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[ 4.5 ] longer by 0-00206 days. Hence, accepting Bháskara s year, we should have 50"-24+7":31 or 57"-55 as the precessional rate. Bhaskara does not state in his Siromaņi any rate deduced by hini, but evidently supports Muñjála's rate of 59":9. Moreover, his adoption of the rate of 60' a year in his Karaya-kutúhala leaves no doubt in our mind as to the rate he used. Similarly, Gaueśa, author of Grabalaghava, makes the year of 365.25856 mean solar days, which is thus longer by 0·00219 days. He ought to have therefore made the precessional rate 50" 24+7":86, or 58" 10 instead of 60' as he has done. Chandrasekhara accepts the length of the year of the Súrya- Siddhanta, and gives 57".615 as the precessional rate (VI. 75). This is just less than the rate we have assumed above by 58":68 - 57"-62, or 1":06. I was surprised to find this close approxi- mation, and could not but ask him the data from which he de- rived the rate. In reply, he said that finding the Súrya-Side dhánta and the S'iromaņi make the ayanámsa either shorter or longer than that observed, he was for some time in a fix about the rate to be followed. Fortunately, while he was studying Játaka-karma-paddhati with the help of the commentary called Játakálavkárs written by Súryadeva some 800 years ago, he accidentally found a passage in which the commentator recorded the ayanínsa as it was observed by him on a particular day of a particular year. This find itself is not less valuable than Chandrasekhara's rate. He gives, however, 22° 26' as the aya- náms'a for the year we have taken for discussion. Muñjála appears to be the earliest writer who has given the date of the year of no ayanáinsa, as well as the rate of preces- Digitized by Google