MEAN LONGITUDE WITHOUT AHARGANA 11 "Reduce the years (elapsed since the beginning of Kaliyuga) to months, and add to them the elapsed months (of the current year). Then multiply the sum by 30, and add the product to the number of (lunar) days elapsed since the beginning of the current month. Multiply that sum by the number of intercalary months (in a yuga) and divide by the number of solar months in a yuga reduced to days: the quotient denotes the number of intercalary months (elapsed). (The remainder is the adhimasaseṣa). Multiply the (complete) intercalary months (thus obtained) by 30 and to the product add the number of solar days (elapsed since the beginning of Kaliyuga) ¹; then multiply that (sum) by the number of omitted lunar days in a yuga and divide by the number of lunar days (in a yuga); the remainder obtained is (the avamaseșa) called āhnika. Then multiply the avamasesa (called ähnika) by the number of intercalary months (in a yuga) and divide by the number of civil days (in a yuga). Add the resulting quotient to the adhimasašesa and divide the sum by the number of lunar months in a yuga: this gives degrees, etc. (This is the total adhimāsasesa.) Next multiply (again) the avamaseșa called ähnika by 60 and divide by the number of civil days in a yuga : the result is in minutes, seconds, and thirds, etc. The number of months elapsed (since the beginning of Caitra) are to be taken as signs and the number of lunar days elapsed (of the current month) as degrees. (The sum of these signs and degrees, and the minutes, seconds, etc. corresponding to the avamašeșa is the grahatanu). From thirteen times and from one time that (grahatanu) severally subtract the degrees, minutes, etc. corresponding to the (total) adhimasaseṣa: the remainders (thus obtained) are stated by the wise astronomers to be the mean longitudes of the Moon and the Sun (respectively) conforming to the teachings of (Arya)bhata." The following is the rationale of the above rule: The fraction of the intercalary month (obtained in the rule) adhimāsasesa solar days in a yuga › in mean lunar months. ¹ By the number of solar days here is meant the number obtained above by 'reducing the years elapsed since the beginning of Kaliyuga to months, then adding to them the number of months elapsed since the beginning of the current year, then multiplying the sum by 30, and then adding to the product thus obtained the number of lunar days elapsed of the current month'.
