two points which are denominated the nodes of her orbit: and the situations of these two points might be ascertained, approximatively, by observing the stars which happen to be near the moon at a time when she is centrally eclipsed, and the place of the sun at his next following eclipse; for the sun, moon, and earth being in the same right line in both these cases, the two former must be at the intersection of each other's paths; and these intersections, or nodes, would be found to be diametrically opposed to each other in the heavens. The places of the planets compared with those of the moon when in their neighbourhood can be conceived to have afforded the means of distinguishing the positions of their apparent paths, and it would be found that they all keep within a small extent, in latitude, on either side of the circle representing the sun's annual path; and, in fact, the breadth assigned to the zodiacal constellations comprehends the traces of all the circles which the planets appear to describe in the celestial sphere.

It must have been impossible, without instruments for measuring the extent of celestial arcs, to have ascertained, directly, that the moon describes her monthly circuit in the heavens with a variable velocity; yet a register of the phenomena of solar and lunar eclipses, kept during a long time, may have led the ancient astronomers to a knowledge of this fact; and, indeed, the notices which, at an early period of astronomical history, are given of the places where the moon's motion is the slowest and the quickest, shew that this important element had not escaped observation. By consulting such a register it might easily be perceived that, in the central or total eclipses, the duration of the passage of the moon over the sun, or of the shadow over the moon, was variable; and consequently that the velocity of the latter, herself, was also variable. Then, if the places of the moon, taken when the duration of the eclipse was the longest and the shortest, were compared, it might be found that they were nearly diametrically opposed to each other in the heavens; a line supposed to join those points is that which was, afterwards, denominated the line of the apsides, and its position might have been, thus, ascertained. The opinion that the real velocity of any celestial body was uniform, being universally

entertained among the ancients; when the eccentricity of the moon's orbit became a received hypothesis, it was concluded that the apparent variation of her velocity depended on her different distances from the earth: hence the points of least and greatest velocity of the luminary were supposed to coincide with those of her greatest and least distances, respectively, of which the former was denominated the apogeum, and the latter, the perigeum. The like points in the circumference of any eccentric circle or orbit were, also, so called; and the angular distance of the moon or of a planet from either, when seen from the earth, was called the anomaly.

To conclude our account of the state of astronomy among the Chaldeans we may observe that this people appear to have noticed from the earliest times some of the comets; those remarkable strangers which so frequently come within sight of the inhabitants of the earth: but the notions entertained concerning them are only to be learned from what has been related by Seneca. This philosopher after remarking that neither Eudoxus nor Conon, both of whom, he says, had diligently studied the astronomy of the Egyptians and had collected such accounts of eclipses as had been preserved by that people, makes any mention of comets; concludes, from thence, that the Egyptians had not cultivated that part of astronomy which relates to their appearances; and then goes on to state that there were two persons, Epigenes and Apollonius of Myndus, who had studied among the Chaldeans, and who do speak of comets, though they differ in the accounts they give of the opinions of that people concerning them; the former alleging that they were considered as bodies kindled in the air, and the latter, that they were of the number of planets or wandering stars. This last opinion coincides remarkably with that which is now universally admitted by astronomers, and, though it could hardly have been expected from the people of that early age, yet it is not impossible that an attentive observer might have been led to form such an hypothesis from a contemplation of the apparent motions of those bodies which, in some respects, resemble the motions of the planets. But when Apollonius asserts that the Chaldeans Nat. Quæst. Lib. III. cap. 7.

knew the courses of the comets, and Diodorus Siculus, that the same people could foretel their risings, or the times when they would become visible, it is evident that they go too far, since, except in a few cases, this is more than can be done by the mathematicians of the present day.

It is remarkable that there is not a word in Ptolemy concerning comets; and this silence makes it probable that, whatever notions the Chaldeans may have formed of them, no account of any observation made by that people to determine their elements, was in existence in the time of that astronomer. But the philosophers of the Greek schools, whose chief talent lay in reasoning concerning the probable causes of natural phenomena, do not seem to have neglected the formation of hypotheses relating to the nature of those bodies; for Aristotle asserts that Anaxagoras and Democritus considered the comets to be produced by the conjunctions of many stars or planets in clusters; and Seneca informs us that Zeno maintained the same opinion; an idea which is not unnatural, since the body of a comet frequently bears a resemblance to some of the nebulous spots in the heavens, and these have, by modern astronomers, been conceived to be formed by an attraction of vast numbers of stars towards the centre of the mass.

C

But it seems that the opinion of Zeno was contested by some of the philosophers of that day who alleged that the known planets were not sufficient in number to constitute all the comets which had been seen; this engages Artemidorus to assert, in support of the ancient opinion, and in accordance with an idea attributed to Democritus, that the number of planets was unknown, and that there may be an infinity of them which, on account of the positions of their circles [orbits] become apparent to us, only while they are describing a certain part of their course; a conception which, if understood of the comets themselves, is very creditable to the sagacity of that philosopher, however he may have merited the censure of Seneca for his notions concerning the constitution of the universe. That the sentiments of some of the ancients regarding comets were much

Bibl. Hist. Lib. II.

Nat. Quæst. Lib. VII. cap. 13.

b Meteor. cap. XVI.

d Seneca, ubi sup.

more rational than those subsequently entertained may be inferred from a passage in Aristotle' where it is said that the Pythagoreans held a comet to be nothing more than a planet, which reappears after a long interval, and which, at the vertex of the curve it describes, approaches as near the sun as is the planet Mercury: Olympiodorus, on the other hand, in his scholia on the work above quoted, at nearly one thousand years after the time of Pythagoras, considering a comet as the origin of the Fable of Phaeton, observes that this personage is said to be the offspring of the sun because a comet is a sublunary body consisting of dry vapours set on fire by that luminary; his driving through the heavens in the chariot of the sun is made an emblem of the [diurnal] motion of a comet, and his destruction by Jupiter is supposed to indicate that a comet is ultimately extinguished by the moist vapours of the earth. In the writings of the ancients we find no hint, and this circumstance is worthy of observation, that these strange visitants then inspired any of the terror with which, from an opinion that they were the harbingers of evil to the human race, they were viewed by the eye of superstition. The opinion was extensively entertained in Europe before the revival of sound philosophy; but, happily, it has now passed away with many other dreams of ignorance; and the discoveries of Halley and Newton have shewn that comets are of the same nature, and subject to the same laws, as the other planetary bodies of the system to which we belong.

Meteor. Lib. I.

CHAPTER V.

DIVISIONS OF THE CELESTIAL SPHERE.

The ancient manner of estimating the visible distances of the stars from each other, and the visible diameter of the sun.-Manner of dividing the ecliptic.—The lunar mansions.-Determination of the colures.-The extent of the sun's movement northward and southward.-Manner of dividing the circumference of a circle.-The circles of the celestial sphere imagined.— Division of the year into months and weeks.-Division of the day into hours.-Difference between the temporary and equinoctial hours.—Advantages of reducing astronomical phenomena to a system. The hypothesis of material spheres.-The planetary orbits supposed to be circular and eccentric.-Ignorance of the ancients respecting the distances of the planets from the earth.

IN estimating by the eye the small distances of stars or planets from each other, and from the moon at the times of the appulses, the ancient astronomers, besides comparing those distances with the visible diameter of the moon, referred sometimes to the measures of length in ordinary use; thus Aratus, wanting to express the distance of a certain star from the nebula in Cancer, says it is about equal to a pygon, or cubit. Now this distance, as is observed by Delambre, is known to be equal to 3° 20′; therefore what was called a cubit in the heavens may be considered as equivalent to that quantity. This mode of designating such spaces appears to have been occasionally employed even after instruments were invented, at least where great accuracy was not attempted, for we find the same expression in the works of the Arabian writers of the middle ages.

Macrobius, in his commentary on the Dream of Scipio, explains a method supposed to have been used by the Egyptians for measuring the angular diameter of the sun, which, from its simplicity, is likely to have been very early put in practice: he says they observed on the day of the equinox the direction assumed by the shadow of the gnomon of an equatorial dial at b Lib. I. cap. 20.

a Phænomena.