Hipparchus' Catalogue was revised by Ptolemy in his famous work the _Almagest_. Ptolemy reduced the positions of the stars given by Hipparchus to the year 137 A.D.; but used a wrong value of the precession which only corresponded to about 50 A.D.; and he probably adopted the star magnitudes of Hipparchus without any revision. Indeed, it seems somewhat doubtful whether Ptolemy made any observations of the brightness of the stars himself. Ptolemy's catalogue contains 1022 stars. Prof. De Morgan speaks of Ptolemy as "a splendid mathematician and an indifferent observer"; and from my own examination of Al-Sufi's work on the Fixed Stars, which was based on Ptolemy's work, I think that De Morgan's criticism is quite justified. Al-Sufi's _Description of the Fixed Stars_ was written in the tenth century and contains 1018 stars. He seems to have adopted the _positions_ of the stars given by Ptolemy, merely correcting them for the effects of precession; but he made a very careful revision of the star magnitudes of Ptolemy (or Hipparchus) from his own observations, and this renders his work the most valuable, from this point of view, of all the ancient catalogues. Very little is known about Al-Sufi's life, and the few details we have are chiefly derived from the works of the historians Abu'-l-faradji and Casiri, and the Oriental writers Hyde, Caussin, Sedillot, etc. Al-Sufi's complete name was Abd-al-Rahmän Bin Umar Bin Muhammad Bin Sahl Abu'l-husaïn al-Sufi al-Razi. The name Sufi indicates that he belonged to the sect of Sufis (Dervishes), and the name Razi that he lived in the town of Raï in Persia, to the east of Teheran. He was born on December 7, 903 A.D., and died on May 25, 986, so that, like many other astronomers, he lived to a good old age. According to ancient authorities, Al-Sufi--as he is usually called--was a very learned man, who lived at the courts of Schiraz and Baghdad under Adhad-al-Davlat--of the dynasty of the Buïdes--who was then the ruler of Persia. Al-Sufi was held in high esteem and great favour by this prince, who said of him, "Abd-al-Rahmän al-Sufi taught me to know the names and positions of the fixed stars, Scharif Ibn al-Aalam the use of astronomical tables, and Abu Ali al-Farisi instructed me in the principles of grammar." Prince Adhad-al-Davlat died on March 26, 983. According to Caussin, Al-Sufi also wrote a book on astrology, and a work entitled _Al-Ardjouze_, which seems to have been written in verse, but its subject is unknown. He also seems to have determined the exact length of the year, and to have undertaken geodetic measurements. The al-Aalam mentioned above was also an able astronomer, and in addition to numerous observations made at Baghdad, he determined with great care the precession of the equinoxes. He found the annual constant of precession to be 51"·4, a value which differs but little from modern results.