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of apparent rest or indecision, now takes place; after which the movement is again reversed, aud resumes its original direct character. On the whole, however, the amount of direct motion more than compensates the retrograde; and by the excess of the former over the latter, the gradual advance of the planet from west to east is maintained. Thus, supposing the Zodiac to be unfolded into a plane surface, (or repre. sented as in Mercator's projection, art. 283. taking the ecliptic EC for its ground line,) the track of a planet when mapped down by observation from day to day, will offer the

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appearance PQRS, &c.; the motion from P to Q being direct, at Q stationary, from Q to R retrograde, at R again stationary, from R to S direct, and so on.

(460.) In the midst of the irregularity and fluctuation of this motion, one remarkable feature of uniformity is observed. Whenever the planet crosses the ecliptic, as at N in the figure, it is said (like the moon) to be in its node; and as the earth necessarily lies in the plane of the ecliptic, the planet cannot be apparently or uranographically situated in the celestial circle so called, without being really and locally situated in that plane. The visible passage of a planet through its node, then, is a phenomenon indicative of a circumstance in its real motion quite independent of the station from which we view it. Now, it is easy to ascertain, by observation, when a planet passes from the north to the south side of the ecliptic: we have only to convert its right ascensions and declinations into longitudes and latitudes, and the change from north to south latitude on two successive days will advertise us on what day the transition took place; while a simple proportion, grounded on the observed state of its motion in latitude in the interval, will suffice to fix the precise hour and minute of its arrival on the ecliptic. Now, this being done for several transitions from side to side of the ecliptic, and their dates thereby fixed, we find, universally, that the interval of time elapsing between the successive passages of each planet through the same node (whether it be the ascending or the descending) is always alike, whether the planet at the moment of such passage be direct or retrograde, swift or slow, in its apparent movement.

(461.) Here, then, we have a circumstance which, while it shows that the motions of the planets are in fact subject to certain laws and fixed periods, may lead us very naturally to suspect that the apparent irregularities and complexities of their movements may be owing to our not seeing them from their natural center (art. 338. 371.), and from our mixing up with their own proper motions movements of a parallactic kind, due to our own change of place, in virtue of the orbitual motion of the earth about the sun.

(462.) If we abandon the earth as a center of the planetary motions, it cannot admit of a moment's hesitation where we should place that center with the greatest probability of truth. It must surely be the sun which is entitled to the first trial, as a station to which to refer to them. If it be not connected with them by any physical relation, it at least possesses the advantage, which the earth does not, of comparative immobility. But after what has been shown in art. 449., of the immense mass of that luminary, and of the office it performs to us as a quiescent center of our orbitual motion, nothing can be more natural than to suppose it may perform the same to other globes which, like the earth, may be revolving round it; and these globes may be visible to us by its light reflected from them, as the moon is. Now there many facts which give a strong support to the idea that the planets are in this predicament.

(463.) In the first place, the planets really are great globes, of a size commensurate with the earth, and several of them much greater. When examined through powerful telescopes, they are seen to be round bodies, of sensible and and even of considerable apparent diameter, and offering distinct and characteristic peculiarities, which show them to be solid masses, each possessing its individual structure and mechanism; and that, in one instance at least, an exceedingly

artificial and complex one. (See the representations of Mars, Jupiter, and Saturn, in Plate III.) That their distances from us are great, much greater than that of the moon, and some of them even greater than that of the sun, we infer, lst, from their being occulted by the moon, and 2dly, from the smallness of their diurnal parallax, which, even for the nearest of them, when most favourably situated, does not exceed a few seconds, and for the remote ones is almost imperceptible. From the comparison of the diurnal parallax of a celestial body, with its apparent semidiameter, we can at once estimate its real size. For the parallax is, in fact, nothing else than the apparent semidiameter of the earth as seen from the body in question (art. 339. et seq.); and, the intervening distance being the same, the real diameters must be to each other in the proportion of the apparent ones. Without going into particulars, it will suffice to state it as a general result of that comparison, that the planets are all of them incomparably smaller than the sun, but some of them as large as the earth, and others much greater.

(464.) The next fact respecting them is, that their dis· tances from us, as estimated from the measurement of their angular diameters, are in a continual state of change, periodically increasing and decreasing within certain limits, but by no means corresponding with the supposition of regular circular or elliptic orbits described by them about the earth as a center or focus, but maintaining a constant and obvious relation to their apparent angular distances or elongations from the sun. For example; the apparent diameter of Mars is greatest when in opposition (as it is called) to the sun, i. e. when in the opposite part of the ecliptic, or when it comes on the meridian at midnight, — being then about 18", - but diminishes rapidly from that amount to about 4", which is its apparent diameter when in conjunction, or when seen in nearly the same direction as that luminary. This, and facts of a similar character, observed with respect to the apparent diameters of the other planets, clearly point out the sun as having more than an accidental relation to their movements.

(465.) Lastly, certain of the planets, (Mercury, Venus, and Mars,) when viewed through telescopes, exhibit the appearance of phases like those of the moon. This proves that they are opaque bodies, shining only by reflected light, which can be no other than that of the sun's; not only because there is no other source of light external to them sufficiently powerful, but because the appearance and succession of the phases themselves are (like their visible diameters) intimately connected with their elongations from the sun, as will presently be shown.

(466.) Accordingly it is found, that, when we refer the planetary movements to the sun as a center, all that apparent irregularity which they offer when viewed from the earth disappears at once, and resolves itself into one simple and general law, of which the earth's motion, as explained in a former chapter, is only a particular case. In order to show how this happens, let us take the case of a single planet, which we will suppose to revolve round the sun, in a plane nearly, but not quite, coincident with the ecliptic, but passing through the sun, and of course intersecting the ecliptic in a fixed line, which is the line of the planet's nodes. This line must of course divide its orbit into two segments; and it is evident that, so long as the circumstances of the planet's motion remain otherwise unchanged, the times of describing these segments must remain the same. The interval, then, between the planet's quitting either node, and returning to the same node again, must be that in which it describes one complete revolution round the sun, or its periodic time; and thus we are furnished with a direct method of ascertaining the periodic time of each planet.

(467.) We have said (art. 457.) that the planets make the entire tour of the heavens under very different circumstances. This must be explained. Two of them— Mercury and Venus

- perform this circuit evidently as attendants upon the sun, from whose vicinity they never depart beyond a certain limit. They are seen sometimes to the east, sometimes to the west of it. In the former case they appear conspicuous over the western horizon, just after sunset, and are called evening stars : Venus, especially, appears occasionally in this situation

with a dazzling lustre ; and in favourable circumstances may be observed to cast a pretty strong shadow.* When they happen to be to the west of the sun, they rise before that luminary in the morning, and appear over the eastern horizon as morning stars: they do not, however, attain the same elongation from the sun. Mercury never attains a greater angular distance from it than about 29°, while Venus extends her excursions on either side to about 47°. When they have receded from the sun, eastward, to their respective distances, they remain for a time, as it were, immovable with respect to it, and are carried along with it in the ecliptic with a motion equal to its own; but presently they begin to approach it, or, which comes to the same, their motion in longitude diminishes, and the sun gains upon them. As this approach goes on, their continuance above the horizon after sunset becomes daily shorter, till at length they set before the darkness has become sufficient to allow of their being seen. For a time, then, they are not seen at all, unless on very rare occasions, when they are to be observed passing across the sun's disc as small, round, well-defined black spots, totally different in appearance from the solar spots (art. 386.). These phenomena are emphatically called transits of the respective planets across the sun, and take place when the earth happens to be passing the line of their nodes while they are in that part of their orbits, just as in the account we have given (art. 412.) of a solar eclipse. After having thus continued invisible for a time, however, they begin to appear on the other side of the sun, at first showing themselves only for a few minutes before sunrise, and gradually longer and longer as they recede from him. At this time their motion in longitude is rapidly retrograde. Before they attain their greatest elongation, however, they become stationary in the heavens; but their recess from the sun is still maintained by the advance of that luminary along the ecliptic, which continues to leave them behind, until, having reversed their

* It must be thrown upon a white ground. An open window in a whitewashed room is the best exposure. In this situation I have observed not only the shadow, but the diffracted fringes edging its outline. ---H. Note to the edition of 1833. Venus may often be seen with the naked eye in the daytime.

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