a complete run more than the sloweet one and has over-
taken him from oehind. When this happens, the meteoroids will
bo scattered all around th«i orbit, and we shall have a shower in
November of every year. The f^ that has not yet happened shows
that they have been revolving for only a limited length of tinte,
probably only a very few thousand years.

Although the total mass of these bodies is very small, yet their
number is beyond all estimation. Professor Nbwtok has estimated
that, taking the whole earth, about seven million siiooting stan are
encountered every twenty-four hours. This would make between
two and three thousand million meteoitrfds which an thus, as it
were, destroyed every year. But the number wliich the earth can
encounter in a year is only an iudgnilloant fraction of tlie total
number, even in the solar system. It may be interesting to calculate
the ratio of the space swept over by the earth in the coarse of a yeiur
to the volume of the sphere surrouiiding the son and nteading out
to the orbit of Ntotuns. We shall find this ratio to be oa^ m one
to about three millions of milUoos. If we meaaore by tiia Bomber
of meteoKrids in a euMc mile, we mla^t oonrfdar theSii very thinly
scattered. Then ia, in fact, only a wigle meteor to aevmnal million
cuUe kilometres of space iin the heavens. Tet the to^ number
is immensely great, because a globe including the orUt of l!l(^fititme
would contain millions of millions of mllUoas of millions of cubic
kilometres.* If we reflect, in addition, that the meteoroids probably

*The compotathma leading to this nsnlt naj be mads in the fd-
knrhur manner:

I. TttfinithaeUbuatifaM mmptO^tmgk JyAssafAAi tiU tawnnf
at/ear. If weput irforthentfoof thedraoafereiiMoraclndetolts
dfcuneler, and p for the nKlins of the eaithtttiasarflMW of aplaaescetiM
of the earth passing thraoii^ lu centre wIO bs «^. Mvmtijlng tUa
by the droumferenoe of the earth's orbtt, we shall have the
quired, whkli we readil|y And to he more than W.OM i
minions of kihNMtres. BfaMM, in sweepbig throiuh tMs
earth enoounteni shoot 9Bto mJUDns of meteoroids. it '

sn again until about
ftoon are seen erery
leteoroids ii endleea,
1, while in the cam
group.

ber Bieteoroids have
t it beyond all prob-
lions of such bodieo
STcn if they had the
ni of the planeta on
imet diHerent. The
hoae which bad the
urther ahead of the
of them, and would
n. The twiftert and
) raee-horaea running
tt the Bwifteat hone
■t one and baa orer-
, the meteoroida will
«H have a shower in
t yet happened ahows
lited length of time,

I very nnaU, yet their
[■WTOM has eatioMted
lion shooting stars are
would make between
which are thus, as It
which the eartii can
fraction of the total
intereetingtocftkulate
In the ooorse of a year
Hin and octeading out
«tioto beoBlyaaone
eaaore bj tlw Bomber
dder themT«rythiiily
itflor to several muiion
ret tiie to^ number
S the orUt of Kt^tMrn
» of ndlUona of oubio
ke meteonrfds probably

US be made fai the f ol-
ifenoMotadHdetota

ba& have the «»• m-
km 80.000 mfHoiiB of

w il fcL. 1 .-^.■zliW.lBB.aii ' ^S J J t W ! ".' ' * ! " ! ' ' "*;

THE ZOUtACAL LIOIIT.

387

on-

welghbttta few grains each, we ihallseo how it istliattboy aru
tirely invisible to vision, even with powerful telescopes.

The Sodiaoal Light. — ^If we observe tho westeni nVy
during the winter or spring montlis, al)out the end of tho
evening twrilight, we shall see a Btream of faint light, a
little like tho Milky Way, rising oliliquely from tho west,
and directed along the eoliptio toward a point south-wcHt
from the zenith. This is called the zodiacal light. It
may also be seen in the east before daylight in the morn-
ing daring the autumn months, and has sometimes lieen
traced all the way across the heavens. Its origin is still
involved in obscurity, but it seems probable that it arises
from an extremely thin cloud either of meteoroids or of
Bemi-gasoons matter like that composing the tail of a
comet, spread all around the sun inside tho earth's orbit.
The researches of Professor A. W. Wbioht show that its
spectrum is probably that of reflected sunlight, a result
which gives color to the theory that it arises from a cloud
of meteoroids revdTing round the sun.

there is only one meleoioid to more than ten millions of cubic kil-

iKe$paiitmef*fkroiigklgih»tartkina

Let us put r for the ^-

maoo of Seearth from the sun. Then the distance of Neptune may
be taken as 80 r, and this wiU be the radius of the sphere. The cir-
cumference of the oarth'a orbit will than be 8 irr. and the space swept
over wUl be 9 «• r «i^. The aphere of Neptun* will be

I ir80» f» = 86,000 «• r», nearly.

Tlie ratio of the two i

I will be

1 8.000 f*

8.000

, nearly.

The ratio - ia mote than 98.000, showing the required ratio to be

about three millioM of mUlioM. The totol number of seattend mete-
ondda la tbmfore to be redraoed by ndllkma of mlllkma of milliona.

Wl*?^faMMMPte9K%^f^|^[^^

CHAPTER XIII.

COMKTS.
^ 1. ABPBOT OF CX)1I1T8.

CoMfTTH are <UHtingiu»h«<l from the plancte l>otl» by their
agpecte and their ..u»ti«,nB. They come into view w.t^iout
anything to herald their approach, continue in wght f..r a
few weeks or months, and then gradually vanwh in the
distance. TUey are commonly considered a* co»npo«od of
three parts, the nudeu*, the cmui (or hair), and the tml.
The nucleus of a ooiiiet is, to the naked eye, a point of
light resembling a star or planet. Viewed in a teWpe,
it generaUy has a small disk, but shades off so graduaUy
tliat it is difficult to estimate ite magnitude. In hu^
comets, it is sometimes several hundred miles in diameter,
but never approaches the size of one of the larger planets.
The nucleus is always surrounded by a mass of foffljy
liirht, which is called the eama. To the naked eye, the
nucleus and coma together look like a star seen through a
mass of thin fog, which surrounds it with a sort of halo.
The coma is brightest near the nucleus, so that it is hardly
possible to tell where the nucleus ends and whero the
Soma begins. It shades off in every direction so gradually
that no definite boundaries can be fixed to it. Ohe
nucleus and coma together are generally called the head

of the comet. ... t »i.a

The taU of the comet is simply a continuation of the
coma extending out to a great distance, and always di-
,«cted away from the sun. It has the appearance of a
stream of milky light, which grows fainter and broader

rw rnn'ms m ^"

ASl'KVr Of VO.VKTH.

381)

uta lK)th by their
ito view without
no in fliglit for a
ly vanish in the

as oompoflod of
r), and the tail.

eye, a point of
d in a t«loBcopo,
off 80 gradually
itude. In largo
nilea in diameter,
lie larger planets.
M nuM of foggy
naked eye, the
it seen through a
\i a sort of halo.

that it is hardly
3 and where the
Btion so gradually
led to it. The
r called the Kead

atinuation of the
B, and always di-

1 appearance of a
inter and broader

iiM it ruciMlt from titu liuud. Lilcu tltu count, it HliadeH oti
HO ^niduully tliiit it itt iinpoHMllilu to fix iiiiy iNMiiMlariuH to
it. Till) li)ii;;th ot tlir tiiil variuH fnnii '2^ or l\° to W" «»r
more. Uuiiurally thu nioru orilliaiit tliu liuad of tliu coiitut,
tliu loii^c'iitHl Itriglii riri thu tail. It iHalHo uftuii hriglitor
and nioru Mwirply dutinud at onu cdgu tlian at tliu othur.

Tliu alMivu dt'M-riptioii appliuH to iM>inut«( which can Ih)
plainly ttuuii by thu iiakud uyu. After ii^ti'uiioiuurH Intgaii
to (iwuup thu liuavuns carefully with tuluMCoputt, it watt
found that many comuts caiiiu into Hight which would
uiitirely e8ca))u thu unaided viHioii. TIiuhu aru called tel-
f«atj>ic mmeUi. Homutimes hIx or muru of hucIi comutH aru
discovered in a siiiglu yuar, wliilu oiiu of thu brighter claut
may not be 6uo>t for ten years or mure.

Fio. 101.

lOOlUR
OUT A MUOLBVB.

;- VJn.lOB.— VBLMCWPIOOOMBT
WITH A NUOLBUa.

When comets are studied with a telescope, it is found
tluit they are subject to extraordinary changes of structure.
To understand these changes, wo must begin by saying that
comets do not, like the planets, revolve around the sun m
nearly oironlar orbits, but always in orbits so elongated
that tiie oomet is visible in only a very small parf of its
oonne. When one of these objects is first seen, it is gen-
erally approaching the sun from the celestial spaoes.
At this time it is nearly always devoid of a tail, and some-
times of a nucleus, presenting the aspect of a thin patch
of cloudy light, which may or may not have a nucleus in

390

ASlTtaJrOMY.

its centre. Ab it approaches the sun, it is generally seen
to grow brighter at some one [)oint, and there a nucleus
gradually forms, being, at, iirst, so faint that it can scarcely
be distinguished from the surrounding nebulosity. The
latter is generally more extended in the direction of the
sun, thus sometimes giving rise to the erroneous impres-
sion of a tail turned toward the sun. Continuing the
watch, tlie true tail, if formed at all, is found to liegiii
very gradually. At first so small and faint as to be almost
invisible, it grows longer and brighter every day, as long
as the comet continues to approach the son.

g 2. THE VAPOBOTTS JDfVELOFEB.

If a comet is very small, it may undergo no changes of
aif«pect, exc^ then just described. If it is an unusually
bright one, the Bext object noticed by tdeieqyie examina-
tion wOl be B b<»ir ■anrounding ihe nodeas on the side
toward the ton* T\a» bow wiU gradwlly rise up and
spread o||l4n afl ridWy finally alMimbig tiw fonn of a
semicjieteliiviig tii» Imoleng in Hieaalie, or, to speak
with mora jtieeiSon , tiie form of s jHrnbda i»Ting the
nucleus near Ma loens. The two etiik tf ^ parabola
will extend out fnrther and further so as to form a part
of the tail, and finally be lost in it. Oontinning the
watch, other bows will be found to form around the nn-
clens, all slowly rising from it like «douds of vapor.
These distinct vaporous masses are called the etwdopet :
they sbsde off gradually into the ooma so as to be with
difficulty distinguished from it, and indeed may be con-
sidered as part of it. The inner envelope is sometimes
connected with the nudens by one or more fan-shqied
appendages, the centre of the fan being in the nnelens,
and the envelope forming its round edge. This a^iear-
ance is apparently caused by masses of wpat streaming
up from that nde of the nudens nearest the son, and grad-
oally spreading around the comet on eadi aide. Hie

ENVELOPES OF 00MET8.

■ -J
891

generally seen
there a nucleus
it can scarcely
bulosity. The
irection of the
moouB impres-
^ontinuing the
'onnd to liegin
as to be almost
ry day, as long

) no changes of
is an nnuBually
letq^ksexaniina-
«B on ihe side
ly riM up and
^ fofm of a
«, ottfU* speak
da iMiving the
f 0k purabok
to form a part
Dontinning the
around the nit-
udiK of vapor.
i the envelope* :
M to be with
3d may be con-
w i« sometimes
dore fan-shaped
in the nnoleos,
. This aj^iear-
rupor streaming
teson, and grad-
Mk aide. Tko

form of a bow is not the real form' of the envdopcs, but
only the apparent one in which we see them projected
against the background of the sky. Their true form is
similar to that of a paraboloid of revolution, surrounding
the nucleus on all sides, except that turned from the sun.
It is, therefore, a surface and not a line. Perhaps its form
can be best imagined by supposing the sun to bo directly
above the comet, and a fountain, throwing a liquid hori-
zontally on (dl sides, to be built upon that part of the
comet which is uppermost. Such a fountain would throw
its water in the form of a sheet, falling on all sides of the
cometic nucleus, bat not tonching it. Two or three vapor
surfaces of this kind are sometimes seen around the comet,
the outer one ^jf^oAkg each of the iimer <»cs, but no two
tonching eadtililL

WiB. IM.— voBHAnoir oi^

To give a dlM> conoBpt l on of the lo n p et k m sad iDotimi of the
envdoiwi, we p> lS B t two ilgares. tiie lint of these rtMms the q^
pewanoe of tiie eavdopes m four •ueoeariTe iteges of their eourw,
and anr be rqpaded as seedoas of the vesl mabteUxhsped mr-
fwMS wMch flwj tesm. In all tiiese fgores, the mib b ami^fiimi to
be sboTO tbe oobmI in the figure, sad the tail of the oomet to be
dinged dowsamad. Id • the riM«t ct vapor has jnat besoa to
titk la > It ii fiiea aad expaaded yet farther. la < ii has B«nm
to aove aw«r a*id mm agovad tine oooiet oa aU lidee. " naally,
in d this Ian bm^mi 1mm ooae lo far that the higher portkHW
have aesiijr disaroeared, me larger part of the awtter havinig
moved awav toirwd tha taiL Before the st^^e « is raaohsd, a
■eooad mrmofm will eoauaoa^ b^a to rise as at «, ao iltat two
or thsee aaiy be virfUft at the nune tfaae, encloaed within eseh

la tiM next figure the actual motioa of the matter oompos-

ASTRONOMY.

ing the eavclo|)c8 \s shown by the courses of the several dotted
lines. This motion, it will be seen, is not very unlike that of
water thrown up from a fountain on the part of the nucleus
nearest the sun and then falling down on all sides. The point in
which the motion of the cometio matter differs from that of the
fountain is that, instead of being thrown in continuous streams,
the action is intermittent, the fountain throwing up successive
sheets of matter instead of continuous streams.

From the gradual expansion of these envelopes around the head
of the comet and the continual formation of new ones in the im-
mediate neighborhood of the nucleus, they would seem to be due
to a process of evaporation going on from the surface of the latter.
Bach layer of vapor thiu formed rises u|> and spreads out con-
tinually until the part, next the sun attains a certdn maximum
height. Then it gradually moves away from the sun, keeping its
distance from the comet, at leaat until it passes the latter on every
side, and contiaues onward to form the tuL

Fio. 101— imuutioK or omanrVi taou

Theak jAeaomem w«n felly obwrvad ia tiM
18U, «fee obaervatiiMM of wfcMi w«n ciMMIIr
M4lPMif«HbrBgiii>,^r " "^

^MM ^fln* 'ttOVM

•«d the iuMT oiM <*. f

aoth tx « ImI^ «f fdNMi 1'.

%liM^ lonwur, ■ItMrdluid tmmmL ilMciaeawl r
%ipHk(M< w M to tikif th* |ttm«l Am Int
«i»< l ofw i ia ril wan Mw to An fnMtUi«««|BL4w|M
men^ on October MA, whni all Am often M Mm ^UtitH^iiiMk.
The Mto at idiiA Mm envelopea aneaiM: mw g«MMd|jr Imw f# to
60 Uiometna par Imw, the ordinary ONed 4rf ft nttwnr^nin.

The flm OM roM to a hdglit of abottft aO^OOO IdlWMlm, bat it
WM flnally ^Sfaalpatod. Bat the mooearive eaea ^^mmammH at •
lower and lower elevation, the sixtb brtur loat ai^t of at • h eirt i t
of about 10^000 kilonetraeu

.Uffttl.W l lWl. ' Wjl iN eyr i II I H | [j^. Wi iWtViv -r*-v xx»*;^qi«Ki>-^

The mmofrn'^iimt

^it MW I UW Mlte

Boveral dotted
unlike that of
>f the nucleus

The point in
om tliut of the
nuous streamg,

up successive

'ound the head
ones in the im-
seem to be due
Be of the latter,
ireads out con-
rtain maximum
tun, keeping its
I bitter on every

8PE0TRA OF COMETS.

393

IL.

■MOlyCmnMle
llwnp4nlB.
JloMtm, bal ft

hlMataheli^

In the great comet of 1861, eleven envelo])e8 were seen between
July 3d, when portions of three were in sight, and the 19th of
the same month, a new one rising at regular mtervals of evenr sec-
ond day. Their evolution and dissipation were accomplished with
much greater rapidity than in the case of the great comet of 18S8,
an envelope requiring but two or three days instead of two or three
weeks to paaa through all its phases.

8 8. THE PHTSIOAL OOlTSTrFUTIOir OF OOKBTS.

To tell exactly what a comet is, wo should be able to
show how all the phenomena it presents would follow from
the properties of matter, as we learn them at the surface
of the earth. This, however, no one has been able to do,
many of the phenomena being sneh as we should not ex-
pect from the known constitution of matter. All we can
do, therefore, ii to present the principal eharacteristics of
comets, as shown by ofaiervation, and t» explain what is
wanting to rewmeile these ehancteristieB with the known
properties of nuttter. i i •!^\

In the first place, idl eomets which )a»r« been examined
with the spedMieope diow a speetnim otnnposed, in part
at least, of bright llnea or baa^ These Knee have been
supposed to be identified wiA those of carbon; but
although the similarity ci aqieot ia Tetryatrildng, the idm-
tiity cannot be regaided aa pnyven.

:nPk'Mlb«

bi Hie anHBced flgoM flw vipfn tfmktm. A, it ihat of onlMm
tak«iiaolc«aBt»[kaBdth«l9w«roB«,B,«|MtofaeoaMt TImm
raeotra te««rpNt«d la Ami umal way would iadioite, flntly, that
the conit isaaawNia; teooadly, that the gwes wUdh compotfs it
are so hot as to ridae by their own U^t, But we cannot admit

804

A8TR0N0MT.

these interpretations without bringing in some additional theory.
A mass of gas surrounding so minute a body as the nucleus of a
telescopic comet would expand into space hj virtue of its own
elasticity unless it were exceedingly rare. HoreoTer, if it were
incandescent, it would speedily cool off so as to be no longer self-
luminous. We must, therefore, propose some theory to account
for the continuation of the lumfnonty through numy centuries,
such as electric activity or phosphorescence. But without further
proof of action of these causes we cannot accept their reality. We
are, therefore, unable to say with certainty now the light in the
spectrum of comets which produces the bright lines has its origin.

In the last chapter it was shown that swarms of ininuto
])urticles called meteoroids follow certain comets in their
orbits. This is no donbt true of all comets. We can only
regard these meteoroids as fragments or debris of the
oomet. The latter has therefore been considered by Pro-
fessor Nkwton as made up entirely of meteoroids or small
detached masses of matter. These masscis are so small and
so numerous that they look like a dond, and the light
whidt they reflect to our eyes has tiie milky i4)pearanoe
peculiar to a omnet On tlus theory a telescopic comet
which has no nucleus is simply a doud of these minute
bodies. The nudeus of the brighter comets may either
be s more condensed mass of such bodies w it noay be a
solid w liquid body itsdf.

If the reader has auy.difflonlty in reoondling this theory
of detached pariides with the view already presented,
tluH tkit Hn^ilepai teon v^^iii Hm tail ^.Hn «oaiet is
lummA oouiil «if hg^en of ivpoi^ ka ttoat Mmen^Mr thai
MiMia, aiiah aa QlMd% &f , and aniol% «m»
9y composed of minute separate partides of watfM^ or

«r tt« Oooaara «BiL— Tbe taS <tf iba
it not a poniMBMttt appendago, not ia eompoaed of tin
masses of vapor whidi we have ahready deaoribed as aa-
oending from the nudeos, and afterward moving away
from tiie sttn. The tail whidi we see on one evening is
not abeolutdy the same we saw the evening before, a

• n-'-sxjj»t«M»»niasaSB««B«nt*<««*4rt*a:-:

gE'iiniiiiwiBwiiii'iri II I iBwiiMiiiflKi

litionsl theory.
ke nucleus of a
ue of its own
rer, if it were
no longer self-
ory to account
lany centuries,
rithout further
ir reality. We
ie light in the
B has its origin.

ns of minute
mets in their
We can only
Uhrig of the
lered by Pro-
roids or small
) 80: sniall and
Old the light
:y i^pearanoe
secopic comet
these minute
ts may either
•r it may be a

ng tiiie theory
iy presented,
ttW OOOMt is

as of wat^r or

MOTIONS OF COMETS.

395

L<rf«lM

ipowl el liw
Miibed as as-
moving away
>iie evening is
dng before, a

poiiiion of the latter having been dissipated, while new
matter has taken its place, as with the stream of smoke from
a steamship. The motion of the vaporous matter which
fonns the tail being always away from the sun, there
seems to be a repulsive force exerted by the sun upon it.
The form of the comet's tail, on the supposition that it is
composed of matter thus driven away from the sun with
a uniformly accelerated velocity, has been several times
investigated, and found to represent the observed form of
the tail so nearly as to leave little doubt of its correctness.
We may, therefore, regard it as an observed fact that the
vapor wUch rises from the nucleus of the comet is repelled
by the ran instead ol being attracted towaid h, as larger
masses of mattw WPS.

I force' 1am

ever been

1 in its

UlalllB attoac-

by their

'%o one of

titWilaponthe

entireh

No iAafMto emit— ttott of tUa nohiMtc
given. H ]N% iHdad^ iMtt tmgirtiiiit tlit

oluuaol|if^'lii!iiliia>^«B0'.'Wi:|p^:

electriilSlS K & KMNrMMv «M

the nMH.MlMil |(Mmw>i BWiairtsil tiflr^

oomet%,- Jwl||iS|aii'^

oonwtVtW Jt ti> W MSMAit a» ^.WIHWWMWI tHi entirely

iK>Iate|'l|pi^Mpyt taf tn-^acmk snMitii|Mt Jiiiy liliiit^stiwhred
fact of ^

In
coDwta
phyrio% _^^

■■WbO WfppNP:- N||R|||^,lMnKd BB QV -'w

If iiAM'ml^^imm^ii^it^immi^wi***^

of eonnta mu W« koow iriuit fonaa awttar n
diiemrt itaok tlUMawe And it to hav« aaauJMd'in oar labota
tt^jjes. Thia ia a question whidi we merely angaeat wUhooi
attempdiw to apecolato optm It. R can be answenu onty by ex-
perintnitd neeanAea in dieiiiiatry and i^ysica.

g 4. MOVIOIIS OV OUMJm.

Previow to the time of KxwroNy no certain knowledge
respecting the aetnal motions of comets in tho heav«DS
had bean aoqnired, except t^ they did not move aionnd

396

ABTRONOMT.

the snn like the planets. When Newton invefltigatod the
mathematical rosnlts of the theory of gravitation, he found
that a body moving nndor the attraction of the sun might
describe either of tlie throe conic sections, the ellipse, par-
abola, or hyperbola. Bodies moving in an ellipse, as the
planets, would complete their orbits at regular intervals
of time, according to laws already laid down. But if the
body moved in a parabola or a hyperbola, it would never
return to the sun after once passing it, but would move off

"Wtti, lW.^4n>iimio MMD

to infinity. It was, therefore, very natoral to qondude
that comets might be bodies which resmnble the plan^ in
moving under the sun's attraction, but which, instead of
describing an oKipse in regular poriods, lilce the phmeCs,
move in parabolic or hyperbolic orbits, and ther^ore
<mly approadk the bub a angle time duing their wh(^
existence. '

UtiB theory is now known to be essentially tme int

aatmt

wum

ORIilTS OF VOMKm.

897

iBtigatod the
)n, he found
e sun might
ellipse, par-
lipse, as the
lar intervals
But if the
i^ould never
lid move ofi

to oondnde
tbe pkn^ in
h, instead iA

the phmeto,
nd iher^iffe
% ikuwt wbofe

idly tone hxt

most ot Wwi observed comets. A few are indeed found to
be rovolviMjr around the sun in elliptic orbits, which differ
from tho8{' of the planets only in l)oing nmch more eccen-
tric. But tli.> greater nmnbcr which have been observed
have receded ?rom the sun in orbits which wo are unable
to distingaiBJt ?rom parabolAs, though it is possible they
may be extillaely elongated ollipsee. Comets are thwe-
fore divided i/f^h respects their motions into two claaies :
(1) periodic vknete, which ve known to move in ellipiio
orbits, and tf^um to.the «an at fixed intervals ; and (9)
farahdio otmO^ a||fMM^jr aMviag in panbdflw, ntver
to return. ^

Tlie first ditfbperjr el Hi* |»«liodWty «f a ,«««« Vas
made by ISiKum vai ,*l mmi i Am with «be gretfft^ei»l^i| of
1682. K»«^ tl»>forfi ^ iilaiM II Am, iHit Jimd
that a oonwimving in mn^ ^ < i M|tt.iua i > l t wtllritttet of
1682 had «eJHN>en ill -^..Ml^ V^fljim'WSi&X.
He was tfieil^ ^ to {^oeii^^ioii tlm-^i,..., _
comets WiMl^ally <!ihe andf Hie same olijeet, i«tiii^& to
<>vik^ of about t5 or t6 yeus. He tfaibre-
itliMitWOnld appevr iigain about ^year
BVck a pawdietion rei^t be a year or nwre in
to the effect of the i^traction of the phutets
upon the ilinet. In the mean time the methods of calcu-
lating tl^ ttttraotion ^i the Janets were m> f«r in^roved
that it biiiiMsM pooBi^le tomake a more aeonn^e fHfedic-
iioUi A«^^yeMr 1759 approached, the necessary com-
putations were made by the great French geometer Clai-
BAinr,7^M> essigned April 13th, 1769, as the day on which
the «ii|M»t would pass its perihelion. This prediction
watt ;^||ipai|cri>1y (MHTect. The oomet was fint j«en on
Cb^iil)^M-4ay, 1768, and passed its perihelion^ Maroh*
1 Jtht 1769, iXiij one month before the piedioted .tune.
'£^e eonaiBt wtiurQed again in 1836, within three dikys of
ttie moment ]^»dioted by Dk Poircfioooi^inr, the most
suooeMfnl ealeohtor. The next return will iHt>babfy take

the sun
fore pre
1768. B
error, o

898

AHTRONOMY.

place ill ton or tl»I2, tlio exact tiiiio being »til^ unknown,

because the neceasary coinputatiuius have noi >et been

made.
We give a figure nhowing the position of the orbit of

Hallkt's c(nuet relative to the orbits of tlio four outer

planH.s. It attain-
ed itib greatest dis-
t8iK<e from the snii,
ftu' '/eyond the or-
bit of Neptune,
4i)Hnittheyearl878,
and then oom-

Jeikced its return
<Hnt^. Thefig-
lire «li0WB the prob-
able pJDsitioii of the
onii^t in 1874. It
wrilf'ihen far be-
jort^ the reach of
thf i»0Bt powerful
telesoopt), bnt its distance and direction ii4>nit of beuig
calculated with so mnoh precision that a ^osoope oould
be pointed at it at any required moment H?'

We have already stated that great nnmbell^ of comets,
too faint to be seen by the nakc^ eye, ara dii^tovered by
telescopes. A considerable number of these telescopic
comets have been found to be periodic. In ii.>0Bt cases,
the period is many centuries in length,. so that tlio comets
have only been noticed at a single virit. Eight or
nine, however, have been found to be of a period ^ shoft
that they have been observed at two or uiortf n^O'^v

We present a table of such of the periodic e(ptt«to as
have been actually observed at two or more rMonis. A
number of others are known to be periodic, bnt have Xi^n
observed only on a sii^le viut to our system.

OP ■A&unr's oomr.

>;WH«Btr ^ii^mmmsm^mimmmsx:--

M t H *mm»ummiJi ^

400

ASTRONOMY.

Theory of Oometary Orbits.— Tliora is ajproiicrtjr

uiidentanuiiig of which will

of all c»r
bit* of bodioa around the miti, an

enable tu to form a clear idea of lonio causeit which affect the
motion of cometa. It mav bo cxpreaMNl in the following theorem :
The nuitn dittanee of a hmly J'rom the *u», or the ntajor inrit of the
ellipee in which it revolves, de|>ends only upon the velocity of the
iHidy at a given distance from the sun, and may be found by the
formula,

It =

H r

a M — r «"

in which r is the distance from the sun, « the velocity with which
the body is movinut and fi a constant proportional to the mass of
the 8>.n and depenains on the units of time and length we adopt

To understand this fonuula, let us imagine ourselves in the celes-
tial spaces, with no planets in our neighborhood. Suppose we have
a great number of balls and shoot them out with the same velocity,
but in different directions, so that they will describe orbits around the
Mun. Then the bodies will all describe different orbits, owing to
the different directions in which we threw them, but these orbits
will all possess the remarkable jwoperty of having equal UMJor
axes, ana therefore equal mean distances from the sun. Sinoe, by
Kbplbr's third law, the ijerio-Jio time depends only upon the
mean distance, it follows thiat ilvf bodies will have the same time
of revolution around the bub. Coasequentiy, it we wait patiently
at the point of projection, they will all make a revolution in the
same time, and will all oome back again at the same moment, each
one ooming from a direction the opposite of that in which it was
thrown.

In the above formula the aujor axis is given by a fraction, having
the expression 3 ^ — r e* for itt denominator ; it follows that it the

square of the velocity is almost equal to — ^, the Taloe of a will

become very S'^t, because the denominator of the fraction will be
very small. 11 tan relooity is soeh tiiat 9 ^ — r •* is lero, the cnean
distance will become inllnite. Heaee, in this ease the body will

a' off to an inflaite distance from the sun and never ivtnm.
ich less will it return if the Telocitv is still granter. Such a
Telodty will make the value of a slgebraioally negative and will
correspond to the hyperbola.

If WW take one kilometre per second as the unit of velocity, and
the mean distance of the eaith ftramthecnn as Uw unit of distanea,
the value of ^ will be representMl by the nomber 87S, so that the

f ormuU for e will be a = -—_———. Fran this equation, we may

eiiteulate what velocity a body movins around the son must bave
at any {j^ven distance r, in order thai it may move in a pandioUc

ahall vaniih.

orbit— that k, that the denominator of the fraetlon
TUs omidition will give

1750

At the diataneeof the earth

OUJUHt OF VOMKTK

Itcrty of »•• "•■-
; of which wilt
rhich affect the
)winK theorem :
major lurit of the
1) velocity of the
bo found by the

•city with which
1 to the moHit of
ingth we adopt,
lives in the celes-
Buppow we have
le same velocity,
orbits around the
orbits, owing to
but these orbits
ing equal major
3 sun. Since, by
I only upon the
e the same time
re wait patiently
revolution in the
me moment, each
i in which it was

a fraction, having
bllowb that if the

ke value of a will

le firaction will be
is aero, thecnean
ise «he body will
nd never ivtnm.
gfVKter. Booh a
M^ve and will

t of vehicity, and
BOiitof diataaee,
■ 875, M that the

equation, we nuqr

le nin must bsve
oive in ajMrabolio
tloB shall vMiieh.

itaaoe of tlie earth

from the sun we have r = 1, so that, at that diHtancc, t will h< tli<>
M|uare root of 17S0, or nearly 43 kilometres |H)r Mccond. The fur
ther we K*'t out from the huh, the Icmm it will )h! ; and we may remark,
H8 an interesting theorem, that whenever the eomet is at the dis-
tance of one of the planetary orbits, its velocity must Imi c(|unl ti>
that of the iilanet multiplied by the square root of 2, or 1-414, etc.
Hence, if the velocity of any planet were suddenly incream>d by a
little more than -,% ot its amount, its orbit would lie changed into
a paralM>la, and it would flv away from the Hun, never to return.

It follows from all this that if the astronomer, by observing the
course of a comet along its orbit, can determine its exact velocity
from point to point, he can thence calculate its mean distance from
the sun and its periodic time. But it is found that the velocity of
a large majority of comets is ho nearly equal to that required for
motion in a parabola, that the difference eludes oliservation. It is
hence concluded that most comets move nearly in parabolas, and
will either never return at all or, at best, not until after the laiiseof
many centuries.

$; 6. omonr or ocmmn.

All that wo know of comets leems to indicate that tbey
did not originally belong to oor system, bnt became mem-
liera of it through the tKitovbing forces of the planets.
From what was said in tin bit SMtion, it wid be seen tiiat
if a comet is moving in a pandxdie (nrbit, and its vdooUy
is diminished at any point by ever so small an amount, ite
orbit will be changed into an "tUipse ; for in order that the
orbit may be parabolic, the quantity 2 /*— r v' most remain
exactly zero. Bnt if we then diminish v by the smallest
amount, this expression will become finite and positive,
and a will no longer be infinite. Now, the attraction of
a phmet may have either of two opposite effects ; it may
eidier increase or diminish the velocity of the c<miet.
Hence if Haa latter be moving in a parabolic orbit, the at-
traotioit ef a phmet mi^^t either thh>w it out into a hyper-
bolic orbit, so tlMt it would never again return to the sun,
but wander irnvrw through the celestial spaoee, or it
might change its ortrit into a more or less elongated ellipse.

Suppoie CJ^ to represent a small portion of the cnbit
of the planet aitd AB% small poHion of the orbit of a
comet passlBg near it. Suppose -also that-the eomet passes

ASTItOHOMY.

a little in fnmt <>f the plniiot, and that the alinultanenuii
{HMitiuiiH of the two bodied are ropn»oiit«<l hy the conre-
apondiiig lottore of the alplmlHjt, a, A, o, </, etc. ; tlie aliortoat
distance of the two botlie* will Imj the line o c, and it is
then that the attraction will be the most jioworful.
between o v and d d the planet will attract the comet ahno«t
directly Uckward. It follows then that if a comet p»«8
the planet in the way hero represented, its velocity will be
retarded by the attraction of the latter. If therefore it be
a parabolic comet, tlie orbit will be changed into an
ellipse. The nearer it passes to the pUmet, the greater
will be the change, so long as it passes in front of it. If

it passes belund, the
reverse effect will
follow, and the mo-
tion will be aocele*
rated. The orbit will
then be changed into
a hyperbola. The or-
bit finally described
after the oomet leaves
|onr ■ystem will de-
ind npon whether
its velodty is aooele-
rated or retarded by
tile oombined attrMstion of all the planets.

All the studies which have been made of comets seem
to show that they originally moved in pMraboliooibita, and
were brought into elliptic orbits in this way by the attvao'
tion of some planet. The planet which has thus hronght
in the greatest number is no doubt JttpUar. In fact, the
orbits of several of the periodic comets peas very near to
that phmet. It mi^t seem that these oHbits oii|^t dmoat
tointmectthatof thephu)etwhididumgedth«n. Thia
would be true at first, but owing to the constant diange in
the position of the oometary cn^it, produced by the at*
traction oi the plaiMits, the orbits would gradndly mo^

108.— AmuonoH or ruurarr ok

OOMMT.

iuMWiiii>M i >. i t8i i y 'i .ni i w wwi

wamm

ORUUN OF VOMKIK

4U3

siinnltancouR
»y tlio corre-
; thuBliortost
0, aiid it is
»t iwworful.
couiot abiiuHt
a cuiiiut p»M
looity will be
liereforo it be
tgud into ail
t, the greater
ont of it. If
8 behind, the
effect will
and tlie mo-
ill be aooele-
Tlio orbit will
) changed into
•bola. The or-
ally described
le oomet leaves
item will de-
ipon whether
M)it/ is acoele-
>r retarded by

comets seem

olio ortiita, and

by the altnus-

B tbns bronght

In fact, the

IS very near to

oQl^t almost
dthem. This
itant change in
oed by the ai-
pradwdly move

away from oach other, tH> that in time there might be no
approach whatever of the pUnet to the comet.

A rumarkabh case of this sort was afforded by a comet
()i»cuvored m Jtme, 1770. It wan obsorvud in all nearly
four months, and was for some time visible to the naked
uyu. On calculating its orbit from all the oliservations,
the astronomers were astonished to find it to be an ellipse
with a |)eriod of only five or six years. It ought dieref ore
tu have appeared again in 1776 or 1777, and should have
rutnmed to its perihelion twenty times before now, and
should also have been visible at returns previonsto that at
which it was first seen. But not only was it never seen
before, but it has never been seen since I The reason of
its disappearance from view was bronght to light on cal-
culating its motions after its flrat discovery. At its re-
turn in 1770, the earth was not in the right part of its
orbit for seeing it. On passing ont to it* aphelion again,
about the beginning of 1779, it oneounterad the planet
Jwjnter, and approached so near it that it was impoauble
to determine on which side it passed. This approach, it
will be remembered, wold not be observed, beoanse the
comet wa* entirely ont of sight, bntH was calenlated with
absolute certainty from the theoiy of the comet's motion.
The attraction of JitpUetf therefore, threw it into aom»
orbit so entirely different that it has never bMn seen since.

It is abo hi|^y ptobable that the oomet had jnst been
brought in hj the attraetion of Jitter on the rery revo-
lution in which it was first observed. Its history is this :
ApproMhing the son fmn the steUar spaces, probably for
the first time, it passed so near Jupiter In 1767 that its or-
bit was flliangBd to an eOipae of abort period. It noade
two complete revolutions around the sun, and in 1779
again mat the planet near the same phuse it had met him
iiefore. The orMt was again ahwed so mnoh that no tel-
eaoope Yum fonnd the oomet ainee. No other case so re-
markaUe as this ha* evnr been noticed.

Not <«ly are new oometa oeearionaUy brought in from

SI-

404

ASTRONOMY.

#' i

the stellar spaces, but old ones may, as it were, fade away
and die. A case of this sort is afforded by Biela's comet,
which has not been seen since 1S52, and seems to have en-
tirely disappeared from the heavens. Its history is so in
structive that we present a brief synopsis of it. It was first
observed in 1772, again in 1805, and then a third time in
1836. It was not until this third apparition that its peri-
odicity was recognized and its previous appearances iden-
tified as those of the same body. The perioil of revolu-
tion was found to bo between six uid seven years. It was
BO small as to be visible in ordinary telescopes only when
the earth was near it, which would occur only at one re-
turn out of three or four. So it was not seen again until
near the end of 1845. Nothing remarkable was noticed in
its appearance nntil January, 1846, when all were aston-
ished to find it separated into two c<.mplete comets, one a
little brighter than the other. The computation of Pro-
fessor MiTBBABD makes the distance of the two bodies to
have been 200,000 mWes.

The next observed rotnm was that of 1852, when the
two comets were again viewed, but far more widely
separated, their distance having increased to about a mil-
lion and a half of miles. Their brightnetn was so nearly
equal that it was not poerible to dedde which should be
considered the principal comet, nor to determine with
certainly which one should be oonsidered aiB identical with
the comet seen during the jo^vious apparition.

Thoni^ carefully looked for at every subsequent return,
neidier oomet hasbem fieen since. In 1872, Ur. Poosoir,
of Madras, thought that he got a monMataryiview of the
comet tiirongh an opening l«tween the dondson a stormy
evening, but the position in which he rappoied himself to
observe it was so far from the oahmlated (hm that'his obser-
vation has not been aoeepted.

Instead of the cornet^ however, wo had a meteorio i^Miwer.
The orbit of tiiis comet almoBt interseots that ni tlie enrtii.
It was therefo«« to be <»pected that the latter, OH passing

REMARKABLE COMETS.

406

ero, fade away
Mela's comet,
ms to have en-
listory i8 so in
It was first
\ third time in
1 that its pcri-
tearances iden-
o\ of revolu-
yeans. It was
pes only when
>nly at one re-
en again until
was noticed in
Jl were aston-
I comets, one a
itation of Pro-
two bodies to

852, when the
more widely
to abont a mil-
I was so nearly
lioh should be
etermine with
I identical with
loo.

leqnent return,
I, Mr. Poofloir,
ry<Tiew of the
ids on a stormy
used himself to
that'his obMr-

steocio idioiwer.
It of tibs earth,
ter, oiipMMing

the orbit of the comet, would intersect tlie fragmentary
meteoroids supposed to follow it, as explained in the last
chapter. According to the calculated orbit of the comet, it
crossetl the point of intersection in September, 1872, while
the earth passes the same point on November 27th of each
year. It was therefore predicted that a meteoric shower
would be seen on the night of November 27th, the radiant
point of which would be in the constellation Andromeda.
This prediction was completely verified, but the meteors
were so faint tiiat though they succeeded each other quite
rapidly, they might not have been noticed by a casual
observer. They all radiated from the predicted point witli
such exactness iiiat the eye could detect no deviation what-
ever.

We thus have a third case in which meteoric showers
are associated with the orbit of a oomet In this case, how-
ever, the comet has been completely dissipated, and proba-
bly has disappeared forever from telescopic vidon, tliough
it may be expected that from time to time its invirible
fragments will form meteors in the earth's ^mosphero.

ft 6. BJDMABXABLB OQHXM.

It is &miliarly known that bright comets were in former
yecjs objects of great terror, being supposed to prewge
the fall of empires, the death of monarch*, tiie vpfHimAi
of earthqnakM, wan,, peatilenoe, and eveiy otho* odamity
which eoold affliet mankind. In showing the entire
gronndleasnea of loeh fean, soimoe has rendered one of its
graptert benefit* to mankind.

bi 1456, the oomflt known as Hallkt's, appearing
when tihe TnrkiirMW making war onCShrisfeoidom, censed
snoh terrw that Pc|ie OxuxTva. wrdend pnqrers to be
oierod in the Indies for praleetion againit it. TW*
is BUiqpoasd to be the origin of the popohr myth that tike
P(me oooe imwd a ball agiinsi the oomet

The nnmber of comets visible to the naked eye, so far as

■N

406

ASTRONOMY.

recorded, has generally ranged from 20 to 40 in a cen-
tury. Only a small portion of these, however, have been
BO bright as to excite nniversal notice.

Oomat of 1880. — One of the most remarkable of these
brilliant comets is that of 1680. It inspired sach terror
that a medal, of wlueh we ]»<eseBt a fignre, was struck
npon tiie Oontineiit of ]&m>pe toqui^ a^«hei»i<m. A
free tiwidatkm of the insoription is : " T^ star thveetens
evil things ; trost «dy I God will torn them to good:*'
What makes this wnxA espeoiaUy rraiarinUe in histcwy
is that NswTOH oaloalated its orUt, and diowed that it
moved around the sun in a conic section, in obedience to
the law of gravitation.

eeMR o« i«M.

Otaet OiMMt of 1811. -.1%. 119 alttim ili geneml ap-
peaiwoe. It has a period of oivier MOO yean, and its
a^fBliQB^iiCai|O0i8abeat4O^OOQ»O9O,O<N>^iiiaM. .

QKm:^mm of lS48..--Oiie of l^mat hOXmA mm-
ets whidi kmmappoarad dnfibg;^ priaiml . ow ilwy -iww
tha^ of fefani^^lMS. It v» viaSbfe Jn irii 4MiMit
oIoBeto.tbeMui. Oonaldenlile tuwor into«««^ri fe^Moe

whuhJiidlMfln peMkled lor thai yew ^^mUm,: Ai
periiielitiii it pooied neafer the son than Miy oiker body
has ever been known to pass, the kMt diilaMe bdng only
abont one filth <rf Ike nm's seni-dlameler. WA « tMy
eiight ohange of its original motkU) itwotid kave astMlly
Men into the son.

40 in a cen-
mr, Lave been

kable of these
k1 sach terror
re,.WMstniek
dwnikm. A
BtartlnmitenB
urn to goodi"
lUe in hiskwy
bowed that it
I obedienee to

mim.
i»igmiml§!p.

nwVt ■

Jdi4i^t

GREAT COMET OF 1868.

407

0(Mt OooMl of 18B8. — ^Another remarkable comet for
the length of time it ranained -viable was that of 1868.
It is f reqnentlj oallad after th« nsme of DosAn, its iin»t
diMMMrerar. Mo oamet Hik&ni^ ov Mighboriiood in

wiuiswteiyUft iftpw

the ob«0nratioiMnia(b ttpovithftve already been preaented!

flu. lll.-HpaMA«'t MMIf m

iii»0 l tl^ i ^mmmmAV'.ms-:M.'m%tfM-A ' '-' ■ -^^:^-:-'r

HWll l Uiailli..i'/Hl.imil i l

ENOKtrS COMET.

Its greatest brillianoy oecnrred about the beginning of
October, when its tail was iO* in length and 10° in breadth
at its outer end.

DoHATi'g omnet had not l<Hig been obaenred when it
was found that ita orbit was deddedljr elliptioal. After it
disappeared, the observatioiia were all earefnlljr investigaiad
by two Biathematidansy Dr. Yov Asm, of Oermaay,
and Mr. O. !¥. Uttx, of this eoontry. The hitter found
a period of 1960 yean, whieh is probably within a half a
oentnrjr of the truth. I| is probable, therefora, that this
comet appeared about the ilrst eentuiy before the Chris-
tian era, and will rrtum again about the year 8800.

tioa^

kaowa MrlMp's eontt h» fuMi kt Wfmm Hkm mtA four

1^ M Si ii i»a t^t»Mr aast o«e smST ^iS« the msI fH«%

°' g i^ '*i' ' ^ ^J!/g*^*'^ *° »* ""^ n^ TlwdwwMlaaflt
*^ ^^^ ^ '■'^ *>*''>*^ *<> *^ «(«Mt ii tlM tiM obMmiloat
wUab kave tepi aude Upoa It mmi to iwll«t|s tkat it to gnms^
amoMttilgiksnB. BtwaB attrfboted tUs diai^ ia ila ocSSig
tM>MMMM^«Ma«l ireriitt^

VMa^r M«*wto Mim lftto^fariad^^
lO* «om*wM asiaallr «nK4tlM MB.

>ai HMr .ynioa of 'BMip *s (OoiBtt awMt bs dHi%

iSiySJWi^ *W»^ MBlst MiMii' iMMnNr the Mtt'lhatf aM»

52f i2'-*2S ISSSf^iLf* ««I««w»» to isttls. Wfiiol to
«w ay <w<>ii| ilWIIIi Mjit aaoiatftos fat ttidr awtioaa wlMnra-

tdntf «ha| «• di^idrftom Ohm of UwplsS!.

fe MPA'llil^lW ' 'ti'*V'-^W«WW WW ^ ^ ^%sm»Wiw<i i H« i i»)g |i iJa!!MiwMMM' aa W !MaiUi i .i !

PART III.

THE UNIVERSE AT URGE.

INTRODUCTION.

Ik onr stndies of the lieavenly bodies, we have hitherto
been occupied almoet entirely with those of the solar sys-
tem. Although this system comprises the bodies which
are most important to us, yet they form only an insignifi-
cant part of creation. Besides the earth on which we
dwell, only seven of the bodies of the solar system are
plainly visible to the naked eye, whereas it is well jjpwni
that 8000 Stan or more can be seen on any clear ^^t
We now have to describe the visible universe in its hugest
extent, and in doing so shall, in imagination, step over
the bounds in which we have hitherto confined onnelvM
and fiy through the immensity of space.

The material univene, as revealed by modem telescopic
investigation, consists principally of shining bodies, many
milHona in number, a few of the nearest and brightest of
which ap« visible to the naked eye as stars. They extend
ontas&raathe moa*: powerful telescope can penetrate,
and no 4|w knows how much &rther. Our sun is simply
one of then stan, and does not, so far as we know, differ
from its f^rws in any esMiitial oharaeteristic. Frran ihe
most caraM estimates, it is rather less bri^t than the
avcfige «^|he nearer stars, and overpowen them by its
briOiaiMgr ^ty because it is so much nearer to us.
Tbe i^anoe of the stan from each other, and th««fore

412

A8TH0N0MT.

from the sun, is immenflely greater than any of the dis-
tiuicu8 which we have hitherto had to consider in the Bolar
system. Suppose, for instance, that a walker through
the celestial spaces could start out from the sun, taking steps
8000 miles long, or equal to the distance from Liverpool to
New York, and making 120 steps a minute. This speed
would carry him around the earth in about four seconds ;
he would walk from the sun to the earth in four hours, and
in five days he would reach the orbit of Neptiu,ne. Yet if
he should start for the nearest star, he would not reach it
in a hundred years. Long before he got there, the whole
orbit of N«]^iwMy supposing it a visible object, would
Ihiave been raduced to a point, and finally vanish from
sight altogether. In fact, the nearest known star is about
seven thousand times as f ar aa the planet NepUkM, If
we suppose the orbit of this planet to he represented by a
child's hoop, the nearest star would be three or four miles
away. We have no reason to suppose that oontignons
stMSl ire, on the average, nearer than this, ezoept in special
eMi|l^ where they are oolleoted together in olnsters.

9^ total number of the stars is estimated by millions,
and they are probably separated by theM wide intervals.
It loUowB that, in going from the sun to the nearest star,
;J|i» wonld be simply taking one step in the universe. The
most distant stars visible in great tdesoopes are probably
sevovl thousand times more distant than the nearest one,
and we do not know what may lie beyond.

The point we wish prindpdUy to impress on the foftder
in this connection is that, although the stan and plan^ px«-
sent to the naked eye so great a similarity in appearance,
there is the greatest possible divenity in their distances
and characters. The planets, though many millions of
miles away, are comparatively near as, and fcurm a little
family by themselves, which ii oalled the soihr lyatem.
The fixed stars are at distances inmm^parably yeatair the
nearest star, aa jnst stated, beii^ thoiuands of timaatnore
distant than the farthest phuiet The phmets we, ao far

i. ,, T l »i jl,HM-W l - ' J-! ^

,^,,u ii|i m

»!f HI**'. iflmsv ' S T -S ' ••

THE UNIVBR8K AT LA ROB.

118

than any of the du-

consider in the solar
i a walker through
1 the sun, taking steps
oe from Lirerpool to
ninnte. This speed

about four seconds ;
th in four hours, and
of Neptrune. Yet if
9 wonld not reach it
got there, the whole
sible objeet, wonld
finally vanish from

known star is about
lanet Neptune, If
be represented by a
) three or four miles
ose that contig^oos
ilia, exeept in special
■ in clusters,
imated by millions,
leMwide intervals.
I to the nearest star,
the universe^ The
oopes are probably
an the nearest (me,
>nd.

press on the iMder
twn and planets ]Hre-
rity in appeavaaoe,
'in tlmr distanoes

naany niilli<Hu of
, aad form a little
1 the solar lyatom.
nably |^«at«r-4he
mds of tiaMi titafe
pknelB aie, ao f«r

as we can see, worlds somewhat like this en which we live,
wliile the stars are suns, generally larger and brighter than
our own. Each star may, for aught we know, have plan-
ets revolving around it, but their distance is so immense
that the largest planets will reuuun invisible with the most
powerful telescopes man can ever hope to construct.

The clasrification of the heavenly bodies thus leads us to
this curious conclusion. Our sun is one of the family of
stars, the other members ol whidi stud the heavens at
night, or, in other words, the stars are suns like that which
makes the day. The planets, though they look like stars,
are not such, but bodies more l^e the earth on which

we live.

The great universe of stars, including the creation in its
largest extent, is called the ateUar «y«feti», or tieUa/r
uniiferte. We have first to oonnder how it looks to the
naked eye.

■^

CHAPTER I.

THE CONSTELLATIONS.

g 1. ammajLL asfbot of thb HBAnmi.

When we view the heavens with the unasHisted eye, the
Btara appear to be scattered nearly at random over Uie
fiurfaoe of tlie celestial vault. The only deviation from an
entirely random distribution which can be noticed is a cer-
tain grouping of the brighter ones into constellations.
We notice also that a few are comparatively much bri^ter
than the rest, and that there is every gradation of bril-
liancy, from that of the brightest to those which are barely
visible. We also notice at a glance that the fainter stars
outnumber the bright ones ; so tluit if we divide the stars
into classes according to their brilliancy, the fainter classes
will be far the more numerous.

Tlie total number one can see will depmd very lai^ly
upon the clearness of the atmosphere and the keenness of
the eye. From the most careful estimates whidi have
been made, it would appear that there are in the whole
celestial sphere about 6000 stars visible to an <M!dinarily
good eye. Of these, however, we can never see more than
a fraction at any one time, be<»U8e one half of the sphere is
always of necessity below the horizon. If we could see a
star in the horizon as well as in the zenith, one half of the
whole number, or 8000, would be visible on any dear night.
But stare near the horizon are seen through so grMt a
thickness of atmosphere as greatly to obscure their light ;
consequently only the brightest ones can there be seen. As

CLASaSa OF Hl'AHH.

415

lasHiBted eye, the
andoin over tlie
eviation from an
I noticed is a oer-
confltellations.
ly much bri^ter
nidation of bril-
which are barely
the fainter stars
\ divide the stars
he fainter ohuwes

end v«ry lai^ly
the keenness of
ites whidi have
LTB in the whole
to an <M!dinarily
rer see more than
f of the sphere is
f vre ooidd see a
I, one half of the
lanydearnight.
rough so gfMt a
sore their light;
lere be seen. As

a result of this obscuration, it is not likely that more than
2()00 Stan can ever be taken in at a single view by any
ordinary eye. About 2000 other stars are so near the
South Pole that they never rise in our latitudes. Hence
out of the 6000 supposed to be visible, only 4000 ever
come within the range of our vision, unless we make a
journey toward the equator.

The Oalazy.— Another feature of the heavens, which is
less striking than the stars, but has been noticed from
the earliest times, is the Oalmyy or MUky Way. This
object consists of a magnificent stream or Iielt of white
milky light 10* or 16" in breadth, extending obliquely
around the celestial sphere. During the spring mouths, it
nearly coincides with our horizon in tlie early evening,
but it can readily bo seen at all other times of the year
spanning the heavens like an arch. It is for a portion of
its length split longitudinally into two parts, which remain
separate throng many degrees, and are finally united
a^n. The student will obtain a better idea of it by
actual examination than from any description. He will
see that its irregularities of form and lustre are such that
in some phces it looks like a nuss of brilliant clouds. In
the aonthem hemisphere there are vacant spaces in it
which the navigates call coal-sacks. In one of these,
5° by 18% there is soaroely a sini^ star visible to the
naked eye (see Figs. 191 and 183).

Luold tad TslMNwpto Mum. — When we view the
heavflu with a teksoope, we find that there are innumer-
able Stan too small to be seen by the naked eye. We
may therefwe divide the stars, with respect to brightness,
into two great wlasswi.

Looid Man are those whidi are visible vithout a tele-
scope.

TMMOopio Sins are those which are not m visible.

When Gaulbo first directed his telescope to the heav-
ens, about the year 1610, he perceived that the Hil^
Way was composed of stars too faint to be individually

MHM

41(1

A8rnoNoMr.

■oon hy the unaidud oyv. We tliiM have the iiitoresting
fact that although tolowopic Htam cannot Ikj seen one by
one, yet in tho region of the Milky Way they are ho numor-
oua that they aliine in inaiiBOH like brilliant clouds. IIuy-
OHBMH in 1056 reaolvfxl a largo portion of the Galaxy into
■tars, and condndod that it was compofled entirely of thoni.
Kki'lkh congiderod it to bo a vast ring of Btars sarronnd-
ing the solar systeni, and remarked that the sun most bo
situated near the centre of the ring. Tliis view agrees
very well with the one now received, only that the stan
which form the Milky Way, instead of lying around the
solar system, are at a distance so vast as to elude all our
powers of calculation.

Such are iii brief tlie more salient phenomena which
are presented to an observer of the starry heavens. We
sliall now ooDisider how these phenomena have been olas-
sitied by an arrangemont of the stars aocording to their
brilliancy and their situation.

S a. KAOiriTUDiB or ths stabb.

In ancient times, the stan were arbitrarily oUssified into
six orders of magnitude. The fourteen brightest visible in
our latitude were derignated asof thetintnugnitude, while
those which were barely visible to the naked eye were said
to be of the sixth magrdtnde. This ohMofioation, it will
be noticed, is entirely arbitrary, since there are no two
stars which are absolutely of the same brOlianoy, while if
all the stars were arranged in the order of their aotnal
brilliancy, we should find a reguhr gradation from the
brightest to the faintest, no two being precisely the same.
Therefore the brightest star of any one magnitude is
about of the same brilliancy with the faintest one of the
next higher magnitude. It depends upon the judgment
of the olisenrer to what magnitude a given star shal) be
awigned I so that we cannot expect an agreement on ^is
point. The most recent and careful division into magni-

^^ j^fmrnmrnm

■i muw.Hiii|JLi..,a,wwiiiUjii,,,i!«

MAONlTUDKa OK tiTAna.

417

thu intorasting
Im) Buun Olio by
luy uru m iiniiior-
t oluiida. IIuY-
the Galaxy into
Diitiroly of tliuiii.
' atars Barrouiid-
ho 8nn raiut bo
riiis view agroea
ily that the itan
)ring around the

to elude all our

lenomena which
f heaveiu. We
have been olaa-
Bording to their

BTAB8.

ly obwrified into
^teat visible in
Mgnitnde, while
id eye were said
ifioation, it will
9re are no two
llianoy, while if
of their actual
ation fimn the
siaely the mmo.
le magnitude is
itest one of the
> the judgm«it
ren atar ahil} be
reement on ftia
ion into magni-

tiidua has been made by IIkis, of Qermany, whoso results
with respect to nninbers are as follows. Between tlie
North Pole and 86° south declination, there are :

H Stan of the first magnitude.

48 " «♦ second "
162 " " third •'
813 " '♦ fourth '♦
864 " " fifth
8974 " " aixth

6866 of the first six magnitudes.

Of these, however, nearly 2000 of the sixth magnitude
are so faint that they can be seen only by an eye of extra-
ordinary keenness.

In order to Moure a more acourate ol s is ifl catioB and exprewion of
brightneH, Han and others have divided each magnitude into
three orders or ■ub-magnitudes, making eighteen orders in all
visible to the naked eye. When a star was considered as falling be-
tween two BBagnitttdes, both flgnres were written, potting the mag-
nitude to which the star most nearly approaohed first For in-
stance, the faintest stars of the fourth magnitude were called 4-S.
The next order below this would be the bri^test of tiie fifth
msgnitude ; these were called 9 '4. The stars of the average fifth
magnitude were called 8 aimply. The fainter ones were caltod 5-6,
and lo on. Iliis notation is still used by some astronomers, but
those who aim at ar s at e r order and preewmi exurefs the magni-
tudes in tenths. For instance, the faintest stan of the fifth magni-
tude they would call 4*6, those one tenth fainter 4-7, and soon
until they reached the avaraaa of the fifth mamitode. which
would be i-O. The divkioa into tenths of msgaitodes is as mi-
nute a one as the ordinary eye is able to make.

This method of desigMting the brilliaaey of a star on a scale of
msonitudes Is not st aU accurate. Several attempts have been
maae in receot thaes to obtabi more aecuratc determinations, by
measuring the light of the stars. An instrument with which this
can be done is oalled a pht t omt t m-. The results obtsiiliBd with the
photometer have been used to correct the scale of magnitudes
and make it give a mwe aoenrate expression for the light of the
Stan. The. study of auch measures shows thst, for the most part,
the htighhi sss of the stan incnases in geometrical progressimi ss
the mapiihides vsiy in siiflimetioal pro(p«ssion. The stan of one
BMgnitade are geaierally about U t&nea as bti^t as those of the
magaitiide next Mow it. Therefore if wo take the light of a star

|J!!1L j' lyU. MWULj

418

ASTRONOMY.

of the sixth magnitude, which is just visible to the naked eye, as
unity, we shall nave the following scale :

Magnitude 6th, brightness 1
5th, " 24

4th, " 6i

8d, '* 16 nearly

2d, " 40

Ul»t " 100

4i
it

Therefore, according to these estimates, an average star of the
first magnitude is about 100 times as bright as one of the sixth.
There is, however, a deviation from this scale in the case of the
brighter magnitudes, an average star of the second magnitude
being perhaps three times as bright as one of the third, and most
of the stars of the first magnituck brij^ter than those of the second
in a yet larger ratio. Indeed, the first magnitude stars differ so
greatlv in brightness that we cannot say how bright a standard
star of that magnitude really is. Bbrwu, for instance, is probably
500 times as bright as a rixth magnitude star.

The logarithm of 2i being very nearly 0*40, we can readily find
how many stars of any one magnitude ara necMsary to make one of
the higher magnitude by multiplying the difference of the magni-
tude by 0*40, aira taking the numoer corresponding to this logarit£m.

This scale will enabu us to odculate in a rough way the mujni-
tude of the nnallest stars which can be seen with a telesco^ of given
aperture. The quantity of light which a telescope admits is diractly
as the aquare of its aperture. Hie amount of ught emitted by the
faintest star visible in it is therefore inversely as this Bquare. If we
increase the aperture 50 per cent, we increase the seeing power of
our telescope about one magnitude. More exactly, the r«uo of in-
crease of aperture is 4^ Si, or 1 -58. The pufrfl of the eye k probably
equivalent to a telescope of about |^ of an inch in aperture ; that
is, in a telescope of this size the faintest visible star would be about
of the sixth magnitude. To find the exact magnitude of the
faintest star visible with a larger teleaoi^e, we recall that the
quantity of light received by the objective is prf^portional to the
square of the aperture. As just shown, every time we multiply the
square of tiie aperture by %k, ot the apertare itself by the aouace
root of this quantity, we add one magnitude to tiie power of our
teleioope. Therefore, if we call a* tiie aperture of a telesoope
which would just show a star one magnitude brighter tiwn the
first (or tOMg. 0), the aperture neoenary to show aatar of magnltiide
m win be found by mltiplying a, by 1'58 m timec-^tiiai is, it wiU
be 1 .58* Ot. Bo, calling a this aperture, we have :

tf = !•»• «• = («• f 8.6".

Tsking the logariihma of botb sides of the eqnatlmi, ami aalnf ap-
proKimate nrand numbers whirb are exiiet saoiqjh for tUa purpose :

Iag.a=:mlog. 1-58 + log.a« = ^ log.SS -»■ log. a* » ^ + Iat'««-

mmmm.

i tfiiiw^i i i.w ' j-'

mmm

NAMBa OF THB BTAR8.

419

the naked eye, u

riy

rerage itarof the
one of the sixth,
n the case of the
lecond magnitude
third, and most
hoae of the second
ide Stan differ so
bright a standard
tanoe, is probably

can readily find
ry to make one of
Doe of the magni-
; to this logarithm,
fa way the uuwni-
kteleseopeofgnren
admits udiractly
ht emitted by the
'hisBQWue. If we
e seeing power of
y, the rano of in-
Oie eye is probably
in iqwrture; that
ar would be about
magnitude of the
re reeidl that the
r<<portional to the
w we multiply the
lelf by the
the power of our
re of a teloKope
brighter tium the
star of magnitude
la-tiiat is, it wiU

km, and usmg ap-
hw this purpeas :

Now. M Just found when m = 6. a = VVi = 6-4 millimetres.
With these values or a and m we find ;

log. a« = - 1 -800 in fractions of an laeh.

— — 0-887 in fraetions of a millimetre.
Hence, when the magnitude Is given, and we wish to find the aperture :

1<W- « = 5 - 1 -808 [will give aperture in inehes.]

log.a = ^' - 0-887 [will give aperture in millimetree.j

If the aperture is given, and we reqaira the limiting magnitude .

m = 8 loir, a -f 8-0 [if a is in inclies.]
m = 6 Ing. a + 80 [if a is in millimetim]

The magnitudea for diflbrent apertures is shown in the fdlowinv
table:

Apntara.

FMMfe.

Apeitare,

VUMIt.

*?©•

^-0

Inehw.
0-5

"^r

8-8

18-S

10-5

18-5

18-8

11-4

100

14-0

11-7

11-0

14-8

ISO

180

14-4

18-8

150

14-8

18-5

18-0

16-8

187

8«0

10- 1

18-8

84-0

16-6

8. THB oamna:iLA,Tzoini akd k

OF TBI

The earliest artronomfflv divided the 8tan into groups,
called constellatiiHw, and fj^ye apedai propor names both
to these groaps and to many of the more eonsi^ononB
stam. We hare no reo<nd of the prooen bj which this
was done, or of the eonsidarations which led to it It was
long befofe the oommenoement of history, as we maj in-
fer fivm dil^pent attiwons to the stan and oonstdlatiom
in the book of Jnhf which is supposed to be among the

420

A8TSON0MT.

must ancient writings now extant. We have evidence
that more than 3000 years before the commencement of
the Christian chronology the star SiritUf the brightest in
the heavens, was known to the Egyptians under the name
of Sothis. Arcturus is mentioned by Job himself. The
seven stars of the (Tr^jS^or, so conspicuous in our north-
ern sky, were known under that name to Homeb and He-
sioD, as well as the group of the Pleiades, or Seven Stars,
and the constellation of Orion. Indeed, it would seem
that all the earlier civilized nations, Egyptians, Ohinese,
Greeks, and Hindoos, had some arbitrary division of the
surface of the heavens into irregular, and often fontastic
shapes, which were distinguished by names.

In early times, the names of heroes and animals were
given to the constellations, and these designations have
come down to the present day. E!ach object was sup-
posed to be painted on the surface of the heavens, and the
stars were designated by their position upon some portion
of the object. The ancient and medieval astronomera
would speak of "the bright star in tlie left foot of
<?no»," "theeyeofthe^tiW," "theheartof theiVf*., '
" the head of P«r«cw»," etc. These figures are stiu'
tained upon some star-diarts, and are useful where >v>»
desired to compare the older descriptions of the constelUiP
tions with our modem maps. Otherwise they have ceased
to serve any purpose, and are not generally found on maps
designed for astronomical uses.

The Arabians, who used this clumsy way of d6a%nating
stars, gave special names to a large number of ^he brighter
ones. Some of these names are in oomm<m use at the
present time, as Aldebarant FomtMatU, etc. A few other
names of bri^t stars have come dovm from prduatoric
times, that of Ardurut for instance : they are, 1m>w-
evw, gradually falling out of use, a system ot ntnaaenela-
ture introdnoed in m^em times having been subttitntid.

la 16M, Batsb, of Germany, nuq>p^ d<yim the ooivtd-
lKti(»B upon charts, dengnating tiMft brin^ter stem of «ii^

i>aSai!iM t lMfciJi.Mftl.miKMWftl8 l i^^

NAMINO THB 8TAR8.

421

have evidence
mencement of
e brightest in
nder the name
himself. The
B in our north-
OMEB and He-
>r Seven Stars,
it would seem
tians, Ohinese,
livision of the
often fantastic

animals were
agnations have
bjeot was snp-
Bavens, and the
a some portion
'al astronomers
B left foot of
tof ihe7w» '
KB are stii
ful whore
)f the constelia-
ley have ceased

ound on maps

of defdgnating
of ^he brighter
Hon uae «t the
AfewoUier
'om preluatoric
are, how-
nmneaelfr-
na subtdtnted.
wntheooQitil-
Nr iteii of ««dk

hey
of

constellation by the letters of the Greek alphabet. When
this alphabet was exhausted, he introduced the letters of
the Boman alphabet. In general, the brightest star was
designated by the first letter of the alphabet or, the next
by the following letter /), etc. Although this is sometimes
supposed to have been his rule, the Greek letter affords
only an imperfect clue to the average magnitude of a star.
In a great many of the constellations there are deviations
from the order, the brightest star being /3 ; but where stars
differ by an entire magnitude or more, the fainter ones
nearly dways follow the brighter ones in alphabetical order.

On this system, a star is designated by a certain Greek
letter, followed by the genitive of the I^tin name of the
constellation to which it belongs. For example, a Cania
Moforis, or, in English, a of the Great Dog, is the desig-
nation of SHritu, the brightest star in the heavens. The
seven stars of the OretU ^dor are called a Urace Mc^oru,
P UrtOB Jfyoritj etc Areturtu is a BooHb. The
reader will here see a resemblance to our way of designat-
ing individuals by a Christian name followed by the fi^nily
name. The Greek letters furnish tiie Christian names of
the aqpante stars, while the name of the constellation is
that of the family. As there are only fifty letters in the
two alphabets used by Batkb, it will be seen that only the
fifty bri|^test stars in each constellation could be desig-
nated by tins meihod. In most of the constellations the
number thus ohoseiik is much less than fifty.

When by the t&A of the telescope many more Btan than
these wera< laid down, some other mediod of denoting
ihran became neeesMury. Fi.Ai(8nncD, who obaerved be-
fore uA after 1700, prepared an extensive catalogiu of
Stan, in which those of eiioh constellation wererdesignated
by nnmben in the order of right ascension. These nam-
ben wow entirely independent of the designations of
BAHn fliat is, he did not omit the Batbb stan from
his fyitem of nunben, but numbered them aa if they had
no Gndc letter. Henoe those stan to w)uch Batkr ap-

4S»

ABTBONOMT.

plied letton have two designatioiu, the letter and the
number.

Fi.AiifmtBD*B nnmbera do not go much above 100 for
any one constellation — Taurut, the riehest, haying 189.
When we consider the q^ore nomerons minute stara, no
systematic method of naming tliem is possible. The star
can be designated only by its position in the heavens, or
the number which it bears in some well-known catalogue.

f, 4. DMOBIFFIOir OV THE OQNmOAATIONS.

The aspect of the starry heavens is so pleasing that
nearly every intdligent person desires to possess some
knowledge of the names "and forms of the principal ooa-
steUations. We therefore present a brief description of
the more striking ones, illustrated by figures, so that the
reador may be Me to recognise them when he sees them
<Hi a dear nigbt.

We h^n with the oonsteUations near the pole, beoanw
they ean be sem <m'hny dear ni^t, while the sonttiena
ones can, for tSie most part, G6lj be seen during onrtain
seasons, or at oertun hours of the ni|^i TheaoewnMnj-
ing %iire shows all the stars within 60* of the pole fliP^i
iff tibe fourth magnitude indnaive. The Bopun wmf9nik
aniBBd the maigin show the meridiana of r^t ■winiaion,
one for tivwy hour. In order |q lusn 1^ -mi^ j w pre s ini t
the northern opnsteUatiens ezad<l(f 99 ^ajr axe^ H inaat be
held so that the hour of sideraal tbne alwjiidh lliftobaerrar
is looking at the heavens dudl be at tliNiv|k)p of the map.
Sui^o^ng the observer to look i^.nfaM 0-dook in the even-
ing, the months around the maigin of the map diow the
regions near the senith. He has therefore onty to hold the
map with the mtmth upward and ftoe the nearth, when he
will have the n<Mihem heavens as they afpuint taaeftk
that ib» stars near the bottmn of the map ^^ be ent oHf
by thehoriaon.

The first oonsteUation to be looirad for la Vtm Jfi|^,

ww^wpiiwwiiaawKww Lj.uiJuk ' wwi^^ .,

etter and the

bove 100 for
;, liaYing 139.
inute Stan, no
>le. The star
le heavens, or
>wn catalogue.

ItULTIOmi.

pleasing that
poMCM some
prinoipal ooa-
desoription of
9S, BO that the
a he sees them

I pole,

the aouthieni
during oMrtain
lieaooomMiijr.
the pole f||Mni

k^i

m^ftiVtiirt be
&tll»obMnper
ip of the map.
lokintheeviNi-
miip diow the
ntytoholdtiw
lai^, when he

itffl he enl etf

I VnaMifforf

TBB CONSTtCLLAl'lONa.

433

the Great Bear, familiarly known as " the Dipper " The
two extreme stan. in this constellation point toward the
poJe-3tar as already exphuned in the opening chapter.

Ur»a Minor, sometimes caUed « the LitUe Dipper," is
the oonsteUation to which the pole-star belongs. About

itt—juf «v tarn

wnaaajntutm.

Ifi ftom the pole, in fi|^t aaeenskm XV. hoon, is a star

{* ^• F'W ■ *» ' A ottrved row of three small stan lies
befcWt^B ^#iM t«o bri^t ones, and fonns the hwdle of

ABTRONOMT.

Cassiopeia, or " the Lady in the Chair," is near hour I
of right aBcension, on the opposite side of the pole-star
from Ursa Mtyor, and at nearly the same distance.
The six brighter stars are supposed to bear a rude resem-
blance to a chair. In mythology, Cassiopeia was the qneen
of CepheuSy and in the mythological representation of the
constellation she is seated in tlie chair from which she is
issuing her edicts.

In hour III of right ascension is situated the constelU-
tion Perseus, about 10° further from the pol« than Cas-
siopeia. The Milky Way passes through these two con-
stcjktbns.

JDraoOf the Dragon, is formed prindpalhr of a bng
mw of Stan lying between Ursa Mt^or and Ursa Minor.
The head of the monster is formed of the nOTt hemm oat
three of four bright stars arranged at the ocwiiers o£ a
loeenge between XYII and XYIIIhous of xi^ aseen-

Ctg^lmts k on die oppocite side U Oasnegma fnm
Fmmm, ^yb^ ia tke Mttky Way, about XXH honra of
i^^Wlwioii Ukaiyl a brilliant consteUation.

^ttur OMMtoHatfoBi vm the pole ant Oamehg^f^tilu,
i^mg, and Laeerta \fS^ Liaard), bat they oonlaiii only

01 daittiiilttgilM MBdMm eoMte l hi fc ioiia, ira itaU Idee
liMfW^im^lpB^^ atartj ai^MW cmjionding

raapeo^^. to VX kdwa, ZU hmms XVIXl hours,
and h«iin el iMacMl time or figil mmkm Theae
hours of ooniM OQoiir.fiiiiy da^, tnift not always aft con-
venient times, teeanai liiey wj with the tune of the
year, as explained in Chapter I., Part I.

We shall first suppose the obeerrer to yie# the heavens
at YI honrs of sidereal time, which occurs on. Decem-
ber aist about midnight, January 1st about 11.80 r.M.,
February Ist about 9.80 p.h., Haroh Ist about 7.80
P.M., and so on through the year, two hours earBer eveiy
month. In this position of the sphere, the Millcy Way

p m4ii i . i Mi!Miiw!ife..ii,w ! iiyiitL . MM. .u..K.iimm.\mm>i

ig near hoar I
the pole-star
ime liifltanoe.
mde reflem-
was the qneen
sntation of the
u which she is

the coiistelhi-
wle thaa Cas-
(hflie twocon-

aW of a long
1 UrM Mmor.
\ northummoBt
) oomars o£ a

f Xi|^ UKKOk-

XXUhoum of
aUation.

y oooy&<»l7

mmfbiUtake
mding

XVIE hoow,
These

THE CONBTKLLATWNB.

425

ajtwaya at oon-
le time of tiie

ci# the heavens
lira on. Decein-

Qt 11.80 P.M.,

Ut about 7.30
m eurlier every
beMUkyWay

spans the heavens like an arch, renting on the horizon be-
tween north and north-west on one side, and between
south and south-east on the other. We shall first describe
the constellations which lie in its course, beginning at the
north. C«pheu9 is near the north-west horizon, and above
it is CoMtopeia, distinctly visible at an altitude nearly
equal to that of the pole. Next is Peraetts, just north-
west of Hkb stnitb. Above Pene/ut lies ^iirt^a, the
Chsriotetfi^ whidi mqr be reeagniaed by a brif^t star of
the first mguitade called OoipSlla (the G<Mt), now quite
>" - the mnttli. Amiga b represented as holding a
^^, > his arms, la the be '. ' which the star is situated.
Abi>u. 10" CMt of <Ay«^ IS tlw star ^ A^tifim of the
second insgnitnde.

Going firihsr south, tiie Mitty Way next passes between
Tamrug tilA 0«mM»

Tawmt th* Bun, magr 1» rsoegnked hf Ihb Pleiades,
or " Sev«i» 6t««*" Bwlfy than avs only sk slws in the

group cimi^'dAis m-mit'

nary eyes^ iN#ia|r iy»4ln^
enough tf ^tiiil; «II|(M|n

ably see 't^fmmf^mm

in all. lib mm0'"§atm Ml
interestiq|r «|^e9l «f iHt&a^
with a miiBtwiiiiiniiii mibtty
oreigh<y#iii<ipi|fe
be seen. ':':W^^^0lltlkillM^ finp'
sent a trilii»iii^'#i^ slit|j^
the six hiiq[|i«lMi itfa« «hati
visible to any indinary ey«|
the five next in size tbose
whieh caa be seen by a re>
nuurlably good eyoy sad the
others ttioee wHoh reqidre a telescope. East of the Pleia-
des is UmT br^^ red star Aldebarany or " the Eye of
thia BnB.*' It'Hes in a group called ihe ffyadee, ar-
rtaigeA ia the f<Mmi of the letter Y, and forming the face

Via. I'lli ""'I'BbModVK vnw ov
tarn FMUPM.

42U

ASTBONOMr.

of the Bull. In the middle of one of the legs of the V
will be seen a beautiful {tair of stan of the fourth magni-
tude very close together. They are called Tauri.

Geminiy tlie Twins, lie eaat of tlie Milky Way, and
may be recogniied by the bright stara Ctutor and PoUvaSf
which lie 90° or SO** aonth-eaat or south of the senith.

They are about 5** apart, and PoUum, the sonthemmfwl
one, ig a little brighter than Oattor.

Orum^ the moet brilliant eorateHation in the heavens,
is very near the meridian, lying sonth-east of Tamtu and
souih-weet of Oemmi. It may be readily ieo(^;niaed by
the figure iHiicli we give. Four of its bright akan fonn

wmm

wimmmmmmm^'mmmiim

legs of the V
fonrth magni-
9 Tauri.
Iky Way, and
tr and PoUwDf
of the zenith.

D ionihenmuiil

n the heavens

of Tannnf and

reoogniaed by

akan form

TUK VONaTKLLATlONO.

a rectangle about 15° long from north
° wide. In tliu middle of it is a row of

tlio comerH of

to south, and h'' wmo. in uiu miuaie oi ii la a
three bright stara of the second magnitude, whicJi no one
can fail to recognize. Below this is another row of three
smaller ones. The middle star of this last row is called
t) OrioniSf and is situated in the midst of the great nebula
of Orion, one of the most remarkable telescopic objects in
the heavens. Indeed, to the naked eye tliis star has a
nebulous hazy appearance. The two stars of tlie first
magnitude are a Orionu, or Betdgftete, which is the high-
est, and may be recognized by its red color, and Jiiyd,
or fi Ortonit, a sparkling white star lower down and a
little to the west. The former is in the shoulder of the
figure, the latter in the foot. A little north-west of
JtetelgtMm 9X4 Haee (mMll itan, whioii form llie head.
The row of atam on the WMt lonu his una toad elub, the
latter beiagniiedl •§ if t» iM&e at. Tamm, ifae Bull, on
the west.

Cants m^r, tlw UMb' BOf, Mm «araM the Milky
Way {mm Onm^ $aA tm^ be HBQjpliiiil bgr ^ bright
star Prttmm ni- lk» im/k lUgilriMK. Tk» Hfee stars
PoUwe, frm ffm,mi JBkifii$ \ tm mim • rigbt Wgled tri-
angle, th» fldit aa|^ bifa« it Phv^m .

CanUm^^mOmlJi^lkf^flVfm'mlk^ Orion,
and is easily raeoipiiaed bj 8irw9, Uie brightest fixed star
in the heevens. A number ef bl^t stars south and
south-east ef JSirim bdoag to this oonsteUati(Hi, making
it one of gnat htSXmuBj.

Argo Namt the ship Argo, Ifisneer the south horizon,
partly above it and partly bebw it. Its brightest star is
Camopm, which, next to l^riva, is the bri^test star in
the heavens. Being in 68** of south dedinttdon-, it never
rises to an observer within 58** of the North Pole— that is,
north of 87** of north latitude. In our country it is visi-
ble only in the Southern States, and even there only
between six and seven hours of sidereal time.

We next trsoe out the zodiacal ecmstelktions, which are

«lB>K»^Jf L U IJW ' WW i I

4^8

ASTBONOMY.

Of interoBt hocaiwo it is through thorn that the gnn ««««,
in Its apparent annual cou«e. We shall commence in
the west and go toward the east, in the order of riirht
ascension. ®

Ariety the Ram, is in the west, about one tliird of the
way from the horizon to the zenith. It may be leoognized
by three stars of the second, tliird, and fonrthmairni-
tudes rosiwtively, forming an obtuse-angled triable.
The brightest star is the highest. Next toward thTLt
IS Tm*rm, the BuU, which brings us nearly to the meri-
dian, and east of tlie meridian lies Gemini, the Twins, both
of which oonstelktions have just been described

-ra« wanaujMom uo, thb lk».

K- P ^^'^ '"^^"o'^^orthy object in this constel-

Leo, tiie Lion, Ig from one to two hoan above the
««temhonzon. Ite brightest star is i?i,^,1^rtWrf
of the way from the eastern horizon to Xlenith, wd

BtaiB north of It m a curved line are in the^ form of a

THK VONSTKLnATJONft.

4iQ

3in tliat the snn pames
Vo sliall ooininenoe in
, in the order of right

abont one tliird of the
. It may be reoognized
rd, and fourth inagni-
>btu0e-angled triangle.
Next toward the east
OS nearly to the ineri-
emini, the Twins, both
len deaeribed.

Lao, TBI uov.

nini, but oontainR no
object in this conatel-
}pio Stan, which ap-
inilky light. To we
the moon not in the

wo hours above the
is Btgul/M^ one third
to the zenith, and
titudes. Five or six
in the^ form of a

Hu^klo, of which lieg^du* ia the handle. As the Liun w»m
(Iniwn among thu old uonHtolliitionH, HeanluH forinud hiH
liuart, and wae thoroforu callud (hr Leon'm. Thu Mukle
fonna Im head, and his body and tail extend toward the
horizon. The tail ends nonr the atur Detiebda, which is
quite near the horizon.

Leo Minor lies in the north of Leo, and Sewtaiu, the
Sextant, sontli of it, but neither contains any bright stars.

J^ridantts, the Itivcr Po, south-west of Orion ; Lqms^
the Hare, south of Orion and west of OantM M<yor ;
Oflumba, the Dove, south of Leptts, are constellations in
the south and south-west, which, however, have no strik-
ing features.

The conacelUtions we }iave described are those seen at
fiix hours of sidereal time. If the sky is observed at some
other hour near this, we may find the sidereal time by the
rule given in Chapter I., g S, p. 80, Mid allow for the di-
urnal motion during thd interval.

AppoMMiiM Of Mm OooateUaMima, st IS Houk) Sidereal
Time.— This hour oocura on April 1st at 11.80 p.m., on
May 1st at 9.80 r.M., aud on Juno lat at 7.80 p.m.

At this hour, dm Mqfor is near the senith, and Oaui-
irpeia near or bebw the north hinteoB. mutWfkj Way
is too near the horiz<m to be visMs. g a ab u lis ia* in
the west, and there is no very oonapionons oo n i feHatto i i
in the south. CaOor and Polhm are high np fai Hie
north-west, and Prooyon is abcmt aa howr and a. liilf
above the horizon, a little to the aowft of went AO Ae
oonsteUations in the west and nortb-w«at have Imb pnnri-
ously described, Leo being a little west of the merUfan.
Three zodiacal constellations have, however, risen, wliich
we shall describe.

Virgo, the Virgin, has a single bright star, Spica,
about as bright as Regvihu, now about one hour east of
the mwidian, and but little more than half way from the
zenith to the horizon.

labrOf the Balance, is south-east from Virgo, but lias
no oonsjncuons stars.

480

AHTRONOMY.

SoftrpitM, tlio Scorpion, m just rirting in tho Houtti-eMt,
Init iH not yet high un«»ngh to Ih) well ttuun.

Jlydrti \» II vury long conHtelUtion oxtunilitig from
Cvuiit Minor in a 8outh-ua«t diroction to the Bonth liori-
son. Itg brightost star is a Jlydra, of tliu aeoond magni-
tude, 85° bolow lieffulua.

Corvus, tho Grow, in Ronth of Virffo, and may l>o ruc^ig-
nisod by four or five stans of tho Bocond or third magni-
tude, 15° Bouth-west from «^p«a.

Next, looking north of the zodiacal oonfltollations, we
see :

Coma Berenices, the Hair of Berenice, now exactly on
tho meridian, and about 10° south of tho zenith. It is a
dose irregular cluster of very small stars, unlike any thing
elflo in the heavens. In ancient mythology, Berenice had
vowod hor hair to Venus, but Jupiter carried it away from
the temple in which it was deposited, and made it into a
constellation.

Bootes, the Bear-Keeper, is a laage constellation east of
Coma BeremoM. It is marked by Arcturuty a bright but
somewhat red star of the first magnitude, about 20° east

of the zenith. Bootes is repre-
sented as holding two dogs in a
leiiflh. These dogs are called
Canes VenaUei, and are at the
time supposed exactly in onr ze-
nith chasing Ursa Mt^or around
the pole.

Corona Borealis, the North-.

em Crown, lies next' east of

Bootes in the north-east It is

"^' a bmall but extremely beantiftil

constellation. Its principal stars are arranged in the form

of a semicircular chaplot or crown.

Appaannoe of the OonateUationa at 18 Howni of 8ida-
roal Time. — This hour occurs on July 1st at 11.80 p.m.,
on August Ist at 0.30 p.m., and on September Ist at 7.80

P.M.

FH. IM.— ooKniA.

77/ A' rONSTKLLATlONff.

481

tllO HOUth-OMt,

xtuiuling from
bhe Bunth hori-
J aeound inagnt-

d may »>o rowig-
ir third magni-

oiwtellations, we

, now exactly on
I zenith. It is a
unliko any thing
;y, Berenice had
ried it away from
d made it into a

natellation east of
mu, a bright bat
I, about 30° eaat

Boottt ia repre-
ig two doga in a

dogs are called
I, and are at the
Bxactly in oar ae-
I'M Mt^or aroand

00^, the North-
68 next' east of
north-east It is
tremely beantifal
mged in the form

.8 Hows of Bi'ds-
Bt at 11.80 p.ii.,
temberlstatT.SO

Tn tills position, tlio Milky Way hchmiih oih-o moru to
H|MUi tlio lii'HVuiiH liico nil nn^h, reHtiii^ mi tlio liori/.oii in
tliu north-woHt and Huiitli-voHt. lint wu do not suo tlio
same parts of it which were viHihIe in the first position at
rIx hours of right aenonsion. (Aumopeia is now in the
north-east and (/rta Majw has passed orer to the
west.

Arcturut is two or throe honrs above the western hori*
7!on. We shall commence, as in the flist position of tlie
H[)here, by describing tho constellations which lie along on
tlio Milky Way, starting from Casaiopeia. Above Cam'
npeia we have GepAeut, and then Zaotrta, neither of
which contains any striking stars.

Ojfgnwtf the Bwan, may be recognised by limr or five
Htara forming a cross direotl; in the centre of Jie Milky
Way, and a sliort distance north-east frrtni the zenith.
The brightest of these stars, a OygrU, forms the northern
end of the cross, and is nearly of tiie first inagnitnde.

Lyra, the Harp, is a beantifal const -/.Ation sr. th-wwit
of Oygimt, and nearly in the zenidi. It oor 'ns the
brilliant star Vega, or «
Jjjfntf 9m. nw 9nl mi|
nIttkK and of i \kMt
wMto eokr. Soalli oC>
Fsfi «•' fmu Mm d\
th* JmoA HMgnM
fMnlly Ml flUiqaB pii»i ^
aUalogHm,1ignAfek1te^

iMk 117.— I.TBA, nofkiAi

%■,

iMil

star ol the pAniltelognuny is « Lyrm, a very interesting
object, beoaase it is really oompoeed of two stars of the
fonrth nugnitade, whica ■%:: be seen separately by a very
keen eye. The power u« ;> u this star doable is one of the
best tests of the acnteness of one's vision (see Fig. 122).

fW.tltH<,W} l»^W

I-

4.32

A8TRONOMT.

ftB. 116.— A^riLA, inn.pin

K us, AMD flASITTA.

AquUa, the Eagle, is the next striking constellation in
the Milky Way. It is two hours east of the meridian,

and about midway between the
zenith and horizon. It is readily
recognized by the bright star
AUair or a AguUa, situated be-
tween two smaller ones, the one
of the third and the other of the
fourth magnitude. The row of
three stars lies in the centre of
the Milky Way.

SagiUa, the Arrow, is a very
small constellation, formed of
three stars inamediately north of
AquUa.
Ddphimuj the Dolphin, is a
striking little constellation north-east of AquUa^ neog-
nized by four stars in the form of a lozenge. It is famil-
iarly called " Job's Coffin."

In this position of the oelestial sphere three new sodia>
n\ constellations have arisen.
;#)i«yMM, the 6eofpkmt

M iboti 80** abovw Hki
i0»m, b ^(oito a hmM

itfim, ot m Soor^t % ied>
^:i i a r fl< aevlj tlw ftml
WMJlitft ii H and « imig VMrj
of eitrved stars west of it.

Sagittarius, the Archer,
comprises a large collection
of second magnitude stars in
and near the Milky Way,
and now very near the meridian,
form the arrow of the archer.

119.-HK)oiiniii, tm KOR-
?io».

The weiternmoflt stars

king constellation in
8t of the meridian,
lidway between the
>rizon. It is readily
by the bright star
AquUcB, situated be-
naller ones, the one
md the other of the
itnde. The row of
ies in the centre of
ay.

le Arrow, is a very
illation, formed of
imiediately north of

, the Dolphin, is a
1 of AgiMa, recog-
Msenge. It is famiU

)re three new aodia-

-HMxmpnm. tmm secNt-
?ioir.

w weiternmoBt stara

THB 00N8TBLIATI0N8.

488

Caprioomm, the Goat, >8 now in the south-east, but
contains no bright stars. Aquarivs, the Water-bearer,
which has just rken, and Pmom, the Fishes, which have
partly risen, contain no striking objects.

Ophiuchm, the Serpent-beurer, is a very huge constel-
lation north of Scorpitu and west of the Milky Way.
Ophiuchvs holds in his hands nn immense serpent, lying
with its tail in an opening of the Milky Way, south-west
of Agnila, while its head and body are formed of a ^1-
lection of stara of the third and fourth magnitudes, at-
tending north of Soorphu nearly to Sootet.

IfereuletiBtLyery
large constellation
between Co rona
Jiorealis and Z^r<(.
It is now in the
zenith, but contains
no bright staiB. It
has, however, a
number of interest-
ing telescopic o^
^»6ta, among tha^
the great ehiter of,

^*> *a£^ ^'^'*— w

tntlmoitooai^cfiiiiaMofBtan. The head of 2?^vw»,
afaviu^ dtittlbed, il jolt iioitii o

OmlMlitlttlli rum* •» O Hmm of BMmpmI nua. —
This tine wffl octenr oti October 1st at 11.80 p.m., on
Ifxiifimhur 1st «t 9.80 r.it, on December 1st at 7.80 km.,
aid oil Stftixmtym at 6.80 p.m.

In this position, fheMilky Way appears resting in the
east and west horisons, but in the cenith it is incHned
over tpwud the north. All the opnsteUations, either in
or north of its ootnae, are among those already described.
We shaU therefora oondder only those in the south.

I !. * umi'imiu

434

A8TR0NOMY.

Pegtuut, the Flying Hone, is distingnished by four
Btan of the second magnitude, which form a large square
about 16° on each aide, called the square of Pegemu. The
eastern side of this square is almost exactly on the meri-
dian.

Andromeda is distinguished by a row of three or four
bright stare, extending from the north-east corner of
Pegcufusy in the direction of Peraem.

CeiuSf the Whale, is a large constellation in the south
and south-east. Its brightest star is fi Cetiy standing
alone, 80** above the horizon, and a little east of the
meridian.

Pmcm Auttrality the Southern Fish, lies further west
than CMwr. It has the brin^t star FomalhanUy about
16" aboTe the horison, and an hour west of the meridian.

IB. VUMBntnrOAVDOATAZiOOIIIirOTHB STABS.

As teleaoqnc power is increased, we still find stars of
lunter and fainter Ught. But the number cannot go on
ineNMring forever in tfie same ratio as with the brighter
nuf^i^iidaa, beeaoae, if it did, tiie whole sky would be a
blaM of itariiglit.

If lel«no|MS with poipm far eoEfleeding ow preaent ones
wera made, they would no doubt show new stan of the
90ih and Sltt magnitndea. But it is highly pfobaUe thai
the iMMNJtfr of mxii aaooeinve order* of atan wonld not
increaie in the same ratio as is observed m the 8th, Mi,
and 10th magnitudes, fw example. The eneaBoaa labor
of eatimatmg the number of itan of ao^ elMMas will loi^
prevent the aoenmnlalMMi of atatbtioi <m tibia qneitiim ;
but thiamueh is oertain, that in i^eoial r^gioM of tko ihy;
which have been seawhingly examined by vaifaMa tele-
aoopea of anoeeaaively inemaaing lyartiina, the nnn^ar of
new stars found is by no meao* in propMiioii to Hbm
ineraaaed inatmmental power. Tkm, in ^ eaitnl por-
tions of the nebula of Qritny oaSkj aome half dc n m sla«

MB!sei!KH»4#!>.yA- :ism"

nished by four
a large square
PegatfM. The
r on the meri-

three or four
sast corner of

n in the sonth

CeUf Btanding

■\e east of the

as fortiherwest
nalhmU, about
t the meridian.

}THS8TAB8.

lill find stars of
it cannot go on
ith the brighter
sky wOTild be a

Mur present ones
«w Stan of the
ly prdbdde tiiaft
■tanwoidd not
in the 8th, 9tfa,
•noRMNU labor
elMMawmkng
k tins qiMitioa;

{iaiMoltt»iky«
by TaikiM tfle*

lytheiiiiB^at
opMrtJon to ikm
tiw oastml por-
halldoMi

CATALOQUmO THE STABS.

486

have been found with the Washington 26-inch refractor
which were not seen with the Cambridge 15-inch,
although the visible magnitude has been extended from
16" • 1 to IB" -3. If this is found to be true elsewhere, the
conclusion may be that, after all, the stellar system can be
experimentally shown to be of finite extent, and to contain
only a finite number of stars.

We hare alraady stated that in the whole sky an eye of aTerage
power will aee about 6000 stars. With a telescope this numberia
greatly increased, and the most powerful telescopes of modem times
will {wobably show more than 80,000,000 staiB. As no trustworthy
estimate has ever been made , there is great uncertainty upon this
point, and tiie actual number may range anywhere Mtween
1S,000,000 and 40,000,000. Of this numbeB, not one out of twenty
has ever been eatuogoed at alL

The gradual increase in the number of stars laid down in Tarious
of the older citaloguea is exhiUted in the following table fhun
CHAianas's Bmer^^tiM AMronomf :

OoMmUtA-
noK.

Ptotaur.
b.o.m6l

Tyeho

Bnhe.

A.D.lBni.

. HeTCliaa.
AJkUSO.

FiMMtaed.
A.O. law.

Bode.
A.D. 1800.

Aries

Una lii^r..
Bofltes... . .

Leo

Vlrga......

Tanms

Orion.

18
85
88
85
88
44
88

81
56
88
40
88
48
68

78
58
60
80
51
88

> 80

110
141

148
888

818

8»«

804

The most fanooa and extrndve aeriea of star obsenrations are
noticed bdov.

The aaaBOBMtrks of Batkb, FLAnraDi, AaaBi.An>n, Hlns, and
Qoou»|^etlM lodd stars of oaeorbotii hoiynhafw IsMdowa
OBmi^ 1Wanjqvl»ntedbf th« star ot^alagoM of other
observwi,^wildiacniitnBnbwhMbeeapBUished. TliMalait
were undstlalani Budafy for tiM dateradnattcm of alar piMilioBa btit
tiMjr unrifar^va is an aoalllaigr datna Hu mageitaat of tke star
obaawsd. Whm tiiqr v mnkA so fv as to corer the hMvaaa,
they will aflofd nlaaUa data as to the dislribatkm of ttUm

The

- . .„ of stars nt coMUiltisd ia ttM

in mrMekm O m Hmtm amm i lt, tha jsls* irwfc

mA hh ■■islM l s, mammm mt Baritafmo. It

tfcasfaai tha lut ai— mMMitadsa iftw th» North

iei*w>e«M>;if«(ri:

sum

486

ABTBONOMT.

Pole to 8* of MNith decliDstion. This work wm tiegun in 18S9, and
At its completion a cstalogue of tlie approximate places of no lesB
than 814,926 stars, with a series of sUr-maps, giving the aspect of
the northern heavens for 1855, was published for the use of astrono-
mers. Aboblamdbh's ori^nal plan was to carry this DurekmuOerunif
as far as 28" south, so that every star visible in a small comet-seeker
of Sf inches aperture should be registered. His ori^nal plan was
abandoned, but his former assistant and present successor at the
observatory of Bonn, Dr. BoBdMraLD, is now engaged in executing
this important work. .... . , . .. . ,

The Catalogue of Stars of the British Association for the Ad-
vancement of Science contains 8877 stars in both hemispheres, and
gives all the stars visible to the eve. It is well adapted to
team the unequal distribution of the ludd stars over the celestial
sphere. The Uble on the opposite page is formed from its data.

From this table it follows that the southern sky has many more
Stan of the flnt seven magnitudes than the northern, and that the
lones immediately north and south of the Equator, although greater
in surface than any others of the same width in declination, are
absolutely poorer in such stars.

Tlie meaning of the table will be much better understood by con-
suiting the graphical representation of it on page 488, by PiiooTon.
On tSs chart are laid down all the stars of the British Association
Catalogue (a dot for each star), and beside these the Milky Way is
represented. The relative richness of the various sones can be at
once seen, and perhaps the scale of the map will allow the student
to trace also the zone of brighter stars (lst-8d magnitude), which is
inclined to that of the Milky Way by a few degrees, and is approx-
imately a great circle of the sphere. ^

The distoibntion and number of the brishter ntars (1st- 7th mag-
nitude) can be well understood from this cbart.

In Aboblaiidbb'b Durekm«$t«rHnf of the stars of the northern
heavens, there are recorded as belonging to the northern hemi-
sphere :

10 stem between the 1 magnitude and the 1 -9 Dugnltode.

t«

9^0

•1

198

««

810

«<

i.oie

««

<«

-888

•(

■I

18.808

«■

<•

67,900

•4

987.544

l«

•«

9-6

In all 814,996 stars from the ilrst to the 9-6 oMgnitodea ara «m»-
merated in the aorthmn sky, so that tlMN are aboot 600^000 in tfie
whole heavena.

We nay nadUy compute the aaoank of Ii|^t raerived by tba
evthoB* dear but aMMiileasnli^tftomaMaeetei. U^vmwmamt

mmsimtrnfii^mi^immsii^imi'

I begun in 18S8, and
ate places of no lesa
^▼ing the iwpect of
tr the nae of astrono-
this DurehmuUemng
i small comet-seeker
[g original plan was
int successor at the
Dgaged in executing

KMsiation for the Ad-
ith hemispheres, and
is well adapted to
trs over the celestial
oed from its data.
I sky has many more
rthem, and that the
or, although greater
li in declination, are

r understood by con-
ge 488, by Pbootor.
B British Association
)se the Milky Way is
nous zones can be at
rill allow the student
magnitude), which is
greea, and is approx-

r i«t«rs (Ist-Ttti mag-

ian of the northern
) the northern hemi-

thel-OmagnUode.

8»

9-9

<■

5««

«l

«•

7-9

8-9

9-5

•«

I awgaitodM am wn»
BtlMiat 600^000 in the

Ol^t rsedved hf tlia
>etan. LetustMinM

» 1^

<»

DiaTRIBUTlOJr OF STARS.

Il9 M ^^ N^ ^ H* h^ HA ^A M t^ ^ ^

iliittittttnitiitnil

437

at «o oe 1^ ee «» ee 4) i-i iK A iK ee M iK CN fl» M ei 00 -4 A S^ !^

K to *t ^ ***'-*>*' *^ I-* *!*<•* h' Ca I-* >-' 1^ I-* I-* k^ tS k'

+ +

?^5

+ +

£ssit'ji$sis{s^sesss;:s!Ss^ss!Sisss^s

SSiSSS3SSS£3£S8S;:iSS!SSSSI!S£38g^S§

+ +

SS«;$igg{SIS£SSS33£l^;§^3SS3:3SS;j£S

^SSg£SS::;!SS££S!gSSS:82i$SSi£;SI§^JSi

+ +

!i:S8S6£S!SSS!£:S£$^^S^SS6£Srg

«5ssssssss^s;r,tiS£s:sitsS£tg!^{3SS=

.'»+
«<"?

i'i

:33S£S£;SStSlgSS3SS!^tt@S

S66S8SSSSt8SSS888SSS;SSSSISSSS

^'4

• 1 —

4DOOkaki^eiMeea-e«9o ei-<«>*Miik-9ei>4«4>)e

I I

m%%%wm%u%in%%^um

+ +

%
%

H
R
M

MNMWMRM

iw» ii«i Mmi*wr uKw>»fww^*- "^

BRIOHTlfBBa OF THE aTABS.

430

that the brightneia of «a mrtHgo itar of the first magnitude ia
about 0*5 of that of a Lj/ra. A itar of the 2d magnitude will shine
with a light expressed by 0-S x 0'4=0-80, and so on.

Thetfital

brightneia

Of 10 1st

magnitade state is 60

•«

87 8d

7-4

138 8d

101

•<

«*

810 4th

«i

»-9

l.Olt Sth

180

4.8M«th

881

18,5M 7th

87-8

• 1

57.900 8tb

•1

47-4

Sam = 148-7

It thus appears that from the stars to the 8th magnitude, inclu-
sive, we recMTe 148 tioMs as much light as from a Lyrm. a Lyra
has been determined bj ZSixnu to be about 44,000,000,000 times
fainter than the sun, so that the proportion of starlight to sunlight
can be computed. It alio appears that the stars of nuupitudes too
high to aUow them to be indiTidually Tisible to the nidted eye are
yet so numerous as to affect the genenl brightness of the sky more
than the so-called lucid staia (lsl-4tb magmtude).

■ii'mliiiMitttui.iMi

|M««M)'M>S»i-."5W if

'm^/'.lm.-.a- .-,■ •'Hi, IT.HilM )■ ^>i|iWWHll|i

CHAPTER II.

VARIABLE AND TEMPORABY STABS.

g 1. 8TAB8 BSQITLABLT VABIABLB.

All Stan do not shino with a constant light. JSince
the middle of the seventeenth oentnry, stars variable in
brilliancy have been known, and there are also stars which
periodically change in color. The period of a variable star
means the interval of time in which it goes through all its
changes, and returns to the same brilliancy.

The most noted variable stars are Mira Ceti (o Cett)
and Algd {ft Persei). Mira appears about twelve times
in eleven years, and remains at its greatest brightness
(sometimes as high as the 2d magnitude, sometimes not
above the 4th) for some time, then gradually decreases for
about 74 days, until it becomes invisible to the naked eye,
and so remains for about five or six months. From the
time of its reappearance as a lucid star till the time of its
maximum is about 43 days (Hkis). The mmm. period, or
the interval from minimum to minimum, is about 333
days (Aboblandkr), but this period, as does the maxi-
mum light, varies greatly.

Algd has been known as a variable star since 1667. Its
period is about ^ 20^ 49", and is supposed to be from
time to time subject to slight fluctuations. This star is
commonly of the 2d magnitude ; after remaining so
about 2i ^uw, it falls to 4" in the short time of 4^ hoursi
and T9m0» of 4°> for 80 minutes. It then commences
to increase in brilliancy, and in another 3| hours it is

STARS.

ABUB.

light. Since

ire variable in

Iso stare which

a variable star

through all its

( Ceti (o Cell)
*, twelve times
est brightness
sometimes not
y decreases for
the naked eye,
18. From the
^e time of its
vean period, or
, is about 338
loes the i&axi-

inee 1667. Its
k1 to be from
This star is
remaining so
le of 4^ houiBi
en commences
^ houn it is

VAItTABLS 8TAR8.

again of the 2d magnitude, at which point it remains for
the remainder of its period, about 2'^ 12".

These two examples of the class of variable stare give a
rough idea of the extraordinary nature of the phenomena
they present. A closer examination of othere discloses
minor variations of great complexity and apparently with-
out law.

The following are some of the more prominent vari-
able stare visible to the naked eye :

Nami.

fi PerMl.. .
d Cephei. .
ti Aqaihe..
fl hjm . . .
a Herealiii.

o Ceti

V Hjdne..
n ArguB..

2.4.

l«v.

«.

Decllmtlon,
18W.

+ 10
4-67
+
+ 88
+ 14
- 8
-28

27-2
40U
40-4
127
82-4
84-1
8«-4
01

Period.

(f.

2M
6M
717
12-91
88-0
8800
4880
70ye«n.

ChMRM of

IfNpiltada.

8-7
80

8i
8 1
2

4
1

to
4

4-8
4-7

8-9
10
10

About 90 variable stare are well known, and as many
more are suspected to vary. In nearly all oases the mean
period can be fairly well determined, though anoirtalies of
various kinds frequently appear. Th« principal anomalies
are :

^ir«t. The period is seldom constant. For some stare
the changes of the period seem to follow a regular law ;
for othere no law can be fixed.

Second. The time from a minimnm to the next maxi-
mum is usually shorter thaa from this maximum to the
next minimum.

Third. Some stan (as fi L^ra^ have not onlyone max-
imum between two consecutive principal minima, but
two such maxima. For /9 Zyroi, according to Aboklam-
DSK, S' 9h after the principal minimnm comes the first
maximnti^ ; titon, 8* 7^ after this, aaeeondary minimum in
which ^ itar is l^ no means so funt as in the principal

-I— -, . |ii j> ««ii iu. I i»n,m"^-U ' » ' " WM i J.i | »Ulu i ..t i »J l llilLil.JB I U -

442

ASTRONOMY.

ininimuiii, and finally 3"* 3^ afterward comes the principal
maximum, the whole period being 12*' 21" 47'". The
courae of one period is illustrated below, supposing the
period to begin at O' 0**, and opposite each phase is given
the intensity of light in terms of y Ltfra = 1, according
to photometric measures by Klein.

PhMe.

RotaMve
Intamltjr.

Prineljwl Minimum

Fint Maximam

28"

0-40
0-88

Second MIntmnm

Prindpftl Maxlmani

Prlncl|Mtl Minimum

la*

008
0-88
0-40

11 IS I

The periods of 94 we1Udet«nnined variable stars being
tabulated, it appears tliat they are as follows :

PUtodbetwMn

No. of SUn.

Period iMtwMn

No. of sum.

Id. and 80 d.
80 80
80 100
100 180
180 800
MO 800
NO 800
800 800

1
4
4
5
9
14
18

800 d. and 400 d.
400 480
480 800
800 880
880 800
800 800
680 700
700 780

18
8
8

Z=»4

It is natural that there should be few known variables
of periods of 600 days and over, but it is not a little re-
markable that the periods of over half of these variables
should fall between 250 and 450 days.

The color of over 80 per cent of the variable stan is red
or orange. Red stars (of which 600 to 700 are known)
are now receiving close attention, as there is a strong like-
lihood of finding among them many new variables.

The speokra of variable stars show ohangoo which ap-
pear to be oonneoted with the variations in th«lr li||^t.

66 the principal

21" 47'". Tiie

, Buppoeing the

ti phftfie ia given

= 1, according

RoteMve

IntMMitjr.

0* 0»

0-40

8* »

0-88

6* »»

0-58

JH 12"

0-88

8* 82-

0-40

iable 8

tars being

W8 :

ram

Mo. of Stan.

100 d.

iSO

(50

Xz=9A

known variables
is not a little re-
)f these variables

riable stars is red
700 are known)
9 is a strong like-
variables.
laqgM which ap-
in tiMir lifi^t.

443

TBMPORARY STARS.

Another clau of variatioM oooun awoag th« fixed atan — naaMly,
Tariatiooa in color, «ith«r with or without oomaponding chaogea
of maffnitude.

In tne Urmtomitry, compoaed in the middle of the tenth century
bv the Peraian aatronomer Al Bdri, it ia atated. that at the time of
hia obiervaticma the star Algol waa reddiali — a term which he ap-
pliea alio to the itais Antaru, AUUbartm, and some others. Most
of these still exhibit a reddish aapect But AIm^I now aupeara aa a
white star, without any sign of color. Dr. Klbiii, of Cologne,
discorered that a Vrta ikuorU periodically changes color from an
intense fiery red to a yellow or Tellowlah-red every five weeka.
Wbbkr, of Peckeloh, has obaenrea this atar lately, and finds thia
period to be well establiahed.

% S. TXMPOBABT QB HSW STABS.

There are a few oases Icnown of apparent!;^ new stars
which have suddenly appeared, attained more or less
brightness, and slowly decreased in magnitude, either dis-
appearing totally, or finally remaining as comparatively
faint objects.

The most famous one was that of 1672, which attained
a brightness greater than that of Siriua or Jupiter and
approached to Fmiim, being even visible to the eye in
daylight. Ttoho Bbahk first observed this star in No-
vember, 1573, and watched its gradual increase in light
until its maximum in December. It then began to diminish
in brightness, and in January, 1578, it was fainter than
JupU«r. In February and iLuvh it was of the 1st mag-
nitude, in April and May of the 3d, in July and August of
the 3d, and in October and November of the 4th. It con-
tinued to dimihish until March, 1574, when it became in-
visible, an tiie telescope was not then in use. Ito color,
at first intense white, decreased through yellow and red.
When it arrived at tiie 5th magnitude its color again
became white, and so remained till its cBsippearanoe.
Ttoho measured it/^distance carefully from nine stan near
it, and near it<; phM)e there is now a star of the 10th
or 11th magnitude, which is possibly the same star.

The histcuy ^t temporary stars is in gmeral similar to
that oi the star of 1573, except th&t oon« have ftttainied so

444

ASTHONOifT.

groat a (logrcx) of *;ii <Mi<i/, Moru ^liaii a avoro of Mioh
objects are known i.o ;; o i.^ptTocI, many of them before
the making of accurate obtM^rvations, and the conclusion ia
probable that many have appc ired without recognition.
Among telescopic Btars, there is but a amall chance of de-
tecting a new or temporary star.

Several supposed cases of the disappearance of stars ex-
ist, but here there are so many jiossible sources of error
that great caution is necessary in admitting them.

Two temporary stars have appeared since the invention
of the speutroscoiw (1850), and the conclusions drawn
from a study of their spectra are most important as throw-
ing light upon the phenomena of variable stars in general.

The iirst of these stars is that of 1866, called T Coronat.
It was first seen on the 12th of May, 1866, and was then
of the 2d magnitude. Its changes were followed by vari-
ous observers, and its magnitude found to diminish as
follows :

MM *

Mm 12 8-

10.

14.
15.
16.
17.

May 18 8-8

"•0
•5
•0
•S
•0

10.

81.
88.
88.

«•
6-
7-
7-
8-

By June 7th it liad fallen to 9—0, and July 7th it was
9" -5. SoHMnrr's observations of this star {T CcTanci)y
continued up to 1877, show that, after falling from the
second to the seventh magnitude in nine dayi, its light
diminished very gradually year after year down to nearly
the tenth magnitude, at which it has remained pretty con-
stant for some yean. Butduring the whole period there
have been fluctuations of brightness at tolerably regnhv
intervals of ninety-four days, though of sncoessiyely de-
creasing extent. After the first sudden fall, there seems
.to have been an increase of brilliancy, whidi brought the
star above the seventh magnitude again, in October,
1866, an increase of a full magnitude ; bntrinee that time

■iif.!^iSaM|U«lS

a iM.'oro of Biioh
of them before
ho conduBion ia
lut reoognition.
11 chance of de-

,nce of Btan ex-
ources of error
I them.

le the invention
icluaions drawn
artant as throw-
Btans in general.
Hod T Corona.
3, and was then
>Uowed by vari-
to diminish as

5-5

«0

6-6

7-0

7.B

July 7th it was
ar {TCoron(B\
dling from the
dayi, its light
down to nearly
ined pretty oon-
ole period there
Dlerably regnliMr
SQOoessively de>
all, there seems
dch brought the
n, in October,
trince that time

YARIAHLK STARS.

445

tho cluitigoM liavo boon niiiuh smaller, ntul aru now but
littlo mora than a tenth of a magnitude. Tho uolor ot the
Btar has been pale yellow throughout tho whole course
of observations.

The ■pectroKopic obMrrstions of this iitsr by HnnutNS and
MiLLBR inowed it to har« » speotrom then abaolutely unique. The
report of their obserrationB sayi, " the Mpectruni of thia object ia
twofold, showing that the lioht by which it ihineB hM emankted
from two dietinct sources. The principal spectrum is usIobous
to that of the sun, and is formed of light which wu emitted by
■n incandescent solid or liquid photosphere, and which has suffered
a partial absorption by passing through an atmosphere of vapors at
a lower temperature than the photosphere. Buperpoeed over this
spectrum is a second spectrum consisting of a few hight lines
which is due to light which has emanated from intensely heated
matter ia Uie state of gas."

In November, 1876, Dr. Schmidt discovered a new star in Gyg-
ntM, whose telescopic history Ih nimilar to that given for T Corona.
When discovered it was of tho M magnitude, and it fell rapidly
below visibility to the naked eye.

This new star in Oygnua war. observed by Gobbc, Copblajid, and
VoQBL, by means of the spectroscope ; and from all the observa-
tions it is plain that the hydrogen lines, at first prominent, have
gradually faded. With the decrease in their brilliancy, a lioe
corresponding in position with the brightest of the lines of a nebu-
la has strengtiwned. On December 8th, t876, this last line was much
fainter than F (hydrogen line in the solar spectrum), while on
March 9d, 1877, F was vary much the fsinter of tiie two.

At flnt it exhibited a oontinuous spectrum with numerous bright
lines, but in the latter part of 1877 ft emitted only munochiomatio
light the spsotrum ooudsting of a single bright line, correspond-
ing m poduOTi to the obaraoteriatio line of gaseous nebulc. The
intermediate stages wen eharaeteriied by a gradual fading out,
not only of the continuous spectrum, but also of the bright lines
which orossed it. From this fact, it is inferred that this star, which
has now fallen to 10-S magnitude, has actually become a planetary
nebula, affording an instance of a remarkabla nversal ot the pro-
cess ima^^joMd by La Piju» in his nebular theory.

S 8. CTSOBUB of VABIABLI 8TAB8.

The theory of variable utars now generally aooepted by investi-
gators is founded on the following Benenl oonohisions :

(1) That the only distinction wmoh can be made between the
various classes of stars we have just desoribed is one of degree.
Between stars as r^pilar as AlgU, whiek goes throuj^ its period in
less than three days, and the suddsa uashig out of the star de-

tli

'fi;bl'i

446

ABTHONOMT.

scribed by Ttcbo Brahb, there is every gradstion of irresnlarity.
The only distinction that can be drawn between them is in the
length of the period and the extent and regularity of the changes.
All sooh stars must, therefore, for the present, be included in the
sixffile class of variables.

tt was at one time supposed that newly created stars appeared
from time to time, and that old ones sometimes disappeared from
view. But it is now considered that there is no well-established
eaK either of the disappearance of an old star or the creation of a
new one. The suppmed cases of disappearance aroee from catar-
loffuen accidentally recording stars in positions where none existed.
BwMequent astronomers flnfing no stars in the place concluded
that the star had vanished when in reality it had never existed.
The view that temporary stars are new creations is diqirwed by
the ra|ddity with which they always fade away again.

(S) That all stars may be to a greater or lew extent variable ;

ly in a vast majority of cases the variations are so slight as to be
imperceptible to the eye. If our sun could be viewed from the dis-
tance of a star, or if we could actually measure the amount of Hght
which it transmits to our eyes, there is little doubt that we should
find it to vary with the presence or absence of spots on its surface.
We are therefore led to the result that variability of light may be a
oommon characteristic of stars, and if so we are to look for its
oauae in something common to all such objects.

Thb spots on the sun may give us a hint of the probable cwase of
the variations in the light of the stars. The general analogies of the
universe, and the observations with the spectroscope, all lead as to
the conclusion that the phyrical constitution of the sun and stars is
of the same general nature. As we see spots on the sun which varv
in form, size and number from day to day, w> if we could take • suf-
Iciently close view of t^e faces of the start we should probably see
^ota on a great number of them. In our ann the apots never cover
more than a very small fraction of the surface ; Vut we have no
reason to suppose that this would be die ease with the stan. If
the spots oarnnA a large portion of the sorfaoe of th« star, ttten
their varisitioBa in number anJ extent wooli cause the star to vary
inlk^t.

Tms view does sJK, however, aooount for those cases in which ths
light of a star is suddenly incnased in smount hundreds of
B|it tiw speetanscrale observattons of T Oortim dwi
am^Mor with «»p««noBs going on in our sun. Mr. Hmwnn's ob-
servamms, wUoh we have already dted, seem to show that thsre
was a sadden and extraordinarr ontburst of glowing hydrogen
fjrom the star, which by its owaliight, aa v «U as by heMog np the
whole sorfaoe of the star, eaased an increase in its brilliancy.

Now, we have on a vary small scale sosaething of this aawe kind
going on in oor snn. The red flamaa which are ssea during a
total eclipse are caused by eruptions of hydrogen from the farteror
of ths sua, aad these eraptioas are gSMraUy eoaaected with the
fasaki or portkma wf the son's dkk nKNW briUiank than tb

I the lost of

^mmmmmmmmM^jf^-^

tn of irresalarity.

n them is in the

r of the changes.

included in the

d stars appeared
liaappearea from
> well-established
the creation of a

arose from cata-
lere none existed.

plaee concluded
Id uerer existed.
I is di sp rored by
i;ain.

extent Tariable ;
so slight as to be
ired from the dis-
e amount of Hght
bt that we shoinld
Its on its surface,
of tight may be a
t to look for its

probable caiase of
I analogies of the
[»pe, all lead ns to
le sun and stars b
he sun which Tanr
I could talce a suf-
iwdd probably sea
■pots never eoTer
Vutwe have no
ith the Stan. If
of Oe iter, then
le the star to vaiy

Bases in which the
ladreda of
MS show
If. HiNMiin'a ob-

show tiiat tlMie
llowing hydrogw
liy helping up the
s brilliantiy.

(rf this saue kind
ire seen dnrlaga

1 from the iittarbr
mMMsted wtth the
It than th« feat of

VARIABLE STABS.

447

The general theory of variable stars which has now the most
evidence in its favor is this : These bodies are, from some general
cause not fully understood, subject to eruptions of slowing hydro-
gen gas from their interior, and to the f mrmation of dark spots on
their surfaces. These eruptions and formations have in most casra
a greater or less tendency to a regular period.

In the case of our sun, the period is 11 years, but in the case of
many of the stars it is much shorter. Ordinarily, as in the case of
the sun and of a large majwity of the stars, the variations are too
slight to affect the total quantity of light to any visible extent.
But in the case of the variable stars this spot-producing power and
the liability to eruptions are very much sireater than in the case of
our sun, and thus we have chaoses of light which can be readily
perceived by the eye. Some adutional strength is given to this
theory by the fact just mentioned, that so lan^e • proportion of
the variabh) stars are red. It is well known that glowing bodies
emit a laroer proportion of red rays and a smaller proportion of
blue ones the cooler they become. It is therefore probable that
the red atan have the leasi heat This being the case, it is more
easy to {voduoe spots on their surface ; and if their outside surface
is so cool as to oeoome solid, tHe glowing hydrogen from the in-
terior when it did burst through would do so with mora pown
than if the surrounding shell wtte liauid or gaseous.

Thera is, however, one star of #hum the variations may be due to
an mUMj diffefent canse-^namely, Aifol. The extreme jegularity
with which the ligfat of this object fades away snd disappears siw-
gesta the poasibimy that a dark body may be revolving around it,
and partially eclinttag it at every revohition. The law of variation
of ita li|riit it so &leient from that of the light of other variable
Stan as to soggnfe a diflarcnt catise. Most othen an nefur their
m>«iiniim fot osly a anall Mrt <rf thdr period, while iij;^ is at its
mitTimiiin for nine tenths el it Othen an subject to neariv con-
tinuona ehauna, iMi» tha light of Aiftl remains constant during
nine tenths o? ita period.

CHAPTER III.

MULTIPLE STARS.

§ 1. GHABAOTBB OF DOUBIiE AND MXJVSIPLE

BTABS.

When we examine the heavens with telescopes, we find
many cases in which two or more stars are extremely close
together, so as to form a pair, a triplet, or a group. It is
evident that there are two ways to account for this ap-
pearance.

1. We may suppose that the stars happen to lie nearly
in the same' straight line from us, hut have no connection
with ea<di other. It is evident that in this case a pair of
stars might appear double, although the one was hundreds
or thousands of times farther off than the other. It is,
moreover, impoBsible, from mere inspection, to determine
which is the farther.

2. We may suppose that the stars are really as near
together as they appear, and are to be considered as form-
ing a connected pair or group.

A. couple of stars in the first case are said to be optically
dotMe, and are not generally classed by astronomers as
double stars.

Stars which are considered as really double are those
which are so near together that we are justified in consider-
ing them as physically connected. Such stare are iaid to
be phyiicaU/y doiMey and are generally designated as
double stars simply.

Though it is impossible by mere inspection to decide to
which class a pur of stara should be considered as belong-
ing, yet the calculus of probabilities will enable us to de*

DOUBLE STARS.

440

I KUI/nFIiB

loopes, we find
ixtremely close
I group. It is
nt for this ap-

1 to lie nearly
no connection
case a pair of
3 was hundreds
I other. It is,
n, to determine

really as near
dered as form-
to he opUcaUy
Eustronomers as

ahle are those

ed in consider*

ars are iaid to

designated aa

[>n to decide to
ired as belong-
uble OB to de-

cide in a rough way whether it is likely that two stare not
physically connected should appear so very close together
as most of the double stars do. This question was first
cQusidered by the Rev. John Michell, F.R.S., of Eng-
land, who in 1777 published a paper on the subject in the
Philosophical TramacHona. He showed that if the lucid
stars were equally distributed over the celestial sphere, the
chances were 80 to 1 against any two being within three
miBtuies of each other, and that the chances were 600,000
tol against the six visible stars of the Pleiades being
accidentally associated as we see them. When the mill-
ions of telescopic stars are oonaidered, there is a greater
probability of such accidental juxtaposition. But the
probability of many such cases ooourring is so eztramely
small that astronomers regard all the closest paim as phy-
sically connected. It is now known that of the 600,000
stars of the finrt ten magnitudes, at least 10,000, ot one out
of every 60, has a oompani<m within a disteAed of 30' of
arc. This proportion k many times greater than could
possibly be the result of ulumee.

There are several eases (rf st«n wbkth appear double to
the nake4 e^' Two of tlieae ire have airaMlj described
—nameljr, d Tmiti Mid « Lyn». ITie lattMr k a most
curious and InterMting object, from the liet that each of|
the twoj^aniii^ii tiompoae it k
itHolf donUe. Jitll|»oraiiiikiag
idea of 4iie p«W«#^^ the tdae-
cope oaa -be 'formed- tl mn by
pointing a poweiril ir Aiment
upon this obiect. It w^i' then
be seen that wis minute y.ihv oi
points, capable of i^ing ^JLJa-
gnished only by the mcM t pen^t

eye, k really oompovd of two tJT l».-ra» qvAimorLV
pain of stirs wide ^ uf , with a '^^ ' ^^*^

group of smaller st&n Letwaen 4ind s/onnd them. The
figure shows the appearanoe in a tel«n<jcp<i of oondderable
power.

. I *m. i M -1 1 iji ^ t.jfmj-v.ytum

450

AaTRONOMT.

BvrrtutioiiB of Doubto Btem— Bbuuy Byitanu.— The
most intereeting questioa suggested by double stara is that
of their relative motion. It is evident that if these
bodies are endowed with the property of mutual gravita-
tion, they must be revolving around each other, as the
earth and phuiets revolve around the sun, e]tie they would
be drawn together as a single star. With a iew of detect-
ing this revolution, astronomers measure .he jfOtUion-
mgUy and dutanoe of these objecta. The diOance of the

v^iti

ov i*oiinBV-*Ams>

ponents of the double star is simply the apparent

whieh separates them, as seen by tiie observer. It is

always expraeiied in seconds or fractions of a seccmd of arc.

The an^ of •potiHAon^ or " position-angle" as it isof un

called for brevity, is the angle which the line joining the

two (Mars makes with the line drawn ^m the brightest star

to the north pole. If Uio fainter star is directiy north of

brighter one, this angle is xero ; if east, it is 90**; if southi

Syitenui.— The
uble Stan is that
nt that if these

mutual gravita-
kch oUier, as the

e]«ie they would

a ' lew of detect-
« .;he jHmtion-
« diitanoe of the

»Iy the apparent
iieoheenrer. It is
)f a seocmd of aro.
igle" as it isof UTi
eline joining the
1 the brightest star
direcdy north of
,iti8 90<*;ifBOttth,

DOUBLS 8TAR8.

461

it is 180" ; if west, it is 270°. This is illnstrated by the
figure, which is supposed to represent the field of view of
an inverting telescope pointed toward ^e south. The
arrow shows the direction of the apparent diurnal motion.
The telescope is supposed to be so pointed that the brighter
star may be in the centra of the field. The numbers
around the surroimding drde then show the an^e of po-
sition, supposing the smaller star to be in the direetitm of
the number.

The letters »n., »f^ np, and nf r>how the methocb of
dividing tiie four quadrants, < meantug souUi, n north,
/ following, and j» preceding. Tha two lattw words refer
to the direction of the diur-
nal motion. Fig. 184 is an
example of a pair of stars in
which the position-angle is
about 44°.

If, by measures of this
sort extending through a
series of yean, the distaUM
or poritiou-angle of a pair
of stars is found to clun^
it shows that one stw is re-
volirii^ around the other.
Such a pair is called a
hmary ttar or hinaty «y»~
tern. The only diatiaeliott
whidi we can make between
binary qrstems and ordinary donbk staas is founded on
the presence or absence of obaerred motion. It is prob-
able tibat nearly all the douUe stan»«are really binary sys-
tems, but that many thousands of years we required to
perform a revolution, so that tiie molion has not yet been
detected.

The disnoveiry of Unary systems is one of great sden-
tiflc ittterebt, because from them we learn that the law ot
gravitati<m iaQhulee the stan as well as tSw solar system in

nOlpUl STAlk

453

A8TR0N0MT.

its scope, and may therefore bo regarded as a universal
property of matter.

Oolora of Double Stan.— There are a few notewortliy statistics
in reoard to the colors of the coimmnents of double stars which
may oe j^ven. Among 596 of the orighter double stars, there are
875 pairs where each component has the same color and intensity ;
101 pairs whore the components have same color, but different in-
tensity ; 130 pairs of different colofs. Among those of the same
color, the vast majority were both white. Of the 476 stars of the
same color, there were 295 pairs whose components were both
white ; 118 pairs whose components were both yellow or both red ;
68 pairs whose components were both bluish. When the com-

Eonents are of different colors, the .brighter generally appears to
ave a tinge of red or yellow ; the other of blue or green.

These cbita indicate in part real physical laws. They also are
partly due to the physiological fact that the fainter a star is, the
more bloe it 'vill appear to the eye.

MMMmsas of Pottbto Mun.— Tlie first systematic measures of
the relative poritiMi> of tlia oaalponents of double stars were made
by OwKOHUX MAnn, IMreotw of the Ducv. Observatory of Mann-
heim. 1739, hut it is to 8m WriJJAX HuucHBLthat we owe the ba-
, sis of ear kiiowtodfe «>f tUsbtaach of sidereal astronomy. In 1780
HBMpBBcaMamred 1^ r«latlv« situation of more than 400 double
Stan, and after repeating kia measures smne score of years later,
ke fooad in aboat SO of the peirs evidence of relative motion of
theoofispoMnts. la thia Inat mirvey he foimd 97 stars whose dis-
taaoe was ooder 4', IM iMftireen 4' and 8', 114 between 8' and
16', aod 1«2 between W tuA W.

8iMw }Ii&aaoau.'a obeerv a l i ooa, the discoveries of Bir Joan Hbb-
. temvu, Sir iiMm Boom, Dawm, and many others in England, of
W. Snuvii, ' Ono. Bnora, Kadlbb, SUccbi, Dbmbowski, Dd-
muif ia larope, bm of G. P. Bono, Alvam Olabk, and 8. W.
lUttn^ ia tM Vaitod States, have inc r eased the number of
kBowa dooUa ataia to aboat 1«»000.

fiiesides the doable stars, there are also triple, quadruple, etc.,
-ftuA ' TiMe aw geBeriioany called imd^pb Kara. The most re-
markable multiple star is the Trapmmm, in the c^tre of the nebula
of Orion, comnionly called OriSiii$^ whose ftmr stars are, without
doubt, physically conneeted.

Th^ next combibatioa beyond a multiide star is a (dwiter of stars ;
and beginidng with clusters of T in diameter, such objeefes may be
found up to 80' or more in diameter, every intermediate siae being
represented. These we shall consider shortly.

% t. OBBm or BINABT STAB8.

When it was established that many of the doiible stars were really
revolving around each otner, tt iiecaine of great interest to
detenaiae tiie orbit aud aaoMrlaIn whether it wA an ellipse, with

as a uni venal

tewortliy statiatica
louble stars which
ble stars, there are
lor and intensitv ;
, but different m-
those of the same
lie 476 stars of the
inents were both
bIIow or both red ;
When the com-
nenUly appears to

or green.

>. They also are
dnter a star is, the

matic measures of
le stars were made
erratoryof Mann-
lat we owe the ba-
tronomy. In 1780
« than 400 double
K>re of years later,
relative motion of
n stars whose dis-
between 8' and

I of Bir Jobs Hbb-
)n in England, of
DbmbOwski, Dn-
Ilabk, and B. W.
id the number of

e, quadruple, etc.,

r$. The most re-

mtre of the nebula

stars are, without

taaluaterof Stan;
ich objeeta may be
nediate siae being

ABB.

le stars were really
great interest to
S an elUjMe, with

BINART STARS.

458

the centre of gravity of the two objects in one of the foci ; if so, it
would be shown that gravitation among the stars followed the same
law as in the solar system. As an illustration of how this may be
done, we present the following measures of the position-angle and
distance of the binary star i l^rtas Majoria, which was the first ane
of which the orbit was investigated. The following notation is

used :
star;

the angle of position; $,
the fainter one.

the distance ; A, the brighter

f Ukbm Majorib = 1 1528.*

Epoch.

Obwrrtr.

17820

1808-1

148*8

»7-6

276-4

264-7

201-1

150-0

122-6

96-7

16-5

•
• • • ■

1-00
2-45
2-90
2-56
001

W. HersclieL

1820-1

1821-8

W. Blruve.

1881-8

J. Hersehel.

1840-8

1851-6

1863-2

Dawes.
MKdler.
Dembowskl.

1872-5

DnnCr.

If these measures be plotted on a sheet of squared paper, the
several positions of B will be found to lie in an ellipse. Tais ellipse
is the projection of the real orbit on the plane perpendiculiur to the
line of sight, or line joining the earth with tiie star A. It is a

?|uestion of analysis to determine the true orbit from tbo times and
rom the values of p and j.

If the real orbit m^pened to lie in a pUme perpendiwtfar to tlie
line of 8i|riit, the star A would lie in the fooua of the eftipse. If
this oolnddenee does not take place, thenth« plane of the true or-
bit is aeen obliquely.

IIm flnt two of KBPun's laws can be employud in determiaing
such oittta, but tiie third Uw is inapplicable.

Ittnm of Bfaary 87>tainB.--WIien the panllaz or distance,
the soni-major axis St the orbit, and tiie time of revolution of a
bhiary ^atem are known, we can determine tiie oomUned mass of
the pair of atari in terms of tiie nuas of the son. Let us put :

4^ tlie mean distaaee of the two componeBta aa m easM w d in
seconds;

o, tiieir mean distance from each other in astrononik«l units ;

T, ike time of revolution in yean ;

Jf, Jf*. the msHes of the two coaponrat stars ;

P, tiior annual parallax ;

D, tiieir diatance in aatronomioal unite.

* Z 1588 slgnUea ikaX this star la No. 1AB8 of W. 8im«»\i Dorpat
CatatoffttSi

■^>:^-

484

ASTnONOMY.

From the geneT»»«rtion of Kbplm's third l»w, given by the
theory of gravitation, we liave

M* + M = "rpT'

Fron the formole expUlned in treating of parallax we have

D = I -*- tin. P.

If a' ia the major axie In aeconda. a being the aame quantity In
aatronomical unite, then !

a = D ■ tin. a".

From theoe two equations,

tin. a'
tin. F

a'
F

becauM o' and P are ao amatl tUt the ares may be tetcen for their

Putting this value of a In the equation for Jf ' ■ Jf«>
we liave M + M» = ^j" p»'

have been determined (O'BS and 0' 16) from direct meaanrea. For
T = 770 years; a" = IS'-S ; P = -98 ;

totpOphiwihi,

r= 94-4 years; a" = 4"-70; P = O'le.

If we subeUtnte in the last equntion these values for T, P, and a',

VTA llftTO

jr. 4- if = 0«7 for a Centauri,
jr. ■•- jr= 9-84 forp OpMtuhl

The last number 1» quite uncertain, owing to the diffloalty of mmMr
aring so small a parallu. We c«i only eonelude that the mass of
S two s*"^ not many times greater or leat.tlum the my* of
onrmn. Rom the agreement in these two eaae% it la j^oMiletbiU

"notC,^ if i&n^ «mW be «>^"»»::;; " 'St^
gtaatly d*erent flrom the mass of «jr aw» We ^^^^J^V^'
tion, whiehammmts to supposing JT. + Jr= 1, •PI*/ »• fcm«»»

p = a' f ri

to other biMtriea. and dednco a value te Pin «?* ••f^.^^S'* ••.?H2?
thehypothetloal painllax (Qyld«n), and which to probably not fte

The» are, iMaide binary systems, multipto <»«> aa f OwMrt. y*ere
the distanoe if il and B is O'-S ; and fiom the ntld^ l»tot between

.1 and B to <7to 5"5. The period of revolution of — jj— rtewt is

supposed to be about TM year.. W >» «»• jl-J ^"'^r **"*
r = 780 year* and a" = 6" -6, we have the hypothetleal parallas

BINAnr BTAR8.

law, giren by the

mlUz wfl hftve

the Mme quantity in

ay be Uken for Uiaijr

Htan wlioae parallaxes
direct meaaarea. For

= 0'-98;

=:0'16.

kluea for T, P, and a',
vri,

» tbe difBoolty of maaa-
ilade that the maaa of
r laaa than tha aaaa of
Nik it la pntaMatbat
ilMd, it wottld not be
I Bay OB Mm niMoai-
, apply tha fMnuh

idtaaaawUehkeallai
li ia pfobably not far

maa aa C Cbiwri, whara
Biiddle point bati»«eB

,„C^.fca.l(7ia

I laat fbrmnla w« pat
otiMtleal parallax

Following are giTen the elemenU of several of the more impor*
tif't binary etars. Eight of these have moved through an entire
revolution — 860° — since the first observation, and about 150 are
known which have certainly moved through an arc of over 10° since
they were first obaerved.

In the tablea the semi-major axia, or mean distance, must be
given in seconds, since we have usually no data by which ita vain*
in linear measurea of any kind can be fixed.

Periods of revolution exceeding 120 years must be regarded as
quite uncertain.

ELmBNTa or Binary fh'ABs.

Stab's Naim.

Period
lYewi.)

43 ComeBer....

85-7

( Heroolla

84 6

X 818l»

8708

n Corona Bor. . .

40-9

S Ubne

9S.90

y Cofoue Aas. . .

05-5

( Vna Maj. . . |

80-6
808

f Cancri j

684
60S

aCentaori

850

70Oiriiluefal

92-8

Y GOKMUBBor....

son Z

955

104-4

u Leonia

il4-8

AOphluohi

883-8

/> Bridaal

117-5

1788 2

184-5

fBoMIs

1274

rOpfiiuehi

1750
817-9

V CaHlopee

898-4

44Bo(Rl8.

88M

1988 2

^•Bofltla

880-8

88 Aadnmeda...

849- 1

Y LeoBia

408-8

81 t^ifpii.......

4IS1
488-0

« Cow— Bat.. . .

84S-9

a QantaMfQBi...

1001-8

(Aqnarii...... .

1018-8

Time
of Peri-
Mtron.

1889-9
1884-9
1842-8
1849-9
1889-8
1889-7
1875.6
1870-8
1889-8
1889.9
1874-9
1807-9
1848-7
1884-9
1841-8
1808-9
1817-5
1868-0
1770-7
1886-0
1881-9
1909-2
1788-0

1868-0

1796-8
1741-1
18041

1888-9
17«l-8
18841

Seml-

Azlt

Major.

0'
1

8
2
2

21
4

4
8
1
9
8

1
8
2
10

7
7

•60

-86

-711

•99

-26

-40

-08

•04

•80

•88

•70

-27

-80

-19

-89

« • •

•86

-89

-40

-88

-08

•54

•00

-81

•4

, ^

•88

•48

•64

Iceen-
trieity.

Oaleulstor.

•48
•41
•86
■29
•08
-69
88
•87
•00
-87
-67

-46
-00

•4a

-88
-66

-71
•87
•61
•07
•71

•60

-74

70
•88
•60

Dabiago.

Flammarion.

Doberek.

FlammarioB.

Doberek.

Sohiaparelll.

Hind.

Flammarion.

O. Strove.

Flammarion.

Hind.

Flammarion.

Doberek.

DoberdL

Bohntk.

Doberek..

Dobmek.

Doberdt.

Flammarion.

DobaM*.

DobevA.

Dobank.

Dobesek.

Doberek.
Doberek.

Doberek.
DobardL
Doberek.

•Slfi S algBMaBira 8181 oTW. 9niimii^i Dotpat Oatalogae.

•V •WKfft-,---;.!' Mit'* 'airvM-r*.!^ ■ '— ■

466

ABTRONOMT.

The flnt computation of the orbit of a binary atar waa made by
Savary (Astronomer at the Paris Observatory) about 1826, and his
reaulU were the first which demonstrated that the laws of sravitu-
tion, which we knew to be operative over the extent of the solar
system, and even over the vast space covered by the orbit of
IIallby'i comet, extended even furtner, to the fixed stars. It might
have been before 189fi a hazardous extension of our views to sup-
pose even the near.dt axed stars to be subject to the laws of New-
ton ; but as many of M-'> known binaries have no measurable paral-
lax, it is by no means an unsafe conclusion that every fixed atar
which our best telescopes will show is subjected to the same laws
as those which govern tin- fall of bodies upon the earth.

■tar WM made by
iboiit 1826, and hU
lie law8 of ffravitu-
extent of the solar
1 by the orbit of
xod stars. It might
our views to sup-
9 the laws of Nbw-
) measurable paral-
kt every flxca star
i to the same laws
le earth.

CHAPTER IV.

NEBULuE AND CLUSTERS,
g 1. DISCOVERT OF NBBUUB.

In the star-cat't^ 'uea of Ptolkmv, IlKVEUcg and the
earlier writors, th w iuclnded a class of nebulous or

cloudy stars, whi( o in reality star-clusters. They

appeared to the nu. a oyo as masses of soft diffused light
of greater or less extent. In tliis respect, they were quite
analogous to the Milky Way. When Galilbo first direct-
ed his telescope to the sky, the nebulous appearance of
these spots vanished, and they were seen to consist of
clusters of stara.

As the telescope was improved, great numbers of such
patches of light were found, some of which could be re-
solved into stare, while othera could not. The latter were
called fiMtla and the former star-dwtera.

About 1660, HuYOHBNS described the great nebula of
Orion, one of the most remarkable and brilliant of these
objects. During the last century, Mbssieb, of Paris, made
a list of 103 northern nebulaa, and Laoaiixb noted a few of
those of the southern sky. The careful sweeps of the
heavens by Sir William Hkbsobsl with his great tele-
scopes first gave proof of the enormous number of these
masses. In 1786, he published a catalogue of one thousand
new nebulffi and clusters. This was followed in 1789 by
a catalogue of a second thousand, and in 1802 by a third
catalogue of five hundred new objects of this class. A

458

ASTRONOHr,

■iiiiilnr serios of Hwoop, carriod on hy Sir John IIkr-
twiiKL ill Ijoth homiupliores, added about two thouBand
more nobulai. The i^euoral catalogue of nobulto and cluu-
tore of stare of the latter astronomer, published in 1864,
contains 5079 nebulaj : 6261 arc known in 1879. Over
two thirds of those were first discovered by the IIebschels.
The more enumeration of over 4000 nobuluu is, how-
ever, but a small i>art of the labor done by these two dis-
tinguished astronomers. The son htis left a great number
of studios, drawings, and measures of nebulw, »i ' the
memoirs of the father on the Construction of the Ilti v • n
owe their suggestiveness and much of their value to Jiis
long-continiiod observations on this class of objects, which
gave him the clue to Ids theories.

% a. Oi:.AB8IFIOATIONOFKBBnLJIiLnT''aLn8TBB8.

In studying these objects, the flrst question wo meet is
tliis : Are all these botiies clusters of stars wlii*;!* look
diffused only because they are so distant that ouv twla-
scopes cannot distinguish them separately t or are bovuc .>f
them in reality wlwt they seem to be— namely, difiosed
massefl of matter f

In his early memoirs of 1784 and 1786, Sir William
Hbbsohbl took the first view. He considered the Milky
Way as nothing but a congeries of stars, and all nebnls
naturally seemed to him to be but stellar dusters, so
distant as to cause the indiridnal stars to disappear in a
general milkiness or nebulosity.

In 1791, however, his views underwent a change. He
had discovered a nebulous star (properly so called), or a
star which wa« undoubtedly similar to the surrounding
stars, and which was encompassed by a hala of nebulous
light. *

* TlUa was the 6Mi ndmla of bUfourtk ebmat pluietaiy nebula.
(B. lT.«9.) . ,

Sir John IIkk-
t two tliouiiand
nobulso and cltui-
ibHahodiu 1864,
lit) 1879. Over
>y the IlERScnBLB.

nubuliu ia, how-
ty those two dis-
ft a great number
nubulte, tfi ' the
mof the Ilti V -n
heir value to iii«
of objects, which

estiou wo meet is
stars whi<:lt look
tit that otjv 'm\9-
fi or are bo!u(! >f
-namely, difiosed

r85, SirWauAM
sidered the Milky
K, and ail nebulse
tellar clnsters, so
to disappear in a

it a change. He

y so called), or a

the surrounding

halo of nebulous

of ^snetaiy nebola.

^'°*^ 'IWW

^h^--

CIHM/ICMH

Microfiche

Series.

CIHIVI/ICIVIH
Collection de

Canadian

Inatituta for HIatorlcal MIcroraproductlona / Inathut Canadian da microraproductiona itiatoriquaa

,aw«-i.taaiw.'i i nt

NEBULA AND CLITSI'ERS.

459

lie says : ** Nobulo; can be selected so that an insensible grada-
tion shall take place from a coarse cluster like the Pleiade* down to
a milky nebulosity like that in Oritm, every intermediate step being
represented. This tends to confirm the hypothesis that all are com-
ftosed of stars more or less remote.

'' A comparison of the two eixtremet of the series, as a coarse
cluster and a nebulous star, indicates, however, that the nebudonty
about the darU not of a starry nature.

" Considering H, iv. 69, as atypical nebulous star, and supposing
the nucleus and chevelure to be connected, we may, first, suppose
tlic whole to be of stars, in which case either the nucleus is enor-
mously larger than other stars of its stellar magnitude, or the envelo{Mi
is compoiied of stars indefinitely small ; or, second, we must admit
that the star is invched in a lihmiag fluid of a natwrt totatttfurUmown

to US. \^

" The shining fluid might exist independently of stua. The
light of this fluid is no kind of reflection from the star in the cen-
tre. If this matter is self-luminous, it seems more flt to produce a
star by its condensation than to depend on the star for ita exigence.

" Both diffused nebulosities and planetaiy nebula are better
nccounted for by the hypothesia of a Bbining fluid than by mppos-
ing them to be ^tant atan.'*

This was the first «cact statement of the idea that, beside
stars and star-clusters, we have in the nniverse a totally
distinct series of objects, probably mndi more simple in
their constitution. The observations of Huooihs and
HvAXHi on the spectra of these bodies have, as we shall
see, entirely confirmed the conclusions of Hebsohbl.
' Nebnlee and dusters were divided by Hkbsohsl into
classes. Of his names, only a few are now in general use.
He applied the name planetary nebulcB to certain oircnlar
or elliptic nebula which in his telescope presented disks
like die planets. /^»ir<d nebtila are tiiose whose convo-
lutions have a spiral shape. This class is quite numer-
ous.

The different kinds of nebnlte and dusters will bo better under-
stood from the cuts and descriptions which follow than by formal
definitions. It must be remembered that there is an almost infinite
variety of such shapes.

The figure by Sir Johk Hebschel on the next page gives a good
idea of a spiral or ring nebula. It has a central nucleus and a small
and bright companion nebula near it. In a larger telescope than
llBKscHEiN'a its aspect is even more complicated. See also Fig. 138.

5«S^f«iiBi»?«>'K»*»^w^a»":'

i ifjiH ft.H p wi i i. im mjv J

ASTRONOMY.

The Omega or hor»c»h>e nclnilu, so culled from the resemblance
of the briglitcct end of it to a Greek Q, or to a horde's iron shoe, is
one of the most complex and remarkable of the nebulae visible in
the northern hemisphere. It is particularly worthy of note, as
there is some reason to believe that it has a proper motion. Cer-
tain it is that the bright star which in the figure is at the left-hand
upper comer of one of the squares, and on the left-hand (west)
edge of the streak of nebulosity, was in the older drawtngs placed
on the other side of this streak, or within the dark bay, thus mak-
ing it at least probable that either the star or the nebula has moved.

195;-~4PnUkIi NKBOUL

The Uifid nebula, so called on aocoont of its three branches
which meet aeara central dark space, is a striking object, and
was suspected by Sir Johh Hebsohkl to have a proper motion.
Lator observations seem to confirm this, and in particular th« three
bright stars on the left-hand edge of the right-hand (east) mass are
now more deeply immersed in the nebula ftan they were observed
to be by Hkbschkl (1883) and Mason, of Yale College (1881), In
1784, Sir Wilmam IlEBsciiEii described them as " in the middle of
the [dark] triangle." This description does not apply to their
present situation. (Fig. 127).

)in the rcsomblancu
hoKu's inm shoo, is
le nebulffi visible in
worthy of note, as
Toner motion. Cer-
re 18 at the left-hand
the left-hand (west)
lerdrawinm placed
lark bay, thus mak-
e nebula has moved.

its three branches
itriking object, and
ve a proper motion,
particular th« three
lumd (east) mass are
they were observed
College (1887). In
18 " in the middle of
I not apply to their

4C2 ABTRONOMT.

% 8. STAB 0I.U8TMB8.

The most note*! of all the duaten k the PUtiade$, which have
alieady been briefly described in connection with the constellation
Totmu. The a^eraKe naked eje can easily distingoish t&x stars
wHhin it, bat vnder favorable eoaditioM ten, eleven, twelve, or

be OMwted. With the teleaeope, over ahaadred

stars arc seen. A view of these is given in the map accompanying
the description of the Pldadet, Fig. 118, p. 425. This group con-
tains Trmpbi/s varia1)le nebula, so callecl liecause it has been sup-
posed to be subject to variations of light. This is probably not a
variable nebula.

r-iwijw-

I ^f "

NEnULAS AND OLUaTERS.

463

Pteiade$t which have
irith the conatellation
distlngidsh rix ttara
tent eleven, twelve, or

The chifltcra rnnrcscntiHl in Figs. 120 and IHO arc goml cxampIvR
of their cInsacH. The flrat is globular and containH st^vnntl thousand
small stars. The central regions are densely |)ackud with stars,
and from these radiate curved hairy-looking branches of a ipiral
form. The second is a cluster of about 200 stars, of nuigniludcs
varying from the ninth to the thirteenth and fourteenth, in which
the hnghter stars are scattered in a somewhat unusual manner

Bleaoope, over kluiBdred

the map accompanying

425. This group con-

because it has been sup-

This is probably not a

Flu. 128. — THB BINO RBBin^A IN LTBA.

over the teleaco|dc Held. This duster is an excellent example of
the " compressed ** form so frequently exhibited. In clusters of
this class the spectroscope, shows that each of the individual stars
is a true sun, shining by its native brightness. If we admit that a
cluster is real — that is, that we have to do with a collection of stars
physically connected — the globular dusters become important. It
IS a fact of observation that in general the stars composing such

K*-'

n.\ .mimum.

404

A8TnoN0MY.

vlustors arc aliout of c<|iial niafrnitiiik-, nnil arc more eondciiHcd at
the centre than at tlic edges. They are prohably 8iil>je<t to central

Jmwers or forces. This wua seen by Bir William IIuiuc-iiul in 178<.l.
le says :

" Not only wore routid nobulic and clusters formed by central
powers, but likewise every cluster of 8<tars or nebula that shows a
gradual condensation or increasing brightness toward a centre.
This theory of central power is fully established on grounds of ob-
servation which cannot \m overturned.

*' Cliuters can be found of 10 diameter with a certain desree of
''omprewion and stars of a certain magnitude, and smaller clusters
of 4 , S' or 8' in diameter, with smaller stars and greater compression,
and so on through resolvable nebulsB by imperceptible steps, to the
smalleat and famtaat land most distant] nebula. Other clusters

PlO. IM.— •UMHILUl

thete an, wMoh lead to the belief that dther they are more com-
praased or are composed of Iwrger stars. Spherical dusters are
pimbably not more different in ma among themsAlves than different
individuals of planta of the same species. As it has been shown
that the sphericM figure of a cluster of stars is owing to central
powers, it follows tnt those clusters which, emUrit panbtu, are the
most complete in this figure must have been the longest exposed
to the action of these causes.

" The maturity of d sidereal system may thus be judged from
the dispositioii of :the component ports.

" Though we cannot see any individual nebula pass through all
its stages of life, we can select particular ones m each peculiar
stage," and thus obtain a single view of their entire course of de-
velopment.

NKUULjB.

4«;5

B more condt'iiHcd iit
Illy 8ul)jcft to ci'iitriil
M IIEIWCIIKL ill 1781).

» formed by central

nebula that showB a

i>R8 toward a centre.

id on grounds of ob-

th a certain desree of
and smaller cTusterH
. greater compremlon,
rceptible steps, to the
wke. Other cluatent

Mr they are more com-
^horicat clastera arc
BmselTesthan different
Ab it has been shown
ra is owing to central
eaterU panhu, are the
1 the longest exposed

thus be judged from

ibula pass through all
ones m each peculiar
oir entire course of de-

g 4. SFEOTBA OF NEBUUB AKD OLUSTEBS.

Ill 1HU4, tlvo years after the invention of tlic s|M!ctrosco|K>, Dr.
HiuKiiNH, uf Jjondun, commenced the examination of the spectra
of tlic ncbultc, and was le<l to the discovery that while the siiectru
of Htars were invariably continuous and crossed with dark lines
similar to those of the solar siiectrum, those of many nebula) were
ilimmtinumi*, showing these bodies to bo composed of glowing gos.
The tigure shows the 8])cctrum of one of the most famous planetary
ncbulic. (II. iv. 37.) The gaseous nebulsB include nearly all tho
planetary nebulas, and very frequently liave stellar-like condensa-
tions in the centre.

Singular enough, the most milky looking of any of the nebula:
(that in Andrometla) gives a continuous 8|tc(;truni, while the nebula
uf Orion, which fairly glistens with small stars, has a discontinuous

Via. 181.— flPECTBUH or a FliAHKTART VUBVhA.

spectrum, showing it to be a true ^. Most of these stars are too
faint to be separately examined with the 8pectrosco|K>, so that we
cannot say whether they have the same spectrum as the nebulee.

The spectrum of most clusters is continuous, indicating that the
individual stars are truly stellar in their nature. In a few cases,
however, clusters are composed of a mixture of nebulosity (usually
near their centre) and of stars, and the spectrum in such cases is
compoun'T^ in its nature, so as to indicate radiation both by gaseous
and aoU . > v^tter.

§ 6. DISTBEBXmON OF NEBXTUB Ain> OLUSTEBS
Onr THE SXTBFAOE OF THE CELES-
TIAL SFHEBE.

The follovring map (Pig. 182) by Mr. R. A. Pboctob, gives at a
glance the distribution of the nebulee on the celestial s])here with
reference to the Milky Way, whose boundaries only arc indicated.

UTAJt-Ol.USrKlUi

407

Tlio iMiHitlon of ca<;li iii!l)ulii Ih inarkud l>y n clot ; whuro tlio dotn iiro
thifki'Ht tlioro iH u region rich in nolnilic. A cftHual oxiimiuution
shown that such rich regions arc UiHtant from the Oahixy, ami it
would apiKjar that it in a general law that the ncbulie are diHtri-
Itutcd in greatcHt numlHjr around the two \h>\c» of the gala<tic
circle, ami that in a general way their number at any |X)int of the
Holiero IncroaMcs with their di«tanco from thin circle. Thin wuk
noticed by the elder IIrhhchrI', who constructed a map similar to
the one given. It is precisely the rovcrHc of the law of apparent
distribution of the true star-clusters, which in general lie in or near
the Milky Way.

x.m i i i i>, in '. V I' ' "»< U.-'. -. I W> '

CHAPTER V.

Sl'ECTIlA OF FIXED STAUS.

1. 0HABA0TBB8 OF BTELLAB BFEOTBA.

Soon after thu tllscovory of the Hpcctro8co|»o, Dr. HuofUNB and
Profcsflor W. A. Mii4.kh applied thfa inHtriiinuiit to the examina-
tion of BtoUar spectra, which were found to be, in tlie main, similar
to the solar spectrum— i.e., composed of a continuous band of the

f)ri8mtttic colors, across which dark lines or bands were laid, the
attor iK'ing Wxcd in position. These results showed the fixed stars
to resemble our own sun in gentral constitution, and to be com-
posed of an incandescent nucleus surrounded by a gaseous and
absorptive atmosphere of lower temiteraturo. This atmosphere
around many stars is different in constitution from that of the sun,
as is shown by the different position and intensity of the various
black lines and bands. .« , , « s *

The various stellar spectra have iMJcn classined by Bkcchi into
four t}n>e», distinguished from one unother by marked differences in
the position, character, and number of the dark lines.

Type I is comitosed of the white stars, of which Hinu* and Vega
are examples (the upper spectrum in the plate Fig. 1»8). The snec-
tnim of these stars is continuous, and is crossed by four dark
lines, due to the presence of large quantities of hydrogen in
the envelope. Sodium and magnesium lines are also seen, and
others yet niinter.

Type II is composed mainly of the yellow stars, like our own
»m,^retunu, Capella, Aldtbaran, and Pdlux. The spectrum of
the Bun is shown in the second place in the plate. The vast ma-
jority of the stars visible to the naked eye belong to this class.

TVpe III (see the third and fourth spectra in the plate) is com-
posed of the brighter reddish stars like a OrUmis, Antarea, a Hereulu,
etc. These spectra are much contracted toward the violet end, and
are crossed by eight or more dark bands, these bands being them-
selves resolvable into separate lines. .. ,^ , . , . j u «
These three types comprise nearly all the lucid stars, and it is
not a little remarkable that the essential differences between the
three classes were recognized by Sir Wiiaiam Herschkl as early
as 1798, and published in 1814. Of course his observations were
made without a slit to his spectroscopic apparatus.

us.

BFEOTBA.

Dr. HuoctiNB and
t to the cxamini^
thu main, Himilar
nuous bund of tho
dB weru laid, the
vcd tlie flxod stara
and to be com-
ty a gaiteouB and
Thia atmoflphore
n tliat of the sun,
lity of the various

A by Skcciii into
rkcd differences io
iini'H.

:li Hirius and Vega
g. 188). Tlie snec-
«ed by four dark
I of hydrogen in
re also seen, and

irs, like our own
The spectrum of
;e. The vast mi^
r to this class.
:he plate) is com-
intaret, a Hermlit,
he violet end, and
tHinds being them-

cid stars, and it is
inces between the
iBRscHKii as early
observations were

IS.

UrKLLAH srhxJV'ltA.

401)

•>

m m ^imty ^ f - m . ■ .4<juJi. i i»W > '^ '; il«t '»!»*W W y I' ! **! * '! 'WiW t J' f iflpM ■

470

ASTRONOMY.

Typo IV comprises the red stars, which are mostly telescopic.
The characteristic spectrum is shown in the last figure of the plate.
It is curiously banded with three bright spaces ■epo'ated by
darker ones.

It is probable that the hotter a star is the more simple a spectrum
it has ; for the brightest, and therefore probably the hottest stars,
such as 8iriu$, give spectra ahowing only yery thick hydrogen linea
and a few Terr thin metallic lines, while the cooler stars, such as
our sun, are shown by their spectra to contain a much larger num-
ber of metallic elements than stars of the type of Sirivs, but no
non-metallic elements (oxygen possibly excepted). The coolest
stars give band-flpectra characteristic of compounds of metallic
with non-metallic elements, and of the non-mctaUic elements un-
combiued.

^ a. MOTZOH OF STABS JS THE ZJNE OF SIQHT.

Spectroscopic observations of stars not only give information io
regard to their chemical and physical constitution, but have been
applied so ns to determine approximately the velocity in kilometres
per second with which the stars are approaching to or receding
from the earth along the line joining earth and star. The theory
of such a determination is briefly as follows :

In the solar spectrum we find a ^up of dark lines, as a, }, «,
which always maintain their relative position. From laboratory
experiments, we can show that the three bright lines of incandescent
hydrogen (for example) have always the same relative position as
the solar dark lines a, 1,6. From this it is inferred that the solar
dark lines are due to the presence of hydrogen in it* absorptive
atmosphere.

Now, suppose that in a stellar spectrum we find three dark
lines a', V, e', whose relative position is exactly the same as that
of the solar lines a, b, e. Not only is their relative position the
same, but the characters of the lines themselves, so far as the fainter
spectrum of the star will allow us to determine them, are dso nmi-
lar— that is, a' and a, V and I, e' and e are alike as to thickness,
blackness, nebulosity of edges, ete., ete. From this it is infened
that the star really contains m its atmosphere the substance whose
existence has been shown in the sun.

If we contrive an apparatus by which the stellar spectrum is seen
in the lower half (say) of the eye-piere oi the spectroscope, while
the spectrum of hydrogen is seen just above it, we find in some
cases this remarkable phenomenon. The three dark stellar lines,
a', &',«', instead of being exactly coincident with the tiiree hydro-
gen Unes a,h,e, are seen to be all thrown to one side or the
other by a like amount— that is, the whole group a', J', e, while
preserving its relative distances the same as those of the omnpivi-
son group a, ft, e, is shifted toward either the violet or red end of
the spectrum by a small yet measurable amount. Bepei^ expert-

mostly telescopic.
; figure of the plate,
jaces ■epa'ated by

e simple a spectrum
ly the hottest stars,
liick hydrogen lines
ooler stars, such as
I much larger num-
3 of Siriut, but no
ted). The coolest
pounds of metallic
itallio elements un-

KE or siaHT.

give information ic
ion, but have been
ilocity in kilometres
ling to or receding
d star. The theory

irk lines, wa, h,t,
From laboratory
ines of incandescent
relative position as
erred that the solar
n in its absorptive

ve find three dark
tly the same as that
alative position the
, so f ar M the fainter
them, are also nmi-
ke as to thickness,
n this it is infened
le substance whose

lar speotrum is seen
spectroscope, while
i, we find in some
> dark stellar lines,
ith the three hydro-
to one side or the
oup a', h'j tf, while
>8e of the omnpari-
riolet or red end of
Repeated expeii-

■aBwy . < r f Mi"J' ' »ui i W ! 'i<iiH'>u«Mtwmi.«i^«nw»<ii

STELLAR SPJSGTltA.

471

mentB by diffurent instruments and observers show always a shifting
in the same direction and of like amount. The figure shows the
shifting of the F line in the spectrum of Sirvut, compared with one
fixed line of hydrogen.

This displacement of the
spectral Imes is now ac-
counted for by a motion of
the star toward or from the
earth. It is shown in Phy-
sics that if the source of
the light which gives the
spectrum a', V, e is mov-
ing away from the earth,thi8
group will be shifted toward
the red end of the spec-
trum ; if toward the earth,
then the whole group will
be shifted toward the blue
end. The amount of this
shifting is a function of the
velocity of recession or ap-
proach, and this velocity m
miles per second can be
calculated from the meas-
ured displacement. This has been done for many stars by Dr.
HvoaiNS, Dr. Vookl, and Mr. C'ubibtib. Their results agree well,
when the difllcult nature of the research is considered. The rates
of motion vary from insensible amounts to 100 kilometres per sec-
ond ; and in some cases agree remarkably with the velocities com-
puted from the proper motions and probable parallaxes.

Fio. 131— p-um iH entcTRcif of
snuvs.

CHAPTER VI.

MOTIOJJS AND DISTANCES OF THE STAllS.

§ 1. FBOFSB MOTIONS.

Wk havo already stated that, to the unaided vision, tlio
fixed stars appear to preserve the same relative position in
the heavens through many centuries, so that if the an-
cient astronomers once more saw them, they could hardly
detect the slightest change in their arrangement. But
the refined methods of modem astronomy, in which the
power of the telescope is applied to celestial measurement,
have shown that there are slow changes in the positions
of the brighter stars, consisting in a motion forward in a
straight line and with uniform velocity. These motions
aro, for the most part, so slow that it would require thou-
sands of years for the change of position to be percepti-
ble to the unaided eye. They are called proper moHons.

As a general rule, the fainter the atars the smaller the pro^r mo-
tions. For the most part, the proper motions of the telescopic stus
are so minute that they have not been drteCMsd except in a very
few cases. This arises partly from the actual slowness of the mo-
tion, and partly from the fadt that the positions of these stars have
not generally been well determined. It will be readily seen that, in
order to detect the proper motion of a star, its position must be de-
termined at periods separated by considerable intervals of time.
Since the exact determinaUons of star positions Jia' only been
made since the year 1750, it follows that no proper motion can be
detected unless it is hu^ enough to become perceptible at the end
of a centurr and a quarter, mth very few ezcepnons, no accurate
determination of the positions of telescopic stars was made until
about the beginning of the present century. Consequently, we
cannot yet pronounce upon the proper motions of these stara, and

THE STAllS.

naidcd vision, tho
'elative position in
K) that if the an-
they could hardly
Tangemcnt. But
liny, in which the
itiai measurement,
!8 in the positions
ition forward in a
. These motions
>uld require thou-
in to be percepti-
1 proper moUona.

nailer the proper mo-
>f the telescopic stus
:>M9d except in a verj

slowneM of the mo-
18 of these stars have
I readily seen that, in

position must be de-
le intervals of time,
ions ha.' onlj been
»roper motion can be
erceptible at the end
cepnons, no acemate
stars waa made until
Consequently, we
B of these stan, and

MOTIONS OF TJIK STARS.

473

can only say that, in general, they arc too small to bo detected by
the observations hitherto made.

To this rule, that the smallor stars have no sensible proper mo-
tions, there are a few very notable exceptions. The star Oroom-
hrUIge 1830, is remarkable for having the greatest proper motion of
any in the heavens, amounting to about 7' in a year. It is only of
tlic seventh, magnitude. Next in the order of pro))cr motion comes
tlic double star 61 Gygni, which is alraut of the fifth magnitude.
There are in all seven small stars, all of which have a larger proper
motion than any of the first magnitude. But leaving out these ex-
ceptional cases, the remaining stars show, on an average, a diminu-
tion of proper motion with brightness. In ceneral, the proper
motions even of the brightest stars are only a fraction of a second
in a year, so that thousands of years would be required for them
to change their place in any striking degree, and hundreds of
thousands to make a complete revolution around the heavens.

% 2. PBOFEB HOnON OF THE SUN.

A very interesting result of the proper motions of tlic
stars is that our sun, considered as a star, has a consider-
able proper motion of its own. By olwervations on a star,
we really detennine, not tho proper motion of the star it-
self, but the relative proper motion of the observer and
the star — that is, the difference of their motions. Since
the earth with the observer on it is carried along with the
sun in space, his proper motion is the same as that of the
sun, so that what observation gives us is the difference
l)etween the proper motion of the star and that of the sun.
There is no way to determine absolutely how much of
the apparent proper motion is due to the real motion of
the star and how nmch to the real motion of the sun. If,
however, we find that, on the average, there is a lai'ge pre-
ponderance of proper motions in one direction, we may
conclude that there is a real motion of the sun in an op-
posite direction. The reason of this is that it is more
likely that the average of a great mass of stars is at rest
than that the sun, which is only a single one, should be at
rest. I^ow, obflervation shows that this is really the case,
and that the great mass of stars appear to be moving from
the direction of the xM>nstel1ation Hercules and toward

mms mimmsmmmm

474

ASTRONOMT.

that of the constellation Argots.* A number of astrono-
more have investigated this motion with a view of deter-
mining the exact point in the heavens toward which tlie
gun is moving. Their results are shown in the following
table :

ArfreUnder

O. Strove

Land»bl

Oalloway

MAdler

Airy and Dunkin

DaoltwUlon.

It will be perceived that there is some discordance aris-
ing from the diverse characters of the motions to be in-
vestigated. Yet, if we lay these different points down on
a map of the stars, we shall find that they all fall in the
constellation HerGvUa. Tlie amount of the motion is such
that if the sun were viewed at right angles to the direction
of motion from an average star of the first magnitude, it
would appear to move about one tlurd of a second per
year.

g 3. DISTAITGES OF THE FEEBD STABS.

The problem of the distance of the stars has always
been one of the greatest interest on account of its involv-
ing the question of the extent of the visible universe.
The ancient astronomers supposed all the fixed stars to be
situated at a short distance outside of the orbit of the planet
Saturn, then the outermost known planet. The idea was
prevalent that Nature would not waste space by leaving a
great region beyond Saturn entirely empty..

When CopEKNious announced the theory that the eon
was at rest and the earth in motion around it, the prob-
lem of the distance of the stars acquired a now interest
* This was diBcovoKd by Sir Wiuuam Hbhbobbl in 118S.

DISTANCES OF THE STARS.

4'^5

imber of astrono-
I a view of deter-
toward which tlic
I in the following

DaeliwUion.

88° SC N
87

36' N.

26' N.

23' N.

8»° 54' N.

28° 68' N.

14°
84°

) discordance aris-
motions to be in-
int points dovm on
[ley all fall in the
the motion is such
les to the direction
lirst magnitude, it
, of a second per

3D STABS.

I stars has always
ouut of its involv-
) visible univorac.
le fixed stars to bo
( orbit of the planet
let. The idea was
space by leaving a
ipty.

eory that the snn
»nnd it, the prob-
ad a now interest

tBBCBBL in 1788.

It was evident that if the earth described an annual orbit,
then the stars would appear in the course of u year to os-
cillate back and forth in corresponding orbits, unless they
were so immensely distant that these oscillations were too
small to be seen. Now, the apparent oscillation of Saturn
produced in this way was described in Fart I. , and sliown
to amount to some 6° on each side of the mean position.
These oscillations were, in fact, those which the ancients
represented by the motion of the planet around a small
epicycle. But no such oscillation had ever been detected
in a fixed star. This fact seemed to present an almost
insuperable difficulty in the reception of the Copemican
system. This was probably the reason why Tvoho Bbahk
was led to reject the system. Very naturally, therefore,
as the instruments of observation were from time to time
improved, this apparent annual oscillation of the stars was
ardently sought for. When, about the year 1704,
BoEMEB thought he had detected it, he published his ob-
servations in a dissertation entitled '* Copernicus Trium-
jphansy A similar attempt, made by IIrM)KB of England,
was entitled *^ An Attempt to Prove the Motion of the
Eiirth:'

This problem is identical with that of the annual paral-
lax of the fixed stars, which has been already described in
the concluding section of our opening chapter. This
parallax of a heavenly body is the angle which the mean
distance of the earth from the snn snbtends when seen
from the body. The distance of tlie body from the snn is
inversely as the parallax (nearly>. Thus the mean distance
of Saturn being 9*5, its annual parallax exceeds 6°, while
that of NepbrniSy which is three times as far, is abont 2°.
It was very evident, without telescopic observation, that
the stars could not have a parallax of one half a degree.
They must therefore be at least twelve times as far as
Saturn if the Oo]iemican system were true.

When the telescope was applied to measurement, a eon-
tinually increasing accuracy began to he gained by the

mam

f/mi¥m

476

AUTllONOMY.

i ii

improvement of the instruments. Yet for Bevoral genera-
tions the purallux of the fixed stars eluded nieasurenient.
Very often indeed did observers think they had detected
a parallax in some of the brighter stars, but their succes-
sors, on repeating their measures with better instruments,
and investigating their motltods anew, found their con-
clusions erroneous. Early in the present century it l)e-
came certain that even the brighter stars had not, in gen-
oral, a parallax as groat as 1", and thus it became certain
that they must lie at a greater distance than 2CH),00<) times
that which separates the earth from the sun.

Success in twtually measuring the parallax of the stars
was at length obtained almost simultaneously by two as-
tronomers, l^KssKt. of Kiinigslierg, and Stbuvk of Dorpat.
Bkssbl selected for his star to lie observed 01 Cytjni, and
commenced his observations on it in August, 1837. The
result of two or three years of oliservation was that this
star had a panUlax of 0* • 35, or about one third (»f a sec-
ond. This would make its distance from the sun nearly
fiO(),00() astronomical units. The reality of this paral-
lax has I)oen well established by subsequent investigators,
only it has been shown to be a little larger, and therefore
the star a little nearer than Bksskl supposed. The most
probable parallax is now found to be 0' • 51, corresponding
to a distance of 400,000 radii of the earth's orbit.

The star selected by Strcvr for the meaaure of parallax was the
bright one, a Lurm. His observations were made between Novem-
ber, 18S5, and August, 1888. He first deduced a parallax of 0'-25.
Subsequent observers have reduced this parallax to 0'-20, corre-
sponding to a distance of about 1,000,000 astronomical units.

Short^ after this, it was found by HBHDBRaoN, of England, As-
tronomer Royal for the Cape of Qood Hope, that the star a Cetdauri
had a still larger parallax of about 1*. This is the largest ptmllax
now known in the case of any fixed star, so that a Cmtauri is, be-
yond aP reasonable doubt, the nearest fixed star. ° Tet its distance
is more than 9lCiO,000 astronomical imits, or thirty millions of nat-
ions of kilometres. Light, which passes from the sun to the earth
in 8 minutes, would require S^ years to reach us from a OttUauri,

Two methods of determining parallax have been applied in as-
tronomy. The paratUx found by one of these methods is known as
tAioliUe, that by the other as reutiee paralku. In determining the

JJiaTANCES OF TUK STAItH.

477

For Bevoral gonora-
Itid iiiuauureinuut.
tliey had detected
, but their succes-
>etter instniinonts,
, found their con-
ent century it lie-
's had not, in gen-
it became certain
than 200,000 times
sun.

irallax of tlio stars
noously by two as-
Stbuvk of Dorpat.
iTcd 01 Cyyni, and
ngust, 1837. The
ition was that tliis
one tliird <»f a sec-
OHi tlie sun nearly
dity of this paral-
[uent investigators,
rger, and therefore
>po8ed. The most
• 51, corresponding
•th's orbit.

are of parallax was th«
nade between Novem-
sed a parallax of 0'-25.
mllaxto O'-aO, corre-
tronomical units.
EiuoN, of England, As-
that the star a Oentauri
is the largest parallax
that a Centauri is, be-
star. ' Yet its distance
thirty millions of mlli-
>m tiie sun to the earth
1 OS from a Outtawri.
ra been applied in as-
le methods is known as
t. In determining the

ikksoliitu piirallax, the observer finds thu \wlvLr distanco nf the tttar
im often as possible through a period of one or more years with a
moriilian circle, and then, by a discussion of all his observations,
conchulus what is the magnitude of thu oscillation duo to parallax.
The difficulty in applying this method is that the refraction of the
air and the state of the instrument are subject to changes arising
from varying temperature, so that the observations are always un-
certain by an amount which is important in such delicate work.

In determining the relative paraUax, the astronomer selects two
stars in the same field of view of his tele8C0]M:, one of which is
many times more distant than the other. It is possible to judge
with a high degree of probability which star is the more distant,
from the magnitudes and proper motions of the two objects. It is
nsMumed that a star which is either very bright or has a largo pro-
])cr motion is many times nearer to us than the extremely faint
stars which may be nearly always seen around it. The effect of
parallax will then be to change the apparent position of the bright
star among the small stars around it in the course of a year. This
(iliango admits of being measured with great precision by the mi-
crometer of the equatorial, and thus the relative parallax may be
determined.

It is true that this relative parallax is really not the absolute par-
allax of either body, but the difference of their parallaxes. So we
must necessarily suppose that the parallax of the smaller and more
distant object Is zero. It is bythis method of relative parallax
that the great majority of determinations have been made.

The distances of the stars are sometimes expressed by
the time required for light to pass from tliem to our sys-
tem. The velocity of hght is, it will be remembered,
about 300,000 kilometres per second, or such as to pass
from the sun to the earth in 8 minutes 18 seconds.

The time required for light to reach the earth from
some of the stats, of which the parallax has been measured,
is as follows :

StAK.

Tmr.

Stab.

Yean.

a Oeniatiri

8-5
6-7
83

••4
10-6
11-9
181
18 7
17-9

70 OpkiwM.

t VnaMttjoTU....

Areturui

Y Draeonii

1880 Qroombridge.

Polorii

19- 1

61 qnni

21,115 Lalandtt

« Cmkmri

itGaitieptia

34 OroambrMov. . . .
21,258 Lalan^k....

17,415 Oeltmi.

afrJM

94-8
25-4
851
859
^•4

8077 Bradley.

85 Ptgad

461
64>5

aAwigei.

DraeoniB^

70- 1

u Lgm

1291

i »w?itw L »WJ,ia!#ft^e^;a» sE?gsg^. fe ' ^^iy...'^% ' ..ai^

CHAPTER VII.

CONSTRUCTION OF TUB HEAVENS.

Thb visible univeree, as revealed to us by the telescope,
is a coUcction of many mimons of stars and of several
thousand nebuljB. It is sometimefl caUed the stellar or
sidereal system, and sometimes, as already remarked, the
stellar universe. The most far-reaching question with
which astronomy has to deal is that of tlie form and mag-
nitude of this system, and the arrangement of the stars
which compose it.

It was once supposed that the stars were arranged on
the same general plan as the bodies of the solar system,
being divided up into great numbers of groups or clus-
ters, while all the stars of each group revolved in regukr
orbits round the centre of the group. All the groups were
suppoBed to revolve around some great common centre,
which was therefore the centre of the visible universe.

But there is no proof that this view is correct. The
only astronomer of the present century who held any such
doctrine was Maedlkb. He thought that the centre of
motion of all the stars was m the Pleiades, but no other
astronomer shared his views. "We have abeady seen that
a great many stars are collected into clusters, but there is
no evidence that the stars of these dusters revolve in
regukr orbits, or that the dusters themselves have any
regular motion around a common centre. Besides, the
large majority of stais visible with the telescope do not
appear to be grouped into dusters at alL

8rnucTUiit! OF Tim uka vknh.

479

HEAVENS.

IB by the telescope,
ars and of several
died the stellar or
3ady remarked, the
ling question with
tlie form and mag-
ement of the stars

B were arranged ou
)f the solar system,

of groups or clus- .
revolved in regular
A.11 the groups were
9at common centre,
visible universe.
w is correct. The

who held any such
that the centre of
iades, but no other
ve already seen that
jlusters, but there is

dusters revolve in
lemselves have any
mtre. Besides, the
le telescope do not
IL

The first astronomer to make a careful study of the
arrangement of the stars with a view to learn the structure
of the heavens was Sir William IIebschel. lie published
in the PhiUm/phical Transactions several memoirs on the
construction of the heavens and the arnuigcmunt of the
stars, which have become justly celebrated. We s liall
therefore begin with an account of IIeksoiikl's methods
and nsBults.

IIeksoiiel'b method of study was founded on a mode of
observation which he called sta/r-gaiiging. It consisted in
pointing a powerful telescope toward various parts of the
heavens and ascertaining by actual count how thick the
Bturs were in each region. His 20-foot reflector was pro-
vided with such an eye-piece that, in looking into it, he
would see a portion of the heavens about 15' in diameter.
A circle of this size on the celestial sphere has al)out one
quarter the apparent surface of the sun, or of the full
moon. On pointing the telescope in any direction, a
greater or less number of stars were nearly always visible.
These were counted, and tlie direction in which the tele-
scope pointed was noted. Gauges of this kind were made
in all parts of the sky at which he could point his instru-
ment, and the results were tabulated in the order of right
iiscension.

Tlie following is an extract from the gauges, and gives
the average number of stars in each field at the points
noted in right ascension and north polar distance :

R. P. D.

N. P. D.

B.A.

tr toM°

B.A.

7B« to80>

Jlo of Stm.

NaofStuiu

h. m.

15 10

11 6

16 88

10-6

IS 81

8-4

15 47

106

18 44

16 8

181

18 49

8-9

16 86

18-6

18 8

8-8

16 87

18-6

14 80

I W ' WliiMliMWM II WWi

480

ASmoNOMY.

In this «iniill tiiblo, it iw plain that a «liffuront law of
cluHtcring or of distrilmtion obtaiiiH in the two rogiouH.
Buch diffurenees aro still mor« marked if wu conipai-o the
oxtrenio wuhjs fonnd by IIkbsciikl, aa II. A. = lU"" 41"',
N P D, = 74° 33', nuinbor of stars \hst field ; 588,
and il. A. = 16" 10", N. P. D., 113° 4', number of

stars = l-l.

The number of these stars in certain portions is very
great. For example, in the Milky Way, near OrUm, six
fields of view promiscuously taken gave 110, 60, 70, 90,
70, and 74 stars each, or a mean of 79 stars per field.
The most vacant space in this noighlwrhood gave 63 stars.
So that as Herschkl's sweepa were two degrees wide in
declination, in one hour (15°) there would pass through
the field of his telescope 40,000 or more stars. In some
of the sweeps this number waa as great as 116,000 stars
in a quarter of an hour.

On applying this telescope to the Milky Way, IIeb-
SOHBL supposed at the time that it completely resolved the
whole whitish appearance into small stars. Tliis conclu-
sion he subsequently modified. He says :

" It U very probable that the great stratum called the Milky Way
is that in which the sun is placed, though perhaps not in the very
centre of its thickness. . .^ „ , vi u

"We gather this from the appearance of the Galaxy, which
seems to encompass the whole heavens, as it certainly must do if
the sun is within it. For, suppose a number of stars arranged be-
tween two parallel pbmes, indefinitely extended every way, but at
a given considerable distance from each other, and calling thU a
sidereal stratum, an eye placed somewhere within it will see all
the stars in the direction of the planes of the stratum projected into
a great circle, which will appe&r lucid on account of the accumu-
lation of the stars, while the rest of tiiC heavens, at the sides, will
only seem to be scattered over with constellations, more or less
crowded, according to the distance of the planes, or number of
Stan) contained in vm thickness or sides of the stratum."

Thus in Hbrsobbl^b figure an eye at 8 within the stratum ah
will see the stars in the direction of its length al, or height ed,
with all those in the intermediate situations, projected into the
lucid circle A OBD, while those in the rides me, n», will be seen
scattered over the remaining part of the heavens M VlfW.

STRUVTURE OP THE HEA VEN8.

481

a «liffuront law of
in the two rogioiw.

if w« coiiipiiTO thu
8 R. A. = ID" 41'",
ir» jKsr field; 588,
113° 4', number of

lin portions is very
ITay, near OrUm, hIx
ivo 110, 00, 70, 90,
70 stars per field.
)rhood gave 63 stars,
two degrees wide in
would pass through
[ore stars. In some
■eat as 116,000 stars

3 Milky Way, IIeb-
npletely resolved the
stars. Tliis conclu-
lays :

im called the Milky Wsy
perhaps not in the very

I of the Oalaxy, which
> it cerUdnly must do if
ter of stars arranged bc-
ended every way, but st
other, and calling this a
re within it will see all
le stratum projected into
account of the accumu-
eavens, at the rides, will
istellations, more or less
le planes, or number of
< the stratum."
Sr within the stratum ah
length al, or height ed,
ions, projected into the
des tnv,nw, will be seen

" If the eye were placed somewhere without the stratum, at no
very ^reat (listance, tho apnearance of the stars within it would
assume the form of one of tne smaller circles of the sphere, which

Fio. 1S5.->-hbbbchbl'b thbdbt or ths stbixar sveTBic.

would be more or less contracted according to tho distance of the
eye ; and if this distance were exceedingly increased, the whole
stratum might at last be drawn together into a lucid spot of any

('•'i',"«^'*flK?Mi,5g|0r»^.j:.j>',j;;.

482

A8TR0N0MT.

Mhape, kceording to the length, breadth, and height of the ntn-
turn.

"Riippoae that « Hmaller Mtnitum pq should bninch out (mm
the former in > certain direction, and that it aluo in ronUinetl
between two panllel pluneii, m> that the eye ia conUin«! < within
the great atratum aomewhere iDefore the aeparation, and not far
from the place where the atraU are still united. I'hen this second
Htratum will not be protected into a bright circle like the former,
but it will be seen as a lucid branch proceeding from the first, and
returning into it again at a diaUnoe less than a semicircle.

" In the figure the stars in the small stratum p q will be pro-
jected into a bright uc PRRP, which, after ita separation from
the circle C B D, unitea witii it again at P.

" If the bounding aurfacea are not parallel planes, but irregularly
curved surfaces, analogous appearances must result."

The Milky Way, an we see it, preaents the aspect which
has been just accounted for, in ita general appearance of a
girdle around the heavens and in its bifurcation at a cer-
tain point, and Heksohel's explanation of this appear-
ance, 88 just given, haa never been seriously questioned.
One doubtful point remains: are the stars in Fig. 135
scattered all through the space S — abpdi or are they
near its bounding planes, or clustered in any way within
this space so as to produce the same result to the eye as if
uniformly distributed t

Hbbsohel assumed that they wei-e nearly equably ar-
ranged all through the space in question. He only exam-
ined one other arrangement — viz., that of a ring of stars
surrounding the sun, and he pronounced against such an
arrangement, for the reason that there is absolutely noth-
ing in the size or brilliancy of the sun to cause us to snp-
{lose it to be the centre of such a gigantic system. Mo
reason except its importance to us personally can be all^^
for such a supposition. By the assumptions of Fig. 186,
each star will have its own appearance of a galaxy or milky
way, which will vary according to the situation of the star.

Such an explanation will aooonnt for the general appear-
ances of the Milky Way and of the rest of the sky, sup-
posing the stars equally or nearly equally distributed in
space. On this supposition, tlie system must be deeper

d height of the ntn-

)uld branch out fioin
t it aiRo i» contained
fa it contains I within
eparation, and nut fitr
led. Then this Beconii
circle like the former,
ling from the first, and
a femicircle.
ratum p q will be pro-
ter its separation from

planes, but irregularly
result."

nts the aspect whicli
eral appearance of a
bifurcation at a cer-
ion of this appear-
Briousiy questioned
e stars in Fig. 135
ibpdi or are they
, in any way within
Bsnlt to the eye as if

nearly equably ar-
on. He only exam-
it of a ring of stars
ioed against such an
■e is absolutely noth-
in to cause us to sup-
Igantio system. No
wnally can be all^^
nptions of Fig. 136,
of a galaxy or milky
situation of the star.
>r the general appear-
rest of the sky, sup-
jnally distributed in
item must be deeper

BTRUGTURK OF THK UK A VKIfS.

where the stars appear more niimorouH. The same ovi-
ilunce can be strikingly preouiitud in Hiiotliur way so us to
include the renults of the 8f)Uthern gauges of 8ir J<»hn
IIkkhchel. The Galaxy, or Milky Way, being nearly a
gnifii circle of the Hpliorc, we may compute the position
of its north or south polo; and as the position of our own
))olar points can evidently Iiave no relation to the stellar
nnirene-, we express the position of the gauges in galactio
|)olar dintance, north or south. By subtracting these
polar distances from 90°, we shall have the distance of each
gauge from the central plane of the Galaxy itself, the stars
near 90° of polar disUuce being within the Galaxy. The
average number of stars per Held of 15' for each zone of
15^ of galactic polar distance has been tabulated by Stbuve
and Hbbsohbl as follows:

Zoom or Qalactto

Ayanua Namber
of Sun per

Zone* of

Average Nunilier

North ruiar

Oalactio South Polu

of Htara per
Field of ly.

DIllMM.

n«ld of My.

DUtMce.

0° to 16'

4-88

0* to 15°

605

1S° to 80°

843

15° to 80°

66!)

80° to 45*

881

80° to 45°

908

45° t4. 60°

18 01

45° to 60°

18-49

60° to 78°

2400

80° to 75°

86-29

75* toW

58-48

75° to 90°

59-06

This table clearly shows that the auperjioidl distribution
of stars from the first to the fifteenth magnitudes over the
apparent celestial sphere is such that the vast majority of
them are in that zone of 30° wide, which includes the
Milky Way. Other independent researches havt shown
that the fainter lucid stars, considered alone, are also dis'
tributed in greater ntunber in tliis zone.

HsRsoan. andeavored, in his earhr memoirs, to find the physical
explanation of this inequality of distribution m the theory of the
uniTerse ezemplifled in Fig. 188, which was based on the funda-
mental amumption that, on the whole, the otars wen, nearly equably
distributed in space.

484

ASTRONOMY.

If they were so distributed, then the number of stars visible in
any gauge would show the thickness uf the stellar system in the
direction in which the telescope was pointed. At each pointing,
the field of view of the instrument includes all the visible stars sit-
uated within u cone, having its vertex at the observer's eye, and its
base at the vei7 limits of me system, the angle of the cone (at the
eye) being IS' 4*. Then the cubes of the perpendiculars let fall
from the eye on the plane of the bases of the various visiul cones
are proiiortional tj the solid contents of the cones tliemselves, or, as
the stars are suppoaed equally scattered within all the cones, the
cube roots of the numbers of stars in each of the fields express the
relative lengths of the perpendiculars. A teetion of the sidereal sys-
tem along any great circle can thus be constructed as in the figure,
which is copied from Hbbbchel.

The solar system is supposed to bo at the dot within the mass of
stars. From this point fines are drawn along the directions in
7'hich the gauging telescope was pointed. On theae lines are laid
off lengths proportional to the cube roots of the number of stars in
each gauge.

FlO. 186.— ABBAHOBMBNT OF THB BTABS ON THB HYP0 T HM I8 OF
HQUABLB DIflTRIBanON.

The irregular line joining the terminal points is approximately
the bounding curve of the ^Uar system in the great circle chosen.
Within this line the space is nearly uniformly filled with stars.
Withov* it is empty space. A similar section can be constructed in
any o.her ^reat circle, joA a combination of all such would give a
representation of the shape of our stellar system. The more numer-
ous and careful the observations, the more elaborate the represen-
tation, and the 868 gauges of Hersohbl are sufilcient to mark out
with great precision the main features of the Milky Way, and even
to indicate some of its chief irregularities. This figure may be
compared with Fig. 185.

On the fundamental assumption of Hbrbchbl (equable distribu-
tion), no other conclusions can be drawn from his statistics but
that drawn by him.

This assumption he subsequently modified in some desree, and
was led to regard his gauges as indicating not so much the depth
uf the system in any direction as the clustering power or tendency
of the stars in those special regions. It is clear that if in any

number of stars visible in
f the stellar system in the
pointed. At each pointing,
tides all the visible stars sit-
Eit the observer's eye, and its
:he angle of the cone (at the
the perpendiculars let fall
of the various visual cones
' the cones themselves, or, as
ed within all the cones, the
ach of the fields express the
A teetion of the sidereal sys-
sonstructed as in the figure,

t the dot within the mass of
wn along the directions in
ed. On these lines are laid
>ta of the number of stars in

STRUCTURE OF THE HEAVENS.

485

m ON THR HTPOTHmS Or
3TION.

nal points is approximately
n in the great circle chosen,
iniformly filled with stars.
ectioD can be constructed in
on of all such would give a
r system. The more numer-
aore elaborate the repreaen-
H< are sufficient to mark out
f the Millcy Way, and even
rities. This figure may be

BRSCRBL (equable distribu-
wn from his statistics but

idifled in some desree, and

ing not so much the depth

iistering power or tendenr;

It is clear that if in any

given part of the sky, where, on the average, there are 10 stars
(say) to a field, we should find a certain small portion of 100 or
more to a field, then, on Hgkhciiel's first hypothesis, rigorously in-
terpreted, it would be necessary to suppose a spike-shaped protu-
berance directed from the earth in order to explain the increased
number of stars. If many such places could on found, then the
probability is great that this explanation is wiong. We should
more rationally suppose some real inequality of star distribution
here. It is, in fact, in just such details that the system of Her-
BCHEb breaks down, and the careful « xatnination which his system
has received leads to the belief that it must be greatly modified to
cover all the known facts, while it undoubtedly has, in the main, a
strong basb.

The stars are certainly not uniformly distributed, and any gen-
eral theory of the sidereal system must take into account the varied
tendency to aggregation in various parts of the sky.

The curious convolutions of the Milky Way, observed at various
parts of its course, seem inconsistent with the idea of verv great
depth of this stratum, and Mr. Pboctor has pointed out that the
circular forms of the two " coal-sacks" of the Southern Milky Way
indicate that they are really i^obnlar, instead of being cvundric
tunnels of great length, looking into space, with their axes directed
toward the earth. If they are slobular, then the depth of the
Milky Way in their ndghborhood cannot be greatly dimrent from
their diameters, which would indicate a much sualler depth than
that assigned by HEKscfueL.

In 1817, HBRscHBii published an important memoir on the same
subject, in which his firrt method was largely modified, though
not abtuDdoned entirely. Itv fuodamraital j^ndple was stated or
him as follows :

" It is evident that we cannot mean to affirm that the stars of the
fifth, sixth, and seventh nuwnitudes are really smaller than those
of the first, second, or third, and that we mustascrilM the cause
of the difference in the apparent magnitudes of the stars to a differ-
ence in their relative diMancea fnmi us. On account of the great
number of stars in each daas, we must also allow that the star* of
each succeeding magniti^e, Winning with the first, «re, one with
another, further from ns than thoae of the masnitude inunediately
preceding. The relative magnitudes give only reUtive distances,
and can afford no information as to the real distances at which the
stars are placed.

" A stMidard of reference for the arrangement of the stars may
be had by comparing their distribution to a certain properly mod-
ified equality of scattering. The equality which I propoBe does not
require that the stars should foe at equal distances from each other,
noi- is it necessary that all those of the same nominal magnitude
should be eqqallT distant from us."

It consiBtsof allotting a certain equal portion of space to every
star, so that, on the whole, each equal portion of apace within the
stellar system ccatains an equal number of stars.

486

ASTRONOMT.

The space about each star can be ootuidered spherical. ^ 8up>
poM such a sphere to lurround our own san, its radius will not

differ greatly from the
dirtance of the nearest
fixed star, and this is
taken as the unit of
distance.

Suppose a series of
larger spheres, all
drawn around our sun
as a centre, and having
the radii 8, 5, 7, 9,
etc. The contents of
the spheres beinir as
the cubes of their
diameters, the first
tphtrewIUhaTeS x 8
X 8 = 27 times the
volume of the unit
■phere, and will there-
fore be latge enough
to contain 87 stars ;
tiie second will have
185 times the volume,
•nd will therefore con-
tain 185 stars, and so
with the successive

teres. The figure
ws a section of
portions of these
(qiheres ttp to that
with radius 11. Above
the centre are given
the various orders of
■tars which are situ-
ated between the sev-
eral spheres, while
la the eerrespondin:
•paces below the cen-
tre are given the num-
ber of stars which the rnrfon is large enough to contain ; for in-
stance, the sphere of ramus 7 has room for 848 stan, but of this
space 185 puts belong to the spheres inside of it : there is, there-
fore, room for 818 stars between the spheres of radii 8 and 7.

^■■CBBi. designates the several distances . of these lavers of
stars as orders ; the stars between spheres 1 and 8 are of the first
order of distance, those between 8 and 5 of the second order, and
so on. Comparing the room for stars between the several spliereB
with the number of stars of the several magnitudes, he found the
result to be as follows :

OP SOTAIRSB 09 WttML

STRUCTUBB OF THE HEAVENS.

487

»iiHidered spherical. 8up-
II ■un, its radius will not
differ greatly inm the
dirtance of the nearest
llzed star, and this is
taken as the unit of
distance.

Suppose a series of
larger spheres, all
drawn around our sun
as a centre, and having
the radii 8, 6, 7, 9,
etc. The contents of
the spheres beins as
the cubes of their
dUbmeters, the iirst
■phirewlllhaTeS x 8
X 8 =s S7 times the
Tolume of the unit
sphere, and will there-
fore be latge enough
to contidn 87 stars ;
the second will have
125 times the volume,
and will therefore con-
tain ISS stars, and so
with the successive
spheres. The figure
snows a secUon of
portions of these
■pheres up to that
with radius 11. Above
the centre are given
the various orden of
■tars whkh an situ-
ated between the sev-
eral spheres, while
in tiie oerrespondin :
M, spaces below the cen-
tre are given the num-
■ough to contain ; for in-
i for 848 Stan, but of this
ide of it : then is, there-
eres of radii 5 and 7.
itances . of these layen of
» 1 and 8 an of the first
of the second order, and
tween the several spheres
magnitudes, he found the

Order of iMttnee.

Number of Stars
Uiere la Room for.

Xagnltade.

Nambar of Stara
ortbatMacnitada.

818

896

600

866

1,178

1.588

1
8

5
6
7

206

454

1,161

6,108

6,146

The result of this comparison is, that, if the order of magnitudes
could indicate the distance of the stars, it would denote at first a
gradual and afterward a veij abrupt condensation of them.

If, on the ordinary scale of magnitudes, we assume thebrishtness
of any star to be inversely proportional to the sqiun of Its dis-
tance, it leads to a scale of distance differant from that adopted by
Hebbchei., so that a rizth-magnitnde star on the common scale
would be about of the eighth order of distance according to this
scheme — that is, we must remove a star of the first magmtude to
eight times ita actual distance to make it shine like a star of the
sixth magnitude.

On the scheme hen laid down, Huwchbl subsequently assigned
the ordn* of distance of various objects, mostly star-clusters, and
his estimates of these distances an still quoted. They rest on the
fundamental hypothesis which has been explained, and the error
in the anumption of equal brilliancv for all stars, affecto these esti-
mates. It is perhaps most probable that the hypothecs, of equal
brillimcy for all stan is still mora erroneous ttuw the hypothesis
of equal distribution, and it may well be ttat th«e is a verv large
range indeed in tiie aetoal dimemdonsandin the intrinite brilliaacy
of Stan at the same order of diataace ftom us, so that the tenth-
magnitude stars, for nample, may be scattered tbroiu^iout the
sphmres, which HnuinnD. would asdgn to tiie seveiftfi, eighth,
nintii, tenth, eleventh, twelfUi, and thirteenth magnitudes.

ESnee the tioM of HnnoMXL, one of the most eimnent of the as-
tronomen who have investigatodTthis subject is STBimc the elder,
formerly director of the Pulkowa Observatonr. His reseanhes
wen founded mainly on the numben of stan of the several magni-
tudes found I^BnssL in a zone thirty d^rees wide extending all
around the heavens, 15* on each dide of the equatw. With these
he eomUned the gauges of Sir Willun Hbrschbl. The hypothesis
on which he based his theory was rimilar to that employed by
Hbbschbl in his later reseanhes, in so far that he supposed the
magnitude of the stan to furnish, on the average, a measura of
their nlative distances. Supposing, after Hbbsohbl, a number of
concentric spheres to be drawn around the mn as a centra, the suc-
cessive spaoea between •mtitSx comsponded to stan of the several

488

ASTRONOMY.

maanitudea. ho found that the further out he went, the more the
8tlS wore condensed in and near the Milky Way. This concluston
may be drawn at once from the fact we have ahready mentioned,
that the smaller the stars, the more they are condensed in the re-
gion of the Galaxy. ftniirrB found that if we take only the stare
plainly vUible to the naked eye-that is. th«»^«''" *« *>»« *'*•*
maimitude— they are no thicker in the Milky Way than in other
parts of the heavens. But those of the sixth magnitude are a
little thicker in that region, thoee of the seventh yet thicker, and
soon, the inequality of distribution becoming constantly greater as
the telescopic power is increased.

From all this, dntcvK concluded that the stellar system might
be considered as composed of layers of stars of various densities, all
parallel to the planeof the Milky Way. The stars are thickest in wid
hear the central layer, which he conceives to be spread out as a wide,
thin sheet of stars. Our sun is ntuated near the middle of this
Uyer. As we pass out of this layer, on either side we find the
stars constantly growing thinner and thinner, but we do not reach
any distinct boundary. As, if we could riw in the atmosphere, we
should find the air constantly growUig thinner, but at m gradual a
rate of progress that we could hardly say where it terminated ; so.
on arBuWa view, would it be with the stellar system, if we could
mount up in a direction perpendicular to the Milky Way. SrauvB
gives the following Uble of the thickness of the stars on each side
of the principal plane, the unit of distance being that of the ex-
treme ^stance to which HBBScBUi'B telescope could penetrate :

Meu DiitHiee

betwvMi Ndghbor-

bagStan.

In the principal plane. . . .

0-08 from principal piano

010

0-80

0-40

0-60

OdO

0-70

0-80

0-866

10000

0-48668

0-88888

0-88886

017880

018081

006646

006510

008078

001414

0-C068S

000

87S

458

611

778

878

861

8-688

8-180

4-181

0-788

This condensation of the stars near the central plane and the
gradual thinnhig-out on each dde of it ate onlyde^pied to be the
expression of the general or average distribution of those bodies.
The probability is that even in the central plane the stars are many
times as thick in some regions as in others, and that, as we tawe the
phme, the thimung-out would be found to proceed at very dmerent
rates in different regions. That there may be a gradual thinning-out

wmtum

STRUCTURE OF THE HEAVENa.

489

) went, the more the
Fay. This conclusion
e already mentioned,
condensed in the re-
e take only the stars
Me down to the fifth
cy Way than in other
ixth magnitude are a
enth yet thicker, and
; constantly greater as

stellar system might
I various densities, all
ters are thickest in and
e sprmd out as a wide,
« the middle of this
her side we find the
r, but we do not reach
in the atmosphere, we
ir, but at so gradual a
ere it termini^ed ; so,
ar system, if we could
Milky Way. Srauva
the stars on each side
wing that of the ex-
le could penetrate :

Mean IMrtwee

ingBian.

1000

1279

1-468

1011

irra

1-978 .

8-Ml

8-088

8-180

4-181

0-788

central plane and the
>nly designed to be the
ition of those bodies,
lane the stars are many
nd that, as we leave the
poceed at very different
I a gradual tlunnbg-out

cannot be denied ; but Strovb'b attempt to form a table of it is open
to the serious objection that, like HsRscHEti, he supposed the differ-
ences between the magnitudes of the stars to anse entirely from
their different distances from us. Although where the scattering
of the stars is nearly uniform, this supposition may not lead us into
serious error, the case will be entirely different where we have to
deal with irregular masses of stars, and especially where our tele-
scopes penetrate to the boundary of the stellar system. In the
latter case we cannot possibly distinguish between small stars lying
within the boundary and larger ones scattered outside of it, and
Strutb's gradual thinning-out of the stars may be entirely ac-
counted for by great diversities in the absolute brightness of the
stars.

Distribution of Stan.— The brightness B of any star, aa seen
from tho earth, depends upon Im surface 8, the intensity of its light
per unit of sarfikce, i, and its distanoe D, so that its brightneaa can be
expressed thus :

for another star :
and

B a-i

B' =.«'-<'•

Nuw this ratio of the brightness B 4- JS' is the <mlj fact we usually
know with regard to any two stars. D has been determined for
only a few Btara, and for thetie it variaa between 800,000 and 8.000,000
times the major axis of the earth's orbit. 8 and i are not known for
any star. There la, however, a prol>ability that t does not vary greatly
from star to star, aa the gnat majority of stars are white in color (only
some 700 red stars, for instanoe, are known out of the 300,000 which
have been careftilly examined). Among 470 double stars of Stbuvk's
Hat 295 were white, 08 being bluish, only one fourth, or 118, bdng
yellow or red.

If JB is of the nth mag. ite light in terms of a first magnitude star
is 4* - 1 where 4 = 0- W7. and if JSTIs of the mth mag., ite light is
<>"-', both expressed in terms of the lii^t of a first magnitude star aa
unity (J* = 1).

Therefore we may put J? = d»-', 5' = <J"-', and we have

=: (la — ■> —

jy*

8' iU^

In this general expression we seek tlie ratio -j~ , and we have it

expressed in terms of four unknown quantities. We must therefore
make some supposition in regard to these.

1. Jf M ttar$ ore of equat tHtrintie britiianeif and of equal tke, then

8i, iS* <', and *• -- s= a constant = -==-,

•mmtmtm

mmm

hmh

■ > jrfjfl't*^

M. j ' ,Mf.vr )rg .w.v » u^jir r v<Jt r'ig;

490

A8TR0N0MT.

whence the relative distance of any two stan would be known on this
hypotheiila.

II. Or, iuppote the itart to he uniformly diMr^mUd in »paee, or tiM
■tar-densltjr to be equal in all directions. From this we can also
obtain some notions of the relative distances of stars.

Call Di, Dt.D, D, the average distances of stars of the

1, 3, 8, nth magnitudes.

ir K stars are situated within the sphere of radius 1, then the num-
ber of stars {Qn), situated within the sphere of radius D., is

since the cubic contenta of spheres are as the cnlies of their radii.
Also

«,_, = jr(D.-,)», i

whence

D,^

-V-

«--«

If we knew Q, and Q» - 1, the number of stan contained in the
spheres of radii D% and D» _ i, then the ratio of D, and D» - i would
be known. We cannot know Q., Q, _ i, etc., directly, but we may
suppose these quantities to be proportional to the numbera of stan of
the nth and (n — l)tU magnitudes found in an enumeration of all the
stare in the heavens of these magnitudes, or, lailinff in these data, we
may confine this enumeration to the northern liemispbere, when
LiTTROW has counted the number of stan of each class in AReiLLAH-
OBR's Durehmuiterung. As we have seen (p. ti8)

whence

Q, = 19,(»9 and Q, = 77,794,
1>. _ l/'Q^

^ - i/ V' -
"2>, ~ y Q, ~

and this would lead us to infer that the stan of the 8th magnitude
were distributed inside of a sphere whose radius was about 1 -6 times
that of the corresponding sphere for the 7th magnitiide stars provided
that, 1st, the stara in general are equally or about equally distributed,
and, 2d, that on the whole the stan of the 8 .... » magnitudes are

further away fh>m us than thoae of the 7 (» — 1) munitudes.

We may have a kind of test of the truth of this hypotSesis, and of
the fint employed, as follows, we had :

3b-i - y 0,-1

Also from the firat hypothesis the briirhtnnas S, of a star of the nth
magnitude in terms of a first magnitude star = 1 was

If here, again, we suppose the distance of a fint magnitude star to
be = 1 aira of an nth magnitude star !>.. then

ii iMm» i i. i i).unu

STRUCTURE OF THE HEAVENS.

491

rould be known on this

r^ttd in tpaee, or tho

9*1001 thia we am aleo

ItAtn.

■tanoes of aUrs of the

radiua 1, then the nam-
radina D», ia

lie cabea of their r»dll.

f atara contained in the
of Dn and D, _ i would
., directly, but we may
the numbera of atara of
enumeration of all the
lilinff in theae data, we
urn nemiaphere, where
ich claaa in Abobllah-
486)

794.

ra of the 8th magnhnde
ua waa about 1 -t timea
agnitude atara provided
out equally diatributed,
I .... » magnitndea are
(n — 1) munitudea.
thia hypotoeaia, and of

Bm of a Btar of the nth
= 1 waa

llrat waKnitnde atar to

whence ^;^ - -^==-

Comparing the expreaa i on for ;g-^ >» ^be two caaea, we have

If the ▼alne of d in thia laat expreaaion cmnea near to the value which
haa been deduced for it from direct photometric meaaurea of the
relative intenaity of varioua claaaea of atara, nia., i = 0-40, then thia
will be ao far an argument to ahow that a certain amount of credence
may be given to both hypotheaea I. and II. Taking the valuea of
Q, and Q,, we hanre

'<■•■'= (-^-)*=»*^

From the valuea of Q. and Qt, there reaulta <)(•, t) = 0-45. Theae,
then, agree tolerably well with the independent photometric valuoa
for 6, and ahow that the equation

givea the average diatanee of the atara of the nth magnitude with a
certain approach to aceuncy. For the atan from lat to 8th magni-
tude tiiaae diatancea are :

1 to 1-9 nagaitnde. 100

Sto9-9 •• 184

8to8-9 " «'88

4to4-9 •• 8-84

5to6-9 •• 5-80

8to8-9 " 8-81

7 to 7-9 " 18-88

8to8-9 •* aO-88

Thia preaentaUon of the anbjeet ia eaaentiidly that of Prof. Buoo
GTLOni.

!lllllilllll.Wlt.l|illl JM I

t im m mmxm '

!'■>

CHAPTER VIII.

COSMOGONY.

A THEOEY of the operations by which the nmvewo re-
ceived its present form and arrangement is called CTMmojy-
my. This subject does not treat of the ongin of matter,
but only with its transformations.

Threi systems of Cosmogony have prevailed among
thinking men at different times.

(1.) That the universe had no origin, but existed from
eternity in the form in which we now sec It.

(2.) That it was created in ito present shape m a
moment, out of nothing.

(8.) That it came into its present form through an ar-
rangement of materials which were before " without form

"""TheU seems to be thoidea which has most prevailed
among thinking men, and it receives many ^tnlong con-
firmations from the scientific discoveries of modem times.
^Z Utter seem to show beyond aU "-TJ^^ .^^^
the universe could not always have existed mits present
S^rdi::?deritspresentconditions;ih.ttherew..at^^

when the materials composing it were masses of glowing
vapor, and that there will be a time when the present state
of things wiU cease. The explanation of the procewes
through which this occurs is sometimes called the nefttjtor
AvpoSm*. It was first propounded by the philosopben
SwBDE^BOBO, Kant, and Laplace, and although since
greatly modified in detail, the views of these men have m
tiie main been retained until the present time.

C08M0G0NT.

408

I the tmiverwre-
c is called Coanwg-
j origin of matter,

prevailed among

, bnt existed from

ee it.

Bsent shape in a

rm through an ar-
)re " without form

has most prevailed
many striking con-
BB of modem times,
isonable doubt that
asted in its present
;hat there waa a time
masses of glowing
len the present state
m of the processes
IS called the ndnilar
Dy the philosophers
und although since
f these men have in
mt time.

Wo eliall '. n its consideration by a statement of the
various facts which appear to show that the earth and
planets, as well as the sun, were once a fiery mass.

The first of these facts is the g^dual but uniform in-
crease of temperature as we descend into the interior of
the earth. Wherever mines have been dug or wells sunk
to a great depth, it is found that the temperature increases
as we go downward at the rate of about oite degree centi-
grade to every 30 metres, or one degree Fahrenheit to
every 50 feet. The rate differs in different places, bnt tlie
general average is near this. The conclusion which we
draw from this may not at first sight be obvious, because
it may seem that the earth might always have shown this
same increase of temperature. But there are several re-
suits which a little thought will make clear, although their
complete establishment requires the use of the higher
mathematics.

The first result is that the increase of temperature ean-
not be merely superficial, but must extend to a great
depth, probably even to the centre of the earth. If it did
not so extend, the heat would have all been lost long ages
ago by conduction to the interior and by radiation from
the surface. It is certain that the earth has not received
any great supply of heat from outside since the earliest
geological ages, because such an accession of heat at the
earth's surface would have destroyed all life, and even
melted all the rocks. Therefore, whatever heat there is
in the interior of the earth must have been there from be-
fore the commencement of life on the globe, and rwnained
through all geological ages.

The interior of the earth being hotter than its surface,
and hotter than the spacearoundit, must be losing heat.
We know by the most familiar observation that if any ob-
ject is hot inade, the heat will work its way through to the
surface by the process of conduction. Therefore, since the
earth is a great deal hotter at the depth of 30 metres than
it is at the surface, heat must be continually coming to the

■?.<^?»>»i,'fW™qyi,-^:_^?^-- >

494

ABTRONOMT.

Burfaoe. On reaching the surface, it muBt be radiated off
into space, else the surface would have long ago become
as hot as the interior. Moreover, this Iobb of heat must
have been going on since the beginning, or, at least, since
a time when the surface was as hot as the interior. Thus, if
we recffbn backward in time, we find tliat there must have
been vaote and more heat in the earth the further back
we go, so that Ve must finally reach back to a time when
it was so hot as to be molten, and then again to a time
when it was so hot as to be a mass of fiery vapor.

The second fact is that we find the son to be cooling off
like the earth, only at an incomparably more rapid rate.
The sun is constantly radiating heat into space, and, so far
as we can ascertain, receiving none back again. A snudl
portion of this heat reaches the earth, and on this portion
depends the existence of life aud motion on the earth's sur-
face. The quantity of heat which strikeB the earth is only
'^'^'>^ hiiAmsi o^ ^^ which the sun radiatCB. This
fraction! eipresBes the ratio of the apparent surface of the
eart)l, as seen from the sun, to that of the whole celestial
sphere.

Since the son is losing heat at this rate, it must have had
more heat yesterday than it has to-day ; more two days ago
than it had yesterday, and so on. Thus calcuUting back-
ward, we find that tiie further we go back into time the
hotter the sun must have been. Since we know that heat
expands all bodies, it follows that the sun must have been
larger in past agee than it is now, and we can trace back
this increase in size without limit. Thus we are led to the
conclusion that there must have been a time when the sun
filled up the space now occupied by the planets, and must
have been a very rare mass of glowing vapor. The plan-
ets could not then have existed separately, but must have
formed a part of this mass of vapor. ' The latter was there-
fore the material out of which the kAmx system was
formed.

The aame process maybe continued into the future.

■BBW

<y<

iBt bo radiated off
long ago become
MB of heat must
or, at least, since
interior. Thus, if
it there must have
the farther back
ik to a time when
t again to a time
ry vapor.

n to be cooling off
more rapid rate.
I space, and, so far
t again. A small
nd on this portion
on the earth's sor-
es the earth is only
m radiates. This
•ent surface of the
the whole celestial

I), it must Iwye had
more two days ago
m calculating back-
jack into time the
we know that heat
in must have been
we can trace back
us we are led to the
,time when the sun
e planets, uidmust
vapor. Theplan-
tely, but must have
Sie latter was there-
BoHu system waa

ed into the future.

Since the sun by its radiatioa li sonstantlj ,^>dng heat, it
must grow cooler and cooler as ttge^ advi««wie, and must
finally radiate so little heat that life and motion can no
longer exist on our globe.

The third fact is that the revolutions of all the planets
around the sun take place in the same direction and in
nearly the same plane. We have hero a similarity amongst
the different bodies of the solar system, wfiioh must have
had an adequate cause, and the only cause which has ever
been assigned is found in the nebular hypothesis. This
hypothesis supposes that the sun and planets were once
a great mass of vapor, as large as the present solar system,
revolving on its axis in the same plane in which the
planets now revolve.

The fourth fact is seen in the existence of nebulas. We
have already stated that the spectroscope shows these bodies
to be masses of glowing vapor. We thus actually see mat-
ter in the celestial spaces, under the very form in which
the nebular hypothesis supposes the matter of our solar
system to have once existed. Sinoe these masses of vapor
are so hot as to radiate light and heat through the immense
distance which separates us from them, they most be grad-
ually cooling off. This cooling must at lengUi reach a
point when they will cease to be vaporous and condense
into 6bjects Hke stars and planets. We know that every
star in the heavens radiates heat as our sun does. In the
case of the brighter stars the heat radiated has been made
sendble in the f od of our telescopes by means of the thermo-
multiplier. The general relation which we know to ex-
ist between light and radiated heat shows that all the stars
must, like the sun, be radiating heat into spaoe.

A fifth fact is afforded by Ae physical constitution of
the planets Jupiter and Saturn. The tetoscopie examina.
tion of tiiese planets shows that changes on their surfaces
are constantly going on with a rapidity and violence to
which nothing on the surface of our earth can compare.
Such operations can be kept up only through the ^ncy of

.«..-

ABTRoyonr.

heat or some equivalent furiu uf energy. But at the dis.
tance of Jupiter and Sntum the rayn of the sun are entirely
insufficient to produce changes so violent. Wo are there-
fore led to infer that Jupiter and Saturn must be hot
bodies, and must therefore be cooling off like the sun,
stars and earth.

We are tlius led to tJie general conclusion that, so far
as our knowledge oxtend^, nearly all the bodies of the
universe are hot, and are cooling off by radiating their
heat into space. Before the discovery of the " conserva-
tion of energy," it was not known that this radiation in-
volv«)d the waste of a something which is necessarily Umited
in supply. But it is now known that heat, motion, and
other forms of force are to a certain extent convertible into
each other, and admit of being expressed as quantities of
a general something which is called energy. We may de-
fine the unit of energy in two or more ways : as the quan-
tity which is required to raise a certain weight through a
certain height at the surface of the earth, or to heat a given
quantity of water to a certain temperature. However
we express it, wr know by the laws of matter that a given
mass of matter can contain only a certain definite number
of units of energy. When a mass of matter either gives
off heat, or causes motion in other bodies, we know that
its energy is being expended. Since the total quantity of
energy which it contains is finite, the process of radiating
heat must at length come to an end.

It is sometimes supposed thi^ this cooling off may be
merely a temporary process, and that in time something
may happen by which all the bodies of the oniverse will
receive back again the heat which they have lost. This is
founded upon the general idea of a oompensating process in
nature. As a special example of its application, some have
supposed that the planets may ultimately fall into the sun,
and thus generate so much heat as to reduce the snn once
m<Mre to vapor. All these theories are in direct opposition
to the well-establiahed laws of heat, and can be justified

But at the diB<
i sun are entirely

We are there-
tm must be hot
)S like the sun,

uion that, so far
le bodies of the
»y radiating their
f the " conserva-
this radiation in-
leoessarily limited
lieat, motion, and
it convertible into
d as quantities of
^. We may de-
rays : as the quan-
weight through a
, or to heat a given
rature. However
latter that a given
n definite number
latter either gives
ies, we know that
e total quantity of
rocesB of radiating

ooling off may be
in time something
I the universe will
have lost. This is
)en8ating process in
lication, some have
ly fall into the sun,
educe the sun once
in direct opposition
d can be justified

COSMOGONT.

407

only by fioine gcnoralizutiun which Hhall Im3 fur wider than
any that science has yet reached. Until we have bucIi a
goneralizatiou, every such theory founded upon or consist-
ent with the laws of nature is a neceosary failure. All the
heat that could be generated by a fall of all the planets into
the sun would not produce any change in its constitution,
and would only last a few years. The idea that the heat
radiated by the sun and stan may in some way Ik) collected
and returned to them by the mere operation of natural laws
is equally untenable. It is a fundamental principle of the
laws of heat that the latter can never pass from a cooler
to a warmer body, and that a l>ody can nevor grow warm
or acquire heat in a space that is cooler .nan the body is
itself. All diiferences of temperature tend to equalize
themselves, and the only state of things to which the uni-
verse can tend, under its present laws, is one in which all
space and all the bodies contained in space are at a uniform
temperature, and then all motion and change of tempera-
ture, and hence the conditions of vitality, mtifct cease. And
then all such life as ours must cease also unless sustained
by entirely new methods.

The general result drawn from all these laws and facts
is, that there was once a time when all the bodies of the
universe formed either a single mass or a number of masses
of fiery vapor, having slight motions in various parts, and
different degrees of density in different regions. A grad-
ual condensation around the centres of greatest density then
went on in consequence of the cooling and the mutual at-
traction of the parts, and thus arose a great number of
nebulous masses. One of these masses formed the ma-
terial out of which the sun and planets are supposed to
have been formed. It was probably at first nearly glob-
ular, of nearly equal density throughout, and endowed
with a very slow rotation in the direction in which the
planets now move. As it cooled off, it grew smaller and
smaller, and its velocity of rotation increased in rapidity by
virtue of a well-established law of mechanics, known a*

?j»!rs*-,SS»«-

'"v

.'11

498

ABTRONOMT.

that of the conservation qf curecm. According to tliis law,
whenever a eystem of particles of any kind whatever, which
is rotating around an axis, changes its form or arrangement
by virtue of the mutual attractions of its parts among them-
selves, the sum of all the areas described by each particle
around the centre of rotation in any unit of time remains
constant. This sum is called the areolar vdoeity.

If the diameter of the mass is reduced to one half, sup-
posing it to remain spherical, the area of any plane passing
through its centre will be reduced to one fourth, because
areas are in proportion to the square of the diameters.
In order that the areolar velocity may then be the same
as before, the mass must rotate four times as fast. The
rotating mass we have described must have had an axis
around which it rotated, and therefore an equator defined
as being everywhere 90° from this axis. In consequence
of the increase in the velocity of rotation, the centrifugal
force would also be increased as the mass grew smaller.
This force varies as the radius of the circle described by
the particle multiplied by the square of the angular velocity.
Hence when the masses, being reduced to half the radius,
rotate four times as fast, the centrifugal force at the equa-
tor would be increased i X 4*, or eight times. The gravi-
tation of the mass at the surface, being inversely as the
square of the distance from the centre, or of the radius,
would be increased four times. Therefore as the masses
continue to contract, the oentrifogal force increases at a
more rajad rate than the oentoal attraction. A time would
therefore come when they would balance each other at the
equator of the mass. The mass would then oease to con-
tract at the equator, but at the poles time would be no
centoifugal force, and the gravitation of the mass would
grow stronger and stronger. In consequence the mass would
at length assume the form of a lens or disk very thin in pro-
portion to its extent. The denser portions of this lens
would gradually be inlwn toward the centre, and there
more o^ less solidified by tiie process of cooling. A point

-«■

COSMOGONY.

499

sordingto tluB law,
id whatever, which
rm or arrangement
parts among them-
id by each particle
it of time remains

A to one half, sup-
f any plane passing
>ne fourth, because
of the diameters,
y then be the same
imes as fast. The
b have had an axis
an equator defined
I. In consequence
on, the centrifugal
mass grew smaller,
circle described by
he angular velocity.
I to half the radius,
1 force at the equa-
times. The gravi-
ing inversely as the
, or of the radius,
ef ore as the masses
force inereases at a
ion. A time would
loeeaoh other at the
i then cease to oon-
thwe would be no
of the mass would
lenoe the mass would
[ilk very thin in pro-
ortions of this lens
he centre, and there
)f cooling. A point

would at length be reached, when solid particles would begin
to be formed throughout the whole disk. These would grad-
ually condense around each other and form a single planet,or
they might break up into small masses and form a group of
planets. As the motion of rotation would not be altered
by these processes of condensatioa, these pknets would all
be rotating around the central part of the mass, which is
supposed to have condensed into the sun.

It is supposed that at first these planetary masses, being
very hot, were composed of a central mass of those sub-
stances which condensed at a very high tranperatore, sur-
rounded by the vapors of those substances which were
more volatile. We know, for instance, that it takes a much
higher temperature to reduce lime and platinum to vapor
than it does to reduce iron, zinc, or magnesium. There-
fore, in the original planets, the limes and earths would
condense first, while many other metals would still be in a
state of vapor. The planetary masses would each be
affected by a rotation increasing in rapidity as they grew
smaller, and would at length form masses of melted metals
and vapors in the same way as the larger nuss out of which
the sun and planets were formed. These masses would
then condense into a planet, with satellites revolving
around it, just as the original mass condensed into sun and
planets.

At first the ]danet8 would be so hot as to be in a molten
condition, each of them probably shining like the son.
They would, however, slowly cool off by the radiation of
heat from their surf aoes. So long as they remained liquid,
the surface, as fast as it grbw oocd, would sink into the in-
terior on aooonnt of its greater specific gravity, and its
place would be taken by hotter material rising from the
interior to the surface, there to cool off in its turn. There
would, in fact, be a motion sometiiing like that whidb occurs
whoi a pot of cold watw is set upon the fire to boil.
Whenever a mass of water at the bottom of the pot is
heated, it rises to the surface, and (he co<4 water moves

HmgWWMWJM WHWB tf i i

^H'iepN^f^miRsitmm'm^e^mt'^

500

ASTBONOMT.

down to take its place. Thus, on the who e, m long as
the phinet ,«maiSed liquid, it ^ould <K)ol off «jn^y
throughout its whole mass, owing to the conrtant motion
from the centre to the cL-cumferenoe and back again A
time would at length arrive when many of the earths and
mXlTwouldbegirtosolidify. At first the solid particles
would be carried up and down with the liquid. A time
would finaUy arrive when they would become so large
and nmneious, and the liquid part <>**»»« 8«r[»» "T
become so viscid, that the motion would be obstructed.
The planet would then begin to solidify. Jwo J^ews
have been entertained respecting the process of solidifica-

*Tccording t»> one view, the wtole surface of the planet
would solidify into a continuous crust, as ice forms over a
pond in cold weather, while the interior was still m a
molten state. The interior liquid could Oien no longer
come to the surface to cool off, and could lose no heat
except what was conducted through this crust Hence
the subsequent cooHng would be much slower, and the
Klobe would long remain a mass of lava, covered over by
a comparatively thin soUd crust like that on which we

livQ

The other view is that, when the cooling attoined a cer-
tain stage, the central portion of the globe would be
solidified by the enormous pressure of ^« f P«™^"J?"'
portions, while the exterior was stiU flmd, and that thus
Sie soUdification would take pUM» from the centre out-

ward.

It is still an unsettled question whether the earth is now
soUd to its centre, or whether it is a great globe of molten
matter with a comparatively thin crust Astronomers and
physicists incline to the former view ; geologisto to the
ktter one. Whichever view may be correct, it appears
certain that there are great hikes of bva in the interior
from which volcanoes are fed. ^

It must be understood that the nebukr hypothesis, as

COBMOOONT.

601

I whole, so long as
1 cool off equally
ihe constant motion
ind back again. A
y of the earths and
(t the solid particles
(he liquid. A time
Id become so large
>f the general mass
raid be obstmeted.
lidify. Two views
process of solidifica-

nrfaoe of the planet
, as ice forms over a
terior was still in a
onld then no longer
, could lose no heat
this crust Hence
uch slower, and the
iva, covered over by
9 that on which we

ooling attained a cer-
the globe would be
I the superincumbent
1 fluid, and that thus
Ennn the centre out-

jther the earth is now
gi«at globe of molten
»t Astronomers and
w ; geologistB to the
be correct, it appears
I htvain die interior

lebnlar hypothesis, as

we have explained it, is not a perfectly established scien-
tific theory, but only a philosophical conclusion founded
on the widest study of nature, and pointed to by many
otherwise disconnected facts. The widest generalization
associated with it is that, so far as we can see, the universe
is not self-sustMuing, but is a kind of organism which, like
all other organisms we know of, must come to an end in
consequence of those very laws of action which keep it
going. It must have had a beginning within a certain
number of years which we cannot yet calculate with cer-
tainty, but which cannot much exceed 20,000,000, and it
must end in a diaos of cold, dead globes at a calculable
time in the future, when the sun and stars shall have
radiated away all their heat, unless it is re-created by the
action of forces of which we at present know nothing.

liiiiwili

ns, IB

ram.

'<mmumiumi^>mmm>mmuiit».f!»».r- a^Mw.,

• jawawM'-t '^MfUn^SMUnU W

ii . ' .IUi.ii i m.'Mi l ltWi.'MM

INDEX.

GV Tan index is intended to point out the subjects treated in the
work, and f urtlier, to give references to the pages where technical terms
are defined or explained.

Abemtion'Oonstant, values of,

944.
Aberration of a lens (chromatic),

60.
Aberration of a lens (q>herical),

61.
Aberration of light. 888.
Absolute paralkx of stars defined,

476.
Aooelerating force defined, 140.
Achromatic teleaoc^ described,

60.
ADAin'i work on pettariMtkMis of

Ufamia,8M.
AflJaataMntt of a tiansit fautra-

ment an three ; tot level, for

ooOtmatkn, and for aiimath, 77.
AeroUtea^ 87S.
Aibt'b dstenninntkm of the denri>

ty of the earth. IM.
Algol (variaUe ataiX 440.
Altitude of a star deOned. M.
Annnhv mlUifaat of the sob, 17&,
AottBUMl eqafaun, 110.
Appannt piMe of a star, 985.
Appamt Mml-41«BMier of a oeles-

tMbo47deaaMl.09.
Appnaot thae, 9rj0.
ABAAo'a catalogoe of Aeralites,

87S.
Arc conwlod into ttaaa^ 89.

Arsblaiidbb's DurefamuatCTung,
48S.

Aboblamubr's uranometiy, 48S.

ARUTABCHm detmnines tlie solar
parsllak, 988.

Abiitabchub maintains the rota-
tion of the earth. 14.

Artificial horiion used with sex-
tant on shore. 95.

Aspects of the pknets. 979.

Aann'a. voir, computation of
orMt of Dooati's comet, 400.

Asteroids defined. 968.

Asteralda, Bomber of, 900 in 187B,
841.

Aatenida. their magnitudes. 841.

Afltronomkal fautrumenta (hi gen-
eral), 68.

AstranomieBl onita of lei^ith and
mass, 914.

AatmioBij (defined). 1.

Atmoaphsfe of the mooa, 881.

Atmoaphena of the phuets, «•
Iteauy, Venus, eto.

Axia of flie oelesttat ^ihera da-
fiBed.98.

Axis of th' ^arth defiBBd. 96.

AifaBoth Tof a tnuiBtt bislro-
meat. 77.

BAiLT'a datermbiatioD at the den-
s^jr of the eartt. 199.

BKiaiW«ra*^^SW»rr^-'

604

INDEX.

Batrr's uranometry (10S4), 430.
Bbbr and Mabdlbr'b map of

the moon, 883.
Bbbskl's parallax of 61 Cygni

(1887). 476.
BsflflEL's work on the theory of

Uranus, 866.
BmiJk'B comet, 404.
Binary ittan, 4S0.
Binary stars, their orbits, 403.
Bodb'b catalogue of stars, 485.
BoDE's bw stated, 909.
Bond's disooveiy of the dusky

ring of Saturn. 18S0, 806.
BoMD'a obserrations of Dcmati's

oomet. 880.
BooiD'a tbewy of the oonstttutiou

of Saturn's rings, 800.
Boutabd'b toblea of Uianus, 860.
Bbadlbt diaooven aberration in

1720,240.
Bkadubt's method of ^e and ear

observations (1700). 79.
Brif^tneas of aii the stars of each

magnitude, 488.
Calendar, can it be improved r

261.
Calendar of the Fraoch Republic,

202.
Calmdars, how formed. 24a
Calltfcs. period of, 208.
Caasq^nOnian (reflectiiig) teieaoope,

07.
CAsann diaoovers foaraateUitea of

Saturn (1084-1871). 880.
CAsann's value of the aolar panl-

lax, 9'-8, 220.
Cataloguea (rf atars, goieral ao-

count, 484.
Catakiguee of stars, tbdr arrange-

ment, 200.
Cavbudibh. experiment for deter-
mining the denat^ of the earth,
182.
Celestial mechanics defined. 8.
Celeetial sphera. 14. 41.
Central edipae of the sun, 177.

Centra of gravity of the solar sys-
tem, Wl».

Centrifugal force, a misnomer,
210.

Christie's determination of mo-
tion of starsinlhieof sight, 471.

Chromatic aberration of a lens, 60.

Chronograph used in transit ob-
servations. 70.

Chronology. 240.

Chronometers. 70. '

CuiiRAVT predkits the return of
Halley's oomet (1709), 887.

Ciuotu'a elements of the earth,
202.

Clocks, 70.

Clusters of start are often formed
by central powers, 464.

Coal-sacks bi ttw mllhy way, 410,
480.

Coma of a comet. 888.

Comets defined, 268.

Comets formerly inspired terror,
406-«.

Comets, general account, 888.

ComeU' orbiu, theory of. 400.

Cometo' tails, 888.

ComeU' tails, repulsive force. 880.

Cometa. thdr origin. 401.

Comet8.tlieir pbyskial constitutton.
808.

Comets, their spectra. 898.

Conjunction (of a plaoet with the
aun) defined. 114

Conimation of a tnnait instru-
ment, 77.

Conjug^ foci of a lens defined,
05.

Conateilatkms. 414

Conrtdlattona. in parttenhw. 482.
etteq.

Oonstructkm of the Hmvani, 478.

Co-ordinatea of % atar dcAned. 41.

OoPBLAiiD obwrrai spectrum of
new atar of 1878. 445.

OoRini's ofaeervatkns of spectrum
of new star of 1876. 445.

' . ■ \

Ijiai

at gmvity of the solar sys-

igal force, a misnomer,

ib'h determination of mo-

{ stars in line of siglit, 471 .

tic aberration of a lens, 60.

[;nph used in transit ob-

ions, "lO.

ogjr. 845.

neters, 70. '

DT predicts the return of

r'n comet (1750), 807.

'■ elements of tlie earth,

TO.

of Stan are often formed

itral powers, 464.

ks in Um taiVrj way, 415,

' a comet, 888.

leflned. 268.

formerly inspired terror,

general account, 888.

orbiU, theory of, 400.

tails, 888.

tails, repolslre force, 885.

ttadr origin. 401.

lieir physical oonstitutioa,

their spectra. 896.

UoD (of a plaoet with the

iflned, 114

ion <rf a tnaait Instru-

77.

te foci of a lens defined.

itioni.414.

ttlo&a. in partloidar. 483,

ition of the Hmtw. 478.
itea of • atar deAned. 41.
n> oiMavTM spectrum of
ir of 1878.445.
ofaaemtions of spectrum
star of 1876,445.

ti ,j i wi i j i »w.uji!iaw«aaiii

INDEX.

605

CoKNii ilcterminea the velocity of
li^'hl, 222.

('urrection of a clocli defined, 73.

C'u8niical physics defined. 8.

Cosmogony defined, 482.

Corona, its spectrum, 805.

Coronn (the) is a solar appendage,
802.

Craters of the moon, 838.

Day, how subdivided into hours,
etc., 257.

Days, mean solar, and solar, 259.

Declination of a star defined, 20.

Dispersive powof of glass defined,
01.

Distance of the fixed stars, 413,
474.

Distribution of the stars, 480.

Diurnal motion, 10.

Diurnal paths of stars are circles
12.

Dominical letter, 355.

I3uNATi's comet (1858)^ 407.

Double (and multiple) stars, 44".

Double stars, their colors. 452.

£arth (the), a sphere, 9.

Earth (the) general account of, 188.

Earth (the) is a point in compari>
son with the distance of the fixed
stars. 17.

Earth (the) is isolated in space, 10.

Earth's annual revolution, 98.

Earth's atmosphere at least lUO
miles in heij^t. 880.

Earth's axis renudns pendlel to it-
self during an annual revolution,
109, 110.

Earth's density. 188. 190.

Earth's dimensions, 801.

Earth's hitemal heat. 408.

Earth's mass. 188.

Earth's mass with various values
of sohur parallax (table), 380.

Earth's motion of rotation proba-
bly not unfform, 148.

Eartlis' (the) rel|Uion to the heav-
ens, 9.

Earth's rotation maintained by
Arihtahoiiu.') and Timociiarih,
and opposed by Ptoi.kmv, 14.

£iutb'8 surface is gradually cool-
ing, 498.

Eccentrics devised by the ancienta
to account for the irregularities
of planetary motions. 121.

Eclipses of the moon, 170.

Eclipses of the sun and moon, 108.

Eclipses of the sun, explanation,
172.

Eclipses of the sun. physical phe-
nomena, 207.

Eclipses, their recurrence, 177.

Ecliptic defined, 100.

Ecliptic limits, 178.

Elements of the orbits of the ma-
jor planets, 376.

Elliptic motion of a planet, its
mathematical theory, 125.

Elongation (of a planet) defined.
114

Encke'b comet, 409.

Enokb's value of the solar paral-
lax. 8" -857. 226.

Ehoblmamn'b photometric meas-
ures of Jupiter's satellites. 850.

Envelopes of a comet. 890.

Epicycles, their theory, 110.

Equation of time, 258.

EquatMT (celestial) defined, 19, 34.

Equatorial telescope, description
of. 87.

Equinoctkd defined, 34

Equinoctial year, 807.

Equinoxes. 104

Equino::es; how determined, 105.

Evection. moon's 168.

Eye-pieces of telescopes, 03.

I^ (the naked) sees about 3000
stars. 411. 414

FABBimis observes solar soots
(1611), 888.

Figure of the earth, 108.

FizBAU determines
lij^t, 338.

INDEX.

506

Fi.AMBTEEi>'« catalogue o( 8tar«

PoWAUt.Tdetennlne« the velocity

Future of the solar Bystem. 501
Galaxy, or milky way. *";
GAUI.KO olMorves 9ol8ri.pot«(l6U).

Q W« dl«=overy of satellites

o:srrriiSo:rSfthe.iiwy

OrrSolrves Neptune

(1846). 867.
Geodetic surveys, IW-
Golden number. 252.
Gould's urunometry, 48a.
S«viS»tlon extends to the stars.

OwvltoaJn resides lu each particle

of matter, 189.
Gravitation. Vrrestnal (lU laws).

aiviiy (on the ^U) changes

•with the latitude, 208.

Greek alphabet. 7.

Gregorian calendar, 2W.
GvJiBN.hypotheacal parallax of

GtSh^' the distribution of the

stars. 489. . .

HAi^utv predicts the return of a

comet (1682). 897.
HamJCy'b comet. 898.
HaWb discovery of satellites oi

Mats. 888.
Hall's rototlon-period of Saturn,

hShbbb observes the spectrum
of the corona (1869). 8(».

EauptpurMe of an object We. 61
HAsSfl value of the solar paral

HL^Som^ofthenorthem
sky. 417,

Hklmholtz's meamircB of the
llniHs of imkwl eye vWon, 4.

the8pectraofHtttr«(l7»8).408.

Batellltei of Saturn (1789), 360.
Hbkbchbl (W.). discovers two
""JSS of Uranus (1787) m

HEnflCHKL(W.) discovers Uramis

HeSbMW.) observes double

stars (1780). 462.
llBBflcBEL-fl catalogues of nebu-

las 457.
Hkmciiel's staf-gftuges. 479.

Herbcbbl (W.) Slaves "■
solar system Is In motion (1788),

.- / w N views on the
Herbciielb (W.) view-

nature of nebulas. 458.
llEVBLiBB'fl catalogue of 9tor8.485
Hul^B(0. W.) orbit of Donatis

„S\g%.) theory of Mer-
nSs'lwlngs of Mars (1666).

HoSn(celestlal--^nslble)ofan

nttserver defined, so.
HoSb guess at the «.l«r par-

Ht"«^ of a Star defined 25
SZTi'B investigation of orbit

of Blela's comet, 404.
HoGOWB' determination of mo-

♦J«n of BtMB In line of sight. 471.
H?j;«.rt observe the spectra

of nebulae (1864). 465.
H^^SHliervationsoftiiespec.

traoftheptanete.870.«««?.
HoooWB- and MiLLBB'B obeerva-
^tSTofspectrmnofnewstarof

HlS«t^dMtLLEB'B observa

tions of stellar spectra. 468.
HiTGHKHB discovers a sateUlte of

Saturn (1665), 860.

INDEX.

507

i,T7/B mcamircB of the
of imkwl eye vWon, 4.
Bi, (W.). ttrst ol)H.TVe«
ectraofHlttr«(17»8). 4«8.
Eli (W.), discovers two
tei of Saturn (1789). 860.

an, (W.). discovers two
Ites of Uranus (1787). 868.
lEL (W.) discovers Uranus

). 862. - , ,

HEL (W.) observes double

(1780). 452.

HBL's catalogues of nebu-

nEi/B Star-gauges. 4TO.
,HEL (W.) states that the
r system Is In motion (1788),

ciiEL's (W.) views on the

ire of nebulffi. 408.
:u«s'scatalogueof stars «5^

'B (G. W.) orbit of Donatl s
net, 409. „

•b (G. W.) theory of Mer

S'9^rawlngsofMar.(1666).

^n (celestial-sensible) of an

server defined, 28.

^x'B guess at the solar par-

f«S^ of a star defined 25
BBAW>'» investigation of orbit

r Blela's comet, 404.
oowB' determination of mo-
on of BtaiB In line of BlghvWl^
^WB first obeerveB the spectra

.fnebuln (1864). 465.
lUr^lUvatlonBofJespoc-

tra of the planets. 870. «« «?•
So«8'andMiLLKB'Bob«rva-

JlonBof«pectrmnofnews.arof

l^ii^dMt.i.EB'B objerva

tlons of stellar spectra. 4«».
["tohkhb discovers a sateUite of

Batum (1666). 860.

HiivuiiKNS discovers laws of con-
tra! forces. 136.

lIuvoiiENS discovers the neb-
ula of Orion (10SO), 457.

IIuYouKNs' explanation of the
appearances of Saturn's rings
(165r>), 866.

IluYOiiENs' guess at the solar par-
allax, 220.

IIuvoiiknb' resolution of the milky
way. 410.

Inferior planets defined, 116.

Intramorcurial planets, 822.

Janbsbn first observes solar promi-
nences in daylight, 304.

Jansben's photographs of the sun,
281.

Julian year, 260.

Jupiter, general account, 843.

Jupiter's rotation time, 846

Jupiter's satellites, 846.

Jupiter's satellites, their elements,
851.

Kant'b nebular hypothesis, 492.

Kepler's idea of the milky way,
416.

Kepler's laws enunciated, 126.

Kbflbr'b laws of planetary mo-
tion, 122.

Klbir, photometric measures of
Beta Lyra, 442.

Lacaille's catalogues of nebula,
467.

Langlbt's measures of solar heat,
288.

Laholbt's measures of the heat
from sun spots, 286.

Laplacb investigates the accelera-
tion of the moon's motion,
146.

Laplace's nebular hypothesis, 492.

Laplacb'b investigation of the
constitution of Saturn's rings,
860.

Laplacb'b relations between the
mean motions of Juidter's satel-
Mtes, 849.

Lahskll discovers Noptuno's 8at<
ollite (1847), 8(t9.

Lahsell dittcovers two satcHitcsof
Uranus (1847), 803.

Latitude (geocentric — geographic)
of a place on the earth detlned,
208.

Latitude of a point on the earth is
measured by the elevation of the
pole, 21.

Latitudes and longitudes (celes-
tial) defined, 112.

Latitudes (terrestrial), how deter-
mined, 47, 48.

La Sage's theory of the cause of
gravitation, 150.

Level of a transit instrument, 77.

Lb Verribh computes the orbit of
meteoric shower, 884.

Lb Yerribr's researches on ttte
theory of Mercury, 828.

Lb Yerribr's work on pcrturba<
tlons of Uranus, 866.

Light-gathering power of an ob-
ject glass, 66. "

Light-ratio (of stars) is about 2-5,
417.

Line of colllmatlon of a telescope,
69.

Local time, 82.

LocKTBR's discovery of a spec-
troscopic method, 804.

Longitude of a place may be ex-
pressed in time, 83.

Longitude of a place on the earth
(how determined), 84, 37, 88, 41.

Iiongitudes (celestial) defined, 112.

Lucid stars defined, 415.

Lunar phases, nodea, etc. See
Moon's phases, nodes, etc.

Maedlbb's theory of a central
sun, 478.

Magnifying power of an eyepiece,
66.

Magnifying powers (of telescopes),
which can be advantageously
employed, 68.

1
} i

»'

508

INDEX.

Magnitudes of the stan. 41(1.

Mnjor plnnots defined, 208.

Man, iu surface, S86.

Mars, physical description, 884.

Murs, rotatioD, 886.

Man's satellites discoTered by

Hall (1877), 888.
Mabiub's claim to discovery of

Jupiter's satellites, 848.
Maskrltnb determines the den-
sity of the earth, 103.
Muss and density of. the sun and

planets, 377.
Mass of the sun In relation to

masses of planets, 227.
Masses of the planets, 283.
Maxwell's theory of constitution

of Saturn's rings, 860.
Matbk (C.) flnt observes double

Btnra (1778), 463.
Mean solar time defined, 38.
Measurement of a degree on the

earth's surface, 301.
Mercury's atmosphere, 814.
Mercury, its apparent motions,

810.
Mercury, its aspects and rotation,

818.
Meridian (celestial) defined, 31, 25.
Meridian circle, 83.
Meridfam line defined, 25.
Meridians (terrestrial) defined, 21.
McflBiBR's catalogues of nebulae,

457.
Metonic cycle, 251.
Meteoric showen, 880.
Meteoric showers, orbits, 888.
Meteora and comets, theix rehuton,

888.
Mcteore first visible about 100
miles above the surface of the
earth, 380.
Meteon, general account, 375.
Meteon, their cause, 877.
Metric equivalents, 8.
Miohablsom determines the ve-
locity of light (1870). 9Sa.

Micitrll's researches on distri-
butlon of Stan (1777), 440.

Micrometer (filar), description and
use, 89.

Milky way, 415.

Milky way, its general shape ac-
cording to IlRnsCHKL, 480.

Minimum Vimbile of telescopes

(lable), 410.
Minor planeU defined, 268.
Minor planets, general account,

840.
Mira Oeti (variable star), 440.
Mohammedan calendar, 252.
Months, different kinds, 340.
Moon's atmosphere, 881.
Moon craters, 820.
Moon, general account, 826.
Moon's light and heat, 881.
Moon's light l-618,000th of tlie

sun's, 882.
Moon's motions and attraction,

152.
Moon's nodes, motion of, 150.
Moon's perigee, motion of, 163.
Moon's phases, 154.
Moon's rotation, 164.
Moon's secular acceleration, 146.
Moon's surface, does it change,

838.
Moon's surface, its character, 828.
Motion of Stan in the line of

sight, 470.
Mountains on the moon often

7000 metres high, 880.
Nadir of an observer defined, 33.
Nautical almanac described, 363.
Nebula and clusters, how distrib-
uted, 465.
Nebulas and dustors in general,

457.
Nebula of Orion, the first telescopic

nebuhi discovered (1650), 457.
Nebulae, their spectra, 465.
Nebular hypothesis stated, 407.
N^une, discoveiy of by Lk Vbr-

BiBB and Adams (1846), 867. «

INDEX.

S09

:m.'b roflcarchcs on dlRtri.

>n of stars (1777), 440.

neter (filar), description and

80.

way. 415.

vf^y> it" gdoeml shape ac-

ing to IlKitBcnsL, 4<M.

vm Vimbile of telescopca

»), 419.

planeto defined, 268.

planets, general account,

eti (variable star), 440.
imedan calendar, 252.
I, different kinds, 340.

atmosphere, 881.
raters, 820.
general account, 826.
light and heat, 881.

light l-618,000th of tlie
,882.

motions and attraction,

nodes, motion of, 150.

perigee, motion of, IdS.

phases, 154.

rotation, 164.

secular acceleration, 146.

surface, does it cliange,

surface, its character, 828.

of stars in the line of

470.

Ins on the moon often

netres high, 880.

t an observer defined, 23.

I almanac described, 268.

and clusters, how distrib-

465.

and dusters in general,

>t Orion, the first telescopic
k discovered (1650), 457.
their spectra, 465.
hypothesis stated, 407.
I, discoveiy of by Lk Vbr-
md Adams (1846), 867. »

Neptune, general account, 365.

Neptune's satellite, elements, 86U.

New star of 1876 has apparently
becomn n plunvtary nebula, 445.

New stars, 448.

Nkwtok (I.) calculates orbit of
comet of 1680, 406.

Nkwton (I.) Laws of Force,
184.

Newtonian (reflecting) telescope,
00.

Nkwtom'b (I.) investigation of
comet orbits, 806.

Newton's (II. A.) researches on
meteors, 886.

Newton's (H. A.) theory of con-
stitution of comets, 804.

Nucleus of a comet, 888.

Nucleus of a solar spot, 287.

Nutation, 211.

Objectives (mathematical theory),
08.

Objectives or object glasses, 54.

Obliquity of the ecliptic, 100.

OccultaUons of atars by the nuwn
(or planets), 186.

Olbbrb's hypothesis of the origin
of asteroids, 840, 8^.

Olbbrs predicts the return of a
meteoric shower, 881.

Old style (in dates), 254.

Opposition (of a planet to the sun)
defined, 115.

Oppositions of Mars, 885.

Parallax of Man, 220, 221.

Paralhuc of the sun, 216.

Penumbra of the earth'sor moon's
shadmr. 174.

Photoepheraof the sun, 270.

.PiOABDpubUslies the 0(mntti»$anee
det Tern (1670), 268.

Pickbbiho'b measures of solar
light, 288.

Planets, their relative size exhib-
ited, 260.

PouiiiUn's measures of sokr radi-
ation, 286.

Precession of the equinoxes, 20(t,
201).

I'ToiiK.MY determines the sohir
parallax, 225.

Parallax (annual) defined, 50.

I*arallax (equatorial horizontal) de-
fined, 52.

Parallax (horizontal) defined, 50.

ParaUax (in general) dcfinc«l, 60.

Parallel sphere defined, 80.

Parallels of declination defined, 24.

Parallax of the stars, general ac-
cotmt, 476.

Peihck's theory of the constitu-
tion of Saturn's rings, 850.

Pendulums of astronomical eluckti,
71.

Periodic comets, elements, 800.

Perturbations defined, 144.
I Perturbations of comets by Jupi-
ter, 408.

Photometer defined, 417.

PiAzzi discovera the flnt asteroid
(1801), 840.

Planetary nebulie defined, 459.

Planets ; seven bodies so called by
the ancients, 96.

Planets, their apparent and real
motions, lis.

Planets, Uieir physical constitu-
tion, 870.

Pleiades, map of, ^5.

Pleiades, these stan are physically
connected, 449.

Polar distance of a star, 26.

Poles of the celestial sphere de-
fined, 14, 20, 24.

Podtion angle defined, 00, 460.

Power of telescopes, its limit, 828.

Practical astronomy (defined), 2.

Prime vertical of an observer de-
fined, 25.

Problem of three bodies, 141.

Proctor's map of distribution of
nebulse and clustere, 466.

Proctor's rotation period of Mars,

iii MMy! ' uijwim>^.j,aj.

ft 10

INDKX.

Proper motionN r f sUirs, 473.
I'ro|M'r motion of tliu huh. 47)).
I'Toi.KMVM euUilogiio of HUro,

4l«.
Proi.KMY niaiutnins tho immova-
bility of tliu cartl), 14.
I'ytiiaiiohah' concuption of eryn-

tiilllno HpliercH for llio plaiiutH, Uti.
Ittuliant point of meteor». ]Ml.
Hutu of a clock dcflned, Ti.
Kuiuling microHCope, 81 , 85.
Hcd Htars (variable sturs often red),

442.
Itvtlectiug telescopes, 00.
Kcflecting tokwcopts, thoir advnn-

tiigcB and diHmlvuntuges, 08, (it).
Refracting telescopcH, 53.
Uefraction of light in tho atmos-

])herc, 234.
llefractive power of a lens defined,

05.
Kef nactive power of glass defined,

01.
Uelutivo parallax of stars defined,

47b.
Resisting medium in spaco, 409.
Reticle of a transit instrument, 70.
lietrogradatlons of the planeU ex-
plained, 118.
Right ascension of a star defined,

22.
Right ascensions of stars, how

determined by observation, 31.
Right sphere defined, 27.
BiUen on the moon, 880.
RoBMBR discovers that light moves

wogressively, 289.
Rosbb's measure of the moon's

heat, 882.
8aro» (the), 181.
Batum, general account, 852.
Saturn's rings, 854.
Saturn's rings, their constitution,

350.
Saturn's rings, their phases, 857.
Saturn's satellites, 800.
Saturn's satellites, elements, 361.

Havauv first compiilf* orbit of u
binitry star (1820), 450,

H«'iiiAi>AiiKLi.rs theory of rein-
tious of comets and meteors,
385.

HciiMioT discovers new star in
Cygnus (1870), 445.

Bciimii>t'h observations of new
star of 18(MI, 444.

SciioENFKi.D's Durchmusteruug,
Am.

BciiHOBTKit's observations on the
rotation of Venus, 810.

SciiwABB'a observations of sua
spote, 208.

Seasons (the), 108.

Sbcciu's estimate of solar tempera-
ture 0.100,000° C, 280.

Secciii's types of star spectra,
408.

Secondary spectrum of object
glasses defined, 02.

Secondb pendulum, lengtli, formu-
la for it, 204.

Secular acceleration of the moon's
mean motion, 140.

Secular perturbations defined, 145.

Semi diameters (apparent) of ce-
lestial objects defined, 52.

Semi-diurnal arcs of stars, 45.

Sextant, 92.

Shooting stars, 877.

Sidereal system, its shape accord-
ing to Hbrsobbl, 484.

Sidereal time explained, 29.

Sidereal year, 207.

Signs of the Zodiac, 105.

Silvered glass reflecting telescopes,
00.

Sirius is about 500 times brighter
than a star 6">, 418.

Stars had special names 8000
B.C., 420.

Solar corona, extent of, 209.
Solar cycle, 255.

Solar heat and light, its cause, 806.
Solar heat, its amount, 284.

IV flmt comimtnn orMt t»f u
ry Htur (lHa«). 4W».
■■AiiKLi>rH theory of rulii-
s uf couiutM auil uic'lc'orH,

DT (liBCOvcrH now Btiir iu

nu8 (187U), 44.1.

dt'h obBurvutioua of nuw

of WW, 444.

;npbi.d'8 Durchmustoruug,

ibtkh'h obHcrvatioua on thu
tion of YenuH, 810.
iBB'a obaorvatloiu of sun
8, 2»8.
>8 (the), 108.

ii'h e8tiniato of sohir tempera-
O.IOO.OOO' C, 280.
fi'a types of star spectra,

dary Rpectrum of object
ncH dcflnod, 02.
(L> pendulum, lengtli, formu-
3r it, 204.

ir acceleration of the moon's
kQ motion, 140.
ir perturbations defined, 145.
diameters (apparent) of ce-
ial objects defined, 52.
diurnal arcs of stars, 45.
at, 02.

ing stars, 877.

!al system, its shape accord-
to Hbrsobel, 484.
eal time explained, 29.
jal year, 207.
of the Zodiac, 105.
'ed gl&ss reflecting telescopes,

I is about 500 times brighter
n a star O", 418.
had special names 8000
., 420.

corona, extent of, 299.
cycle, 256.

heat and light, its cause, 806.
heat, its amount, 284.

INliKX.

Holiir nintinn In npnno, 47.1,

Holar piirulliix from liiniirlni><pitili-
ly. 'J3:«.

Holur |)ariillux t'n>ni MufH, 'J'iO.

Bolar piiriillux from velocity of
light, 222.

Holur pariillux, hiatory of attempts
to (Ictermlni! It, 228.

Holur purullux, IIh mouHiires, 210.

Holur purullux prububly uImmiI
8" Ml, 228.

Holur prominences uro gaseouM,
80i).

Holur syHtem deflnoti, 07.

Holur system, description, 207.

Holar system, its future, 80t>, 601.

Holur temperature, 280.

Hoistices, 108, 104.

Spherical aberration of a lens, 01.

Hpherical astmnomy (detined), 2.

Spiral nebulie defined, 450.

Star clusters, 402.

Star-gauges of Hbhsciibi., 470..

Sta;- magnitudes, 410.

Stars of various magnitudes, how
distributed, 486-7.

Stars Eien by the naked eye, about
2000, 411-414.

Stars, their proper motions, 472.

Stars, their spectra, 408.

Stbuvb's (W.) idea of the distri-
bution of the stars, 487.

Sthcvb'b (W.) parallax of alpha
Lym (1838), 476.

Stbuvb's (W.) search for [Nep-
tune], 806.

Struvb'b (O.) supposition of
changes in Saturn's rings, 858.

Suti'B uranometry, 448.

Summer solstice, 110.

Sun's apparent path, 101.

Sun's attraction on the moon
(and earth), 156.

Sun's constitution, 805.

Sun's density, 280.

Sun's (the) existence cannot be in-
definitely long, 406.

Sun's muss over 700 times fhul of

the planets, 272.
Huii'h motion unionjr llio NturH,

lOl.
Hun, phyHicul description, 278.
Sun's proper motion, 47:i.
Sun's rotation tinu', al)out25iluyn,

290.
Hini -spots nnd fiu:ul(D, 2N7.
Huu-Hpots ure continvd to certain

purtH of tl'e <ll8c, 380.
Sun r.pots, cause of their periodic

up|)earui)ce unknown, 2U4.
Sun's surface is griuiuully cooling,

494.
Sun-spots, their nature, 200.
Sun-spots, their periodicity, 202.
Superior plunets (deflneti), 110.
SwEPPNBono's nebular hypothe-
sis, 4Mi.
Swift's supposed discovery of

Vulcan, «28.
8ymbf>l8 used in astronomy, 0, 7.
Telescopes, their advantages, 57,

58.
Telescopes (reflecting), 00.
Telescopes (refracting), 6.1.
Tempbl's comet. Its relntion to

November meteors, 884.
Temporary stars, 448.
Theoretical astronomy (defined), 8.
Tides, 105.

Time converted into arc, 82.
TmocnAUis maintains tlie rota-
tion of the earth, 14.
Total solar eclipses, description of,

297.
Transit instrument, 74.
Transit instrument, methods of

observation, 78.
Transits of Mercury and Venus,

818.
Transits of Venus, 210.
Triangulation, 199.
Tropical year, 207.
Tycho Bbahb's catalogue of stars.

I« 111

512

INDEX.

Tyciio Brahe observes now star

of 1572, 443.
Units of mass and Uiugth enii)loye<l

in astronomy, 218.
Univenal gravitation discovered

toy Newton, 149.
Universal gravitation treated,

131.
Universe (tlie) general account,

411.
Uranus, general account, 302.
Variable and temporary stars, gen-

cntl account, 440.
Variable stars, 440.
Variable stars, their periods, 442.
Variable stars, theories of, 445.
Variation, moon's, 163.
Velocity of light, 244.
Venus's atmosphere, 317.
Venus, its apparent motions, 810.
Venus, its aspect and rotation,

815.
Vernal equinox, 102, 110.
Vernier, 82.
Vogel's determination of motion

of stars in line of sight, 471.
Vookl'b measures of solar actinic

force, 283.
Voobl'b observations of Mer-
cury's spectrum, 314.

Vooei/b observations of spectrum
of new star of 1870, 445.

Vowel's ol>scrvaUous of the spec-
tra of tbe planets, 370, et »eq.

Volcanoes on the moon supposed
to exist by HEitacnBL, 832.

Vulcan, 322.

Watbon'b supposed discovery of
Vulcan, 323, 834.

Wave and armature time, 40.

Weight of a body defined, 189.

Wilson 'b theory of sun-spots, 290.

Winter solstice, 100.

Wolf's researches on sun-spots,
295.

Years, different kinds, 250.

Young observes the spectrum of
the corona (1860), 805.

Zenith defined, 19, 28.

Zenith telescope described, 90.

Zenith telescope, method of observ-
ing, 92,

Zodiac, 105.

Zobllner'b estimate of relative
brightness of sua and planets.
271.

ZoBiiiiNER'B measure of the rela-
tive brightness of sun and moon,
332.

Zone observations, 85.

•agyan*^; . ;. -^

/b obnervations of Bpectruni

cw star of 1870, 44.'}.

/b olHwrvuUoits of tlic spec-

>f tbe plauets, 870, et tieq.

io«8 on the moon supposed

cist by HERBcnBL, 832.

1, 322.

jn's supposed discovery of

:an, 828, 824.

and armature time, 40.

t of a body defined, 180.

«'8 theory of sun-spots, 290.

r solstice, 100.

's researches on sun-spots.

different kinds, 250.
> observes the spectrum of
:orona (1860), 805.
defined, 19, 28.
telescope described, 00.
telescope, method of observ-
92,
, 105.

ner's estimate of relative
itnesa of sun and planets,

eter'b measure of the rela-
brightncss of sun and moon,

ibservations, 85.

^^^

riM

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