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GIFT OF

MICHAEL REESE

UNIVERSITY

CALIFO^L

FRONTISPIECE.

THE GKEAT TELESCOPE OF THE LICK OBSEBVATORV, MI^HAMILTOX, CAL.

'Object-Glass made by A. Clark & Sons : Aperture, 36 in.; Focal Length, 56 ft. 2 in

Mounting by Warner & Swasey.

A TEXT-BOOK

OF

ASTRONOMY

FOR

COLLEGES AND SCIENTIFIC SCHOOLS

BY

CHAKLES A. YOUNG, PH.D., LL.D.

PROFESSOR OF ASTRONOMY IN PRINCETON UNIVERSITY

RKVISKD KDITION

BOSTON, U.S.A., AND LONDON

GINN & COMPANY, PUBLISHERS

1898

ENTERED AT STATIONERS' HALL

COPYRIGHT, 1888, BY

CHARLES A. YOUNG

COPYRIGHT, 1898, BY

CHARLES A. YOUNG

ALL RIGHTS RESERVED

7 7 A, ^/

PREFACE TO FIRST EDITION.

THE present work is designed as a text-book of Astronomy

suited to the general course in our colleges and schools of

science, and is meant to supply that amount of informati- >n

upon the subject which may fairly be expected of every

" liberally educated " person. While it assumes the previ-

ous discipline and mental maturity usually corresponding to

the latter years of the college course, it does not demand the

peculiar mathematical training and aptitude necessary as the

basis of a special course in the science only the most ele-

mentary knowledge of Algebra, Geometry, and Trigonometry

is required for its reading. Its aim is to give a clear, accu-

rate, and justly proportioned presentation of astronomical

facts, principles, and methods in such a form that they can

be easily apprehended by the average college student with a

reasonable amount of effort.

The limitations of time are such in our college course that *

probably it will not be possible in most cases for a class to

take thoroughly everything in the book. The fine print is to

be regarded rather as collateral reading, important to a com-

plete view of the subject, but not essential to the course.

Some of the chapters can even be omitted in cases where it

is found necessary to abridge the course as much as possible ;

e.g., the chapters on Instruments and on Perturbations.

While the work is no mere compilation, it makes no claims

to special originality: information and help have been drawn

from all available sources. The author is under great obliga-

tions to the astronomical histories of Grant and Wolf, and

especially to Miss Clerke's admirable " History of Astronomy

in the Nineteenth Century." Many data also have been drawn

from Houzeau's valuable " Vade Mecum de 1'Astronome."

IV PREFACE.

It has been intended to bring the book well down to date,

and to indicate to the student the sources of information on

subjects which are necessarily here treated inadequately on

account of the limitations of time and space.

Special acknowledgments are due to Professor Langley and

to his publishers, Messrs. Ticknor & Co., for the use of a

number of illustrations from his beautiful book, " The New

Astronomy " ; and also to D. Appleton & Co. for the use of

several cuts from the author's little book on the Sun. Pro-

fessor Trowbridge of Cambridge kindly provided the original

negative from which was made the cut illustrating the com-

parison of the spectrum of iron with that of the sun. Warner

& Swasey of Cleveland and Fauth & Co. of Washington have

also furnished the engravings of a number of astronomical

instruments.

Professors Todd, Emerson, Upton, and McNeill have given

most valuable assistance and suggestions in the revision of the

proof ; as indeed, in hardly a less degree, have several others.

PRINCETON, N. J., August, 1888.

PREFACE TO THE REVISED EDITION.

THE progress of Astronomy has been very rapid since the

first publication of this book in 1889, and, although in the

meantime the author has attempted as far as possible to keep

the successive issues u up to date" by minor changes, notes,

and " addenda," it has at last become imperative to give

the work a thorough revision, rewriting certain portions and

making considerable additions, in order to embody the new

and important results which have been obtained during the

last ten years.

The Appendix has also been enlarged by several articles

giving the demonstration of certain fundamental methods and

PREFACE. V

formulae for which, in previous editions, the student was

referred to other works not always conveniently accessible.

In one or two of these articles the Calculus is necessarily

used.

The various tables have been corrected to correspond with

the latest and most authoritative data ; and a set of illustrative

exercises has been added at the end of nearly every chapter.

While the book has thus been necessarily somewhat increased

in size, the changes have been so managed that no serious diffi-

culty will be encountered in using the new edition along with

the older issues. The original numbering of the articles has

been retained throughout, with only one or two exceptions,

the interpolated matter being designated by numbers with

asterisks.

It is believed that the book, so far as its scope extends,

may now be taken as fairly representing the present state of

the science, although some of the most important recent dis-

coveries are hardly made so prominent as would have been the

case if the revision had not been substantially completed and

prepared for the press more than two years ago; the actual

printing having been much delayed by various causes.

Special acknowledgments are due from the author to the

publishers for the liberality with which they have made the

extensive and expensive changes in the plates, and to Apple-

ton & Co., and Professors Frost, Hale, Holden, and Pickering

for many of the new illustrations.

PRINCETON UNIVERSITY, March, 1898.

TABLE OF CONTENTS.

PAGES

INTRODUCTION . 1-4

CHAPTER I. THE DOCTRINE OF THE SPHERE : Definitions and Gen-

eral Considerations .......... 5-20

^CHAPTER II. ASTRONOMICAL INSTRUMENTS : the Telescope ; Time-

^ "~~ keepers and Chronograph; the Transit Instrument and Accessories ;

the Meridian Circle and Reading Microscope ; the Altitude and Azi-

muth Instrument ; the Equatorial Instrument and Micrometer ; the

Sextant 21-5^^

CHAPTER III. CORRECTIONS TO ASTRONOMICAL OBSERVATIONS: the

Dip of the Horizon ; Parallax ; Semi-diameter ; Refraction ; Twilight ;

Exercises on Chapters I, II, and III ~T"~ . 58-71

CHAPTER IV. PROBLEMS OF PRACTICAL ASTRONOMY : the Determi-

nation of Latitude and its Variation, of Time, of Longitude, of a

Ship's Place at Sea, of Azimuth, and of the Apparent Right Ascen-

sion and Declination of a Heavenly Body ; the Time of Sunrise or

Sunset ; the Rising and Setting of a Star or of the Moon ; Exercises . 72-96

CHAPTER V. THE EARTH: the Approximate Determination of its

Dimensions and Form ; Proofs of its Rotation ; Accurate Determina-

tion of its Dimensions by Geodetic Surveys aiid Pendulum Observa-

tions ; Determination of its Mass and Density ; Exercises . 97-124

CHAPTER VI. THE EARTH'S ORBITAL MOTION: the Motion of the

Sun among the Stars ; the Equation of Time ; Precession ; Nutation ;

Aberration ; the Calendar ; Exercises . . . . . 125-154

CHAPTER VII. THE MOON: her Orbital Motion; DJgiaaCfi and Di-

mensions ; Mass, Density, and Superficial Gravity ; Rotation and

Librations ; Phases ; Light and Heat ; Physical Condition ; Influence

exerted on the Earth ; Surface Structure ; Possible Changes ;

Exercises 155-1

CHAPTER VIII. THE SUN : Distance and Dimensions; Mass and Den-

sity ; Rotation ; Solar Eye-pieces, and Study of the Sun's Surface ;

General Views as to Constitution ; Sun Spots, their Appearance,

Nature, Distribution, and Periodicity ; the Spectroscope . 184-208

Vlll TABLE OF CONTENTS.

CHAPTER IX. THK SPECTROSCOPE AND THE SOLAR SPECTRUM : Chemi-

cal Elements present in the Sun ; the Sun-spot Spectrum ; Dgpulfir's

Principle ; the Chromosphere and Prominences ; the Corona ; Exer-

cises on Chapters VIII. and IX. " " . T . . 209-231

CHAPTER X. THE SUN'S LIGHT AND HEAT : Comparison of Sunlight

with Artificial Lights; the Measurement of the Sun's Heat and Deter-

mination of the Solar Constant ; the Pyrheliometer, Actinometer, and

Bolometer ; the Sun's Temperature ; Maintenance of the Sun's Radia-

tion ; Conclusions as to its Age and Future Endurance . . 232-247

CHAPTER X/L ECLIPSES: Form and Dimensions of Shadows; Lu-

nar Eclipses ; Solar Eclipses, Total, Annular, and Partial ; Ecliptic

Limits, and x Number of Eclipses in a Year ; the Saros ; Occultations ;

Exercises ^~~\ 248-268

CHAPTER XII. CENTRAL FORCES : Equable Description of Areas ;

Areal, Linear, and Angular Velocities ; Kepler's Laws and Infer-

ences from them ; Gravitation demonstrated by the Moon's Motion ;

Conic Sections as Orbits ; the Problem of Two Bodies ; the " Velocity

from Infinity" and its Relation to the Species of Orbit described

by a Body moving under Gravitation; Intensity of Gravitation;

Exercises 269-293

CHAPTER XIII. THE PROBLEM OF THREE BODIES : Disturbing Forces ;

Lunar Perturbations and the Tides ; x Exercises . . . 294-318

HAPTER XIV. THE PLANETS : their Motions, Apparent and Real :

the Ptolemaic, Tychonic, and Copernican Systems ; the Orbits and

their Elements ; Planetary Perturbations ; Exercises . . 319-339

CHAPTER XV. THE PLANETS THEMSELVES : Methods of determining

their Diameters, Masses, Densities, Times of Rotation, etc. ; the

"Terrestrial Planets," Mercury, Venus, and Mars ; the Asteroids ;

Intra-Mercurial Planets and the Zodiacal Light ; Exercises . 340-377

CHAPTER XVI. THE MAJOR PLANETS : Jupiter, Saturn, Uranus, and

Neptune; Exercises 378-406

CHAPTER XVII. THE DETERMINATION OP THE SUN'S HORIZONTAL

PARALLAX AND DISTANCE : Oppositions of Mars and Transits of

Venus; Gravitational Methods; Determination by Means of the

Velocity of Light ; Exercises ....... 407-427

CHAPTER XVIII. COMETS : their Number, Motions, and Orbits ;

their Constituent Parts and Appearance; their Spectra, Physical

Constitution, and Probable Origin ; Exercises . . . 428-464

CHAPTER XIX. METEORS : Aerolites, their Fall and Physical Char-

acteristics ; Shooting Stars and Meteoric Showers ; Connection be-

tween Meteors and Comets ; Exercises ..... 465-482

TABLE OF CONTENTS. IX

CHAPTEK XX. THE STARS : their Nature and Number ; the Constel-

lations ; Star-catalogues ; Stellar Photography ; Designation of Stars ;

their Proper Motions ; Radial Motion, or Motion in Line of Sight ;

the Motion of the Sun in Space ; Stellar Parallax ; Exercises . 483-506

CHAPTER XXI. THE LIGHT OF THE STARS : Star Magnitudes and

Photometry ; Variable Stars ; Stellar Spectra ; Scintillation of the

Stars ; Exercises 507-540

CHAPTER XXII. AGGREGATIONS or STARS : Double and Multiple

Stars ; Clusters ; Nebulae ; Photography of Nebulae ; the Milky Way,

and Distribution of Stars in Space ; Constitution of the Stellar Uni-

verse ; Cosmogony and the Nebular Hypothesis . . . 541-578

APPENDIX. Reduction of Sidereal Time to Solar ; Azimuthal Motion

of Star at the Horizon ; Kepler's Problem and its Solution, Numer-

ically and by the Curve of Lines; Projection and Calculation of

Lunar Eclipses ; Proof that the Orbit of a Body moving under the

Law of Gravitation is a Focal Conic ; Expression for Velocity at any

Point of Orbit ; Apparent Epicycloidal Motion of Planets . 581-599

ASTRONOMICAL CONSTANTS, TABLES .... 601-611

INDEX 613-627

SUPPLEMENTARY INDEX . . . 628-630

INTRODUCTION.

1. ASTRONOMY (aa-rpov vo/xos) is the science which treats of the

heavenly bodies. As such bodies we reckon the sun and moon, the

planets (of which the earth is one) and their satellites, comets and

meteors, and finally the stars and nebulae.

We have to consider in Astronomy :

(a) The motions of these bodies, both real and apparent, and the

laws which govern these motions.

(b) Their forms, dimensions, and masses.

(c) Their nature constitution, and conditions.

(d) The effects they produce upon each other by their attractions,

radiations, or b}' any other ascertainable influence.

It was an early, and has been a most persistent, belief that the

heavenly bodies have a powerful influence upon human affairs, so

that from a knowledge of their positions and "aspects" at critical

moments (as for instance at the time of a person's birth) one could

draw up a "horoscope" which would indicate the probable future.

The pseudo -science which was founded on this belief was named

Astrology, the elder sister of Alchemy, and for centuries As-

tronomy was its handmaid; i.e., astronomical observations and cal-

culations were made mainly in order to supply astrological data.

At present the end and object of astronomical^study is chiefly

knowledge pure and simple ; so far as now appears, its development

has less direct bearing upon the material interests of mankind than

that of an}' other of the natural sciences. It is not likely that great

inventions and new arts will grow out of its laws and principles, such

as are continually arising from physical, chemical, and biological

discoveries, though of course it would be rash to say that such out-

growths are impossible. But the student of Astronomy must expect

his chief profit to be intellectual, in the widening of the range of

thought and conception, in the pleasure attending the discovery of

simple law working out the most complicated results, in the delight

4 INTRODUCTION.

our common schools. At the same time the necessary statements

and demonstrations are so much facilitated by the use of trigono-

metrical terms and processes that it would be unwise to dispense

with them entirely in a work to be used by pupils who have already

become acquainted with them.

In discussing the different subjects which present themselves,

the writer will adopt whatever plan appears best fitted to convey

to the student clear and definite ideas, and to impress them upon

the mind. Usually it will be best to proceed in the Euclidean

order, by first stating the fact or principle in question, and then

explaining its demonstration. But in some cases the inverse pro-

cess is preferable, and the conclusion to be reached will appear

gradually unfolding itself as the result of the observations upon

which it depends, just as its discovery came about.

The occasional references to " Physics " refer to the " Elementary

Text-Book of Physics," by Anthony and Brackett ; Magie's revised

edition, 1897. John Wiley & Sons, N.Y.

THE " DOCTRINE OF THE SPHERE/

CHAPTER I.

THE " DOCTRINE OF THE SPHERE," DEFINITIONS, AND GENERAL

CONSIDERATIONS.

ASTRONOMY, like all the other sciences, has a terminology of its

own, and uses technical terms in the description of its facts and

phenomena. In a popular essay it would of course be proper to

avoid such terms as far as possible, even at the expense of circum-

locutions and occasional ambiguity ; but in a text-book it is desirable

that the reader should be introduced to the most important of them

at the very outset, and made sufficiently familiar with them to use

them intelligently and accurately.

4. The Celestial Sphere. To an observer looking up to the

heavens at night it seems as if the stars were glittering points attached

to the inner surface of a dome ; since we have no direct perception of

their distance there is no reason to imagine some nearer than others,

and so we involuntarily think of the surface as spherical with our-

selves in its centre. Or if we sometimes feel that the stars and

other objects in the sky really differ in distance, we still instinctively

imagine an immense sphere surrounding and enclosing 1 all. Upon

this sphere we imagine lines and circles traced, resembling more or

less the meridians and parallels upon the surface of the earth, and

by reference to these circles we are able to describe intelligently the

apparent positions and motions of the heavenly bodies.

This celestial sphere may be regarded in either of two different

ways, both of which are correct and lead to identical results.

(a) We may imagine it, in the first place, as transparent, and of

merely finite (though undetermined) dimensions, but in some way

so attached to, and connected with, the observer that his > eye always

remains at its centre wherever he goes. Each observer, in this way

of viewing it, carries his own sky with him, and is the centre of his

own heavens.

(b) Or, in the second r -vce, and this is generally the more con-

venient way of reg;r matter, we may consider the celestial

6

i

sphere as mathematically infinite in its dimensions : then, let the

observer go where he will, he cannot sensibly get away from its

centre. Its radius being " greater than any assignable quantity,"

the size of continents, the diameter of the earth, the distance of the

sun, the orbits of planets and comets, even the spaces between the

stars, are all insignificant, and the whole visible universe shrinks

relatively to a mere point at its centre. In what follows we shall

use this conception of the celestial sphere. 1

The apparent place of any celestial body will then be the point

on the celestial sphere where the line drawn from the eye of the

observer in the direction in which he sees the object, and produced

indefinitely, pierces the sphere. Thus, in Figure 1, A, B, C are

the apparent places of a, b, and c,

the observer being at 0. The ap-

parent place of a heavenly body

evidently depends solely upon its

direction, and is wholly independent

of its distance from the observer.

5. Linear and Angular Dimensions.

Linear dimensions are such as may

be expressed in linear units ; i.e., in

miles, feet, or inches; in metres or

millimetres. Angular dimensions

FlG.l.

are expressed in angular units ; i.e.,

in right angles, in radians, 2 or (more commonly in astronomy) in

degrees, minutes, and seconds. Thus, for instance, the linear semi-

1 To most persons the sky appears, not a true hemisphere, but a flattened

vault, as if the horizon were more remote than the zenith. This is a subjective

effect due mainly to the intervening objects between us and the horizon. The

sun and moon when rising or setting look much larger than when they are

higher up, for the same reason.

2 A radian is the angle which is measured by an arc equal in length to radius/

Since a circle whose radius is unity has a circumference of 2 ?r, and contains 360,

or 21,600', or 1,296,000", it follows that a radian contains (f^Y*, or (

\ 2ilf / ^ \

/ 1 9QfiOftO \ "

or ( j ; i.e. (approximately), a radian = 57.3 = 3437.7' = 206264.8".

Hence, to reduce to seconds of arc an angle expressed in

radians, we must multiply it by the number 206264.8; a

relation of -which we shall have to mak u 'at use.

Z7T

diameter of the sun is about 697,000 kilometres (433,000 miles),

while its angular semidiameter is about 16', or a little more than

a quarter of a degree. Obviously, angular units alone can properly

be used in describing apparent distances and dimensions in the sky.

For instance, one cannot say correctly that the two stars which are

known as " the pointers " are two or five or ten feet apart : their

distance is about five degrees.

It is sometimes convenient to speak of " angular area" the unit

of which is a " square degree " or a " square minute " ; i.e., a small

square in the sky of which each side is 1 or l f . Thus we may

compare the angular area of the constellation Orion with that of

Taurus, in square degrees, just as we might compare Pennsylvania

and New Jersey in square miles.

6. Relation between the Distance and Apparent Size of an Object.

Suppose a globe having a radius BC equal to r. As seen from

FIG. 2.

the point A (Fig. 2) its apparent (i.e., angular) semidiameter will

be BA C or s, its distance being A C or R.

We have immediately from Trigonometry, since B is a right angle,

If, as is usual in Astronomy, the diameter of the object is small

as compared with its distance, we may write S = ~B, which gives 5

in radians (not in degrees or seconds). If we wish it in the ordi-

nary angular units,

* = 57.3^ , or s' = 3437.7^ , or s" = 206264.8^

% * R R

where s means s in degrees ; s', s in minutes ; V, s in seconds of arc.

her form of the equation we see that the apparent diameter

8 UU.b'iJMTiUJN AiNJJ

In the case of the moon, R = about 239,000 miles ; and r, 1081

miles. Hence s = ai-f Q ^|T f a radian, which is a little more

than of a degree, or about 933".

It may be r^ntioned here as a rather curious fact that most persons say

that the mo appears about a foot in diameter ; at least, this seems to be

the average e, mate. 1 This implies that the surface of the sky appears to

them only abo^t 110 feet away, since that is the distance at which a disc

one foot in diameter would have an angular diameter of T ^> of a radian,

7. Vanishing Point. Any system of parallel lines produced in

one direct^ i will appear to pierce the celestial sphere at a single

point. The r actually pierce it at different points, separated on the

surface of t le sphere by linear distances equal to the actual dis-

tances betw ',en the lines, but on the infinitely distant surface these

linear distances, being only finite, become invisible, subtending at

the centre angles less than anything assignable. The different

points, therefore, coalesce into a spot of apparently infinitesimal

size the so-called "vanishing point " of perspective. Thus the

axis of the earth and all lines parallel to this axis point to the

celestial pole.

POINTS AND CIRCLES OF REFERENCE.

8. The Zenith. The Zenith is the point, vertically overhead, i.e.,

the point where a plumb-line, produced upwards, would pierce the

sky : it is determined by the direction of gravity where the observer

stands.

If the earth were exactly spherical, the zenith might also be de-

fined as the point where a line drawn from the centre of the earth

upward through the observer meets the sky. But since, as we shall

see hereafter, the earth is not an exact globe, this second definition

indicates a point known as the Geocentric Zenith, which is not iden-

tical with the True or Astronomical Zenith, determined by the direc-

tion of gravity.

9. The Nadir. The Nadir is the point opposite the zeni th-

under oot

Both zenith and nadir are derived from the Arabic, which lan-

; also given us many other

REFERENCE POINTS AND CIRCLES.

10. Horizon. The Horizon 1 is a great circle of the celestial

sphere, having the zenith and nadir as its poles : it is therefore

half-way between them, and 90 from each.

A horizontal plane, or the plane of the horizon, is a plane perpen-

dicular to the direction of gravity, and the horizon may also be

correctly denned as the intersection of the celestial sphere by this

plane.

Many writers make a distinction between the sensible and rational

horizons. The plane of the sensible horizon passes through the

observer ; the plane of the rational horizon passes through the cen-

tre of the earth, parallel to the plane of the sensible horizon : these

two planes, parallel to each other, and everywhere about 4000 miles

apart, trace out on the sky the two horizons, the sensible and the

rational. It is evident, however, that on the infinitely distant sur-

face of -the celestial sphere, the two traces sensibly coalesce into

one single great circle, which is the horizon as first defined.. We

get, therefore, but one horizon circle in the sky.

r

11. The Visible Horizon is the line where sky and earth meet.

On land it is an irregular line, broken by hills and trees, and of no

astronomical value ; but at sea it is a true circle, and of great im-

portance in observation. It is not, however, a great circle, but,

technically speaking, only a small circle ; depressed below the true

horizon by an amount depending upon the observer's elevation

above tiio water. This depression is called the Dip of fff? Horizon,

and will be discussed further on.

12. Vertical Circles, Thes^ are great circles passing through

the zenith and nadir, and therefore necessarily perpendicular to the

horizon secondaries to it, to use the technical term.

Parallels of Altitude, or Almucantars. These are small circles

parallel to the horizon : the term Almucantar is> seldom used.

The points and circles thus far defined are determined entirely

by the direction of gravity at the station occupied by the observer.

13. The Diurnal Rotation of the Heavens. If one watches the

sky for a few hours some night, he will find that, while certain stars

rise in the east, others set in the west, and nearly all the constella-

tions change their places. Watching longer and more closely, it will

1 Beware of the common, but vulgar, pronunciation, Horizon.

MICHAEL REESE

UNIVERSITY

CALIFO^L

FRONTISPIECE.

THE GKEAT TELESCOPE OF THE LICK OBSEBVATORV, MI^HAMILTOX, CAL.

'Object-Glass made by A. Clark & Sons : Aperture, 36 in.; Focal Length, 56 ft. 2 in

Mounting by Warner & Swasey.

A TEXT-BOOK

OF

ASTRONOMY

FOR

COLLEGES AND SCIENTIFIC SCHOOLS

BY

CHAKLES A. YOUNG, PH.D., LL.D.

PROFESSOR OF ASTRONOMY IN PRINCETON UNIVERSITY

RKVISKD KDITION

BOSTON, U.S.A., AND LONDON

GINN & COMPANY, PUBLISHERS

1898

ENTERED AT STATIONERS' HALL

COPYRIGHT, 1888, BY

CHARLES A. YOUNG

COPYRIGHT, 1898, BY

CHARLES A. YOUNG

ALL RIGHTS RESERVED

7 7 A, ^/

PREFACE TO FIRST EDITION.

THE present work is designed as a text-book of Astronomy

suited to the general course in our colleges and schools of

science, and is meant to supply that amount of informati- >n

upon the subject which may fairly be expected of every

" liberally educated " person. While it assumes the previ-

ous discipline and mental maturity usually corresponding to

the latter years of the college course, it does not demand the

peculiar mathematical training and aptitude necessary as the

basis of a special course in the science only the most ele-

mentary knowledge of Algebra, Geometry, and Trigonometry

is required for its reading. Its aim is to give a clear, accu-

rate, and justly proportioned presentation of astronomical

facts, principles, and methods in such a form that they can

be easily apprehended by the average college student with a

reasonable amount of effort.

The limitations of time are such in our college course that *

probably it will not be possible in most cases for a class to

take thoroughly everything in the book. The fine print is to

be regarded rather as collateral reading, important to a com-

plete view of the subject, but not essential to the course.

Some of the chapters can even be omitted in cases where it

is found necessary to abridge the course as much as possible ;

e.g., the chapters on Instruments and on Perturbations.

While the work is no mere compilation, it makes no claims

to special originality: information and help have been drawn

from all available sources. The author is under great obliga-

tions to the astronomical histories of Grant and Wolf, and

especially to Miss Clerke's admirable " History of Astronomy

in the Nineteenth Century." Many data also have been drawn

from Houzeau's valuable " Vade Mecum de 1'Astronome."

IV PREFACE.

It has been intended to bring the book well down to date,

and to indicate to the student the sources of information on

subjects which are necessarily here treated inadequately on

account of the limitations of time and space.

Special acknowledgments are due to Professor Langley and

to his publishers, Messrs. Ticknor & Co., for the use of a

number of illustrations from his beautiful book, " The New

Astronomy " ; and also to D. Appleton & Co. for the use of

several cuts from the author's little book on the Sun. Pro-

fessor Trowbridge of Cambridge kindly provided the original

negative from which was made the cut illustrating the com-

parison of the spectrum of iron with that of the sun. Warner

& Swasey of Cleveland and Fauth & Co. of Washington have

also furnished the engravings of a number of astronomical

instruments.

Professors Todd, Emerson, Upton, and McNeill have given

most valuable assistance and suggestions in the revision of the

proof ; as indeed, in hardly a less degree, have several others.

PRINCETON, N. J., August, 1888.

PREFACE TO THE REVISED EDITION.

THE progress of Astronomy has been very rapid since the

first publication of this book in 1889, and, although in the

meantime the author has attempted as far as possible to keep

the successive issues u up to date" by minor changes, notes,

and " addenda," it has at last become imperative to give

the work a thorough revision, rewriting certain portions and

making considerable additions, in order to embody the new

and important results which have been obtained during the

last ten years.

The Appendix has also been enlarged by several articles

giving the demonstration of certain fundamental methods and

PREFACE. V

formulae for which, in previous editions, the student was

referred to other works not always conveniently accessible.

In one or two of these articles the Calculus is necessarily

used.

The various tables have been corrected to correspond with

the latest and most authoritative data ; and a set of illustrative

exercises has been added at the end of nearly every chapter.

While the book has thus been necessarily somewhat increased

in size, the changes have been so managed that no serious diffi-

culty will be encountered in using the new edition along with

the older issues. The original numbering of the articles has

been retained throughout, with only one or two exceptions,

the interpolated matter being designated by numbers with

asterisks.

It is believed that the book, so far as its scope extends,

may now be taken as fairly representing the present state of

the science, although some of the most important recent dis-

coveries are hardly made so prominent as would have been the

case if the revision had not been substantially completed and

prepared for the press more than two years ago; the actual

printing having been much delayed by various causes.

Special acknowledgments are due from the author to the

publishers for the liberality with which they have made the

extensive and expensive changes in the plates, and to Apple-

ton & Co., and Professors Frost, Hale, Holden, and Pickering

for many of the new illustrations.

PRINCETON UNIVERSITY, March, 1898.

TABLE OF CONTENTS.

PAGES

INTRODUCTION . 1-4

CHAPTER I. THE DOCTRINE OF THE SPHERE : Definitions and Gen-

eral Considerations .......... 5-20

^CHAPTER II. ASTRONOMICAL INSTRUMENTS : the Telescope ; Time-

^ "~~ keepers and Chronograph; the Transit Instrument and Accessories ;

the Meridian Circle and Reading Microscope ; the Altitude and Azi-

muth Instrument ; the Equatorial Instrument and Micrometer ; the

Sextant 21-5^^

CHAPTER III. CORRECTIONS TO ASTRONOMICAL OBSERVATIONS: the

Dip of the Horizon ; Parallax ; Semi-diameter ; Refraction ; Twilight ;

Exercises on Chapters I, II, and III ~T"~ . 58-71

CHAPTER IV. PROBLEMS OF PRACTICAL ASTRONOMY : the Determi-

nation of Latitude and its Variation, of Time, of Longitude, of a

Ship's Place at Sea, of Azimuth, and of the Apparent Right Ascen-

sion and Declination of a Heavenly Body ; the Time of Sunrise or

Sunset ; the Rising and Setting of a Star or of the Moon ; Exercises . 72-96

CHAPTER V. THE EARTH: the Approximate Determination of its

Dimensions and Form ; Proofs of its Rotation ; Accurate Determina-

tion of its Dimensions by Geodetic Surveys aiid Pendulum Observa-

tions ; Determination of its Mass and Density ; Exercises . 97-124

CHAPTER VI. THE EARTH'S ORBITAL MOTION: the Motion of the

Sun among the Stars ; the Equation of Time ; Precession ; Nutation ;

Aberration ; the Calendar ; Exercises . . . . . 125-154

CHAPTER VII. THE MOON: her Orbital Motion; DJgiaaCfi and Di-

mensions ; Mass, Density, and Superficial Gravity ; Rotation and

Librations ; Phases ; Light and Heat ; Physical Condition ; Influence

exerted on the Earth ; Surface Structure ; Possible Changes ;

Exercises 155-1

CHAPTER VIII. THE SUN : Distance and Dimensions; Mass and Den-

sity ; Rotation ; Solar Eye-pieces, and Study of the Sun's Surface ;

General Views as to Constitution ; Sun Spots, their Appearance,

Nature, Distribution, and Periodicity ; the Spectroscope . 184-208

Vlll TABLE OF CONTENTS.

CHAPTER IX. THK SPECTROSCOPE AND THE SOLAR SPECTRUM : Chemi-

cal Elements present in the Sun ; the Sun-spot Spectrum ; Dgpulfir's

Principle ; the Chromosphere and Prominences ; the Corona ; Exer-

cises on Chapters VIII. and IX. " " . T . . 209-231

CHAPTER X. THE SUN'S LIGHT AND HEAT : Comparison of Sunlight

with Artificial Lights; the Measurement of the Sun's Heat and Deter-

mination of the Solar Constant ; the Pyrheliometer, Actinometer, and

Bolometer ; the Sun's Temperature ; Maintenance of the Sun's Radia-

tion ; Conclusions as to its Age and Future Endurance . . 232-247

CHAPTER X/L ECLIPSES: Form and Dimensions of Shadows; Lu-

nar Eclipses ; Solar Eclipses, Total, Annular, and Partial ; Ecliptic

Limits, and x Number of Eclipses in a Year ; the Saros ; Occultations ;

Exercises ^~~\ 248-268

CHAPTER XII. CENTRAL FORCES : Equable Description of Areas ;

Areal, Linear, and Angular Velocities ; Kepler's Laws and Infer-

ences from them ; Gravitation demonstrated by the Moon's Motion ;

Conic Sections as Orbits ; the Problem of Two Bodies ; the " Velocity

from Infinity" and its Relation to the Species of Orbit described

by a Body moving under Gravitation; Intensity of Gravitation;

Exercises 269-293

CHAPTER XIII. THE PROBLEM OF THREE BODIES : Disturbing Forces ;

Lunar Perturbations and the Tides ; x Exercises . . . 294-318

HAPTER XIV. THE PLANETS : their Motions, Apparent and Real :

the Ptolemaic, Tychonic, and Copernican Systems ; the Orbits and

their Elements ; Planetary Perturbations ; Exercises . . 319-339

CHAPTER XV. THE PLANETS THEMSELVES : Methods of determining

their Diameters, Masses, Densities, Times of Rotation, etc. ; the

"Terrestrial Planets," Mercury, Venus, and Mars ; the Asteroids ;

Intra-Mercurial Planets and the Zodiacal Light ; Exercises . 340-377

CHAPTER XVI. THE MAJOR PLANETS : Jupiter, Saturn, Uranus, and

Neptune; Exercises 378-406

CHAPTER XVII. THE DETERMINATION OP THE SUN'S HORIZONTAL

PARALLAX AND DISTANCE : Oppositions of Mars and Transits of

Venus; Gravitational Methods; Determination by Means of the

Velocity of Light ; Exercises ....... 407-427

CHAPTER XVIII. COMETS : their Number, Motions, and Orbits ;

their Constituent Parts and Appearance; their Spectra, Physical

Constitution, and Probable Origin ; Exercises . . . 428-464

CHAPTER XIX. METEORS : Aerolites, their Fall and Physical Char-

acteristics ; Shooting Stars and Meteoric Showers ; Connection be-

tween Meteors and Comets ; Exercises ..... 465-482

TABLE OF CONTENTS. IX

CHAPTEK XX. THE STARS : their Nature and Number ; the Constel-

lations ; Star-catalogues ; Stellar Photography ; Designation of Stars ;

their Proper Motions ; Radial Motion, or Motion in Line of Sight ;

the Motion of the Sun in Space ; Stellar Parallax ; Exercises . 483-506

CHAPTER XXI. THE LIGHT OF THE STARS : Star Magnitudes and

Photometry ; Variable Stars ; Stellar Spectra ; Scintillation of the

Stars ; Exercises 507-540

CHAPTER XXII. AGGREGATIONS or STARS : Double and Multiple

Stars ; Clusters ; Nebulae ; Photography of Nebulae ; the Milky Way,

and Distribution of Stars in Space ; Constitution of the Stellar Uni-

verse ; Cosmogony and the Nebular Hypothesis . . . 541-578

APPENDIX. Reduction of Sidereal Time to Solar ; Azimuthal Motion

of Star at the Horizon ; Kepler's Problem and its Solution, Numer-

ically and by the Curve of Lines; Projection and Calculation of

Lunar Eclipses ; Proof that the Orbit of a Body moving under the

Law of Gravitation is a Focal Conic ; Expression for Velocity at any

Point of Orbit ; Apparent Epicycloidal Motion of Planets . 581-599

ASTRONOMICAL CONSTANTS, TABLES .... 601-611

INDEX 613-627

SUPPLEMENTARY INDEX . . . 628-630

INTRODUCTION.

1. ASTRONOMY (aa-rpov vo/xos) is the science which treats of the

heavenly bodies. As such bodies we reckon the sun and moon, the

planets (of which the earth is one) and their satellites, comets and

meteors, and finally the stars and nebulae.

We have to consider in Astronomy :

(a) The motions of these bodies, both real and apparent, and the

laws which govern these motions.

(b) Their forms, dimensions, and masses.

(c) Their nature constitution, and conditions.

(d) The effects they produce upon each other by their attractions,

radiations, or b}' any other ascertainable influence.

It was an early, and has been a most persistent, belief that the

heavenly bodies have a powerful influence upon human affairs, so

that from a knowledge of their positions and "aspects" at critical

moments (as for instance at the time of a person's birth) one could

draw up a "horoscope" which would indicate the probable future.

The pseudo -science which was founded on this belief was named

Astrology, the elder sister of Alchemy, and for centuries As-

tronomy was its handmaid; i.e., astronomical observations and cal-

culations were made mainly in order to supply astrological data.

At present the end and object of astronomical^study is chiefly

knowledge pure and simple ; so far as now appears, its development

has less direct bearing upon the material interests of mankind than

that of an}' other of the natural sciences. It is not likely that great

inventions and new arts will grow out of its laws and principles, such

as are continually arising from physical, chemical, and biological

discoveries, though of course it would be rash to say that such out-

growths are impossible. But the student of Astronomy must expect

his chief profit to be intellectual, in the widening of the range of

thought and conception, in the pleasure attending the discovery of

simple law working out the most complicated results, in the delight

4 INTRODUCTION.

our common schools. At the same time the necessary statements

and demonstrations are so much facilitated by the use of trigono-

metrical terms and processes that it would be unwise to dispense

with them entirely in a work to be used by pupils who have already

become acquainted with them.

In discussing the different subjects which present themselves,

the writer will adopt whatever plan appears best fitted to convey

to the student clear and definite ideas, and to impress them upon

the mind. Usually it will be best to proceed in the Euclidean

order, by first stating the fact or principle in question, and then

explaining its demonstration. But in some cases the inverse pro-

cess is preferable, and the conclusion to be reached will appear

gradually unfolding itself as the result of the observations upon

which it depends, just as its discovery came about.

The occasional references to " Physics " refer to the " Elementary

Text-Book of Physics," by Anthony and Brackett ; Magie's revised

edition, 1897. John Wiley & Sons, N.Y.

THE " DOCTRINE OF THE SPHERE/

CHAPTER I.

THE " DOCTRINE OF THE SPHERE," DEFINITIONS, AND GENERAL

CONSIDERATIONS.

ASTRONOMY, like all the other sciences, has a terminology of its

own, and uses technical terms in the description of its facts and

phenomena. In a popular essay it would of course be proper to

avoid such terms as far as possible, even at the expense of circum-

locutions and occasional ambiguity ; but in a text-book it is desirable

that the reader should be introduced to the most important of them

at the very outset, and made sufficiently familiar with them to use

them intelligently and accurately.

4. The Celestial Sphere. To an observer looking up to the

heavens at night it seems as if the stars were glittering points attached

to the inner surface of a dome ; since we have no direct perception of

their distance there is no reason to imagine some nearer than others,

and so we involuntarily think of the surface as spherical with our-

selves in its centre. Or if we sometimes feel that the stars and

other objects in the sky really differ in distance, we still instinctively

imagine an immense sphere surrounding and enclosing 1 all. Upon

this sphere we imagine lines and circles traced, resembling more or

less the meridians and parallels upon the surface of the earth, and

by reference to these circles we are able to describe intelligently the

apparent positions and motions of the heavenly bodies.

This celestial sphere may be regarded in either of two different

ways, both of which are correct and lead to identical results.

(a) We may imagine it, in the first place, as transparent, and of

merely finite (though undetermined) dimensions, but in some way

so attached to, and connected with, the observer that his > eye always

remains at its centre wherever he goes. Each observer, in this way

of viewing it, carries his own sky with him, and is the centre of his

own heavens.

(b) Or, in the second r -vce, and this is generally the more con-

venient way of reg;r matter, we may consider the celestial

6

i

sphere as mathematically infinite in its dimensions : then, let the

observer go where he will, he cannot sensibly get away from its

centre. Its radius being " greater than any assignable quantity,"

the size of continents, the diameter of the earth, the distance of the

sun, the orbits of planets and comets, even the spaces between the

stars, are all insignificant, and the whole visible universe shrinks

relatively to a mere point at its centre. In what follows we shall

use this conception of the celestial sphere. 1

The apparent place of any celestial body will then be the point

on the celestial sphere where the line drawn from the eye of the

observer in the direction in which he sees the object, and produced

indefinitely, pierces the sphere. Thus, in Figure 1, A, B, C are

the apparent places of a, b, and c,

the observer being at 0. The ap-

parent place of a heavenly body

evidently depends solely upon its

direction, and is wholly independent

of its distance from the observer.

5. Linear and Angular Dimensions.

Linear dimensions are such as may

be expressed in linear units ; i.e., in

miles, feet, or inches; in metres or

millimetres. Angular dimensions

FlG.l.

are expressed in angular units ; i.e.,

in right angles, in radians, 2 or (more commonly in astronomy) in

degrees, minutes, and seconds. Thus, for instance, the linear semi-

1 To most persons the sky appears, not a true hemisphere, but a flattened

vault, as if the horizon were more remote than the zenith. This is a subjective

effect due mainly to the intervening objects between us and the horizon. The

sun and moon when rising or setting look much larger than when they are

higher up, for the same reason.

2 A radian is the angle which is measured by an arc equal in length to radius/

Since a circle whose radius is unity has a circumference of 2 ?r, and contains 360,

or 21,600', or 1,296,000", it follows that a radian contains (f^Y*, or (

\ 2ilf / ^ \

/ 1 9QfiOftO \ "

or ( j ; i.e. (approximately), a radian = 57.3 = 3437.7' = 206264.8".

Hence, to reduce to seconds of arc an angle expressed in

radians, we must multiply it by the number 206264.8; a

relation of -which we shall have to mak u 'at use.

Z7T

diameter of the sun is about 697,000 kilometres (433,000 miles),

while its angular semidiameter is about 16', or a little more than

a quarter of a degree. Obviously, angular units alone can properly

be used in describing apparent distances and dimensions in the sky.

For instance, one cannot say correctly that the two stars which are

known as " the pointers " are two or five or ten feet apart : their

distance is about five degrees.

It is sometimes convenient to speak of " angular area" the unit

of which is a " square degree " or a " square minute " ; i.e., a small

square in the sky of which each side is 1 or l f . Thus we may

compare the angular area of the constellation Orion with that of

Taurus, in square degrees, just as we might compare Pennsylvania

and New Jersey in square miles.

6. Relation between the Distance and Apparent Size of an Object.

Suppose a globe having a radius BC equal to r. As seen from

FIG. 2.

the point A (Fig. 2) its apparent (i.e., angular) semidiameter will

be BA C or s, its distance being A C or R.

We have immediately from Trigonometry, since B is a right angle,

If, as is usual in Astronomy, the diameter of the object is small

as compared with its distance, we may write S = ~B, which gives 5

in radians (not in degrees or seconds). If we wish it in the ordi-

nary angular units,

* = 57.3^ , or s' = 3437.7^ , or s" = 206264.8^

% * R R

where s means s in degrees ; s', s in minutes ; V, s in seconds of arc.

her form of the equation we see that the apparent diameter

8 UU.b'iJMTiUJN AiNJJ

In the case of the moon, R = about 239,000 miles ; and r, 1081

miles. Hence s = ai-f Q ^|T f a radian, which is a little more

than of a degree, or about 933".

It may be r^ntioned here as a rather curious fact that most persons say

that the mo appears about a foot in diameter ; at least, this seems to be

the average e, mate. 1 This implies that the surface of the sky appears to

them only abo^t 110 feet away, since that is the distance at which a disc

one foot in diameter would have an angular diameter of T ^> of a radian,

7. Vanishing Point. Any system of parallel lines produced in

one direct^ i will appear to pierce the celestial sphere at a single

point. The r actually pierce it at different points, separated on the

surface of t le sphere by linear distances equal to the actual dis-

tances betw ',en the lines, but on the infinitely distant surface these

linear distances, being only finite, become invisible, subtending at

the centre angles less than anything assignable. The different

points, therefore, coalesce into a spot of apparently infinitesimal

size the so-called "vanishing point " of perspective. Thus the

axis of the earth and all lines parallel to this axis point to the

celestial pole.

POINTS AND CIRCLES OF REFERENCE.

8. The Zenith. The Zenith is the point, vertically overhead, i.e.,

the point where a plumb-line, produced upwards, would pierce the

sky : it is determined by the direction of gravity where the observer

stands.

If the earth were exactly spherical, the zenith might also be de-

fined as the point where a line drawn from the centre of the earth

upward through the observer meets the sky. But since, as we shall

see hereafter, the earth is not an exact globe, this second definition

indicates a point known as the Geocentric Zenith, which is not iden-

tical with the True or Astronomical Zenith, determined by the direc-

tion of gravity.

9. The Nadir. The Nadir is the point opposite the zeni th-

under oot

Both zenith and nadir are derived from the Arabic, which lan-

; also given us many other

REFERENCE POINTS AND CIRCLES.

10. Horizon. The Horizon 1 is a great circle of the celestial

sphere, having the zenith and nadir as its poles : it is therefore

half-way between them, and 90 from each.

A horizontal plane, or the plane of the horizon, is a plane perpen-

dicular to the direction of gravity, and the horizon may also be

correctly denned as the intersection of the celestial sphere by this

plane.

Many writers make a distinction between the sensible and rational

horizons. The plane of the sensible horizon passes through the

observer ; the plane of the rational horizon passes through the cen-

tre of the earth, parallel to the plane of the sensible horizon : these

two planes, parallel to each other, and everywhere about 4000 miles

apart, trace out on the sky the two horizons, the sensible and the

rational. It is evident, however, that on the infinitely distant sur-

face of -the celestial sphere, the two traces sensibly coalesce into

one single great circle, which is the horizon as first defined.. We

get, therefore, but one horizon circle in the sky.

r

11. The Visible Horizon is the line where sky and earth meet.

On land it is an irregular line, broken by hills and trees, and of no

astronomical value ; but at sea it is a true circle, and of great im-

portance in observation. It is not, however, a great circle, but,

technically speaking, only a small circle ; depressed below the true

horizon by an amount depending upon the observer's elevation

above tiio water. This depression is called the Dip of fff? Horizon,

and will be discussed further on.

12. Vertical Circles, Thes^ are great circles passing through

the zenith and nadir, and therefore necessarily perpendicular to the

horizon secondaries to it, to use the technical term.

Parallels of Altitude, or Almucantars. These are small circles

parallel to the horizon : the term Almucantar is> seldom used.

The points and circles thus far defined are determined entirely

by the direction of gravity at the station occupied by the observer.

13. The Diurnal Rotation of the Heavens. If one watches the

sky for a few hours some night, he will find that, while certain stars

rise in the east, others set in the west, and nearly all the constella-

tions change their places. Watching longer and more closely, it will

1 Beware of the common, but vulgar, pronunciation, Horizon.

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