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xii Khallikán and Abul Faraj; or else the accepted dates of Omar's and Hasan's deaths (517 and 518 ) must be abandoned for others at least twenty years earlier.

Omar's appointment at Merv mentioned by Nizám ul Mulk was, as we learn from Abul Feda, that of Astronomer Royal. Whilst holding this office Omar compiled some astronomical tables called Záj i Maliksháhi, of which mention is made by Haji Khalfa, and in collaboration with seven other astronomers effected a reform of the old Persian Calendar, somewhat similar to the reform of the Julian Calendar, made under the auspices of Pope Gregory XIII. five centuries afterwards. The object of both reforms was to make the civil year coincide more exactly with the cycle of the seasons, and in both instances this object was sought to be accomplished by an improved system of intercalation. M. Reinaud, the editor of Abul Feda's Geography, says that some authorities even prefer Omar's system to that adopted by Pope Gregory The amended reckoning ran from the 10th Ramazán, 471, and was called Taríkh i Jaláli, after the reigning monarch, Sultan Jaláluddin Maliksháh. Omar was also highly distinguished as a mathematician. A work of his on Algebra has been edited and translated by M. Woepke of Bonn, and another, "On the Difficulties of Euclid's Definitions," is preserved in the Leyden Library. His work on Algebra enjoyed a high reputation for several centuries. Ibn Khaldun