celestial motions, he endeavoured to represent their inequalities in this false hypothesis. Eudoxus had previously imagined for this object, every planet attached to several concentric spheres, endowed with different motions; but this astronomer not having explained in what manner these spheres, by their action on the planets produce the variety of their motions, his hypothesis hardly deserves notice in a treatise on astronomy. A much more ingenious hypothesis consists in moving along one circumference, of which the earth occupies the centre, that of another circumference, on which moves that of a third, and so on, up to the last circumference, on which the body is supposed to move uniformly. If the radius of one of these circles surpasses the sum of the others, the apparent motion of the body round the earth will be composed of a mean uniform motion, and of several inequalities depending on the proportions of these several radii to each other, and the motions of their centres, and of that of the star. By increasing their number, and giving them suitable dimensions, we may represent the inequalities of this apparent motion. Such is the most general manner of considering the hypothesis of cycles and eccentrics, which Ptolemy adopted in his theories of the sun, moon, and planets. He supposed these bodies in motion round the earth in this order of distances-the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn; astronomers were divided in their opinions as to the position of Mercury and Venus; Ptolemy followed the most ancient opinion, and placed them below the sun; others placed them above, and finally, the Egyptians made them move round it. It is singular, that Ptolemy does not mention this hypothesis, which is equivalent to placing the sun in the centre of the epicycles of these two planets, instead of making them revolve round an imaginary centre. But, being persuaded that his system could only be adapted to the three superior planets, he transferred it to the two inferior, and was misled by a false application of the principle of the uniformity of the laws of nature, which, if he had set out from the discovery of the Egyptians, on the motions of Mercury and Venus, would have led him to the true system of the world. But even, if epicycles could be made to represent the inequalities of the motions of the heavenly bodies, still it would be impossible to represent the variations in their distances. In the time of Ptolemy, these variations were almost insensible in the planets, whose apparent diameters could not

then be measured. But his observations on the moon should have taught him that his hypothesis was erroneous, according to which the diameter of the moon perigee, in the quadratures, should be double of the diameter apogee in the sysigies. The motion in latitude of the planets, was another difficulty to be unexplained by this system; and every inequality which the improvements in the art of observing discovered, incumbered this system with a new epicycle, which, instead of being confirmed by the progress of the science, has only grown more and more complicated; and this should convince us, that it is not that of nature. But in considering it as a method of adapting the celestial motions to calculation, this first attempt of the human understanding towards an object so very complicated, does great honour to the sagacity of its author.

Ptolemy confirmed the motion of the equinoxes, discovered by Hipparchus, by comparing his observations with those of this great astronomer. He established the respective immobility of the stars, their invariable latitude to the ecliptic, and their motion in longitude, which he found * 111" in every year, as Hipparchus had suspected.

We now know that this motion is very nearly † 154" annually, which, considering the interval between the observations of Ptolemy and Hipparchus, implies an error of more than one degree in their observations. Notwithstanding the difficulty which attended the determination of the longitude of the stars, when observers had no exact measure of time, we are surprised that so great an error should have been committed, particularly when we observe the agreement of the observations with each other, which Ptolemy cites as a proof of the accuracy of his result. He has been reproached with having altered them, but this reproach is not founded; his error, in the determination of the motion of the equinoxes, seems to have been derived from too great confidence in the result of Hipparchus, relative to the length of the tropical year and the motion of the sun. In fact, Ptolemy determined the longitudes of the stars, by comparing them either with the sun, or with the moon, which was equivalent to a comparison with the sun, since the synodical revolution of the Moon was well known by the means of eclipses. Now, Hipparchus having supposed the year too long,

and consequently the motion of the sun in longitude too slow, it is clear that this error diminished the longitudes of the sun and moon, employed by Ptolemy. The motion in longitude, which he attributed to the stars, is too small by the arc described by the sun in the time, equal to the error of Hipparchus in the length of the year.

In the time of Hipparchus, the tropical year was 365.24234: this great astronomer supposed it 365.24667; the difference is 433", and during this interval the sun describes an arc of 47"; this, added to the annual precession of 111", determined by Ptolemy, gives 158 for the precession, which he would have found, if he had computed from the length of the true tropical year, the error would then have been only 4".

This remark has led to the examination of another question. It had been generally believed, that the catalogue of Ptolemy, was that of Hipparchus, reduced to his time by means of the annual precession of 111". This opinion is founded on this circumstance, that the constant error in longitude of his stars, disappear when reduced to the time of Hipparchus. But the explanation which we have given of the cause of this error, justifies Ptolemy from the reproach which has been imputed to him, of having taken the merit of Hipparchus to himself; and it seems right to believe him, when he asserts that he has observed all the stars of his own catalogue, even to the stars of the sixth magnitude. He adds, at the same time, that he found very nearly the same positions of the stars, relatively to the ecliptic, as Hipparchus, so that the difference between these two catalogues must have been very small. Thus, the observations of Ptolemy on the stars, and the true value which he has assigned to the evection, are proofs of his exactness as an observer. It is true, that the three equinoxes which he has observed, are inaccurate; but it appears that, too much prepossessed in favour of the exactness of the solar tables of Hipparchus, he made his observations of the equinoxes, at that time very difficult, coincide with them, as the derangement of his armillary might have been sufficient to explain the errors.

The astronomical edifice raised by Ptolemy, subsisted near fourteen centuries, and now that it is entirely destroyed, his Almagest, considered as a depositary of ancient observations, is one of the most precious monuments of antiquity. Ptolemy has not rendered

less service to geography, in collecting all the known longitudes and latitudes of different places, and laying the foundation of the method of projections, for the construction of geographical charts. He composed a great treatise on optics, which has not been preserved, in which he explained the astronomical refractions: he likewise wrote treatises on the several sciences of chronology, music, gnomonics, and mechanics. So many labours, and on such a variety of subjects, manifest a very superior genius, and will ever obtain him a distinguished rank in the history of science. On the revival of astronomy, when his system gave way to that of nature, mankind avenged themselves on him for the despotism it had so long maintained; and they accused Ptolemy of having appropriated to himself the discoveries of his predecessors; but in his time, the works of Hipparchus, and of the astronomers of Alexandria, must have been sufficiently known to have rendered excusable his not distinguishing what belonged to them from his own discoveries. As to the long continuation of his errors, it must be attributed to the same causes which replunged Europe into darkness. The fame of Ptolemy has met with the same fate as that of Aristotle and Descartes. Their errors were no sooner recognized, than a blind admiration gave way to an unjust contempt, for even in science itself, the most useful revolutions are not always exempt from passion and prejudice.

[La Place, Exposition du Systême du Monde.]

CHAP. III.

OF ASTRONOMY IN MODERN EUROPE.

It is to the Arabians that modern Europe is indebted for the first rays of light that dissipated the darkness in which it was enveloped during twelve centuries. They transmitted to us the treasure of knowledge which they received from the Greeks who were themselves disciples of the Egyptians; but by a deplorable fatality the arts and sciences disappeared among all these nations, as soon as they had communicated them.

Despotism has for a long period extended its barbarism over those beautiful countries where science first received its origin, and those names which formerly rendered them celebrated, are now unknown in them.

Alphonso, king of Castille, was one of the first sovereigns who encouraged the revival of astronomy in Europe. This science can reckon but few such zealous protectors; but he was ill seconded by the astronomers whom he had assembled at a considerable expense, and the tables which they published did not answer to the great cost they had occasioned.

Endowed with a correct judgment, Alphonso was shocked at the confusion of the circles in which the celestial bodies were supposed to move; he felt that the expedients employed by nature ought to be more simple. "If the Deity," said he, "had asked my advice, "these things would have been better arranged." By these words, which are taxed with impiety, he meant to express that mankind were still far from knowing the true mechanism of the universe.

In the time of Alphonso, Europe was indebted to the encouragement of Frederic II. Emperor of Germany, for the first Latin translation of the Almagest of Ptolemy, which was made from the Arabic version.

We are now arrived at that celebrated epoch when astronomy, escaping from the narrow sphere which had hitherto confined it, raised itself by a rapid and continued progress to the height where