from Père Souciet who, in the second volume of his observations, relates that an astronomer of their nation, in the year 104 Before Christ, measured the extent of the twenty eight constellations by means of an instrument, probably a Clepsydra, and adds that a similar measurement was made 207 years afterward. Again, in a copy of a Chinese map of the heavens, Mr. Ramusat observed that the constellation Orion is designated by a name signifying a conqueror, which seems to correspond with the character of that hero in the Grecian fables; and that the stars in Pegasus are divided between two figures, as in the planisphere at Denderah, but all these coincidences are too uncertain, or have too much the appearance of being accidental, to afford much ground for the opinion that the representations of the celestial sphere were copied by any one of these people from either of the others; and, as it appears that the divisions of the Chinese zodiac were originally situated on the circumference of the equator, though they were, at a subsequent time, reduced to that of the ecliptic, on which circle they were placed, from the first, by all other nations, it is much more probable that the astronomers of the east and west had recourse to their imaginations, independently of each other, when they found it convenient to arrange the stars in particular groups.

Some knowledge of astronomy must have existed among the inhabitants of the American continent long before that continent was, by the voyages of the Spaniards, made known to the people of Europe; and either because man, independently of instruction, is naturally led to adopt similar means for determining the seasons and the divisions of time, or that the first occupiers of that vast region brought with them the processes which they had followed in Asia, from whence they came; the practices of the Peruvians and Mexicans, as far as they went, corresponded nearly with those of the ancient people of the eastern world. According to Acosta " the former observed the days of the equinoxes and solstices by means of gnomons which they erected before the temples of the sun; and it is said that they divided the year (which they made to consist of 365 days) into 12 months of 30 days each, adding, like the Egyptians, five a Novi orbis Historia, Lib. VI. cap. 3.

days at the end of the twelve months, to complete the period: the Mexicans, according to the account given by Gemelli Carreri, in the Giro del Mundo, divided the 360 days into 18 months of 20 days each: they also used a cycle of 13 years, conformably to the number of their gods, and another equal to four of these, or 52 years. The eighteen months were united by threes, in the interior of a ring ornamented with hieroglyphical figures, which was discovered in the country; and Bailly very reasonably supposes that these months are subdivisions of a primary division of the year into six parts; from which it would appear that this people, at one time, like the Hindus and Arabians, made use of a period of two months or 60 days. It is worthy of remark, also, that the general mode of reckoning time, in use among the Tahitians, till they adopted the European calendar, was by the year, which consisted of 12 or 13 months; by the season or half year, and by a month of 30 days *.

a Polynesian Researches, Vol. I. chap. 4.

CHAPTER XVII.

THE ASTRONOMY OF EUROPE DURING THE MIDDLE AGES.

Revival of Astronomy in Europe. The system of eccentric spheres and epicycles adopted by Purbach.-The system of homocentric spheres revived by Fra Castorius.-The force of prejudice in philosophy.-Decline of astrology.-Copernicus proposes a system founded on the movement of the earth about the sun. Explanation of the direct and retrograde movements of the planets according to the system of Copernicus.-The threefold motion of the earth. First use of pendulums for astronomical purposes.-Hypothesis of Copernicus concerning the variations in the positions of the equinoctial points.-The elements of the solar orbit supposed to be variable.—Method of determining the distances of the planets from the sun and earth.-Com- plexity of the system of Copernicus.

THE Science of astronomy which may, in some respects, be said to have advanced towards perfection during the reigns of the Mohammedan princes of Cairo and Bagdad was, through the Arabians who had settled in Spain, communicated to the people of Europe; and, as the learned men of the east had founded all their improvements, on the system of Ptolemy, it was natural that the same system should form the groundwork of the astronomy introduced by them into this part of the world; in fact, we find that the treatises on this science which were then, first, composed by Europeans, consist wholly of compilations from Ptolemy, with comments upon the comments previously made by the Arabians. Such were the works of the astronomers patronised by Alphonsus, king of Castile, all of whom lived about the middle of the thirteenth century; consequently, about the time that learning was on the decline in Asia and Egypt: but these were chiefly persons of the Jewish persuasion, and their writings are disfigured by what appear to be caballistic reveries, which, among that people, then, usurped the place of true philosophy. The prince just mentioned caused to be computed a set of astronomical tables agreeably to the hypotheses of Ptolemy, and containing sundry corrections of the mean

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movements of the planets, with some additional equations formed with reference to the imaginary trepidation of the equinoctial points; a doctrine to which mathematicians, at that time, tenaciously adhered though founded on data which we should now think unworthy of the least confidence. We have mentioned in what manner this pretended libration was supposed to have been proved from a comparison of observations made by Ptolemy with those ascribed to a pseudo-Hermes; and we may now remark that a like inequality in the motion of the equinoctial points was, with as little reason, inferred from a comparison of the place of Spica Virginis, according to the observations of a certain Milleus who cultivated astronomy at Rome in the reign of Trajan, and that assigned to the same star by Alphonsus after an interval of 1160 years. The former observer makes the longitude of Spica equal to 5o 26° 15', and the latter, 6o 13' 48 but the Alphonsines, computing backward with the supposed value of the general precession, [1 degree in 72.8 years,] determined that, if the precession had been uniform, the longitude of the star in the time of Milleus would have been 5° 27° 52'; and they concluded that the difference [1° 37′] was caused by a movement which the equinoctial points had made in a direction contrary to that of the general precession. In fact, however, the longitude of that star in the time of Milleus was equal to 5° 27° 22′, and in that of Alphonsus, 6° 13° 30', the error of the former astronomer being 1° 7' in defect, and of the latter, 18 minutes in excess; and this result will serve to shew the degrees of accuracy with which the observations must have been made.

Like some of the Arabian astronomers, Alphonsus seems to have been little satisfied with the notions then prevalent concerning the planetary systems, and is said to have observed that if the Deity had deigned to consult him at the creation of the universe he could have suggested one less complex. This charge, so improperly preferred against the Author of Nature might have been, with some appearance of justice, urged against the system-makers of his own time; who, in the attempt to

a Ricius de motu octave sphæræ.

unite the material spheres of Calippus or Aristotle with the epicycles of Apollonius and Ptolemy, had produced a clumsy machine utterly inconsistent with that simplicity which has always been conceived to be the essential quality of a work attributed to the immediate agency of the Supreme Intelligence.

The Rabbi Isaac Abensid, to whom was entrusted the formation of the Alphonsine tables, finding that the change which would result, in the places of the equinoctial points, from the law of trepidation assigned by Thebith, was not sufficient to account for the increase in the longitudes of the stars since the time of Ptolemy, made the period in which the oscillatory motion of those points was compensated, equal to 7000 years, and united this movement with that of a uniform progression in the circumference of the ecliptic, which he supposed to be completed in 49000 years; but the adoption of these numbers seems to have no other foundation than the proportion they bear to the sabbatical period of seven years, and to that of the Jubilee, which is equal to forty-nine years.

The century in which the disciples of the Arabian school were cultivating astronomy in Spain was distinguished by the labours of Albertus, Bishop of Ratisbon, who composed a treatise on the sphere, and of the English mathematicians, John Halifax, or Sacro Bosco as he was called, and Roger Bacon; the first of whom executed an abridgment of the Almagest with a commentary; and the last, so celebrated for his erudition and the persecutions he underwent from the ignorance and malice of men of his own order, besides many discoveries in mechanics, chemistry and optics, was the first to shew, probably from observations made by himself, that the days of the equinoxes happened earlier, with respect to the calendar, than they did in the time of Ptolemy; and he concluded, in his Opus Majus, that the anticipation was equal to one day in 125 years, which is nearly correct; in the same work he notices also the error in the period of Calippus, which, he rightly observes, is equal to one day in 304 years; and from these circumstances it is evident, as Bailly has shewn, that this remarkable ecclesiastic had the merit of foreseeing the necessity of correcting the calendar three centuries before that correction was actually made.