Part 2 - The method of calculating Ahargana

The method of calculating ahargana (number of days elapsed since the beginning of kaliyuga) 1. parivarttah svacatustaya garabdhi rasagunayama dvivasutithayah | ravi bhaganona bhanoh savanadivasah kuddivasaste || ravi bhaganaravyabda dvadasagunita bhavanti ravimasah | bhaganantaram rabindrah sasimasah suryamasonah || adhimasah sasimasa strisadgukhita bhavanti sasidivasah | sasisavana divasantara navamani tithih sasamkadinam || 2. kalpaparaddha manavah sat kasya gatascaturyu gatrighanah | trinikrtadinika lergo'gaka gunah sakante'bdah || navanagarasi munikrta nava yamanaganandendavah sakanrpante | sarvamatitamanunam sandhibhiradyantarantagaih || - Brahma-sphuta-siddhanta I. 22-24 Brahma-sphuta-siddhanta I. 26-27

has been given by Brahmagupta and Bhaskara I is almost identical. The rule given in the Brahmasphutasiddhanta¹ may be compared with the following given by Bhaskara I in the LaghuBhaskariya: Add 3179 to the ( number elapsed) years of the Saka era, (then ) multiply (the resulting sum) by 12, and (then) add the (number of lunar) months ( expired ) since the commencement of Caitra. Set down (the result thus obtained) at (two) separate places; multiply (one) by (the number of) intercalary months in a yuga, which are 1,593,336 in a yuga : and divide (the product) by 5,184 * 10,000 (i.e.) by 51,840,000). Add the (resulting complete) intercalary months to the result placed at the other place. Then multiply (that sum) by 30 and (to the product) add the ( lunar) days (i.e. tithis) expired of the current month. Set down (the result thus obtained ) in two places; multiply (one) by the (number of) omitted lunar days in a yuga i.e. by 25,082,580 and divide by 1,603, 000, 080. The resulting (complete) omitted lunar days when subtracted from the result put at the other place give the (required) ahargana. The remainder obtained on dividing (the ahargana) by 7 gives the day beginning with Friday at sunrise (at Lanka) 2 1. kalpagatanda dvadasaghatascaitradimasa yukto'dhah | 'gunito yugadhimasai ravi masa tadhimasa yutah || trimsad gunastithiyutya prthag yugavamaguno yugendu dinaih | bhaktah phalavamono'rka savanahargano'rkadih || 2. nagadraye karita samyuktah sakabda dvadasahatah | caitradimasa samyuktah prthag gunya yugadhikaih || te ca sat trikaramahita nava bhutendavo yuge | bhagaharo'bdhi vastyeka sarasyura yutahatah || adhimasanprthaksthesu praksipya trisatahate | yuttavadinani yatani pratirasya yugavanaih || samgunasya- bararastesudvayastasunyasarah svibhih | chedah khastaviyada vyomakha khagni kharasendavah || labdhanyavam rathani tesu suddha svaharganah | barah saptahrte sese sukradirbhara karodayat | - Brahma-sphuta-siddhanta I. 29-30 -- Laghu-Bhaskariya I. 4-8

Addendum: The mean lunar day (madhyama tithi) may, however, differ from a true lunar day (spasta tithi) by one, so that the ahargana obtained by the above process may sometimes be in excess or defect by one. To test whether the ahar gana (obtained by the above process) is correct, it is divided by seven and the remainder counted with Friday. If this leads to the day of calculation, the ahargana is correct; if it leads to the preceding day, the ahargana is in defect; and if that leads to the succeeding day, the ahar gana is in excess. When the ahargana is found to be in defect. it is increased by one; when it is found to be in excess, it is diminished by one. (K.S. Shukla : Maha-Bhaskariya p. 4-5) Example Calculate the ahargana on October 1,1965. From Indian Calendar we find that October 1,1965 falls on Friday. 7 th lunar day (tithi) in the light half of the 7 th month Asvina in the Saka year 1887 (elapsed). Let us proceed as follows: Adding 3,179 to 1,887. we get 5.066. (1) Multiplying this by 12 and adding 6 (i. e. the number of lunar months elapsed since the beginning of Caitra) we get 60,798. (2). Multiplying this by 1,593,336 and dividing the product by 51,840,000, we get 1,868 as quotient. (The remainder is discarded as unnecessary) (3) Adding this number (i.e. 1,868) to the previous one (i.e.) 60,798) we get 62,666. (4) Multiplying this by 30 and adding 6 (i.e. the number of lunar days elapsed since the beginning of the current month) to the product, we get 1,879,986. (5) Multiplying this by 25,082,580 and dividing the product by 1.603,000.080, we get 29,416 as the quotient. (The remainder is discarded as not necessary). (6) Subtracting this number (ie. 29,416) from the previous one (i.e. 1,879,986) we get 1,850,570. (7) This is the required ahargana. Since division by 7 leaves

as the remainder. we subtract one from it, and get 1,850,569 as the correct ahar gana for the day. An Alternative Rule for Ahargana Both Bhaskara I and Brahmagupta give an alternative rule for calculating out ahargana¹ : Multiply the number of (solar months) elapsed since the beginning of kaliyuga by the number of lunar months (in a yuga) and divide by the number of solar months (in a yuga). Reduce the quotient to days (and add the number of lunar days elapsed since the beginning of the current lunar month); then multiply by the number of civil days (in a yuga) and divide by the number of lunar days (in a yuga ); the quotient denotes the ahargana.