behind and vice versa; but, acting on both, they continue together under its attraction, just as the loose parts of the earth's surface continue to rest upon it. It is, then, in strictness, not the earth or the moon which describes an ellipse around the sun, but their common centre of gravity. The effect is to produce a small, but very perceptible, monthly equation in the sun's apparent motion as seen from the earth, which is always taken into account in calculating the sun's place. The moon's actual path in its compound orbit round the earth and sun is an epicycloidal curve intersecting the orbit of the earth twice in every lunar month, and alternately within and without it. But as there are not more than twelve such months in the year, and as the total departure of the moon from it either way does not exceed one 400th part of the radius, this amounts only to a slight undulation upon the earth's ellipse, so slight, indeed, that if drawn in true proportion on a large sheet of paper, no eye unaided by measurement with compasses would detect it. The real orbit of the moon is everywhere concave towards the sun.

(453.) Here moreover, i. e. in the attraction of the sun, we have the key to all those differences from an exact elliptic movement of the moon in her monthly orbit, which we have already noticed (arts. 407, 409), viz. to the retrograde revolution of her nodes; to the direct circulation of the axis of her ellipse; and to all the other deviations from the laws of elliptic motion at which we have further hinted. If the moon simply revolved about the earth under the influence of its gravity, none of these phenomena would take place. Its orbit would be a perfect ellipse, returning into itself, and always lying in one and the same plane. That it is not so, is a proof that some cause disturbs it, and interferes with the earth's attraction; and this cause is no other than the sun's attraction-or rather, that part of it which is not equally exerted on the earth.

(454.) Suppose two stones, side by side, or otherwise situated with respect to each other, to be let fall together; then, as gravity accelerates them equally, they will retain their relative positions, and fall together as if they formed one mass. But suppose gravity to be rather more intensely exerted on one than on the other; then would that one be rather more accelerated in its fall, and would gradually leave the other; and thus a relative motion between them would arise from the difference of action, however slight.

(455.) The sun is about 400 times more remote than the moon; and, in consequence, while the moon describes her monthly orbit round the earth, her distance from the sun is alternately th part greater and as much less than the earth's. Small as this is, it is yet sufficient to produce a perceptible excess of attractive tendency of the moon towards the sun,

NOM

Fig. 62.

E

above that of the earth when in the nearer point of her orbit, M, and a corresponding defect on the opposite part, N; and, in the intermediate positions, not only will a difference of forces subsist, but a difference of directions also; since however small the lunar orbit M N, it is not a point, and, therefore, the lines drawn from the sun S to its several parts cannot be regarded as strictly parallel. If, as we have already seen, the force of the sun were equally exerted, and in parallel directions on both, no disturbance of their relative situations would take place; but from the non-verification of these conditions arises a disturbing force, oblique to the line joining the moon and earth, which in some situations acts to accelerate, in others to retard, her elliptic orbitual motion; in some to draw the earth from the moon, in others the moon from the earth. Again, the lunar orbit, though very nearly, is yet not quite coincident with the plane of the ecliptic; and hence the action of the sun, which is very nearly parallel to the last-mentioned plane, tends to draw her somewhat out of the plane of her orbit, and does actually do so-producing the revolution of her nodes, and other phenomena less striking. We are not yet prepared to go into the subject of these perturbations, as they are called; but they are introduced to the reader's notice as early as possible, for the purpose of reassuring his mind, should doubts have arisen as to the logical correctness of our argument, in consequence of our temporary neglect of them while working our way upward to the law of gravity from a general consideration of the moon's orbit.

16

CHAPTER IX.

OF THE SOLAR SYSTEM.

TROGRADATIONS.

APPARENT MOTIONS OF THE PLANETS. THEIR STATIONS AND RETHE SUN THEIR NATURAL CENTRE OF MOTION. INFERIOR PLANETS. THEIR PHASES, PERIODS, ETC. DIMENSIONS AND FORM OF THEIR ORBITS. TRANSITS ACROSS THE SUN. - SUPERIOR PLANETS. THEIR DISTANCES, PERIODS, ETC. KEPLER'S LAWS AND THEIR INTERPRETATION.— ELLIPTIC ELEMENTS OF A PLANET'S ORBIT. ITS HELIOCENTRIC AND GEOCENTRIC EMPIRICAL LAW OF PLANETARY DISTANCES;- VIOLATED IN THE CASE OF NEPTUNE. THE ULTRA-ZODIACAL PLANETS.PHYSICAL PECULIARITIES OBSERVABLE IN EACH OF THE PLANETS.

PLACE.

(456.) 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 sixth, Uranus, is barely discernible without a telescope; and niue others-Neptune, Ceres, Pallas, Vesta, Juno, Astræa, Hebe, Iris, Flora- are never visible to the naked eye. Besides these fifteen, 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 ten last-mentioned planets having all been discovered within little more than half a century from the present time.

While this sheet is passing through the press, a sixteenth, not yet named, has been added to the list, by the observations of Mr. Graham, astronomical assistant to E. Cooper, Esq. at his observatory at Markree, Sligo, Ireland.

(457.) The apparent motions of the planets are much more irregular than those of the sun or moon. Generally speaking, and comparing their places at distant times, they all advance, though with very different average or mean velocities, in the same direction as those luminaries, i. e. in opposition to the apparent diurnal motion, or from west to east: all of them make the entire tour of the heavens, though under very different circumstances; and all of them, with the exception of the eight telescopic planets,-Ceres, Pallas, Juno, Vesta, Astræa, Hebe, Iris, and Flora (which may therefore be termed ultra-zodiacal,)—are confined in their visible paths within very narrow limits on either side the ecliptic, and perform their movements within that zone of the heavens we have called, above, the Zodiac (art. 303.)

(458.) The obvious conclusion from this is, that whatever be, otherwise, the nature and law of their motions, they are performed nearly in the plane of the ecliptic- that plane, namely, in which our own motion about the sun is performed. Hence it follows, that we see their evolutions, not in plan, but in section; their real angular movements and linear distances being all foreshortened and confounded undistinguishably, while only their deviations from the ecliptic appear of their natural magnitude, undiminished by the effect of perspective.

(459.) The apparent motions of the sun and moon, though not uniform, do not deviate very greatly from uniformity; a moderate acceleration and retardation, accountable for by the ellipticity of their orbits, being all that is remarked. But the case is widely different with the planets sometimes they advance rapidly; then relax in their apparent speed-come to a momentary stop; and then actually reverse their motion, and run back upon their former course, with a rapidity at first increasing, then diminishing, till the reversed or retrograde motion ceases altogether. Another station, or moment of apparent rest or indecision, now takes place; after which the movement is again reversed, and resumes its original direct character. On the whole, however, the amount of direct motion more than compensates the retrograde; and by the Fig. 63.

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 represented as in Mercator's projection,

art. 283, taking the ecliptic E C for its ground line,) the track of a planet when mapped down by observation from day to day, will offer the appearance P Q R S, &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 centre (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 centre of the planetary motions, it cannot admit of a moment's hesitation where we should place that centre 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