Outlines of astronomy

Part One

NEW YORK P. F. COLLIER & SON

M C M I I

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SCIENCE

SIR JOHN HERSCHEL

Sir John Frederick William Herschel, Bart., the illustrious astronomer, was the only son of Sir F. William Herschel. He was born at Slough, Buckinghamshire, England, in the year 1792. His scholastic education began at Eton, whence, at the age of seventeen, he was sent to St. John's College, Cambridge, where he attained to great eminence in mathematics. After leaving the University, he entered upon the study of astronomy, and in 1820, assisted by his father, completed a mirror of 18 inches diameter and 20 feet focal length for a reflecting telescope. This, as subsequently improved, became the instrument which enabled him to effect the astronomical observations that formed the basis of his fame. In 1821-23 he undertook the re-examination of his father's double stars. For this work he received in 1826 the gold medal of the Astronomical Society, and the Lalande Medal of the French Institute. From 1824 to 1827 he was Secretary of the Eoyal Society, and in 1827 was elected to the Chair of the Astronomical Society, which office he filled on two subsequent occasions. In 1831 the honor of knighthood was conferred on him by William IV"., and he subsequently

4 SIR JOHN HERSCHEL

was made a baronet. His exploration of the southern heavens constituted an epoch in astronomy, and secured for him the distinction of memberships in almost every importaat society in both hemispheres. His "Outlines of Astronomy," here reproduced, first appeared in 1849, and, notwithstanding the disadvantage arising from the practice of stereotyping text- books which relate to progressive sciences, there is no more instructive volume extant on the subject of which it treats. Sir John Herschel died in 1871; his remains are interred in Westminster Abbey, close to the grave of Sir Isaac Newton.

Chapter I

General Notions — Apparent and real Motions — Shape and Size of the Earth — The Horizon and its Dip — The Atmosphere — Refraction — Twilight — Appearances resulting from Diurnal Motion — From Change of Station in General — Parallactic Motions — Terrestrial Parallax — That of the Stars Insensible — First Step toward forming an Idea of the Distance of the Stars — Copernican View of the Earth's Motion — Relative Motion — Motions partly Real, partly Apparent — Geocentric Astronomy, or Ideal Reference of Phenomena to the Earth's Centre as a Common Conventional Station 32

CHAPTER n

Terminology and Elementary Geometrical Conceptions and Relations — Terminology relating to the Globe of the Earth — To the Celestial Sphere — Celestial Perspective 89

CHAPTER HI

Of the Nature of Astronomical Instruments and Observations in General — Of Sidereal and Solar Time— Of the Measurements of Time— Clocks, Chronometers — Of Astronomical Measurements — Principle of Telescopic Sights to Increase the Accuracy of Pointing — Simplest Application of this Principle — The Transit Instrument — Of the Measurement of Angular Intervals — Methods of Increasing the Accuracy of Reading — The Vernier — The Microscope — Of the Mural Circle — The

6 CONTENTS

Meridian Circle — Fixation of Polar and Horizontal Points — The Level, Plumb-line, Artificial Horizon — Principle of Collimation — Collimators of Rittenhouse, Kater and Bohnenberger — Of Compound Instruments with Co-ordinate Circles — The Equatorial, Altitude and Azimuth Instrument — Theodolite — Of the Sextant and Reflecting Circle — Principle of Repetition — Of Micrometers — Parallel "Wire Micrometer — Principle of the Duplication of Images — The Heliometer — Double Refracting Bye-piece — Yariable Prism Micrometer — Of the Position Micrometer — Illumination of "Wires — Solar Telescope and Eye -piece — Helioscopy — Collimation of large Reflectors « lOi

CHAPTER IV

OP GEOGRAPHY

Of the Figure of the Earth — Its Exact Dimensions — Its Form that of Equilibrium Modified by Centrifugal Force — Variation of Gravity on its Surface — Statical and Dynamical Measures of Gravity — The Pendulum — Gravity to a Spheroid — Other Effects of the Earth's Rotation — Trade "Winds — Veering of the "Winds — Cyclones — Foucault's Pendulum — The Gyroscope — Determination of Geographical Positions — Of Latitudes — Of Longitudes — Conduct of a Trigonometrical Survey — Of Maps — Projections of the Sphere — Measurement of Heights by the Barometer . It3

CHAPTER V

OP URANOGRAPHY

Construction of Celestial Maps and Globes by Observations of Right Ascension and Declination — Celestial Objects Distinguished into Fixed and Erratic — Of the Constellations — Natural Regions in the Heavens — The Milky "Way — The Zodiac — Of the Ecliptic — Celestial Latitudes and Longitudes — Precession of the Equinoxes— Nutation — Aberration — Refraction — Parallax — Summary View of the Uranographical Corrections 246

CHAPTER VI

OP THE SUN'S MOTION AND PHYSICAL CONSTITUTION

Apparent Motion of the Sun not Uniform — Its Apparent Diameter also Variable — Variation of its Distance Concluded — Its Apparent Orbit an Ellipse about the Focus— Law of the Angular Velocity— Equable Description of Areas — Parallax of the Sun — Its Distance and Magnitude — Copernican Explanation of the Sun's Apparent Motion — Parallelism of the Earth's Axis — The Seasons — Heat Received from the Sud

CONTENTS 7

in Different Parts of the Orbit — Effect of Excentricity of the Orbit and Position of its Axis on Climate — Mean and True Longitudes of the Sun — Equation of the Centre — Sidereal, Tropical and Anomalistic Years — Physical Constitution of the Sun — Its Spots — Faculae — Probable Nature and Cause of the Spots — Recent Discoveries of Mr. Dawes — Of Mr. Nasmyth — Potation of the Sun on its Axis — Its Atmosphere . — Supposed Clouds — Periodical Recurrence of a More and Less Spotted State of its Surface — Temperature of its Surface — Its Expenditure of Heat — Probable Cause of Solar Radiation 281

CHAPTER YII

Of the Moon — Its Sidereal Period — Its Apparent Diameter — Its Parallax Distance, and Real Diameter — First Approximation to its Orbit — An Ellipse about the Earth in the Focus — Its Excentricity and Inclination — Motion of its Nodes and Apsides — Of Occupations and Solar Eclipses Generally — Limits within which they are Possible — They Prove the Moon to be an Opaque Solid — Its Light Derived from the Sun — Its Phases — Synodic Revolution or Lunar Monlh — Harvest Moon — Of Eclipses more Particularly — Their Phenomena — Their Periodical Recurrence — Physical Constitution of the Moon — Its Mountains and other Superficial Features — Indications of former Volcanic Activity — Its Atmosphere — Climate — Radiation of Heat from its Surface — Rotation on its own Axis — Libration — Appearance of the Earth from it — Probable Elongation of the Moon's Figure in the Direction of the Earth — Its Habitability not Impossible — Charts, Models and Photographs of its Surface ......... 333

CHAPTER Till

Of Terrestrial Gravity — Of the Law of Universal Gravitation — Paths of Projectiles ; Apparent, Real — The Moon Retained in her Orbit by Gravity — Its Law of Diminution — Laws of Elliptic Motion — Orbit of the Earth Round the Sun in Accordance with these Laws — Masses of the Earth and Sun Compared — Density of the Sun — Force of Gravity at its Surface — Disturbing Effect of the Sun on the Moon's Motion . . . 336

CHAPTER IX

OF THE SOLAR SYSTEM

Apparent Motions of the Planets— Their Stations and Retrogradations— The Sun their Natural Centre of Motion — Inferior Planets — Their Phases, Periods, etc. — Dimensions and Form of their Orbits — Transits across the Sun — Superior Planets — Their Distances, Periods, etc. — Kepler's

O CONTENTS

Laws and their Interpretation — Elliptic Elements of a Planet's Orbit — Its Heliocentric and Geocentric Place — Empirical Law of Planetary Distances ; Violated in the Case of Neptune — The Asteroids — Physical Peculiarities Observable in each of the Planets 319

CHAPTER X

OP THE SATELLITES

Of the Moon, as a Satellite of the Earth — General Proximity of Satellites to their Primaries, and Consequent Subordination of their Motions — Masses of the Primaries Concluded from the Periods of their Satellites — Maintenance of Kepler's Laws in the Secondary Systems — Of Jupiter's Satellites — Their Eclipses, etc. — Telocity of Light Discovered by their Means — Satellites of Saturn — Of Uranus — Of Neptune . 444

TO

THE REV. W. RUTTER DAWES, F.R.A.S.,

My dear Mr. Dawes — In availing myself of your permission to dedicate to you an Edition of these Outlines, enriched by accounts of several of your own recent discoveries, 1 should ill acquit myself to my own feelings if I did not add to the expression of that grateful sense of your many and important services to our common Science, which every astronomer must acknowledge, that of affectionate esteem and regard, the natural result of a prolonged and most friendly intercourse.

Believe me,

Yery truly yours,

Collingwood, Feb. 15, 1858.

Preface To The First Edition

The work here offered to the Public is based "upon and may be considered as an extension, and, it is hoped, an improvement of a treatise on the same subject, forming Part 43 of the Cabinet Cyclopaedia, published in the year 1833. Its object and general character are sufficiently stated in the introductory chapter of that volume, here reprinted with little alteration; but an opportunity having been afforded me by the Proprietors, preparatory to its reappearance in a form of more pretension, I have gladly availed myself of it, not only to correct some errors which, to my regret, subsisted in the former volume, but to remodel it altogether (though in complete accordance with its original design as a work of explanation); to introduce much new matter in the earlier portions of it; to rewrite, upon a far more matured and comprehensive plan, the part relating to the lunar and planetary perturbations, and to bring the subjects of sidereal and nebular astronomy to the level of the present state of our knowledge in those departments.

The chief novelty in the volume, as it now stands, will be found in the manner in which the subject of Perturbations is treated. It is not — it cannot be made elementary, in the sense in which that word is understood in these days of light reading. The chapters devoted to it must, therefore, be considered as addressed to a class of readers in possession of somewhat more mathematical knowledge than

(ii)

12 PREFACE TO THE FIRST EDITION

those who will find the rest of the work readily and easily accessible; to readers desirous of preparing themselves, by the possession of a sort of carte du pays, for a campaign in the most difficult, but at the same time the most attractive and the most remunerative of all the applications of modern geometry. More especially they may be considered as addressed to students in that university, where the "Principia" of Newton is not, nor ever will be, put aside as an obsolete book, behind the age ; and where the grand though rude outlines of the lunar theory, as delivered in the eleventh section of that immortal work, are studied less for the sake of the theory itself, than for the spirit of farreaching thought, superior to and disencumbered of technical aids, which distinguishes that beyond any other production of the human intellect.

In delivering a rational as distinguished from a technical exposition of this subject, however, the course pursued by Newton in the section of the "Principia" alluded to, has by no means been servilely followed. As regards the perturbations of the nodes and inclinations, indeed, nothing equally luminous can ever be substituted for his explanation. But as respects the other disturbances, the point of view chosen by Newton has been abandoned for another, which it is somewhat difficult to perceive why he did not, himself, select. By a different resolution of the disturbing forces from that adopted by him, and by the aid of a few obvious conclusions from the laws of elliptic motion which would have found their place, naturally and consecutively, as corollaries of the seventeenth proposition of his first book (a proposition which seems almost to have been prepared with a special view to this application), the momentary change of place of the upper focus of the disturbed ellipse

Preface To The First Edition 13

is brought distinctly under inspection: and a clearness of conception introduced into the perturbations of the excentricities, perihelia, and epochs which the author does not think it presumption to believe can be obtained by no other method, and which certainly is not obtained by that from which it is a departure. It would be out of keeping with the rest of the work to have introduced into this part of it any algebraic investigations; else it would have been easy to show that the mode of procedure here followed leads direct, and by steps (for the subject) of the most elementary character, to the general formulae for these perturbations, delivered by Laplace in the Mecanique Celeste. 1

The reader will find one class of the lunar and planetary inequalities handled in a very different manner from that in which their explanation is usually presented. It comprehends those which are characterized as incident on the epoch, the principal among them being the annual and secular equations of the moon, and that very delicate and obscure part of the perturbational theory (so little satisfactory in the manner in which it emerges from the analytical treatment of the subject), the constant or permanent effect of the disturbing force in altering the disturbed orbit. I will venture to hope that what is here stated will tend to remove some rather generally diffused misapprehensions as to the true bearings of Newton's explanation of the annual equation. 2

If proof were wanted of the inexhaustible fertility of astronomical science in points of novelty and interest, it would suffice to adduce the addition to the list of members

1 Livre ii. chap. viii. art. 67.

2 Principia, lib. i. prop. 66, cor. 6.

14 PREFACE TO THE FIRST EDITION

of our system of no less than eight new planets and satellites during the preparation of these sheets for the press. Among them is one whose discovery must ever be regarded as one of the noblest triumphs of theory. In the account here given of this discovery, I trust to have expressed myself with complete impartiality; and in the exposition of the perturbative action on Uranus, by which the existence and situation of the disturbing planet became revealed to us, I have endeavored, in pursuance of the general plan of this work, rather to exhibit a rational view of the dynamical action, than to convey the slightest idea of the conduct of those masterpieces of analytical skill which the researches of Messrs. Leverrier and Adams exhibit.

To the latter of these eminent geometers, as well as to my excellent and esteemed friend the Astronomer Koyal, I have to return my best thanks for communications which would have effectually relieved some doubts I at one period entertained had I not succeeded in the interim in getting clear of them as to the compatibility of my views on the subject of the annual equation already alluded to with the tenor of Newton's account of it. To my valued friend, Professor De Morgan, I am indebted for some most ingenious suggestions on the subject of the mistakes committed in the early working of the Julian reformation of the calendar, of which I should have availed myself, had it not appeared preferable, on mature consideration, to present the subject in its simplest form, avoiding altogether entering into minutiae of chronological discussion.

Collingwood, April 12, 1849.

Preface To The Fifth Edition

The rapid progress of science renders it necessary frequently to revise and bring up elementary works to the existing state of knowledge, under penalty of their becoming obsolete. In former editions of this work, this has been done, so far as it could be done without incurring the necessity of an almost total typographical reconstruction. But Astronomy, within the last few years, has been enriched by so many and such considerable additions, that it has been considered preferable (another edition being called for), not indeed to recast the general plan of the work, but to incorporate these in it in due order and sequence, thereby materially enlarging the volume, and giving it in many respects the air of a new work. The articles thus introduced are distinguished from those of the former editions between which they have been inserted by the addition to the last current number of an italic letter — thus, between Arts. 394 and 395 will be found inserted 394 a, 394 b, and 394 c. The inclosure of any passage in brackets [ ] indicates its having been introduced in the Fourth or some subsequent Edition. The index references in this as in former editions, being to the articles and not to the pages, are thus preserved. Together with these recent accessions to our knowledge, I have taken the opportunity of introducing several things which might justly have been noted as deficient in the former editions — as, for instance, the account of the methods by which the mass of the Earth has been determined,

16 PREFACE TO THE FIFTH EDITION

and that of the successful treatment, and it is presumed final subjugation, of those rebellious ancient Solar Eclipses which have so much harassed astronomers. A brief account of M. Foucault's remarkable pendulum experiments, and of that beautiful instrument, the gyroscope, is introduced: as are also notices of Professor Thomson's speculations on the origin of the Sun's heat, and his estimate of its average expenditure, as well as of some curious views of M. Jean Keynaud, on the secular variation of our climates, supplementary to those put forward in former editions of this work. I could have wished that its nature and limits would have permitted some account of Mr. Cooper's magnificent contributions to sidereal astronomy, in his catalogue of upward of 60,000 previously unregistered ecliptic stars; of Mr. Bishop's ecliptic charts and those of M. Chacornac; of Mr. Carrington's elaborate circumpolar catalogue; and of Mr. Jones's immense work on the zodiacal light, forming the third volume of the account of the United States' Japan Expedition, which reached me too late to allow of drawing up a fitting analysis of his results. These gentlemen will severally please to accept, however, this respectful tribute of my admiration for their important labors. Some new speculations are also hazarded; as, for instance, on the subject of the Moon's habitability, the cause of the acceleration of Encke's comet, etc., and a few numerical errors are corrected which have hitherto escaped notice and public comment as blemishes — as, for example, in some of the numbers in Art. 422 in the explanation of the phenomena of a lunar eclipse, in the evaluation of the total mass of the atmosphere, Art. 242, and in the distance of the Moon, Art. 403 (for which, however, I am not answerable).

Preface To The Fifth Edition 17

In the numerical statement of special astronomical elements, it is unavoidable that slightly different values of the same quantity should from time to time come to be substituted for those before received, as its determination acquires additional exactness. To have altered the figures in such cases wherever they occur, throughout the letter-press, would have entailed, a great probability of error and confusion; and, as the Synoptic Tables of astronomical elements at the end of the work have been carefully revised in conformity with the best current authorities, the reader is requested, whenever he may observe any discrepancy of this nature, to prefer the tabulated values.

Several of the woodcuts, which were originally drawn correctly, have been inverted right hand for left by the engraver. So far as explanation goes, this is not of the slightest moment. To a reader in the Southern Hemisphere, they are right as they stand; and one in the Northern has only to imagine himself so situated.

Collingwood, February 17, 1858.

Note (added in 1865). The views of M. Reynaud, above referred to, though no doubt original on his part, are, however, completely anticipated by certain speculations of Sir Charles Lyell, in his "Principles of Geology" (p. 110, Ed. of 1830), expanded and further reasoned out to conclusions identical with those of M. Reynaud, in a paper by the author of the present work, "On the Astronomical Causes which may influence Geological Phenomena, ' ' read before the Geological Society on December 15, 1830, and published in the Transactions of that Society. This, however, had completely escaped his recollection when perusing the works of M. Reynaud referred to in the note to Art. 369 c, which occurring while the additions to the Fifth Edition were in preparation, with all the force of novelty, led to their insertion in Art. 369 b, and to the above notice of them in the preface.

Preface To The Tenth Edition

Since the publication of the last edition of this work, the progress of astronomical discovery has been continuous and rapid ; to keep up with which, so far as consistent with its general object, it has been necessary to extend some of the Notes added in former editions and to annex others. Among these recent additions to astronomical knowledge may be mentioned more especially those which relate to the physical constitution of the central body of our own system, on which so vast and unexpected an amount of information has accumulated from various quarters as to place us at the opening out of a new vista of solar discovery. Within the limits of our own system, too, the meteorites have at length acquired a firm footing as a distinct group of members, while their now established and most unexpected connection with periodic comets in some instances, presents the latter class of bodies under a new aspect, increasing, if anything can increase, the mysterious interest which already hangs about them. The group of asteroids, too, has received an accession of no less than fifteen to their list as it stood at the end of 1866. The elements of these are given in the Appendix (from the Berlin "Ephemeris" for 1871), so as to complete the list up to the present time. The correction indicated in a former edition, as required in the distance of the sun (and by necessary implication in the dimensions of all the planetary orbits and the magnitudes of the sun and planets themselves), has moreover received (18)

Preface To The Tenth Edition 19

an unexpected confirmation from Mr. Stone's critical reexamination of the calculations of that distance from the recorded observations of the celebrated transit of Venus in 1769, the result of which is here brought under the notice of our readers.

Beyond the limits of our own system, the application of spectrum analysis has disclosed the amazing fact of the gaseous constitution of many of the nebulae (a constitution long suspected on general cosmological grounds): by which is meant their analogy to matter not in that state of luminosity presented by the photosphere of our sun, but in that in which are maintained the luminous prominences and appendages which fringe its disk in total eclipses, a state to which the epithet of incandescent- gaseous as distinct from flame or a state of combustion seems most appropriate. Thus a real line of demarcation between nebulae proper and sidereal clusters is decisively drawn. These delicate applications of optical science to chemistry have also afforded strong grounds for concluding with considerable confidence the presence of several of our terrestrial elementary bodies in the sun and fixed stars: while in one instance prismatic observation has afforded, with a certain approach to probability, evidence of the recess of the most conspicuous among them from our system, and even supplied a measure of its rapidity.

Collingwood, July 17, 1869.

Introduction

(1.) Every student who enters upon a scientific pursuit, especially if at a somewhat advanced period of life, will find not only that he has much to learn, but much also to unlearn. Familiar objects and events are far from presenting themselves to our senses in that aspect and with those connections under which science requires them to be viewed, and which constitute their rational explanation. There is, therefore, every reason to expect that those objects and relations which, taken together, constitute the subject he is about to enter upon will have been previously apprehended by him, at least imperfectly, because much has hitherto escaped his notice which is essential to its right understanding: and not only so, but too often also erroneously, owing to mistaken analogies, and the general prevalence of vulgar errors. As a first preparation, therefore, for the course he is about to commence, he must loosen his hold on all crude and hastily adopted notions, and must strengthen himself, by something of an effort and a resolve, for the unprejudiced admission of any conclusion which shall appear to be supported by careful observation and logical argument, even should it prove of a nature adverse to notions he may have previously formed for himself, or taken up, without examination, on the credit of others.

Such an effort is, in fact, a commencement of that intellectual discipline which forms one of the most important ends of all science. It is the first movement of approach toward that state of mental purity which alone can fit us for a full and steady perception of moral beauty as well as physical adaptation. It is the "euphrasy and rue" with which we must "purge our sight" before we can receive and contemplate as they are the lineaments of truth and nature.

(2.) There is no science which, more than astronomy, stands in need of such a preparation, or draws more largely on that intellectual liberality which is ready to adopt whatever is demonstrated, or concede whatever is rendered highly probable, however new and uncommon the points of view may be in which objects the most familiar may thereby become placed. Almost all its conclusions stand in open and striking contradiction with those of superficial and vulgar observation, and with what appears to every one, until he has understood and weighed the proofs to the contrary, the most positive evidence of his senses. Thus, the earth on which he stands, and which has served for ages as the unshaken foundation of the firmest structures, either of art or nature, is divested by the astronomer of its attribute of fixity, and conceived by him as turning swiftly on its centre, and at the same time moving onward through space with great rapidity. The sun and the moon, which appear to untaught eyes round bodies of no very considerable size, become enlarged in his imagination into vast globes — the one approaching in magnitude to the earth itself, the other immensely surpassing it. The planets, which appear only as stars somewhat brighter than the rest, are to him spacious, elaborate, and habitable worlds; several of them much greater and far more curiously furnished than the earth he inhabits, as there are also others less so; and the stars themselves, properly so called, which to ordinary apprehension present only lucid sparks or brilliant atoms, are to him suns of various and transcendent glory— effulgent centres of life and light to myriads of unseen worlds. So that when, after dilating his thoughts to comprehend the grandeur of those ideas his calculations have called up, and exhausting his imagination and the powers of his language to devise similes and metaphors illustrative of the immensity of the scale on which his universe is constructed, he shrinks back to his native sphere, he finds it, in comparison, a mere point; so lost — even in the minute system to which it belongs — as to be invisible and unsuspected from some of its principal and remoter members.

(3.) There is hardly anything which sets in a stronger light the inherent power of truth over the mind of man, when opposed by no motives of interest or passion, than the perfect readiness with which all these conclusions are assented to as soon as their evidence is clearly apprehended, and the tenacious hold they acquire over our belief when once admitted. In the conduct, therefore, of this volume, I shall take it for granted that the reader is more desirous to learn the system which it is its object to teach, as it now stands, than to raise or revive objections against it; and that, in short, he comes to the task with a willing mind; an assumption which will not only save the trouble of piling argument on argument to convince the sceptical, but will greatly facilitate his actual progress; inasmuch as he will find it at once easier and more satisfactory to pursue from the outset a straight and definite path, than to be constantly stepping aside, involving himself in perplexities and circuits, which, after all, can only terminate in finding himself compelled to adopt the same road.

(4.) The method, therefore, we propose to follow in this work is neither strictly the analytic nor the synthetic, but rather such a combination of both, with a leaning to the latter, as may best suit with a didactic composition. Its object is not to convince or refute opponents, nor to inquire, under the semblance of an assumed ignorance, for principles of which we are all the time in full possession — but simply to teach what is known. The moderate limit of a single volume, to which it will be confined, and the necessity of being on every point, within that limit, rather diffuse and copious in explanation, as well as the eminently matured and ascertained character of the science itself, render this course both practicable and eligible. Practicable, because there is now no danger of any revolution in astronomy, like those which are daily changing the features of the less advanced sciences, supervening, to destroy all our hypotheses, and throw our statements into confusion. Eligible, because the space to be bestowed, either in combating refuted systems, or in leading the reader forward by slow and measured steps from the known to the unknown, may be more advantageously devoted to such explanatory illustrations as will impress on him a familiar and, as it were, a practical sense of the sequence of phenomena, and the manner in which they are produced. We shall not, then, reject the analytic course where it leads more easily and directly to our objects, or in any way fetter ourselves by a rigid adherence to method. Writing only to be understood, and to communicate as much information in as little space as possible, consistently with its distinct and effectual communication, no sacrifice can be afforded to system, to form, or to affectation.