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Page 347
Philips supplies a similar list (Handbook of Oriental History, Royal Historical Society Guides and Handbooks, p. 32), giving Tir for the fourth month, Azor for the ninth month, and De for the 10th month.
The total of days in the year is thus (316) + (305) + 29 = 365 days in common years and 366 in leap years. The calendar attempts to balance the number of days in two halves of the year according to the current actual ratio of the number of days in springsummer versus the number of days in autumnwinter, as opposed to a balance based on simple arithmetic. By so doing, the calendar more easily is synchronized with the vernal equinox.
The leap year rule is relatively complex. The effect of the rule is, first, to produce a very accurate average solar year length and, second, to keep the error at any given time small. Put another way, the variation in average error is constrained to be small. Where the Gregorian calendar waits a century to accumulate an error of one day and then corrects the books by eliminating an entire day, the Persian Solar calendar constantly adjusts fractional days. The overall scheme is one of sliding cycles, in which a leap year occurs regularly every four years for a period of about 30 years and then waits until the fifth year before starting another 30-year cycle. In effect, the calendar is constantly dropping fractional days, which cumulatively represent the difference between the Julian quadrennial rule and the actual length of the solar year. See the test program DTLT_136.C for details.
Although this rule produces a very accurate year length over shorter periods, the disadvantage of a computationally complex rule is incurred. As a result, no straight-forward computational method for interconverting dates and Julian Day numbers seems to exist for this calendar, compelling the use of the method of summation of days, which is computationally time consuming. (See Borkowski, Earth, Moon, and Planets, v74, n3, p.223230.) Again, the purpose of the rule is to maintain synchronicity of the calendar with the actual vernal equinox.
The epoch of the calendar, 1 Farvardin 1 A.H.S., is the date A.D. 622 March 19 in the Julian calendar, some 119 days before the traditional date of the Hegira on A.D. 622 July 16.
The Hegira is thought to have occurred on A.D. 622 September 20, which corresponds to the eighth day of the third month of the Islamic calendar. It is well established that Mecca observed a kind of lunisolar calendar prior to this period, in common with most Middle Eastern cultures of the time. This calendar involved the intercalation of a 13th month.
According to Saha and Lahiri (p. 180), the Islamic calendar has been shown to have been originally lunisolar as well. Up to the last year of the life of Mohammed (A.D. 632 or A.H. 10), a 13th month was intercalated when necessary. The system was a common one for the area.
This view holds that intercalation was applied in the years up to A.H. 10. The consequence which logically follows from the acceptance of this historical research is that the epoch of the Islamic calendar requires repositioning to an earlier date. It

 
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