and the contrary, did not, perhaps, for some time excite attention. The opinion that the real velocities of the planets were uniform must have had its supporters as late as the time of Pliny, for that distinguished philosopher observes that the planets appear to move slowest when in the highest circuit [in apogeo], not because there is any acceleration or retardation of their true motions, which are uniform for each planet, but because, at different distances from the centre of observation, unequal angular movements are described by the radii drawn to the planet.

Now, with respect to the inferior planets, the fact that they never deviate beyond a certain distance from the sun, and that they alternately approach to, and recede from him, might be supposed to afford an argument that their movements depended, in some measure, on that luminary; and could the phases the inferior planets present to a spectator on the earth, and their transits over the sun's disc, have been seen without the aid of a telescope, the former, from their resemblance to the phases of the moon, and the latter, from their occurrence between the disappearance of the planets in the sun's light at his rising, and their emergence from thence after sun-set, would, at once, have led to the discovery that those planets revolve about the sun; but this being impossible, it is less surprising that the true nature of their movements should have been mistaken or quite unknown. Any observations made by the naked eye would be insufficient to determine whether the movements were rectilinear or circular with respect to the sun; and, if a circular movement were supposed, it would be still uncertain whether the sun was, or was not, included within the orbits: but, admitting that the inferior planets revolved about the earth, it must have been obvious that they were carried with the sun in his annual course; and this appearance probably led to the opinion of the motion of the planets in epicycles, which afterwards became so general.

It was impossible for the ancients to have any proof of the different distances of the planets from the earth, except such as

"Nat. Hist. Lib. II. cap. 13.

might be obtained from the difference in the degrees of their brightness, or of their apparent velocities about the earth; having adopted the principle that the paths of all the celestial bodies were circular, and their true movements uniform and equal, it would seem to follow that those which had the slowest motions were the most remote. The ancients invariably arranged the superior planets in the same order. Saturn was supposed to be on the exterior, then followed Jupiter and Mars, in succession towards the earth, which was placed in the centre of the system; they all agree, likewise, in considering that the sun and moon revolved with the other planets about the earth in orbits within that of Mars, and that the moon's orbit was the nearest to the earth. But a difference of opinion existed among the ancients about the disposition of Venus and Mercury; according to Achilles Tatius 2, some of them placed the sun between the spheres of those planets, but, he observes, the Egyptians placed the latter between the spheres of Mars and the sun, probably 'because Venus and Mercury were never seen to pass over the sun's disc, and they supposed the former to be nearer the earth than the latter perhaps because it appears brighter; this disposition was adopted by Plato and is mentioned in his dialogue Timæus: on the other hand, in the system of the later Greeks, and, as Alpetragius states, in those of the Babylonians and Hindus, the orbits of Venus and Mercury are placed between those of the sun and moon; that of Mercury being nearest to the moon or earth because his conjunctions with the sun occur more frequently than those of Venus.

* Tatius, Isagoge, cap. 16. in Petav. Uranolog.

b Ib. cap. 17.

CHAPTER VI.

NATURE OF THE ANCIENT ASTRONOMICAL CYCLES.

Determinations of the solar and lunar years.-Probability that the Sothaic period was used by the Egyptians.-The Persian cycle.-Possibility that the Egyptians had discovered the movement of the equinoctial points.The commencement of the year was variable among the ancients.-The Egyptian agricultural year regulated by the heliacal rising of Sirius.-The Chaldean cycles.—Ancient planetary cycles.-The restitutions of the moon's inequalities of movement supposed to have been known to the Chaldeans and Hindus.-The ancient manner of determining the moon's periodical revolutions.

THE manner in which the ancient Egyptians and Chaldeans determined the length of the year is doubtful, but there are two methods capable, as we have shewn, of affording an approximation to it, and either of them might have been adopted in the infancy of astronomy; these are the heliacal risings of stars and the lengths of the shadows of a gnomon. The interval between two heliacal risings of any star would include a period nearly equal to that which is known by the name of the sidereal year; and that between the days of the two longest or two shortest shadows, which indicate the days of the winter and summer solstice respectively, would give the length of the tropical year. If we are not allowed to suppose that a gnomon was used for the purpose of ascertaining the tropical year, or that on which the seasons depend, we may remark that the same could be rudely determined as soon as men had learned to trace a meridian line, or one at right angles to it; for, by simply looking, at morning and evening, in the latter direction, the days of the vernal and autumnal equinox would be known since, then, the sun rises and sets precisely in the eastern and western points of the horizon. It has been supposed that the faces of the Pyramids of Egypt had their particular directions in order to allow this kind of observation; and M. Biot remarks, that two of the faces of the temple at Denderah were disposed so that the Recherches sur l'Astronomie Egyptienne.

e a more accurate knowledge of the length of the t, if they did so, no public use was made of it in liny states that, according to the Egyptians, the vas rendered complete in a period of four years, and eriod produced the return of the winds and bad the same days; alluding, no doubt, to its advantages inus vagus, or sacred year, which consisted of 365 ut a fraction. He observes, also, that the period of when introduced into Greece, had the name of the s of Eudoxus, and this philosopher may, therefore, be to have brought it from Egypt. The Egyptians themcribe the discovery of the additional quarter of a day, most of their improvements in the sciences, to one of mes. But, according to Geminus, they designedly ar of 365 days without a fraction, in order that their festivals might not be fixed to one season of the year. citer alleges that it was a common error among the to suppose that the festival of Isis happened always at ter solstice; this, he says, was true 120 years before his but he observes that it now takes place about a month and as Geminus lived about 77 years B. c. it is evident period at which the festival so occurred must have been 200 years B. C. Formerly, he adds, on the authority of a ntary on the Octaëterides, or cycles of eight years, asto Eratosthenes, the same festival was celebrated as early summer solstice: and as the quarter of a day, by which lian year exceeds that of the Egyptians, will amount to year in 730 years of the latter kind, it is evident that the alluded to by Eratosthenes must have been about the year c. or at a period earlier either by 1460 years or by some le of that number of years. The ancient Hindus used solar and a lunar year, and they considered each to be d into 360 parts called days; but these appear to have fictitious, and used only for the purpose of facilitating astronomical computations: it is probable therefore that division was not made by that people till the science

a Nat. Hist. Lib. II. cap. 17.

b De Apparentiis Coelestibus, cap. De Mensibus.