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.-Complexity 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

A A

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 5o 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 5o 27° 22′, and in that of Alphonsus, 6o 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.

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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

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.

A dark period in the history of astronomy extends from the end of the thirteenth, to the middle of the fifteenth century, when Purbach, in his Theorice novæ Planetarum which was published in 1460, proposed a return to the hypothesis of material spheres, invented by the more ancient philosophers to keep the bodies composing the solar system in their eternal paths; to this he was induced, probably, by a desire to avoid the difficulty, which then, from the attention beginning to be paid to physical subjects, seems to have been felt, in conceiving why those bodies should, without any known cause, describe in space the circumferences of imaginary circles whose centres moved also upon the circumferences of other circles equally imaginary. In the system of Purbach, as in that proposed by Albategnius and Alfraganus, the exterior and interior surfaces of the spherical shells were not concentric; between the interior surface of the outer shell and the exterior surface of the next interior shell, as between two walls, another spherical shell, bearing the planet, revolved in the manner of an epicycle, in a direction contrary to that of the deferent; and, to produce these movements, two different motive powers (anima) were supposed to act. The earth was still supposed to be the centre of the universe: the system of shells constituting the eighth sphere, or that of the fixed stars, was made to include the seven systems of spheres immediately connected with the planets, and to revolve about the earth with the diurnal motion.

The dispositions and movements of the planetary spheres may be imagined from the following explanation of the system proposed by Purbach for the lunar orbit. According to this astronomer, the moon may be supposed to be accompanied by seven chrystalline shells, or hollow spheres, constituting three deferents or principal orbs, surrounding the earth at certain distances, and two, or rather four epicycles. The exterior surface of the first orb x, [Plate IV. fig. 2,] was supposed to be concentric with the earth, E, and to coincide with the interior surface of the lower orb belonging to the system of Mercury; the centre of the interior surface of x may be supposed at c, at a certain distance from the earth: within, and concentric with this surface, were two other orbs y and z, the former in contact, but the