or which, otherwise, would have remained for ages undiscovered by observation.

The general motion of the celestial bodies about the earth, from east to west, it would, immediately, be attempted to explain by supposing them to be attached to the concave surface of a hollow sphere which, being endowed with that movement of revolution, would, consequently, carry all those bodies along with it; but the movements of the planets being found to be variable in velocity and direction, it would be necessary to suppose them independent of the sphere of the inerratic stars and, either to move by themselves in free space, or each of them to be attached to a separate sphere by whose motion it might be conveyed about the earth: the latter supposition seems to have been immediately preferred, probably because no satisfactory reason could, at first, be assigned why, if left to themselves, they should not fall from their places, agreeably to what was constantly observed of bodies near the earth's surface when left without support.

But whether attached to spheres or not, the phenomena of the movements of the superior planets might, naturally enough, lead to the opinion that these movements were performed about the earth in orbits which were perfectly or nearly circular; because, at different times, they appear to be in every different part of the circumference of an imaginary circle in the heavens. Now the first opinions of men concerning the heavenly bodies seem to have been drawn from a supposed perfection in all their qualities rather than from observation of their phenomena, and it became an established point that the movements must be performed in orbits correctly circular, and with uniform velocities; hence, from the observed variability of the planets' motions, it was early concluded that the circular orbits. could not be concentric with, though they were supposed to enclose the earth; for by making an orbit eccentric, it is evident that a body, really moving with a uniform angular motion about the centre, would appear to move faster, when in that part of the orbit which is nearer the spectator, and slower, when in that more remote than the point of mean distance from him. The changes in the apparent movements of the planets from direct to retrograde,

a

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

a 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 frequently than those of Venus.

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

occur more

b Ib. cap. 17.

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

a Recherches sur l'Astronomie Egyptienne.

horizontal lines passing along the foot of their walls tended southward of east and northward of west about as much as the amplitude of the sun at rising and setting on the days of the winter and summer solstice respectively; consequently those days might be found and, from thence, the length of the year, by simply directing the sight in a line parallel to the same faces. This method of determining the year is by Simplicius, expressly stated to have been practised; and it is probable that it gave rise to the formation of a year of six months, which was that used by the Carians and Acarnanians, and in which as Censorinus observes the days increased during one year and decreased during the next, alternately; for such would be the case if the first year was made to commence at midwinter, and the other at midsummer. The difference between the sidereal and tropical year being only about twenty minutes, by which the former exceeds the latter, on account of the retrogradation of the equinoctial points, would be long imperceptible from the uncertainty of the day on which any star first rises heliacally and the uncertainty of the precise moment when the shadow of the gnomon is the longest or shortest.

By the testimony of Diodorus Siculus the year of the Chaldeans and Egyptians originally consisted of thirty days; it must, therefore, have been formed by taking that number of days as a lunar period, or interval between two consecutive changes of the moon; and this writer, in the same book, assigns to the latter people the honour of regulating the year, subsequently, by the sun instead of the moon; he alleges that they made the solar year consist of twelve months, of thirty days each, and added five days and a quarter after each twelfth month, to complete the circuit. But it seems as if a year of 360 days only, was, for a certain time, used in Egypt and, as it is not likely that an error of five days should have been made in determining the length of the solar year by any of the methods above mentioned, we can only imagine that such a length was purposely chosen for the sake of the round number. The sun is said by Manetho to have been the son of Vulcan and the inDe Die natali, cap. 16.

a Comment. 46, Lib. II. De Cœlo.

Biblioth. Hist. Lib. I.