The Kali Epoch and Ahargana: Part 3: Varahamhira’s Epoch

According to Varahamihira’s Pancha Siddhantika, Varahamihira’s Epoch started in Chaitra Shukla Pratipada of Saka Year 427 on a Monday.

Converting Saka year 427 to Gregorian year, we arrive at

Gregorian Year (from Chaitra Shukla Pratipad to 31st Dec) = Saka Year + 78 = 505 AD

The details of the Chaitra Shukla Pratipada in 505 AD is as follows:

Date:          February 22, 505
Time: 5:51:54
Time Zone: 5:03:00 (East of GMT)
Place: 75 E 46' 00", 23 N 11' 00"
Ujjain, India
Altitude: 0.00 meters

Lunar Yr-Mo: Parthiva - Adhika Chaitra
Tithi: Sukla Pratipat (Su) (100.00% left)
Vedic Weekday: Saturday (Sa)
Nakshatra: Poorvabhadra (Ju) (22.48% left)
Yoga: Subha (Su) (44.96% left)
Karana: Kimstughna (Ma) (100.00% left)
Hora Lord: Mars (5 min sign: Cn)
Mahakala Hora: Mars (5 min sign: Aq)
Kaala Lord: Sun (Mahakala: Sun)

Sunrise: 6:34:11 (February 21)
Sunset: 17:57:16 (February 21)
Janma Ghatis: 58.2382

Ayanamsa: 3-02-46.30
Sidereal Time: 15:57:49

Which, when looked up at Sunrise, the details are:

Date:          February 22, 505
Time: 6:33:23
Time Zone: 5:03:00 (East of GMT)
Place: 75 E 46' 00", 23 N 11' 00"
Ujjain, India
Altitude: 0.00 meters

Lunar Yr-Mo: Parthiva - Adhika Chaitra
Tithi: Sukla Pratipat (Su) (97.22% left)
Vedic Weekday: Sunday (Su)
Nakshatra: Poorvabhadra (Ju) (19.76% left)
Yoga: Subha (Su) (42.02% left)
Karana: Kimstughna (Ju) (94.44% left)
Hora Lord: Sun (5 min sign: Le)
Mahakala Hora: Sun (5 min sign: Aq)
Kaala Lord: Sun (Mahakala: Sun)

Sunrise: 6:33:22
Sunset: 17:57:45
Janma Ghatis: 0.0005

Ayanamsa: 3-02-46.30
Sidereal Time: 16:39:25

This however does not coincide with Varahamihira’s opinion that it started on a Monday. Upon a closer look we found that there is yet another Sun-Moon conjunction on 23rd March 505, indicating that the year started on this date, the previous being a Adhikamasa or Malamasa and can’t be considered as beginning of the year.

The epoch started on March 23rd, 505 AD which is a Monday at 7:45 pm and coincides with Varahamihira’s own observation. Varahamihira observes that Sun has set at that time.

Date:          March 23, 505
Time: 19:45:46
Time Zone: 5:03:00 (East of GMT)
Place: 75 E 46' 00", 23 N 11' 00"
Ujjain, India
Altitude: 0.00 meters

Lunar Yr-Mo: Parthiva - Nija Chaitra
Tithi: Sukla Pratipat (Su) (100.00% left)
Vedic Weekday: Monday (Mo)
Nakshatra: Revati (Me) (3.80% left)
Yoga: Vaidhriti (Ju) (7.59% left)
Karana: Kimstughna (Mo) (100.00% left)
Hora Lord: Mercury (5 min sign: Aq)
Mahakala Hora: Mercury (5 min sign: Pi)
Kaala Lord: Mercury (Mahakala: Mercury)

Sunrise: 6:05:38
Sunset: 18:08:30
Janma Ghatis: 34.1718

Ayanamsa: 3-02-50.33
Sidereal Time: 7:48:18

However, if we were to follow the epoch start at following Sunrise, we will face with a problem. The weekday changes to Tuesday. Additionally Sun moves into Aries. Hence, we need to accept that if the Epoch starts happens before Sunrise, the previous day needs to be considered as Start day, instead of the day that comes after Sunrise.

Date:          March 24, 505
Time: 6:04:38
Time Zone: 5:03:00 (East of GMT)
Place: 75 E 46' 00", 23 N 11' 00"
Ujjain, India
Altitude: 0.00 meters

Lunar Yr-Mo: Parthiva - Nija Chaitra
Tithi: Sukla Pratipat (Su) (55.93% left)
Vedic Weekday: Tuesday (Ma)
Nakshatra: Aswini (Ke) (60.98% left)
Yoga: Vishkambha (Sa) (61.63% left)
Karana: Kimstughna (Ju) (11.87% left)
Hora Lord: Mars (5 min sign: Sc)
Mahakala Hora: Mars (5 min sign: Sc)
Kaala Lord: Mars (Mahakala: Mars)

Sunrise: 6:04:37
Sunset: 18:08:49
Janma Ghatis: 0.0009

Ayanamsa: 3-02-50.39
Sidereal Time: 18:08:52

Computation of Ahargana according to Varahamihira

The computation of Ahargana involves these steps

  1. Year Elapsed: Find the Saka Year Elapsed from the beginning of the Epoch. Note: Although Varahamihira has given the computation with regards to Saka Year, this can be extended to Vikrama year as well, as long as the Chaitra Shukla Pratipada calendar is followed. If say, we are to find the Ahargana (from Varahamihira’s Epoch) on the 10th Tithi in Vashakh Month in Saka Year 1000. We need to determine the year elapsed by Subtracting off 427 (Varahamihira’s epoch). We arrive at (1000–427)= 573.
  2. Intercalary Lunar Months: Then we need to determine the intercalary Lunar Months in the years elapsed. Before that we need to convert the Year elapsed into Solar months. This is 12 * years elapsed. To this we add, the lunar months elapsed in the current year (which in this case is 1. Chaitra =0, Vaishakh =1 and so on). In this example, Solar months = 573 * 12 + 1 = 6877. Then we derive the intercalary months in a given number of Solar months. This can be derived using the formula, Solar Months * 7/228. Which means in 228 Solar months, there are 7 intercalary months. In this example it is 6877 * [7/228] = 211.13 . Here the decimals have to be dropped. We take 211 interracial and add to this number of solar months, we arrive at the lunar months. In this example, Lunar months = 6877 + 211 = 7088 lunar months. Lunar days = Lunar months * 30 + days elapsed in current date = 7088 * 30 + 10 = 2,12,650 Lunar days elapsed from the beginning of the epoch.
  3. Omitted Lunar days: To determine the omitted Lunar days, we multiply the Lunar days arrived above by 11, add to it 514 and divide the sum by 703. In our example, it is [2,12,650 * 11 + 514] / 703 = 2339150.76. Removing the decimal places (i.e., quotient) represent the Ahargana starting from the Varahamihira epoch. So the Ahargana of 10th Tithi in Vaishakh Month in Saka Year 1000 is 23,39,150.

The same concept can be used with other ratios given by other authors such as Surya Siddhanta, Romaka Siddhanta etc., to first determining the number of lunar days and then determining number of omitted lunar days. Ahargana = Lunar days — Omitted Lunar days.

The Kali Ahargana can be derived by adding the Savana Days elapsed from the beginning of the Kali yuga to Varahamihira’s Epoch, which will be covered in the next article.

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