results which he has given as observations are merely computed from the tables of Hipparchus. He never in any instance cites a single observation more than is just necessary for the object he has immediately in view, and consequently, by precluding all comparison of one observation with another, has deprived us of the means even of guessing at the probable amount of the errors of his solar, lunar, and planetary tables. If an astronomer, as Delambre justly remarks, were to adopt the same course at the present day, he would be certain of forfeiting all claim to confidence ; but Ptolemy stood alone ; he had neither judges nor rivals; and now no one condescends to calculate the few observations he has left us. His catalogue contains only 1022 stars, and is therefore less extensive than that of Hipparchus, but it is exceedingly valuable on account
of its details.
Astronomy of the Arabians.
The most celebrated of the Arabian astronomers was Albategni, or Muhammed Ben Geber Al-Batani, so called from Batan, a city of Mesopotamia, where he was born about 850. He was a prince of Syria, and resided at Rakka in Mesopotamia ; but many of his observations were made at Antioch. Having studied the Syntaxis of Ptolemy, and made himself acquainted with the methods practised by the Greek astronomers, he began to observe, and soon found that the places assigned to many of the stars in Ptolemy s tables were considerably different from their actual situa tions, in consequence of the error which the latter had com mitted with regard to the precession of the equinoxes. Albategni measured the rate of the precession with greater accuracy than had been done by Ptolemy; and he had still better success in his attempt to determine the eccentricity of the solar orbit-^ is value of which differs extremely little from that which results from modern obser vations. In assigning the length of the year, however, he fell into an error of more than two minutes ; but this pro ceeded, as has been shown by Dr Halley, from too great confidence in the observations of Ptolemy. Albategni aldo remarked that the place of the sun s apogee is not immovable, as former astronomers had supposed, but that it advances at a slow rate, according to the order of the signs, a discovery which has been confirmed by the theory of gravitation. A new set of astronomical tables, more accurate than those of Ptolemy, likewise resulted from the indefatigable labours of Albategni ; and his observations, important in themselves, are doubly interest ing on account of the fact that they form a link of connec tion between those of the astronomers of Alexandria and of modern Europe. The works of Albategni were pub lished in 1537 under the title of De Scientia Stellarum.
Ibn-Junis, who flourished at the beginning of the 11th century, constructed a set of tables, and composed a sort of celestial history, in which he has recorded numerous observations of his own and of other astronomers belonging to the same country. This work, imperfectly known through some extracts, long excited the curiosity of astro nomers, as it was supposed to contain observations tending to establish the acceleration of the mean motion of the moon. A manuscript copy of it, belonging to the Uni versity of Leyden, was, in 1804, transmitted to the French Institute, and translated by Professor Caussin. It contains 23 observations of eclipses from the year 829 to 1004; seven observations of the equinoxes ; one of the summer solstice; one of the obliquity of the ecliptic made at Pamas- cus, by which the value of that element is found to be 23 35 ; and likewise a portion of tables of the sun and moon, with some other matter illustrative of the state of astronomy among the Arabians. The observations which regard the acceleration of the mean lunar motion are two eclipses of the sun and one of the moon, observed by Ibn- Junis, near Cairo, in the years 977, 978, and 979, and they agree with theory in confirming the existence of that phenomenon.
Ulugh Begh, a Tartar prince, and grandson of the great Tamerlane, not only encouraged the study of astronomy, but was himself a diligent and successful observer. At Samarcand, the capital of his dominions, he established an academy of astronomers, and caused the most magnificent instruments to be constructed for their use. By means of a gnomon 180 feet in height, he determined the obliquity of the ecliptic to be 23 30 20", the precession of the equinoxes at 1 in 70 years, and obtained elements for the- construction of tables which have been found to be scarcely inferior in accuracy to those of Tycho Brahe. The ancient astronomy had produced only one catalogue of the fixed stars, that of Hipparchus. Ulugh Begh has the honour of having formed a second, after an interval of sixteen centuries.
Revival of Astronomy in Europe.
After the death of Ulugh Begh, astronomy received no farther accessions in the East. But the seeds of knowledge had now begun to take root in a more propitious soil, and Europe, destined to carry the development of the human energies to its fullest extent, began to awake from the lethargy in which it had continued during so many ages.
The 14th century produced no astronomer from whose labours the science gained any accessions. George Purbach, or Beurbach, so named from a small town in Austria, where he was born in 1423, obtained great celebrity as a professor. He studied at Vienna, and after giving proofs of exceptional talent, he travelled into Italy, where he was favourably received by Cardinal de Cusa, who himself cultivated astronomy. On his return to Vienna he under took a translation of the Almagest; and although ignoranl both of Greek and Arabic, his perfect acquaintance with the subject enabled him to correct many errors which had been introduced through the carelesness or ignorance of former translators. Purbach had the good fortune to form a disciple who executed many of the plans which had been interrupted by his premature death. This was the celebrated John Müller of Konigsberg, better known by the name of Regiomontanus. Attracted to Vienna in his youth by the great reputation of Purbach, he continued to study there during ten years, and on the death of his master repaired to Rome for the purpose of acquiring the Greek language, and of making himself, through it, acquainted with the Almagest. At Rome he continued his obser vations, and translated into Latin the works of Ptolemy, the Conies of Apollonius, and some other treatises of ancient science. In 1471 he retired to Nuremberg, where, with the aid of Bernard Valther, a wealthy burgess, he founded an observatory and furnished it with excellent instruments principally of his own invention, by means of which he was enabled to detect many errors in the ancient tables. After the death of Regiomontanus, Walther continued to observe at Nuremberg during thirty years. His observa tions were collected by order of the senate of Nuremberg, and published by Schoner in 1544, a second time by Snellius, and, lastly, along with those of Tycho Brahe. In 1484 Walther began to make use of clocks, then a recent invention, to measure time in celestial observations. He was also the first who employed the planet Venus in deter mining the longitudes of the stars.
nomer of some celebrity. John Werner was the first who explained the method, which was afterwards brought into general use by Maskelyne, of finding the longitude at sea,
by observing the distance between a fixed star and the