Chapter 1: On Middle Motion

Now he describes the calculation of the Ahargana The "Ahargana" is the total number of civil days elapsed from a fixed epoch to a desired date, essential for calculating planetary positions.—

Subtract 1442 from the Shaka year; divide the result by eleven. The quotient is called the Chakra (Cycle). Multiply the remainder by twelve and add the months elapsed since Chaitra. Set this sum in two places. To one, add twice the Chakra and ten; divide by thirty-three to find the Adhimasa (intercalary months). Add these to the sum of months. Multiply by thirty and add the elapsed lunar days (tithis). Add one-sixth of the Chakra (ignoring fractions). Set this in two places. Divide one by sixty-four to find the Kshaya-ahas (omitted days). Subtract these from the other to get the Ahargana. To find the weekday, add five times the Chakra to the Ahargana and divide by seven; the remainder counted from Monday gives the day. || 4-5 ||

Now, the calculation of the Ahargana is explained in two verses beginning with "Subtract 1442..." First, an example is written: From the reign of the illustrious King Vikramaditya, 1669 years have passed; likewise, in the Shaka era of King Shalivahana, 1534 years. On the full moon day of the bright half of Vaishakha, a Monday, at 54 ghatis and 10 palas, with the moon in the Vishakha nakshatra (39 ghatis, 55 palas) and the Variyan yoga (0 ghatis, 59 palas), the Ahargana is calculated to observe a lunar eclipse.

In this case, the Shaka year is 1534. Subtracted by "two-four-one" (1442), the resulting group of years is 92. This is divided by eleven. The quotient in one place is 8, named the Chakra. The remainder is 4. Multiplied by twelve, it is 48. Adding the one elapsed month from Chaitra to the desired time, it becomes 49. This is placed in two spots. The Chakra doubled is 16. Adding this to the 49 and adding ten, we get 75. Divided by thirty-three, the quotient for intercalary months is 2. Adding this to the 49, the total months are 51. This multiplied by thirty is 1530. The elapsed lunar days are 14. Adding these, we get 1544. Adding one-sixth of the Chakra (which is 1), it becomes 1545. This is placed in two spots and divided by sixty-four; the quotient for omitted days is 24. Subtracting these from the total, the civil Ahargana is 1521.

Now for the weekday: The Chakra (8) multiplied by five is 40. Adding this to the Ahargana (1521) gives 1561. Divided by seven, the remainder counted from Monday original: "abja" (the Moon/Monday) indicates the day. The result is Monday.

Now for a special rule: If the desired weekday does not result from the Ahargana, one should add or subtract one to match the desired day. Furthermore, if the division by eleven results in a remainder of zero, a difference of two days may occur in the resulting weekday.

Example of this:

In Shaka 1674, on the first day of the bright half of Chaitra, the Ahargana is calculated for a Sunday. There, the Chakra is 12 and the remainder is 0. The Ahargana is 32. Here, Tuesday results, but Sunday is expected. In such cases, the Ahargana should be adjusted by subtracting or adding two.

Furthermore, there is another special rule for years containing an intercalary month. If, when calculating the Ahargana for months prior to the intercalary month, a higher number of intercalary months appears compared to the previous year, it should not be taken; rather, the count from the previous year should be used. For example, in Shaka 1666, on the first day of the bright half of Chaitra, a Friday. In this year, there is an intercalary Vaishakha. Calculating the Ahargana for the first of Chaitra: Shaka 1666 minus 1442 is 223. Divided by eleven, the Chakra is 20 and the remainder is 3. Multiplied by twelve, it is 36. Adding the months elapsed from Chaitra (0), it remains 36. Doubling the Chakra (40) and adding it gives 76; adding ten gives 86. Divided by thirty-three original: "amara" (the gods/33), the intercalary months result as 2. Since this intercalary month occurs after Vaishakha, it is not accepted here; one must subtract one. Thus, the intercalary month is 1. Adding this to the 36 and multiplying by thirty gives 1110. Adding the elapsed lunar days (0) and one-sixth of the Chakra (3), we get 1113. Divided by sixty-four, the omitted days are 17. Subtracting these, the Ahargana is 1096. To match the desired Friday, one is added, making the Ahargana 1097. If the calculation were done with the raw intercalary months, it would be 1124; even subtracting one for the weekday would yield 1123, which is incorrect because it would cause a discrepancy in the resulting planetary positions. Therefore, an intercalary month is not accepted before it actually occurs. Conversely, in months following an intercalary month, if the calculation does not show it, it must still be included. For example, in Samvat 1669 (Shaka 1530), there is an intercalary Bhadrapada. Calculating for the first of Kartika, a Saturday: Shaka 1530 minus 1442 is 88. Divided by eleven, the Chakra is 8, remainder 0. Multiplied by twelve is 0. Adding 7 months from Chaitra gives 7. Doubling the Chakra (16) and adding it gives 23. Adding ten—