earth's. The efficacy of muscular power to overcome weight is therefore proportionally nearly 28 times less on the sun than on the earth. An ordinary man, for example, would not only be unable to sustain his own weight on the sun, but would literally be crushed to atoms under the load.*

(451.) Henceforward, then, we must consent to dismiss all idea of the earth's immobility, and transfer that attribute to the sun, whose ponderous mass is calculated to exhaust the feeble attractions of such comparative atoms as the earth and moon, without being perceptibly dragged from its place. Their centre of gravity lies, as we have already hinted, almost close to the centre of the solar globe, at an interval quite imperceptible from our distance; and whether we regard the earth's orbit as being performed about the one or the other center makes no appretiable difference in any one phenomenon of astronomy.

(452.) It is in consequence of the mutual gravitation of all the several parts of matter, which the Newtonian law supposes, that the earth and moon, while in the act of revolving, monthly, in their mutual orbits about their common center of gravity, yet continue to circulate, without parting company, in a greater annual orbit round the sun. We may conceive this motion by connecting two unequal balls by a short stick, which, at their common center of gravity is suspended by a long string and made to gyrate conically round a point vertically below that of suspension. Their joint system will circulate as one pendulous mass about this imaginary center, while yet they may go on circulating round each other in subordinate gyrations, as if the stick were quite free from any such tie, and merely hurled through the air. If the earth alone, and not the moon, gravitated to the sun, it would be dragged away, and leave the moon behind — and vice versâ; 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 center of gravity. The effect is to produce

-

*A mass weighing 12 stone or 168 lbs, on the earth would produce a pressure of 4687 lbs. on the sun,

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. a proof that some cause disturbs it, and earth's attraction; and this cause is no attraction or rather, that part of it exerted on the earth.

That it is not so, is interferes with the other than the sun's which is not equally

(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 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

NOM

Σ

1

the sun, 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.

301

CHAPTER IX.

OF THE SOLAR SYSTEM.

APPARENT MOTIONS OF THE PLANETS. THE STATIONS AND RETROGRADATIONS.-THE SUN THEIR NATURAL CENTER 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 PLACE.-EMPIRICAL LAW OF PLANETARY DISTANCES;-VIOLATED IN THE CASE OF NEPTUNE. THE ASTEROIDS.-PHYSICAL PECULIARITIES OBSERVABLE IN EACH OF THE PLANETS.

(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 so discernible, while the rest of which about fifty are already known, and probably many more remain to be discovered, are visible only through telescopes, and with one exception (that of Neptune) can only be known among the multitude of minute stars those instruments reveal to us by watching them from night to night and attending to their

* One only, Vesta, is said to have been once seen by Schröter with the naked eye.

changes of place. All these have been discovered since the commencement of the current century, and forty-five of them since 1844. A list of their names, discoverers, and the dates of their respective discovery will be found in the Appendix. All of them but Neptune belong to a peculiar and very remarkable class or family of planets to which the name of Asteroids has been assigned.

(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 certain among the telescopic planets, 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 plané, 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