still very much in the dark. They move in long or very eccentric ellipses. The comet which Sir Isaac Newton observed in 1680 approached the Sun so closely in its perihelion as to be greatly within the orbit of Mercury, and in its remotest point or aphelion, was calculated to be 150 times farther from the sun than the earth is. A Comet appeared two years after, which Halley identified by careful observation and happy conjecture with the comet of 1531 and 1607; and accordingly he foretold its re-appearance after a period of 76 or 77 years:—a prediction which was verified in 1759; and again in 1835. This is the only comet of which many successive returns have been accurately observed, and the nature of whose orbit is well understood, with the exception of three small telescopic comets, which are called 'planetary' because their orbits are included within that of Jupiter. They are known by the names of their discoverers, Encke's, Biela's, and Faye's.

All these bodies, then, taken together,—the Sun, Planets, Planetoids, Moons, and Comets-constitute the system of which our little world is a part. Their movements in space are all produced by an impulse originally communicated to each, which is controled and regulated by the continual action of a centripetal force, exerted by, and directed to, the Sun. The original impulse, acting alone, would have carried the

1 That is, 150 times 95,000,000 of miles,-a distance which it baffles imagination to conceive.

CENTRIFUGAL AND CENTRIPETAL FORCES. XV

planets straight forward into infinite space, in the line of their first projection; it being an axiom in physics, that any body to which motion is communicated will continue to move on for ever, uniformly and constantly, in the direction given, unless it be affected by some disturbing cause. The centripetal force, again, supposing it acted alone on the planets at rest, would make them fall into the body of the Sun with a continually accelerated motion; just as a stone let fall descends to the earth. And the descent of the planet, like the fall of the stone, would be merely an instance of the great truth established by Sir Isaac Newton, that all bodies whatever mutually attract each other, with a force directly proportional to their quantity of matter as measured by weight, and inversely to the square of the distance. Hence it follows that the sun tends or gravitates to the planets, as well as the planets to the sun; and both sun and planets revolve round a common central point within the system; a point, however, which, owing to the prodigiously greater mass of matter in the sun, is within his body, and never distant from his centre so much as one-fourth of the solar diameter. "If we tie two stones together by a string, and fling them aloft, we see them circulate about a point between them, which is their common centre of gravity; but if one of them be greatly more ponderous than the other, this common centre will be proportionally nearer to that one, and even within

its surface; so that the smaller one will circulate, in fact, about the larger, which will be comparatively but little disturbed from its place." As the two

be

causes of motion we have spoken of, the centrifugal and centripetal force, do not act singly, nor per saltum, but conjointly and unceasingly, their combined effect is to compel the planets to describe a curvilinear path, concave to the Sun. This effect may more easily comprehended by adverting to the familiar fact, that the rower of a boat, in making directly for the nearest point on the opposite side of a rapid stream, is compelled to land considerably below the point he aimed at. If there were no current, the plying of the oars would convey him to the point right opposite; if he ceased to ply in the current, the boat would go down the stream; the two forces acting together carry him in the diagonal, and land him at a lower point on the opposite bank.

The curve into which the planets are turned aside from a rectilinear path by the force of solar attraction, is an ellipse, more or less eccentric, but seldom differing much from a circle. The sun is not in the centre of circular orbits, but in one of the foci of an ellipse, and every planet has therefore an aphelion or point in its orbit where it is farthest from, and a perihelion, where it is nearest to the Sun. The difference between the greatest and the smallest distance in the

2

1 Sir John Herschel's Astronomy, p. 193.

2 See Appendix. Note C.

30

case of the Earth is 3,290,100 miles, or th part of its mean distance. The points in the orbit corresponding to the aphelion and perihelion are termed the apsides, and have a slow angular motion in the heavens, in consequence of which they mutually change their positions, after an interval of about 10,470 years. At the present epoch, the Earth is in her aphelion about the beginning of July, and in her perihelion about the beginning of January. And yet, in our northern hemisphere, it is coldest when the Earth is nearest the Sun, and vice versâ ; a result which is due to the shorter duration of the day, and the greater obliquity of the solar rays as they fall on the earth's surface.

The luminous points which twinkle in the firmament (for the planets shine with a steady light) are called fixed stars, because they never change their relative positions, that is, their apparent angular distances from one another. It is thus they are distinguished from the planets, (λavytai, wanderers, from Thavaouat, erro,) whose motions among the heavenly bodies appear to the observer on this earth to be altogether irregular and anomalous. Such apparent irregularity is a necessary result, when two bodies, the one observed and the other observed from, are both in motion, with different velocities and in different directions. To the ancients, such seemingly capricious movements were perplexing and inexplicable, unless they had followed out the

b

idea started by Pythagoras, that the Sun was the centre of the universe,—an idea which, strange to say, seems to have found no favour among the later philosophers of antiquity.1

as

Vast as the distances are found to be among the bodies composing the solar system, they are nothing when compared with the distance of the fixed stars from our earth. Of its immensity some idea may be formed from the fact, that a star observed in the zenith (i.e. directly overhead) through a long narrow tube, will still be seen in the zenith, if the observation be repeated six months after; and yet the observer is then on the opposite side of the earth's orbit, at the distance across of 190,000,000 of miles. In other words, if that diameter of the

1 It is creditable to Cicero that, though unable to explain or account for these seeming anomalies, he never allows them to shake his faith in the perfect order and regularity of the celestial movements, or in the existence of a divine intelligence from which they proceed. So firm are his convictions, that even when recording and describing these unaccountable phenomena, he denies the propriety of the epithet λavnra, in the words that follow :

"Maxime vero admirabiles sunt motus earum quinque stellarum, quæ falso vocantur errantes; nihil enim errat quod in omni æternitate conservat progressus et regressus, reliquosque motus constantes et ratos. Quod eo est admirabilius in his stellis quas dicimus, quia tum occultantur, tum rursus aperiuntur ; tum abeunt, tum recedunt; tum antecedunt, tum subsequuntur: tum celerius moventur, tum tardius; tum omnino ne moventur quidem, sed ad quoddam tempus insistunt."-CIC. DE NAT. DEOR. II., 20.

These puzzling appearances do not prevent Cicero from concluding thus in the next chapter, "Coelestem ergo admirabilem ordinem incredibilemque constantiam, ex qua conservatio et salus omnium omnis oritur, qui vacare mente putat, is ipse mentis expers habendus est."-Ib., 21.