Concise Manual on Planetary Motion with Commentary

The following section presents a mathematical ratio for calculating intercalary months (Adhimasa) based on the relationship between solar and lunar cycles.

$\frac{\text{K. A. Ma.} \times \text{I. Sau.}}{\text{K. Sau.}} = \frac{\text{I. Sau.}}{\frac{\text{K. Sau.}}{\text{K. A. Ma.}}} = \frac{\text{I. Sau.}}{32 | 16 | 4}$ K. A. Ma. = Kalpa Adhimasa (Intercalary months in an eon); I. Sau. = Ishta Saura (Elapsed solar months); K. Sau. = Kalpa Saura (Solar months in an eon). The value 32|16|4 represents the interval in months between intercalary additions.

In place of this value (32|16|4), the Teacher referring to the author of the astronomical treatise has adopted the number 33. Because this divisor is larger, the resulting quotient is smaller than the true value. This difference between the true and calculated values over one cycle Chakra: a specific period of years used in this system equals the residual of two months. Therefore, the number of cycles is multiplied by two. Furthermore, at the commencement of this text, there was a remainder of ten months; thus, their sum constitutes the desired intercalary months. By adding these intercalary months—calculated as $\frac{\text{I. Sau.} + 2 \text{ Ch.} + 10}{33}$—to the count of solar months, we obtain the lunar months. This is because the difference between solar and lunar months is defined as the intercalary month. This month-count is multiplied by thirty and added to the elapsed lunar days Tithis to find the total lunar days.

Now, the desired omitted days Avama: days deleted to synchronize the lunar and solar calendars are calculated as:
$= \frac{\text{K. Ava.} \times \text{I. Chan. Di.}}{\text{K. Chan. Di.}} = \frac{\text{I. Chan. Di.}}{\frac{\text{K. Chan. Di.}}{\text{K. Ava.}}}$

$= \frac{\text{I. Chan. Di.}}{63 + \frac{9}{10}}$

However, the Teacher has used $\frac{\text{I. Chan. Di.}}{64}$ here due to the very small difference. But in one cycle, the omitted days actually equal $63 \frac{9}{10}$. Therefore, $64 - 63 \frac{9}{10} = \frac{1}{10}$ has been taken in excess for each cycle. By multiplying the cycle count by this $\frac{1}{10}$ and adding it to the previously calculated omitted days, we get the true omitted days. Thus, the lunar days minus these omitted days $= \text{I. Chan. Di.} + \frac{\text{Ch.}}{64}$ formula simplified for calculation results in the civil day-count Ahargana: the number of days elapsed since a fixed epoch at sunrise. This is proven because Lunar Days - Civil Days = Omitted Days.

The derivation for determining the day of the week:
The remainder of one cycle divided by seven is 5. Therefore, multiply the cycle count by five, add it to the desired day-count, and divide by seven. Since the day the text commenced was a Monday original: "Chandra-vara", the result indicates the number of days elapsed from Monday. The reason for discarding the remainders of the intercalary and omitted days is well-explained in the standard astronomical treatises Siddhantas. It is not detailed here for fear of making the text too long. Thus, all is proven. || 4-5 ||

Subtract 1452 from the desired Shaka era year; the quotient when divided by 11 is called the Cycle Chakra. Multiply the remainder by 12, add the lunar months elapsed since the start of the year (Chaitra), and place this in two positions. In one position, add 10 and twice the Cycle number, then divide by 33. Add the resulting intercalary months to the months set aside in the other position and multiply by 30. To this, add the number of lunar days Tithis elapsed in the current month, then add one-sixth of the Cycle number. Place this in two positions. Divide one by 64 and subtract the resulting "loss days" from the other position. The result is the day-count Ahargana for sunrise on the desired day.

Add five times the Cycle to the day-count and divide by 7; the remainder gives the day of the week starting from Monday. || 4-5 ||

Meditating on the twin feet of Sri Kali, the "Lord of the Age" and the "Day," I now set forth the example of my own son's birth.

Birth Chart (Janma-patri)

May Uma, Gauri, Shiva, Durga, Bhadra, Bhagavati, and the family goddess Chamunda always protect this child. || 1 ||
May the Sun and all the planets, the lunar mansions, and the zodiac signs grant long life to him whose birth chart this is. || 2 ||