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Three cases of Planetary perturbation distinguished. Of inequalities

dependent on the excentricites. Long inequality of Jupiter and

Saturn. Law of reciprocity between the periodical variations of the

elements of both planets. Long inequality of the Earth and Venus.

Variation of the epoch. Inequalities incident on the epoch affecting

the mean motion. Interpretation of the constant part of these ine-

qualities. Annual equation of the Moon. Her secular acceleration.

Lunar inequalities due to the action of Venus. Effect of the sphe-

roidal figure of the Earth and other planets on the motions of their

satellites. Of the tides. Masses of disturbing bodies deducible from

the perturbations they produce. Mass of the Moon, and of Jupiter's

satellites, how ascertained. Perturbations of Uranus resulting in the

discovery of Neptune ----- Page 454

PART III.

Or SIDEREAL ASTRONOMY.

CHAPTER XV.

Of the fixed stars. Their classification by magnitudes. Photometric

scale of magnitudes. Conventional or vulgar scale. Photometric

comparison of stars. Distribution of stars over the heavens. Of the

Milky Way or galaxy. Its supposed form that of a flat stratum

partially subdivided. Its visible course among the constellations. Its

Internal structure. Its apparently indefinite extent in certain direc-

tions. Of the distance of the fixed stars. Their annual parallax.

Parallactic unit of sidereal distance. Effect of parallax analogous to

that of aberration. How distinguished from it. Detection of paral-

lax by meridional observations. Henderson's application to a cen-

tauri. By differential observations. Discoveries of Bessel and Struvc.

List of stars in which parallax has been detected. Of the real magni-

tudes of the stars. Comparison of their lights with that of the Sun -

519

CHAPTER XVI.

Variable and periodical stars. List of those already known. Irre-

gularities in their periods and lustre when brightest. Irregular and

temporary stars. Ancient Chinese records of several. Missing stars.

Double stars. Their classification. Specimens of each class. Binary

systems. Revolution round each other. Describe elliptic orbits

under the Newtonian law of gravity. Elements of orbits of several.

Actual dimensions of their orbits. Coloured double stars. Pheno-

menon of complementary colours. Sanguine stars. Proper motion of

the stars. Partly accounted for by a real motion of the Sun. Situa-

tion of the solar apex. Agreement of southern and northern stars
in giving the same result. Principles on which the investigation of

the solar motion depends. Absolute velocity of the Sun's motion.

Supposed revolution of the whole sidereal system round a common

centre. Systematic parallax and aberration. Effect of the motion of

light in altering the apparent period of a binary star - Page 554

CHAPTER XVII.

OF CLUSTEBS OF STABS AND NEBULA.

Of clustering groups of stars. Globular clusters. Their stability dyna-

mically possible. List of the most remarkable. Classification of

nebulas and clusters. Their distribution over the heavens. Irregular

clusters. Resolvability of nebulas. Theory of the formation of clus-

ters by nebulous subsidence. Of elliptic nebulas. That of Andro-

meda. Annular and planetary nebula;. Double nebulae. Nebulous

stars. Connection of nebula? with double stars. Insulated nebulas of

forms not wholly irregular. Of amorphous nebula;. Their law of

distribution marks them as outliers of the galaxy. Nebula; and

nebulous group of Orion — of Argo —of Sagittarius—of Cygnus. The

Magellanic clouds. Singular nebula in the greater of them. The

zodiacal light. Shooting stars ..... 591

PART IV.

OF THE ACCOUNT OF TIME.

CHAPTER XVIIL

Natural units of time. Relation of the sidereal to the solar day affected

by precession. Incommensurability of the day and year. Its incon-

venience. How obviated. The Julian Calendar. Irregularities at

its first introduction. Reformed by Augustus. Gregorian reformation.

Solar and lunar cycles. Indict ion. Julian period. Table of Chrono-

logical eras. Rules for calculating the days elapsed between given

Dates. Equinoctial time. ..... 622

APPENDIX.

I. Lists of Northern and Southern Stars, with their approximate

Magnitudes, on the Vulgar and Photometric Scales - - 645

n. Synoptic Table of the Elements of the Planetary System - 647

III. Synoptic Table of the Elements of the Orbits of the Satellites,

so far as they are known ..... 649

IV. Elements of Periodical Comets at their last Appearance - 652

Index ..... . . 653

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(1.) Evert 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 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 ot 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 any thing 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

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