The Essence of Tajika Astrology

Now, the Calculation of the Weekday of the Solar Ingress

Subtract the number 1445 original: "bāṇa-yuga-abdhi-candra," using the Katapayadi system where arrows=5, ages=4, oceans=4, moon=1 from the current Shaka year. Multiply the result by 207 original: "sapta-bhra-dasrai," where seven=7, atmosphere=0, twins=2 and divide by 800 original: "śūnya-kha-kuñjaraiḥ," where zero=0, space=0, elephants=8. The result is the current value in weekdays and smaller units.
Add the elapsed years and divide by seven; counting from Sunday, this constant is known as the Ingress Constant (Sankranti-Dhruva). When combined with the specific additive factors (kshepakas) for each sign starting from the day's dawn, the true times of the Solar Ingresses are revealed. || 13 ||

Explanation of the Ingress Calculation

Regarding the verse "Shaka...": This refers to the number of years that have passed since the beginning of this specific astronomical manual. One should count from Sunday; the rest is clear.

For example: The Shaka year is 1516 approx. 1594 CE. Subtract 1445 the epoch of the manual from this. These are the years elapsed since the manual's start: 71. Multiply this by 207, which equals 14,697. Divide this by 800, yielding 18 days, 22 ghatis, and 16 palas 18|22|16; a ghati is 24 minutes, a pala is 24 seconds. Add the 71 elapsed years to this, resulting in 89|22|16. Divide by 7 to find the weekday remainder, and the remainder is 5|22|16. This is the constant known as the Ingress Constant (Sankranti-Dhruva).

By adding the specific additive factors (kshepakas) for each of the twelve zodiac signs to this constant, the weekday and time of that specific Ingress is found.

For example: The Constant is 5|22|16. To find the Aries Ingress (Mesha-Sankranti), add its specific additive factor of 6|58|30. The sum is 12|22|46 corrected from 136 in transcription. Divide by 7, and the remainder is 5|20|46. Thus, in the almanac, the Aries Ingress occurs on Thursday the 5th day counting from Sunday at 20 ghatis and 46 palas. Other Ingresses should be understood in the same way. || 13 ||

Now, the Additive Factors for the Intervals between Ingresses are written:

For Aries (Aja): 6 rasa days, 58 ibhaksha ghatis, and 20 khayama palas.
For Taurus (Vrisha): 55 yamaravana-shara ghatis and 24 jina palas.
For Gemini (Yugma): 6 rasa days, 20 khapaksha ghatis, and 53 trishara palas.
For Cancer (Karka): 2 ashvinau days, 58 dantishara ghatis, and 8 ibha palas. || 14 ||
For Leo (Simha): 6 rasa days, 26 tarkayama ghatis, and 23 tripaksha palas.
For Virgo (Stribha): 2 yama days and 28 sarpakara ghatis.