A treatise on astronomy

Front matter

Glass Q3 - .-

Book M^l .

113 +

Chapter I

General Notions — Form and Magnitude of the Earth — Horizon and its Dip — The Atmosphere — Refraction — Twilight — Appearances resulting from diurnal Motion — Parallax — First Step towards forming an Idea of the Distance of the Stars — Definitions - - 14

Chapter II

Of the Nature of astronomical Instruments and Observations in general— Of sidereal and solar Time — Of the Measurement of Time — Clocks, Chronometers, the Transit Instrument — Of the Measurement of angular Intervals — Application of the Telescope to Instruments destined to that Purpose — Of the Mural Circle — Determination of polar and horizontal Points — The Level — Plumb Line — Artificial Horizon — Collimator — Of compound Instruments with co-ordinate Circles, the Equatorial — Altitude and Azimuth Instrument— Of the Sextant and Reflecting Circle — Principle of Repetition 66

Chapter III. Of 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 Earth's Rotation— Trade-winds — Determination of geographical Positions — Of Latitudes — Of Longitudes — Conduct of a trignometrical Survey — Of Maps — Projections of the Sphere — Measurement of Heights" by the Barometer 105

Chapter IV. Of Uranograpiiy

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 — Uranographical Problems - - - - 151

4 CONTENTS.

Chapter V. Of The Sun's Motion

Page 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 Sun in different Parts of the Orbit 176

Chapter VI

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 Eccentricity and Inclination— Motion of the Nodes of its Orbit — Occultations — Solar Eclipses — Phases of the Moon — Its synodical Period — Lunar Eclipses — Motion of the Apsides of its Orbit — Physical Constitution of the Moon — Its Mountains — Atmosphere — Rotation on Axis — Libration — Appearance of the Earth from it - 203

Chapter VII

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 221

Chapter VIII. 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, &c— Dimensions and Form of their Orbits —Transits across the Sun— "Superior Planets, their Distances, Periods, &c. — Kepler's Laws and their Interpretation — Elliptic Elements of a Planet's Orbit— Its heliocentric and geocentric Place— Bode's Law of Planetary Distances— The four ultra-zodiacal Planets—Physical Peculiarities observable in each of the Planets - 231

Chapter IX. Of 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, &c— Velocity of Light discovered by their Means— Satellites of Saturn— Of = Uranus- -.---------• 2/2

COxVTENTS. 0

CHAFrER X.

OF COMETS.

Page Great Number of recorded Comets — The number of unrecorded probably much greater — Description of a Comet — Comets without Tails— Increase and Decay of their Tails— Their Motions — Subject to the general Laws of planetary Motion — Elements of their Orbits — Periodic Return of certain Comets — Halley's — Encke's — Biela's — Dimensions of Comets — Their Resistance by the Ether, gradual Decay, and possible Dispersion in Space - 284

Chapter XI. Of Perturbations

Subject propounded — Superposition of small Motions — Problem of three Bodies — Estimation of disturbing Forces — Motion of Nodes — Changes of Inclination — Compensation operated in a whole Revolution of the Node — Lagrange's Theorem of the Stability of the Inclinations — Change of Obliquity of the Ecliptic — Precession of the Equinoxes — Nutation — Theorem respecting forced Vibrations— Of the Tides — Variation of Elements of the Planet's Orbits —Periodic and secular — Disturbing Forces considered as tangential and radial — Effects of tangential Force — 1st, in circular Orbits ; 2d, in elliptic — Compensations effected — Case of near Commensurability of mean Motions — The great Inequality of Jupiter and Saturn explained — The long Inequality of Venus and the Earth — Lunar Variation — Effects of the radial Force — Mean Effect of the Period and Dimensions of the disturbed Orbit — Variable Part of its Effect — Lunar Evection — Secular Acceleration of the Moon's Motion — Permanence of the Axes and Periods — Theory of the secular Variations of the Eccentricities and Perihelia — Motion of the lunar Apsides — Lagrange's Theorem of the Stability of the Eccentricities— Nutation of the lunar Orbit — Perturbations of Jupiter's Satellites 294

Chapter XII. Of Sidereal Astronomy

Of the Stars generally — Their distribution into Classes according to their apparent Magnitudes — Their apparent Distribution over the Heavens — Of the Milky Way — Annual Parallax — Real Distances, probable Dimensions, and Nature of the Stars — Variable Stars — Temporary Stars — Of double Stars — Their Revolution about each other in elliptic Orbits — Extension of the Law of Gravity to such Systems — Of coloured Stars — Proper Motion of the Sun and Stars — Systematic Aberration and Parallax — Of compound sidereal Systems — Clusters of Stars — Of Nebula? — Nebulous Stars — Annular and planetary Nebula? — Zodiacal Light 349

a2

6 CONTENTS a

CHAPTER XIII. Page

Of the Calendar 38I

Synoptic Table of the Elements of the Solar System - - -389

Synoptic Table of the Elements of the Orbits of the Satellites, so far

as they are known 390

I. The Moon 390

II. Satellites of Jupiter 390

III. Satellites of Saturn 391

IV. Satellites of Uranus 391

Index - 393

TREATISE

ON

ASTRONOMY,

Introduction

(1.) In entering upon any scientific pursuit, one of the student's first endeavours ought to be, to prepare his mind for the reception of truth, by dismissing, or at least loosening his hold. on, all such crude and hastily adopted notions respecting the objects and relations he is about to examine as may tend to embarrass or mislead him ; and to 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 towards 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 onwards 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 vastly 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

INTRODUCTION. 9

our belief when once admitted. In the conduct, therefore, of this volume, we shall take it for granted that our 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 ourselves the trouble of piling argument on argument to convince the skeptical, 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 our road.

(4.) The method, therefore, we propose to follow 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. Our 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 we know. The moderate limit of a single volume, 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, we can afford to make no sacrifice to system, to form, or to affectation.

(5.) We shall take for granted, from the outset, the Copernican system of the world ; relying on the easy, obvious, and natural explanation it affords of all the phenomena as they come to be described, to impress the student with a sense of its truth, without either the formality of demonstration or the superfluous tedium of eulogy, calling to mind that important remark of Bacon : — -" Theoriarum vires, arcta et quasi se mutuo sustinente partium adaptatione, qua, quasi in orbem cohaerent, firmantur;"* nor failing, however, to point out to the reader, as occasion offers, the contrast which its superior simplicity offers to the complication of other hypotheses.

(6.) The preliminary knowledge which it is desirable that the student should possess, in order for the more advantageous perusal of the following pages, consists in the familiar practice of decimal and sexagesimal arithmetic ; some moderate acquaintance with geometry and trigonometry, both plane and spherical; the elementary principles of mechanics ; and enough of optics to understand the construction and use of the telescope, and some other of the simpler instruments. For the acquisition of these we may refer him to those other parts of this Cyclopaedia which profess to treat of the several subjects in question. Of course3 the more of such knowledge he brings to the perusal, the easier will be his progress, and the more complete the information gained ; but we shall endeavour in every case, as far as it can be done without a sacrifice of clearness, and of that useful brevity which consists in the absence of prolixity and episode, to render what we have to say as independent of other books as possible.

(7.) After all, we must distinctly caution such of our readers as may commence and terminate their astronomi-

* The confirmation of theories relies on the compact adaptation of their parts, by which, like those of an arch or dome, they mutually sustain each other, and form a coherent whole.

INTRODUCTION'. 1 1

cal studies with the present work (though of such, — at least in the latter predicament, — we trust the number will be few), that its utmost pretension is to place them on the threshold of this particular wing of the temple of science, or rather on an eminence exterior to it, whence they may obtain something like a general notion of its structure ; or, at most, to give those who may wish to enter, aground-plan of its accesses, and put them in possession of the pass-word. Admission to its sanctuary, and to the privileges and feelings of a votary, is only to be gained by one means, — a sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science, as can entitle him to form an independent opinion on any subject of discussion within their range. It is not without an effort that those who possess this knowledge can communicate on such subjects with those who do not, and adapt their language and their illustrations to the necessities of such an intercourse. Propositions which to the one are almost identical, are theorems of import and difficulty to the other ; nor is their evidence presented in the same way to the mind of each. In teaching such propositions, under such circumstances, the appeal has to be made, not to the pure and abstract reason, but to the sense of analogy, — to practice and experience : principles and modes of action have to be established, not by direct argument from acknowledged axioms, but by bringing forward and dwelling on simple and familiar instances in which the same principles and the same or similar modes of action take place ; thus erecting, as it were, in each particular case, a separate induction, and constructing at each step a little body of science to meet its exigencies. The difference is that of pioneering a road through an untraversed country, and advancing at ease along a broad and beaten highway ; that is to say, if we are determined to make ourselves distinctly understood, and will appeal to reason at all. As for the method of assertion, or a direct demand on the faith of the student (though in some complex cases indispensable, where illustrative explanation would defeat its own end by becoming* tedious and burdensome lo both parties), it is one which we shall neither adopt ourselves nor would recommend to others.

(8.) On the other hand, although it is something new to abandon the road of mathematical demonstration in the treatment of subjects susceptible of it, and teach any considerable branch of science entirely or chiefly by the way of illustration and familiar parallels, it is yet not impossible that those who are already well acquainted with our subject, and whose knowledge has been acquired by that confessedly higher and better practice which is incompatible with the avowed objects of the present work, may yet find their account in its perusal, — for this reason, that it is always of advantage to present any given body of knowledge to the mind in as great a variety of different lights as possible. It is a property of illustrations of this kind to strike no two minds in the same manner, or with the same force ; because no two minds are stored with the same images, or have acquired their notions of them by similar habits. Accordingly, it may very well happen, that a proposition, even to one best acquainted with it, may be placed not merely in a new and uncommon, but in a more impressive and satisfactory light by such a course — some obscurity may be dissipated, some inward misgiving cleared up, or even some link supplied which may lead to the perception of connexions and deductions altogether unknown before. And the probability of this is increased when, as in the present instance, the illustrations chosen have not been studiously selected from books, but are such as have presented themselves freely to the author's mind as being most in harmony with his own views ; by which, of course, he means to lay no claim to originality in all or any of them beyond what they may really possess.

(9.) Besides, there are cases in the application of mechanical principles with which the mathematical student is but too familiar, where, when the data are before him, and the numerical and geometrical relations of his problems all clear to his conception, — when his forces are estimated and his lines measured, — nay, when even he has followed up the application of his technical processes, and

INTRODUCTION. 13

fairly arrived at his conclusion, — there is still something wanting in his mind — not in the evidence, for he has examined each link, and finds the chain complete — not in the principles, for those he well knows are too firmly established to be shaken — but precisely in the mode of action. He has followed out a train of reasoning by logical and technical rules, but the signs he has employed are not pictures of nature, or have lost their original meaning as such to his mind : he has not seen, as it were, the process of nature passing under his eye in an instant of time, and presented as a whole to his imagination. A familiar parallel, or an illustration drawn from some artificial or natural process, of which he has that direct and individual impression which gives it a reality and associates it with a name, will, in almost every such case, supply in a moment this deficient feature, will convert all his symbols into real pictures, and infuse an animated meaning into what was before a lifeless succession of words and signs. We cannot, indeed, always promise ourselves to attain this degree of vividness in our illustrations, nor are the points to be elucidated themselves always capable of being so paraphrased (if we may use the expression) by any single instance adducible in the ordinary course of experience ; but the object will at least be kept in view ; and, as we are very conscious of having, in making such attempts, gained for ourselves much clearer views of several of the more concealed effects of planetary perturbation than we had acquired by their mathematical investigation in detail, we may reasonably hope that the endeavour will not always be unattended with a similar success in others.

(10.) From what has been said, it will be evident that our aim is not to offer to the public a technical treatise, in which the student of practical or theoretical astronomy shall find consigned the minute description of methods of observation, or the formulae he requires prepared to his hand, or their demonstrations drawn out in detail. In all these the present work will be found meagre, and quite inadequate to his wants. Its aim is entirely different ; being to present in each case the mere ultimate rationale of facts, arguments, and processes ; and, in all cases of mathe-

B matical application, avoiding whatever would tend to encumber its pages with algebraic or geometrical symbols, to place under his inspection that central thread of common sense on which the pearls of analytical research are invariably strung ; but which, by the attention the latter claim for themselves, is often concealed from the eye of the gazer, and not always disposed in the straightest and most convenient form to follow by those who string them. This is no fault of those who have conducted the inquiries to which we allude. The contention of mind for which they call is enormous ; and it may, perhaps, be owing to their experience of how little can be accomplished in carrying such processes on to their conclusion, by mere ordinary clearness of head; and how necessary it often is to pay more attention to the purely mathematical conditions which insure success, — the hooks-and-ojes of their equations and series, — than to those which enchain causes with their effects, and both with the human reason,— that we must attribute something of that indistinctness of view which is often complained of as a grievance by the earnest student, and still more commonly ascribed ironically to the native cloudiness of an atmosphere too sublime for vulgar comprehension. We think we shall render good service to both classes of readers, by dissipating, so far as our power lies, that accidental obscurity, and by showing ordinary untutored comprehension clearly what it can, and what it cannot, hope to attain.

Chapter I

General Notions — Form and Magnitude of the Earth — Horizon and its Dip — The Atmosphere — Refraction — Twilight — Appearances resulting from diurnal Notion — Parallax — First Step towards forming an Idea of the Distance of the Stars — Definitions.

(11.) The magnitudes, distances, arrangement, and motions of the great bodies which make up the visible universe, their constitution and physical condition, so far as they can be known to us, with their mutual influences and actions on each other, so far as they can be

CHAP. I.J GENERAL NOTIONS. 1ft

traced by the effects produced, and established by legitimate reasoning, form the assemblage of objects to which the attention of the astronomer is directed. The term astronomy* itself, which denotes the law or rule of the astra (by which the ancients understood not only the stars properly so called, but the sun, the moon, and all the visible constituents of the heavens), sufficiently indicates this ; and, although the term astrology, which denotes the reason, theory, or interpretation of the stars,t has become degraded in its application, and confined to superstitious and delusive attempts to divine future events by their dependence on pretended planetary influences, the same meaning originally attached itself to that epithet.

(12.) But, besides the stars and other celestial bodies, the earth itself, regarded as an individual body, is one principal object of the astronomer's consideration, and, indeed, the chief of all. It derives its importance, in a practical as well as theoretical sense, not only from its proximity, and its relation to us as animated beings, who draw from it the supply of all our wants, but as the station from which we see all the rest, and as the only one among them to which we can, in the first instance, refer for any determinate marks and measures by which to recognise their changes of situation, or with which to compare their distances.

(13.) To the reader who now for the first time takes up a book on astronomy, it will no doubt seem strange to class the earth with the heavenly bodies, and to assume any community of nature among things apparently so different. For what, in fact, can be more apparently different than the vast and seemingly immeasurable extent of the earth, and the stars, which appear but as points, and seem to have no size at all ? The earth is dark and opaque, while the celestial bodies are brilliant. We perceive in it no motion, while in them we observe a continual change of place, as we view them at different

* A<rr>j£, a star ; vo^oj, a law ; or vtpsiv, to tend, as a shepherd his flock j so that x<rr?ovo/*og means "shepherd of the stars." The two etymologies are, however, coincident.

t Aoyos , reason, or a word, the vehicle of reason ; the interpreter of thought, hours of the day or night, or at different seasons of the year. The ancients, accordingly, one or two of the more enlightened of them only excepted, admitted no such community of nature ; and, by thus placing the heavenly bodies and their movements without the pale of analogy and experience, effectually intercepted the progress of all reasoning from what passes here below, to what is going on in the regions where they exist and move. Under such conventions, astronomy, as a science of cause and effect, could not exist, but must be limited to a mere registry of appearances, unconnected with any attempt to account for them on reasonable principles. To get rid of this prejudice, therefore, is the first step towards acquiring a knowledge of what is really the case ; and the student has made his first effort towards the acquisition of sound knowledge, when he has learnt to familiarize himself with the idea that the earth, after all, may be nothing but a great star. How correct such an idea may be, and with what limitations and modifications it is to be admitted, we shall see presently.

(14.) It is evident, that, to form any just notions of the arrangement, in space, of a number of objects which we cannot approach and examine, but of which all the information we can gain is by sitting still and watching their evolutions, it must be very important for us to know, in the first instance, whether what we call sitting still is really such : whether the station from which we view them, with ourselves, and all objects which immediately surround us, be not itself in motion, unperceived by us ; and if so, of what nature that motion is. The apparent places of a number of objects, and their apparent arrangement with respect to each other, will of course be materially dependent on the situation of the spectator among them ; and if this situation be liable to change, unknown to the spectator himself, an appearance of change in the respective situations of the objects will arise, without the reality. If, then, such be actually the case, it will follow that all the movements we think we perceive among the stars will not be real movements, but that some part, at least, of whatever changes of relative place we perceive among them must be merely

CHAP. I.] GENERAL NOTIONS. 17

apparent, the results of the shifting of our own point of view ; and that, if we would ever arrive at a knowledge of their real motions, it can only be by first investigating our own, and making due allowance for its effects. Thus, the question whether the earth is in motion or at rest, and if in motion, what that motion is, is no idle inquiry, but one on which depends our only chance of arriving at true conclusions respecting the constitution of the universe.

(15.) Nor let it be thought strange that we should speak of a motion existing in the earth, unperceived by its inhabitants : we must remember that it is of the earth as a whole, with all that it holds within its substance, or sustains on its surface, that we are speaking ; of a motion common to the solid mass beneath, to the ocean which flows around it, the air that rests upcn it, and the clouds which float above it in the air. Such a motion, which should displace no terrestrial object from its relative place among others, interfere with no natural processes, and produce no sensations of shocks or jerks, might, it is very evident, subsist undetected by us. There is no peculiar sensation which advertises us that we are in motion. We perceive jerks, or shocks, it is true, because these are sudden changes of motion, produced, as the laws of mechanics teach us, by sudden and powerful forces acting during short times ; and these forces, applied to our bodies, are what we feel. When, for example, we are carried along in a carriage with the blinds down, or with our eyes closed (to keep us from seeing external objects), we perceive a tremor arising from inequalities in the road, over which the carriage is successively lifted and let fall, but we have no sense of progress. As the road is smoother, our sense of motion is diminished, though our rate of travelling is accelerated. Those who have travelled on the celebrated rail-road between Manchester and Liverpool testify that but for the noise of the train, and the rapidity with which external objects seem to dart by them, the sensation is almost that of perfect rest.