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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.

(396.) Lastly, certain of the planets, 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 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.

(397.) 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.

(398.) We have said (art. 388.) that the planets make

the entire tour of the heavens under very different circumstances. This must be explained. Two of them

sun.

-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 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. 330.). 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

*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 no only the shadow, but the diffracted fringes edging its outline. — Author.

orbits, just as in the account we have given (art. 355.) 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 motion, and become again direct, they acquire sufficient speed to commence overtaking him-at which moment they have their greatest western elongation; and thus is a kind of oscillatory movement kept up, while the general advance along the ecliptic goes on.

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(399.) Suppose PQ to be the ecliptic, and ABD the orbit of one of these planets, (for instance, Mercury,) seen almost edgewise by an eye situated very nearly in its plane; S, the sun, its center; and A, B, D, S successive positions of the planet, of which B and S are in the nodes. If, then, the sun S stood apparently still in the ecliptic, the planets would simply appear to oscillate backwards and forwards from A to D, alternately passing before and behind the sun; and, if the eye happened to lie exactly in the plane of the orbit, transiting his disc in the former case, and being covered by it in the latter. But as the sun is not so stationary, but apparently carried along the ecliptic P Q, let it be supposed to move over the spaces S T, TU, U V, while the planet in each case executes one quarter of its period. Then will its orbit be apparently carried along with the

sun, into the successive positions represented in the figure; and while its real motion round the sun brings it into the respective points B, D, S, A, its apparent movement in the heavens will seem to have been along the wavy or zigzag line ANH K. In this, its motion in longitude will have been direct in the parts A N, N H, and retrograde in the parts Hn K; while at the turns of the zigzag, at H, K, it will have been stationary.

(400.) The only two planets - Mercury and Venuswhose evolutions are such as above described, are called inferior planets; their points of farthest recess from the sun are called (as above) their greatest eastern and western elongations; and their points of nearest approach to it, their inferior and superior conjunctions,—the former when the planet passes between the earth and the sun, the latter when behind the sun.

(401.) In art. 398. we have traced the apparent path of an inferior planet, by considering its orbit in section, or as viewed from a point in the plane of the ecliptic. Let us now contemplate it in plan, or as viewed from a station above that plane, and projected on it. Suppose, then, S to represent the sun, a b c d the orbit of Mercury, and ABCD a part of that of the earth-the

S

B

direction of the circulation being the same in both, viz. that of the arrow. When the planet stands at a, let the earth be situated at A, in the direction of a tangent, a A, to its orbit; then it is evident that it will appear at its greatest elongation from the sun, -the angle a A S, which measures their apparent interval as seen from A, being then greater than in any other situation of a upon its own circle.

D

(402.) Now, this angle being known by observation, we are hereby furnished with a ready means of ascer

taining, at least approximately, the distance of the planet from the sun, or the radius of its orbit, supposed a circle. For the triangle S A a is right-angled at a, and consequently we have S a: SA:: sin. SA a: radius, by which proportion the radii S a, S A of the two orbits are directly compared. If the orbits were both exact circles, this would of course be a perfectly rigorous mode of proceeding: but (as is proved by the inequality of the resulting values of S a obtained at different times) this is not the case; and it becomes necessary to admit an excentricity of position, and a deviation from the exact circular form in both orbits, to account for this difference. Neglecting, however, at present this inequality, a mean or average value of Sa may, at least, be obtained from the frequent repetition of this process in all varieties of situation of the two bodies. The calculations being performed, it is concluded that the mean distance of Mercury from the sun is about 36000000 miles; and that of Venus, similarly derived, about 68000000; the radius of the earth's orbit being 95000000.

(403.) The sidereal periods of the planets may be obtained (as before observed), with a considerable approach to accuracy, by observing their passages through the nodes of their orbits; and, indeed, when a certain very minute motion of these nodes (similar to that of the moon's nodes, but incomparably slower,) is allowed for, with a precision only limited by the imperfection of the appropriate observations. By such observation, so corrected, it appears that the sidereal period of Mercury is 87d 23h 15m 43.9s; and that of Venus, 224d 16h 49m 8.0s. These periods, however, are widely different from the intervals at which the successive appearances of the two planets at their eastern and western elongations from the sun are observed to happen. Mercury is seen at its greatest splendour as an evening star, at average intervals of about 116, and Venus at intervals of about 584 days. The difference between the sidereal and synodical revolutions (art. 353.) accounts for this. Refer

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