(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.

(102.) Our first chapter has been devoted to the acquisition chiefly of preliminary notions respecting the globe we inhabit, its relation to the celestial objects which surround it, and the physical circumstances under which all astronomical observations must be made, as well as to provide ourselves with a stock of technical wordsof most frequent and familiar use in the sequel. We might now proceed to a more exact and detailed statement of the facts and theories of astronomy; but, in order to do this with full effect, it will be desirable that the reader be made acquainted with the principal means which astronomers possess, of determining, with the degree of nicety their theories require, the data on which they ground their conclusions; in other words, of ascertaining by measurement the apparent and real magnitudes with which they are conversant. It is only when in possession of this knowledge that he can fully appreciate either the truth of the theories themselves, or the degree of reliance to be placed on any of their conclusions antecedent to trial: since it is only by knowing what amount of error can certainly be perceived and distinctly measured, that he can satisfy himself whether any theory offers so close an approximation, in its numerical results, to actual phenomena, as will justify him in receiving it as a true representation of nature.

(450.) In the annual circuit of the earth about the sun, it is constantly attended by its satellite, the moon, which revolves round it, or rather both round their common center of gravity; while this center, strictly speaking, and not either of the two bodies thus connected, moves in an elliptic orbit, undisturbed by their mutual action, just as the center of gravity of a large and small stone tied together and flung into the air describes a parabola as if it were a real material substance under the earth's attraction, while the stones circulate round it or round each other, as we choose to conceive the matter.

(451.) If we trace, therefore, the real curve actually described by either the moon's or earth's centers, in virtue of this compound motion, it will appear to be, not an exact ellipse, but an undulated curve, like that represented in the figure to article 272., only that the number of undulations in a whole revolution is but 13, and their actual deviation from the general ellipse, which serves them as a central line, is comparatively very much smaller — so much so, indeed, that every part of the curve described by either the earth or moon is concave towards the sun. The excursions of the earth on either side of the ellipse, indeed, are so very small as to be hardly appreciable.

(289.) In the foregoing chapters, it has heen shown that the apparent path of the sun is a great circle of the sphere, which it performs in a period of one sidereal year. From this it follows, that the line joining the earth and sun lies constantly in one plane; and that, therefore, whatever he the real motion from which this apparent motion arises, it must be confined to one plane, which is called the plane of the ecliptic.

(290.) We have already seen (art. 118.) that the sun's motion in right ascension among the stars is not uniform. This is partly accounted for by the obliquity of the ecliptic, in consequence of which equal variations in longitude do not correspond to equal changes of right ascension. But if we observe the place of the sun daily throughout the year, by the transit and circle, and from these calculate the longitude for each day, it will still be found that, even in its own proper path, its apparent angular motion is far from uniform. The change of longitude in twenty-four mean solar hours averages 0° 59′ 8″·33; but about the 31st of December it amounts to 1° 1′ 9″·9, and about the 1st of July is only 0° 57′ l l″·5. Such are the extreme limits, and such the mean value of the sun's apparent angular velocity in its annual orbit.

(369.) The reader has now been made acquainted with the chief phenomena of the motions of the earth in its orbit round the sun, and of the moon about the earth. —We come next to speak of the physical cause which maintains and perpetuates these motions, and causes the massive bodies so revolving to deviate continually from the directions they would naturally seek to follow, in pursuance of the first law of motion, and bend their courses into curves concave to their centers.

(370.) Whatever attempts may have been madehy metaphysical writers to reason away the connection of cause and effect, and fritter it down into the unsatisfactory relation of habitual sequence, it is certain that the conception of some more real and intimate connection is quite as strongly impressed upon the human mind as that of the existence of an external world, —the vindication of whose reality has (strange to say) been regarded as an achievement of no common merit in the annals of this branch of philosophy. It is our own immediate consciousness of effort, when we exert force to put matter in motion, or to oppose and neutralize force, which gives us this- internal conviction of power and causation so far as it refers to the material world, and compels us to believe that whenever we see material objects put in motion from a state of rest, or deflected from their rectilinear paths, and changed in their velocities if already in motion, it is in consequence of such an EFFORT somehow exerted, though not accompanied with our consciousness.

(161.) Geography is not only the most important of the practical branches of knowledge to which astronomy is applied, but is also, theoretically speaking, an essential part of the latter science. The earth being the general station from which we view the heavens, a knowledge of the local situation of particular stations on its surface is of great consequence, when we come to enquire the distances of the nearer heavenly bodies from us, as concluded from observations of their paralax as well as on all other occasions, where a difference of locality can be supposed to influence astronomical results. We propose, therefore, in this chapter, to explain the principles, by which astronomical observation is applied to geographical determinations, and to give at the same time an outline of geography so far as it is to be considered a part of astronomy.

(162.) Geography, as the word imports, is a delineation or description of the earth. In its widest sense, this comprehends not only the delineation of the form of its continents and seas, its rivers and mountains, but their physical condition, climates, and products, and their appropriation by communities of men. With physical and political geography, however, we have no concern here.

(338.) The moon, like the sun, appears to advance among the stars with a movement contrary to the general diurnal motion of the heavens, but much more rapid, so as to be very readily perceived (as we have before observed) by a few hours' cursory attention on any moonlight night. By this continual advance, which, though sometimes quicker, sometimes slower, is never intermitted or reversed, it makes the tour of the heavens in a mean or average period of 27d 7h 43m 11s·5, returning, in that time, to a position among the stars nearly coincident with that it had before, and which would be exactly so, but for causes presently to be stated.

(339.) The moon, then, like the sun, apparently describes an orbit round the earth, and this orbit cannot be very different from a circle, because the apparent angular diameter of the full moon is not liable to any great extent of variation.

(340.) The distance of the moon from the earth is concluded from its horizontal parallax, which may be found either directly, by observations at remote geographical stations, exactly similar to those described in art. 302., in the case of the sun, or by means of the phenomena called occultations (art. 346.), from which also its apparent diameter is most readily and correctly found.

(627.) Time, like distance, may be measured by comparison with standards of any length, and all that is requisite for ascertaining correctly the length of any in. terval, is to be able to apply the standard to the interval throughout its whole extent, without overlapping on the one hand, or leaving unmeasured vacancies on the other; to determine, without the possible error of a unit, the number of integer standards which the interval admits of being interposed between its beginning and end; and to estimate precisely the fraction, over and above an integer, which remains when all the possible integers are subtracted.

(628.) But though all standard units of time are equally possible, theoretically speaking, all are not, practically, equally convenient. The tropical year and the solar day are natural units, which the wants of man and the business of society force upon us, and compel us to adopt as our greater and lesser standards for the measurement of time, for all the purposes of civil life; and that, in spite of inconveniencies which, did any choice exist, would speedily lead to the abandonment of one or other. The principal of these are their incommensurability, and the want of perfect uniformity in one at least of them.

(581.) Besides the bodies we have described in the foregoing chapters, the heavens present us with an in numerable multitude of other objects, which are called generally by the name of stars. Though comprehending individuals differing from each other, not merely in brightness, but in many other essential points, they all agree in one attribute, — a high degree of permanence as to apparent relative situation. This has procured them the title of “fixedstars;” an expression which is to be understood in a comparative and not an absolute sense, it being certain that many, and probable that all are in a state of motion, although too slow to be perceptible unless by means of very delicate observations, continued during a long series of years.

(582.) Astronomers are in the habit of distinguishing the stars into classes, according to their apparent brightness. These are termed magnitudes. The brightest stars are said to be of the first magnitude; those Avhich fall so far short of the first degree of brightness as to make a marked distinction are classed in the second, and so on down to the sixth or seventh, which comprise the smallest stars visible to the naked eye, in the clearest and darkest night.

(387.) The sun and moon are not the only celestial objects which appear to have a motion independent of that by which the great constellation of the heavens is daily carried round the earth. Among the stars there are several, — and those among the brightest and most conspicuous, — which, when attentively watched from night to night, are found to change their relative situations among the rest; some rapidly, others much more slowly. These are called planets. Four of them, — Venus, Mars, Jupiter, and Saturn, — are remarkably large and brilliant; another, Mercury, is also visible to the naked eye as a large star, but, for a reason which will presently appear, is seldom conspicuous; a fifth, Uranus, is barely discernible without a telescope; and four others, — Ceres, Pallas, Vesta, and Juno, — are never visible to the naked eye. Besides these ten, others yet undiscovered may exist; and it is extremely probable that such is the case, — the multitude of telescopic stars being so great that only a small fraction of their number has been sufficiently noticed to ascertain whether they retain the same places or not, and the five last, mentioned planets having all been discovered within half a century from the present time.

(388.) The apparent motions of the planets are much more irregular than those of the sun or moon.