An introduction to astronomy; designed as a text book for the students of Yale college

Introduction

ASTRONOMY

DESIGNED AS A

TEXT BOOK

STUDENTS OF YALE COLLEGE

EE VISED EDITION,

WITLT NUMEROUS ALTERATIONS AND ADDITIONS, INCLUDING THE LATEST DISCOVERIES.

BY DEKOT OUISTP, LL.D.

PROFESSOR OF NATURAL PHILOSOPBT AND ASTRONOMY,

NEW YORK:

$3 4$

Entered, according to Act of Congress, in the year 1854,

Stereotyped by

RICHARD C. VALENTINE,

17 Dutch-st., cor. of Fulton.

REVISED EDITION

The great progress of astronomical discovery, during the last few years, has induced the author of this work to prepare, with much labor and expense, a new edition, which should fully exhibit the features of the science in their latest physiognomy. Since the stereotype edition was first published, in 1844, numerous and important discoveries have been made, both in the solar system and among the fixed stars. The dimensions of the planetary system have been nearly doubled by the addition of the planet Neptune ; the number of the Asteroids has been increased from four to twenty-seven; interesting discoveries have been made in the Rings of Saturn, and an eighth member has been added to his retinue of satellites ; and the subject of Comets has received a new impulse by the appearance of the remarkable comet of 1848.

Meanwhile, the introduction into practical astronomy of Telescopes greatly exceeding in light and power those previously directed to the heavens, has disclosed new wonders among the fixed stars, and especially among the Nebulao ; a problem, which had eluded the eager pursuit of astronomers, — that of finding the distances of the fixed stars, — has been solved ; stellar astronomy has been greatly enriched by the observations of Sir John Herschel in the southern hemisphere ; our knowledge of the proper motions of the stars has been enlarged, and crowned with several most interesting results ; some progress has been made towards determining the magnitudes of the stars, the nature of their orbits, the velocities of their motions, and the periods of their revolutions ; and recent investigations inspire the hope, that the mechanism of the universe will shortly be understood as perfectly as is that of the solar system.

Besides a notice of these important results, there will also be found, in the present edition, a concise statement of the phenomena and causes of Meteoric Showers. — a topic which, for peculiar reasons, the author has forborne to introduce into the text of previous editions, but it is now inserted in conformity with the example of Sir John Herschel, Humboldt, and other distinguished writers of astronomical works, who have not scrupled to assign to the periodical meteors a distinct place in the solar system. The Numerical Relations of the sun and planets — a subject which has heretofore appeared only in the Addenda — is now incorporated with the text ; and, illustrated as it is by a variety of curious and interesting problems, it will lead the pupil to form just and accurate ideas of those relations, and of the laws that govern them.

The part of astronomy which relates to the Earth, the Sun, and the Moon, has undergone, of late, but few changes ; but that which relates to the Planets and Fixed Stars has been enriched by so many new discoveries, that it has been necessary to re-write it, and to cast it anew. With these improvements, it is believed the present work will be found to be as well suited to initiate the student of astronomy into the mysteries of this noble science, and to inspire a taste for its pursuits, as can reasonably be expected of any work comprised within such narrow limits.

Yale College, January, 1854.

Preface

Neably all who have written Treatises on Astronomy, designed for young learners, appear to have erred in one of two ways ; they have either disregarded demonstrative evidence, and relied on mere popular illustration, or they have exhibited the elements of the science in naked mathematical formulae. The former are usually diffuse and superficial ; the latter, technical and abstruse.

In the following Treatise, we have endeavored to unite the advantages of both methods. We have sought, first, to establish the great principles of astronomy on a mathematical basis ; and, secondly, to render the study interesting and intelligible to the learner, by easy and familiar illustrations. We would not encourage any one to believe that he can enjoy a full view of the grand edifice of astronomy, while its noble foundations are hidden from his sight; nor would we assure him that he can contemplate the structure in its true magnificence, while its basement alone is within his field of vision. We would, therefore, that the student of astronomy should confine his attention neither to the exterior of the building, nor to the mere analytic investigation of its structure. We would desire that he should not only study it in models and diagrams, and mathematical formula?, but should at the same time acquire a love of nature herself, and cultivate the habit of raising his views to the grand originals. Nor is the effort to form a clear conception of the motions and dimensions of the heavenly bodies, less favorable to the improvement of the intellectual powers, than the study of pure geometry.

But it is evidently possible to follow out all the intricacies of an analytical process, and to arrive at a full conviction of the great truths of astronomy, and yet know very little of nature. According to our experience, however, but few students in the course of a liberal education will feel satisfied with this. They do not need so much to be convinced that the assertions of astronomers are true, as 1hey desire to know what the truths are, and how they were ascertained ; and they will derive from the study of astronomy little of that moral and intellectual elevation which they had anticipated, unless they learn to look upon the heavens with new views, and a clear comprehension of their wonderful mechanism.

Much of the difficulty that usually attends the early progress of the astronomical student, arises from his being too soon introduced to the most perplexing part of the whole subject, — the planetary motions. In this work, the consideration of these is for the most part postponed until the learner has become familiar with the artificial circles of the sphere, and conversant with the celestial bodies. We then first take the most simple view possible of the planetary motions by contemplating them as they really are in nature,, and afterwards proceed to the more difficult inquiry, why they appear as they do. Probably no science derives such signal advantage from a happy arrangement, as astronomy ; — an order, which brings out every fact or doctrine of the science just in the place where the mind of the learner is prepared to receive it.

ANALYSIS.

DESIGNED AS A BASIS FOR REVIEW AND EXAMINATION.

PRELIMINARY OBSERVATIONS.

Astronomy defined,

Descriptive Astronomy,

Physical do. 1

Practical do. 1

History. — Ancient nations who cultivated astronomy,

Pythagoras — his age and country,

His views of the celestial motions, 1

Alexandrian School — when founded — by whom — introduction of astronomical instruments, 2

Hipparchus — his character, 2

Ptolemy — the Almagest, 2

Copernicus, Tycho Brahe, Kepler and

Galileo — respective labors of each,.... ! Sir Isaac Newton — his great discovery.

La Place — Mecanique Celeste, 2

Astrology — Natural and Judicial — object of each, 2

Accuracy aimed at by astronomers, 3

Copernican System — its leading doctrines, 3

Plan of this work, 3

Part I.— OF THE EARTH. Chapter 1. — of the figure and dimensions

OF THE EARTH, AND THE DOCTRINE OF THE SPHERE.

Figure of the earth, 4

Proofs, 4

Dip of the horizon, 4

How found, 5

Table of the dip — its use, 6

Exact figure of the earth, 6

Its circumference, 6

Small inequalities of the earth's surface, 6

Diameter of the earth how determined, 7 How to divest the mind of preconceived

erroneous notions, 8

Doctrine of the Sphere, defined, 9

Great and small circles defined, 9

Axis of a circle — pole, 9

Situation of the poles of two great circles which cut each other at right angles, 9

Points of intersection of two great circles — how many degrees apart, 10

Page.

Page. When a great circle passes through the

pole of another, how does it cut it ? . 10

Secondary defined, 10

Angle made by two great circles how

measured, 10

Terrestrial and Celestial spheres distinguished, 10

Horizon defined, 1

Sensible horizon, 1

Rational do 1

Zenith and Nadir, 1

Vertical circles, 1

Meridian, 1

Prime Vertical, 1

How the place of a celestial body is determined, 11

Altitude — azimuth — amplitude, 12

Zenith Distance — how measured, 12

Axis of the earth — axis of the celestial

sphere, 12

Poles of the earth — poles of the heavens, 12

Equator — terrestrial and celestial, 12

Hour circles, 13

Latitude, 13

Polar Distance, how related to latitude, 13

Longitude, 13

Standard Meridians, 13

Ecliptic, 13

Inclination of the ecliptic to the equator, 13

Equinoctial points, 13

Equinoxes — Vernal and autumnal, 13

Solstitial points, 14

Solstices, 14

Signs of the ecliptic enumerated, 14

Colures — Equinoctial and Solstitial,... 14

Right ascension, 15

Declination, 15

Celestial Longitude, 15

Celestial Latitude, 15

North Polar Distances, how related tc

latitude, 15

Parallels of Latitude, 15

Tropics, 16

Polar circles, 16

Zones, 16

Zodiac, 16

VI

ANALYSIS.

Page.

Elevation of the pole — to what is it

equal? 16

Elevation of the equator, 16

Distance of a place from the pole, to

what equal ? 16

Chapter II. — diurnal revolution — artificial GLOBES ASTRONOMICAL PROBLEMS.

Circles of Diurnal Revolution, 17

Sidereal day defined, 17

Appearance of the circles of diurnal

revolution at the equator, 17

A Right Sphere defined, 18

A Parallel Sphere, 19

An Oblique Sphere, 19

Circle of Perpetual Apparition, 20

Circle of Perpetual Occupation, 20

How are the circles of daily motion cut by the horizon in the different

spheres? 20

Explanation of the peculiar appearances of each sphere, from the revolution of the earth on its axis, 21

Artificial Globes — terrestrial and celestial, 22

Their use, 23

Meridian — how represented — how graduated, 23

Horizon — how represented — how graduated, 23

Hour Circles, how represented, 23

Hour Index described, 23

Quadrant of Altitude, 24

Its use described, 24

To rectify the globe for anyplace, 24

Problems on the terrestrial Globe — To find. t)\e latitude and longitude

of a place, 24

To find a -place, its latitude and longi-

gitude being given, 25

To find the bearing and distance of

two places, 25

To determine the difference of time of

two places, 25

The hour being given at any place, to tell what hour it is in any other part

of the world, 25

To find the antosci, periceci, and antipodes, 25

To rectify the globe for the sun's place, 26 The latitude of the place being given, to find the time of the sun's rising

and setting, '

Problems on the celestial Globe. — To find the right ascension and declination, 26

To represent the appearance of the

heavens at any time,

To find the altitude and azimuth of a star, .. !

Page

To find the angular distance of two stars from each other, 27

To find the su/i's meridian altitude, the latitude and day of the month being given,. 28

Chapter III. — Parallax — Refraction — Twilight. Parallax defined, 23

Horizontal Parallax, 29

Relation of parallax to the zenith distance, and distance from the center

of the earth, 29

To find the horizontal parallax from

the parallax at any altitude, 29

Amount of parallax in the zenith and

in the horizon, 30

Effect of parallax upon the altitude of

a body, 30

Mode of determining the horizontal

parallax of a body,.. 30

Amount of the sun's hor. par 31

Use ofy parallax, 31

Refraction. — Its effect upon the altitude of a body, 32

Its nature illustrated, 32

Its amount at different angles of elevation, 32

How the amount is ascertained, 33

Sources of inaccuracy in estimating the

Effect of refraction upon the sun and

moon when near thehoi*izon, 35

Oval figure of these bodies explained,. 35 Apparent enlargement of the sun and

moon near the horizon, 36

Twilight. — Its cause explained, 37

Length of twilight in different latitudes, 37 How the atmosphere contributes to diffuse the sun's light, 37

Chapter IV.— Time. Time defined, 38

What period is a sidereal day, 38

Uniformity of sidereal days, 38

Solar time, how reckoned, 39

Whv solar days are longer than sidereal, 39

Apparent time defined, 39

Mean time, 40

An astronomical day, 40

Equation of time defined, 40

When do apparent time and mean

time differ most? 40

When do they come together? 40

Effect of a change in the place of the

earth's perihelion, 40

Causes of the inequality of the solar

days, 41

Explain the first cause, depending on

the unequal velocities of the sun,... . 4l

ANALYSIS.

Vll

Page

Explain the second cause, depending

on the obliquity of the ecliptic, 42

When does the sidereal day com-

mence ? 44

The Calendar. — Astronomical year defined, 45

How the most ancient nations deter.

mined the number of days in the year, 45 Julius Caesar's reformation of the calen.

dar explained, 45

Errors of this calendar, 45

Reformation by Pope Gregory......... . 46

Rule for the Gregorian calendar, 46

New style, when adopted in England, 46 What nations still adhere to the old

style? 46

What number of days is now allowed

between old and new style ? 47

How the common year begins and ends, 47

How leap year begins and ends, 47

Does the confusion of different calendars affect astronomical observations ? 47

Chapter V. — Astronomical Instruments and Problems — Figure and Density of the earth. How the most ancient nations acquired

their knowledge of Astronomy, 48

Use of instruments in the Alexandrian

School, 48

Ditto, by Tycho Brahe, 48

Ditto, by the Astronomers Royal, 48

Space occupied by 1" on the limb of an

instrument, 48

Extent of actual divisions on the limb, 49

Vernier, defined, 49

Its use illustrated, 49

Chief astronomical instruments enumerated, 50

Observations taken on the meridian.. . 50

Reasons of this, 50

Transit Instrument defined, 51

Ditto described, 51

Method of placing it in the meridian. . 51

Line of collimation defined, 52

System of wires in the focus, 52

Its use for arcs of right ascension, 52

Astronomical Clock, — how regulated, 52

What does it show ? 52

How to test its accuracy, 53

How corrected, 53

Mural Circle, its object, 54

Describe it, 54

How the different parts contribute to

the object, 54

Mural Quadrant, 55

Use of the Mural Circle for arcs of declination, 56

Altitude and Azimuth Instrument defined, 56

Page.

Its use, 56

Describe it, 57

Sextant described, 58

How to measure the angular distance

of the moon from the sun, 59

How to take the altitude of a heavenly

body 59

Use of the artificial horizon, 59

In what consists the peculiar value of

theSextant? 60

Astronomical Problems. — Given the the sun's right ascension and declination, to find his longitude and the

obliquity of the ecliptic, 61

Napier's Rule of circular parts, 62

Given the sun's declination to find his rising and setting at any place whose

latitude is known, 63

Given the latitude of a place and the declination of a heavenly body, to determine its altitude and azimuth when on the six o'clock hour circle, 64 The latitudes and longitudes of two celestial objects being given, to find

their distance apart, 6b

Figure and Density of the Earth — reason for ascertaining it with great

precision, 66

How found from the centrifugal force, 66 From measuring an arc of the meridian, 67 From observations with the pendulum, 68

From the motions of -the moon, 68

Density of the earth compared with

water, 68

How ascertained by Dr. Maskelyne, . . 69 Why an important element, 69

Chapter 1. — The Sun — Solar Spots — Zo 1 diacal Light. Figureof the sun, 70

Angle subtended by a line of 400 miles, 70

Distance from the earth, 70

Illustrated by motion on a railway car, 70 Apparent diameter of the sun — how

found, 72

How to find the linear diameter, 71

How much larger is the sun than the

Its density and mass compared with

the earth's, 71

Weight at the surface of the sun, 72

Velocity of falling bodies at the sun ... 72

Solar Spots. — Their number, 72

Description, 72

What region of the sun do they occupy, 73

Proof that they are on the sun, 73

V1U

ANALYSIS.

Page.

How we learn the revolution of the sun

on his axis, 73

Time of the revolution, 73

Apparent paths of the spots, 74

Inclination of the solar axis, 74

Sun's Nodes — when does the sun pass

them? 75

Cause of the solar spots, 76

Faculae, 76

Zodiacal Light. — Where seen, 76

Its form, , 76

Aspects at different seasons, 76

Its motions, 77

Its nature, 77

Chapter II. — Apparent Annual Motion

of the Sun — Seasons — Figure of the Earth's Orbit.

Apparent motion of the sun, 78

How both the sun and earth are said to

move from west to east, 79

Nature and position of the sun's orbit,

how determined, 79

Changes in declination how found, 79

Ditto, in right ascension, 80

Inferences from a table of the sun's declinations,... 80

Ditto, of right ascensions, 81

Path of the sun, how proved to be a

great circle, 81

Obliquity of the ecliptic, how found, 81

How it varies, 81

Great dimensions of the earth's orbit, 81

Earth's daily motion in miles, 82

Ditto,hourly ditto, 82

Diurnal motion at the equator per

hour, 82

Seasons. — Causes of the change of seasons, 82

How each cause operates,. 82

Illustrated by a diagram, 83

Change of seasons had the equator been

perpendicular to the ecliptic, 84

Figure of the Earth's Orbit. — Proof

that the earth's orbit is not circular, 85

Radius vector defined, 85

Figure of the earth's orbit how obtained, 86

Relative distances of the earth from the

sun, how found, 86

Perihelion and Aphelion denned, 87

Variations in the sun's apparent diameter, 87

Angular velocities of the sun at the perihelion and aphelion, 87

Ratio of these velocities to the distances, 87

How to calculate the relative distances of the earth from the sun's daily motions,

Pago Product of the angle described in any given time by the square of the distance, 88

Space described by the radius vector of

the solar orbit in equal times, 83

How to represent the sun's orbit by a diagram, 89

Chapter III. — Universal Gravitation. Universal Gravitation defined, 90

Why is it called attraction, 90

History of its discovery, 90

How was the gravitation of the moon

to the earth first inferred ? 91

Laws of Gravitation. — If a body revolves about an immovable center of force, and is constantly attracted

to it, how will itmove ? 92

If a body describes a curve around a center towards which it tends by any force, how is its angular velocity related to the distance, 93

In the same curve, the velocity at any

point of the curve varies as what ? 93 If equal areas be described about a center in equal times, to what must the

force tend? 94

How is the distance of any planet from the sun at any point in its orbit, to its distance from the superior focus ? 94 Case of two bodies gravitating to the same center where one descends in a straight line, and the other revolves

in a curve, 95

Velocity of a body at any point when

falling directly to the sun, 97

Relation between the distances and periodic times, 99

Kepler'' s three great laws, 99

Motion in an Elliptical Orbit, 100

Idea of a projectile force, 100

Nature of the impulse originally given

to the earth, 100

Two forces under which a body revolves, 100

Illustrated by the motion of a cannon

ball, 101

Why a planet returns to the sun, 102

Illustration by a suspended ball, 103

Chapter IV. — Precession of the Equinoxes — Nutation — Aberration — Mean and True Places of the sun.

Precession of the Equinoxes defined, 104

Why so called, 104

Amount of Precession annually, 104

Revolution of the equinoxes, 104

Revolution of the pole of the equator

around the pole of the ecliptic, 105

ANALYSIS.

IX

Page.

Changes among the stars caused by

precession, 105

The present pole star not always such, 105 What will be the pole star 13,000

years hence ? 105

Cause of the precession of the equinoxes, 105

Explain how the cause operates, 106

Proportionate effect of the sun and

moon in producing precession, 107

Tropical year defined, 107

How much shorter than the sidereal

year, 107

Use of the precession of the equinoxes

in chronology, 107

Notation, defined, 108

Explain its operation, 108

Cause of Nutation, 108

Aberration, defined,.. 108

Illustrated by a diagram, 109

Amount of aberration, . . 109

Effect on the places of the stars, 109

Motion of the Apsides, the fact stated, 109

Direction of this motion, 110

Time of revolution of the line of Apsides, 110

Present longitude of the perihelion,. . 110

When was it nothing? 110

Mean and True Places of the Sun, 1 11

Mean Motion defined, Ill

Illustrated by surveying a field, Ill

Mean and true longitude distinguished, Ill

Equations defined, Ill

Their object, Ill

Mean and True anomaly defined,.... 112

Equation of the Center, 112

Explain from the figure, 112

Chapter V. — The Moon — Lunar Geography — Phases of the Moon — Her Revolutions. Distance of the moon from the earth, 113

Her mean horizontal parallax, 113

Her diameter, 113

Volume, density, and mass, 113

Shines by reflected light, 113

Appearance in the telescope, 113

Terminator defined, 113

Its appearance, 113

Proofs of Valleys, 114

Form of these, 114

Best time for observing the lunar

mountains and valleys, 114

Names of places on the moon double, 115

Dusky regions how named, 115

Point out remarkable places on the

map of the moon, 115

Explain the method of estimating the

height of lunar mountains, 115

Page.

Specify the heights of particular

mountains, 117

Volcanoes, proof of their existence, — 117

Has the moon an atmosphere? 117

Improbability of identifying artificial

structures in the moon, 117

Phases of the Moon, their cause,.... 118 Successive appearances of the moon from one new moon to another, .... 118

Syzygies defined, 118

Explain the phases of the moon from

figure 46, 119

Revolutions of the moon. Period of her revolutions about the earth, . 119

Her apparent orbit a great circle, 120

A sidereal month defined, 120

A synodical do. 120

Length of each, 120

Why the synodical is longer, 120

How each is obtained, 120

Inclination of the lunar orbit, 121

Nodes defined, 121

Why the moon sometimes runs high

and sometimes low, 121

Harvest moon defined, 122

Ditto explained, 122

Explain why the moon is nearer to us when on the meridian than when

near the horizon, 122

Time of the moon's revolution on its

axis, 123

How known, 123

Librations explained, 123

Diurnal Libration, 124

Length of the Lunar days, 124

Earth never seen on the opposite side

of the moon, 124

Appearances of the earth to a specta-

toron the moon, 124

Why the earth would appear to remain fixed, 125

Ascending and descending nodes distinguished, 125

Whether the earth carries the moon

around the sun, 126

How much more is the moon attracted towards the sun than towards

When does the sun act as a disturbing

force upon the moon ? 126

Why does not the moon abandon the

earth at the conjunction? 126

The moon's orbit concave towards the

, 127

How the elliptical motion of the moon about the earth is to be conceived

Illustrations, 127