The Kali Epoch and Ahargana: Part 4: Kali Ahargana

The Kali Epoch started in -3179 Saka or -3044 Vikram. The Vikram samvat is usually reckoned as solar calendar. However, here I am assuming that the Vikram Samvat coincide with the Chaitra Shukla Pratipada, to simplify the reckoning of Ahargana. My suggestion for all practical purpose is to reckon using Saka Era, as that mostly follows the Lunar Calendar.

We can extent Varahamihira’s rule of computation of Ahargana to the beginning of Saka Era i.e., using the same ratios to determine the Intercalary Lunar days and the Omitted Lunar days. However, instead of starting with Year — 427, we start with Year + 3179.

Lets find the KALI AHARGANA of 7th April 2016 which happens to be the Chaitra Shukla Pratipada of Saka 1938.

  1. Elapsed year = 1938 + 3179 = 5117. Solar months = 5117 * 12 = 61,404
  2. Elapsed Lunar Month and days = 0
  3. Intercalary Lunar months = Solar Months * 7/228 = 61,404 * 7/228 = 1885.21 = 1885 (drop the decimals)
  4. Lunar days = (Solar Months + Intercalary Lunar months + current lunar month) * 30 + current lunar day = (61,404 + 1885 + 0) * 30 + 0 = 18,98,670
  5. Omitted Tithis = [Lunar days*11 + 514] / 703 = [18,98,670*11 + 514] / 703 = 29709.65 = 29709 (drop the decimals)
  6. Ahargana = 18,98,670–29709 = 18,68,961

Now, how accurate this is? To know, let us find out the Ahargana of the Varahamihira Epoch using the key elements for a Mahayuga and also Varahamihira’s formula.

Determining the Kali Ahargana of the Varahamihira Epoch using Key elements of Mahayuga

Solar Year = Saka Year + 3179 = 3606

Solar month = 3606 x 12 = 43,272

Intercalary month = There are 15,93,336 intercalary months in a mahayuga = 15,93,336 / 43,20,000 x 3,606 = 1,329.993

Lunar month = Solar months + Intercalary months = 43,272 + 1,329.993 = 4,935.993

Lunar days= 4,935.993 x 30 = 13,38,059.79

Omitted Lunar days = There are 2,50,82,580 omitted tithis in a yuga = 2,50,82,580 / 43,20,000 x 3,606 = 20,936.987

Ahargana = Lunar days - Omitted Lunar days = 13,38,059.79 - 20,936.987 = 13,17,122.803

Determining the Kali Ahargana of the Varahamihira Epoch using Varahamihira’s equation

Solar Year = Saka Year + 3179 = 3606

Solar month = 3606 x 12 = 43,272

Intercalary month = Solar Months \* 7/228 = 1328.526

Lunar month = Solar months + Intercalary months = 43,272 + 1328.526 = 44,600.526

Lunar days= 44,600.526 \* 30 = 13,38,015.78

Omitted Lunar days = \[Lunar days\*11 + 514] / 703 = \[13,38,015.78\*11 + 514] / 703 = 20,936.967

Ahargana = Lunar days - Omitted Lunar days = 13,38,015.78 - 20,936.967 = 13,17,078.813

We observe that there is a difference of 43.99 days in the Ahargana days based on the computation using key elements of Mahayuga and Varahamihira’s equations which are based on approximations.

So we will use the method based on the computation of key elements in a Mahayuga. This yields better accuracy, although not fully accurate. There is an error of 1 or 2 days which cause error in the weekday. We need to apply a weekday correction to arrive at the right Kali Ahargana.

Weekday Correction: Say the Ahargana of Varahamihira Epoch is 13,17,122 (after dropping the decimals). Since we know that Kali yuga started on a Thursday, if we divide the Kali ahargana by 7 and count the weekday from Thursday, we should get the weekday of the day under consideration. If we divide 13,177,122 by 7, the quotient is 2. Here 0=Thursday, 1=Friday 2=Saturday. Since we know that Varahamihira’s epoch on 23rd March 505 is a Monday, we have to add 2 to the Ahargana so arrived, so that the resultant when divided by 7, yields a reminder of 4, which is equivalent to Monday. Thus the Accurate Kali Ahargana of Varahamihira Epoch is 13,17,122 + 12 = 13,17,124.

Determining the KALI AHARGANA of 7th April 2016 which happens to be the Chaitra Shukla Pratipada of Saka 1938, using Mahayuga elements.

Solar Year = Saka Year + 3179 = 1938 + 3179 = 5117

Solar month = 5117 x 12 = 61,404

Intercalary month = There are 15,93,336 intercalary months in a mahayuga = 15,93,336 / 43,20,000 x Solar year = 0.36882777777778*5117 * 5117 = 1887.29173888890026

Lunar month = Solar months + Intercalary months = 61,404 + 1887.29173888890026 = 63291.29173888890026

Lunar days= Lunar months * 30 = 63291.29173888890026 x 30 = 1898738.7521666670078

Omitted Lunar days = There are 2,50,82,580 omitted tithis in a yuga = 2,50,82,580 / 43,20,000 x Solar Year = 5.80615277777778 * 5117 = 29710.08376388890026

Ahargana = Lunar days - Omitted Lunar days = 1898738.7521666670078 - 29710.08376388890026 = 1869028.66840277810754 = 1869028

There are 1577917500 civil days in a mahayuga of 432000 solar years. If we use this, in 5117 solar year, we will have 1577917500 / 432000 * solar days = 365.25868055555556 * 5117 = 1869028.66840277780052 = 1869028 civil days. This matches with our computation above.

If we actually count the days from the Kali Epoch, we arrive at 18,69,021 days. This is equivalent to having 1577911025.9917920672 civil days in a Mahayuga of 43,20,000 solar years. In the next article, we will examine the elements of the Mahayuga and check whether some adjustments needed.

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